Abstract
In this paper, we delve into the evolving landscape of vibration-based structural damage detection (SDD) methodologies, emphasizing the pivotal role civil structures play in society's wellbeing and progress. While the significance of monitoring the resilience, durability, and overall health of these structures remains paramount, the methodology employed is continually evolving. Our focus encompasses not just the transformation brought by the advent of artificial intelligence but also the nuanced challenges and future directions that emerge from this integration. We shed light on the inherent nonlinearities civil engineering structures face, the limitations of current validation metrics, and the conundrums introduced by inverse analysis. Highlighting machine learning's (ML) transformative role, we discuss how techniques such as artificial neural networks and support vector machine's have expanded the SDD's scope. Deep learning's (DL) contributions, especially the innovative capabilities of convolutional neural network in raw data feature extraction, are elaborated upon, juxtaposed with the potential pitfalls, like data overfitting. We propose future avenues for the field, such as blending undamaged real-world data with simulated damage scenarios and a tilt towards unsupervised algorithms. By synthesizing these insights, our review offers an updated perspective on the amalgamation of traditional SDD techniques with ML and DL, underlining their potential in fostering more robust civil infrastructures.
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1 Introduction
The natural or manmade risks can cause damage or collapse to civil engineering structures. In addition to the loss of human lives and financial losses, an unexpected failure of a structural system can have severe societal consequences. In order to reduce the risk of sudden failures in structures, structural damage detection is essential, especially at its early stage. According to the definition by Rytter et al. (1993), damage identification consists of four phases: identifying damage, determining damage location, measuring damage severity, and finally predicting the remaining service life of structures, which he refers to characteristics that impair its performance, safety, reliability, or service life (Cosenza and Manfredi 2000; Frangopol and Curley 1987). The definition of damage does not always imply a complete failure of the system, but rather a decrement in functionality that leads to poor performance (Kaouk and Zimmerman 1994; Zimmerman and Kaouk 1994; He and Zhu 2011). In the absence of remedial action, the damage may grow, eventually resulting in failure. Damage to systems may occur gradually or abruptly (Farrar et al. 2007; Çatbas et al. 2012). For instance, corrosion and fatigue fail over time, while earthquakes and fire-related damage cause rapid failures (Farrar and Worden 2013a).
The vibration response of a monitored structure is recorded and analyzed to assess structural damage and determine structural health using vibration-based damage detection techniques (Wu and Jahanshahi 2018). These vibration techniques have emerged as pivotal tools in the realm of civil engineering, responding to the ever-growing demand for safe and enduring structures. Since then, different vibration-based structure-damage-detection (SDD) techniques have been proposed, proven effective, and widely accepted (Doebling et al. 1998). Structure-damage detection methods include non-destructive testing (NDT) and vibration methods. The former contains local techniques that are incapable of detecting damage within structures or damage encased in non-structural components. On the other hand, vibration-based damage identification methods examine changes in structural global vibration parameters and are considered global methods that have gained much attention in recent decades. In this paper, we only discuss vibration-based methods for detecting damage in civil-infrastructures. Due to the abundance of novel published work in recent years, it is crucial for real time practitioners to find the suitable approach to solve problem. The significance of this paper stems from the pressing need to consolidate and understand these varied detection methodologies, their evolutions, and their relevance in today's engineering practices.
There have been several articles reviewing and summarizing early vibration-based damage detection methods. Using vibration-based damage detection methods, Doebling et al. (1996) and Sohn et al. (2003) reviewed vibration-based methods for the detection of damages to diverse structures before 1996 and between 1996 and 2001. Using natural frequency changes, Salawu (1997) examined damage detection methods. Only publications from 1996 to 2003 were examined by Carden and Fanning (2004). A review of ANNs and the Hilbert–Huang transform (HHT) for damage detection has been conducted by Hakim and Razak (2014) and Chen et al. (2014a). Kong et al. (2017) reviewed recent literature on predicting the remaining life of structures. Cao et al. (2017) reviewed damping-based damage detection techniques in depth. Huang et al. (2019a) examined recent progress in Bayesian inference's detection and assessment of structural damage. Weng et al. (2019) reviewed dynamic sub-structuring methods for identifying large-scale damage to structures. A recent study conducted by Gordan et al. (2017) examined the use of data mining in damage analysis and structural health monitoring (SHM) since 2000. Bao et al. (2019a) examined data science and modeling in SHM. Several bridge damage detection methods were compiled by An et al. (2019) between 2011 and 2017. In our review paper, we particularly address the recently published novel techniques.
Vibration-based Structural Health Monitoring (SHM) has become essential for ensuring the safety and integrity of civil structures. Yang et al. (2021) highlighted the importance of early damage detection, emphasizing the connection between a structure's health and its natural symmetry. They brought attention to ISO standards and national codes but indicated a need for more detailed technical codes for practical applications. Hou and Xia (2021) offered insights into machine learning and AI's role in damage identification, but their review is limited to developments until 2019, pointing to the necessity of addressing post-2019 advances and practical applicability challenges. Walber et al. (2022) discussed sensors and instrumentation in the aerospace context, potentially missing out on detailing other civil structures. Zhang et al. (2022a) made significant contributions to understanding signal processing in SHM but overlooked the broader context of vibration-based damage detection. Niyirora et al. (2022) spotlighted machine learning and its applications in bridge maintenance, yet a broader exploration of these techniques during initial construction stages remains unaddressed. Luo et al. (2022) detailed the temperature's influence on damage detection, pointing towards the need for clearer distinctions and synergy in damage detection methods.
Azhar et al. (2023) underlined the significance and diversity of SHM systems, emphasizing the importance of precision in interpreting results and the need for enhanced robustness. Fitriyah et al. (2023) concentrated on truss bridges, potentially limiting their findings' broader applicability. Sheng and Hakim (2023) discussed machine learning's advantages but missed out on real-world challenges and deeper connections with vibration-based damage detection. Tiboni et al. (2022) and Tefera et al. (2023) concentrated on rotating machinery, leaving a gap in applicability to civil engineering. Eltouny et al. (2023) explored unsupervised learning methods, signaling the difficulty of transitioning research methods to practical civil engineering applications. Chaupal and Rajendran (2023) provided valuable insights into laminated composite structures, while Avci et al. (2021) transitioned from traditional to modern ML and DL techniques. Luleci et al. (2022) emphasized GANs but had a narrower focus. Flah et al. (2021) examined the potential of ML in SHM, indicating a need for a dedicated review focusing solely on vibration-based detection.
In response to these studies, our review addresses the observed gaps, offering an updated, comprehensive perspective on vibration-based damage detection in civil engineering structures, blending traditional and recent methodologies to provide actionable insights for practitioners. This synthesis is crucial, not just academically but practically, ensuring that professionals in the field can apply the most up-to-date and comprehensive strategies.
Over the past decade, information technology advancements, particularly in sensing, signal processing, and AI, have propelled vibration-based damage identification methods (Adewuyi and Wu 2009; Bandara et al. 2014a; Catbas et al. 2012; Yao and Pakzad 2012; Yager and Zadeh 1992; Khan and Yairi 2018). Key considerations include damage detection under varied conditions, real-time SHM, and optimal sensor placement. Figure 1 illustrates a typical damage detection system, featuring components like accelerometers, velocimeters, and strain gauges (Adewuyi and Wu 2009; Bandara et al. 2014a). These systems utilize signal-processing algorithms to translate data into insightful information (Catbas et al. 2012; Yao and Pakzad 2012). With tech progression, ML and deep learning (DL) has been integrated into engineering applications, outpacing conventional methods, especially when managing imprecise or noisy data (Yager and Zadeh 1992; Khan and Yairi 2018). ML applications in structural engineering range from identifying structural systems to monitoring structural health (Zhang et al. 2008; Oh 2008; Omran et al. 2016; Yan et al. 2013; Rafiei and Adeli 2017; Salehi and Burgueño 2018). In recent years, machine learning, especially ANNs and DL has become instrumental in developing models for civil structures' vibration-based SDD. Their efficacy has been validated through numerous studies. Therefore, this paper is devoted to discussing the challenges and future trends in vibration-based damage detection of civil engineering structures.
Civil structural damage identification system design
In this review, recent studies have extensively explored non-destructive techniques for predicting and identifying damage. Additionally, the integration of artificial intelligence into civil engineering has gained traction. Given this, there was a pressing need to consolidate and assess these cutting-edge methods to determine their suitability for specific situations, enabling professionals to apply them in real-world contexts. In this review, we give an easy-to-understand overview of this topic. The flow of this review paper has been described in the table of contents provided in the start.
2 Damage recognition practices focus on structural vibration
Damage detection metrics are crucial in assessing the effectiveness of various methods used for damage detection in structures. Different methods employ different types and sizes of damage detection, allowing for a comprehensive analysis of structural integrity. In recent research, several metrics have been proposed for damage detection, such as the root mean square deviation (RMSD) (Stepinski et al. 2013), modal strain energy (MSE) (Wang et al. 2020), modal assurance criterion (MAC) (Li et al. 2021), and damage index (DI) (Cheraghi and Taheri 2007). These metrics enable the identification of different types of damage, including cracks, delamination, corrosion, and structural instability, across a range of sizes, from micro-scale to macro-scale damage. Additionally, other methods such as acoustic emission analysis (Chen et al. 2022), infrared thermography (Bagavathiappan et al. 2013), and digital image correlation (Pan et al. 2009) have been employed for damage detection in different materials and structures. These methods provide valuable insights into damage initiation, propagation, and severity, allowing for efficient and accurate structural health monitoring.
Damage detection metrics play a crucial role in assessing the structural integrity of various systems. Recent research has witnessed advancements in damage detection methods, accompanied by the development of novel metrics. For instance, in 2022, Li et al. (2022) proposed the use of the wavelet transform-based energy entropy (WTEE) as a damage metric for structural health monitoring. This metric enhances the sensitivity to damage by capturing high-frequency signal components associated with localized damage. In 2023, Zhang et al. introduced the concept of damage-sensitive dissimilarity (DSD) as a metric for damage detection in composites (Zhang et al. 2023a). The DSD metric utilizes statistical measures to quantify the dissimilarity between the damaged and undamaged states of a structure, enabling the identification of damage types such as fiber breakage and delamination.
In terms of the type and size of damage detected, recent studies have explored various damage scenarios. For instance, Wu et al. (2022) investigated the detection of micro-cracks and corrosion in steel structures using ultrasonic-guided waves. Wang et al. (2022a) focused on the identification of fatigue cracks in metallic components using modal strain energy and frequency change analysis. Furthermore, advances in imaging techniques have facilitated the detection of larger-scale damage. For example, infrared thermography has been employed to identify structural defects, such as voids and de-bonding, in composite materials (Wu et al. 2011).
These recent developments reflect the ongoing progress in the field of damage detection, with a focus on improving the accuracy, sensitivity, and versatility of the metrics utilized. These advancements contribute to the refinement of structural health monitoring systems and aid in ensuring the reliability and safety of various engineering structures. In the early 1980s civil engineers began exploring vibration-based damage detection of bridges using methods developed in aerospace and mechanical engineering (Farrar et al. 2001). Methods that rely on vibration can detect structural damage based on changes in vibration parameters, such as frequency and mode shape (Sohn et al. 2003). A vibration-based damage detection method can be categorized according to vibration parameters: time domain, frequency domain, and time–frequency domain. Response history is utilized in time domain methods, whereas frequency domain methods use modal parameters. Analyzing time–frequency data is the basis for time–frequency domain methods. Depending on the algorithms used, non-model-based or data-driven methods and model-based methods can be classified into two categories. In the following sections, a variety of vibration-based damage detection methods are presented.
2.1 Classical approaches based on FEM
Classical approaches based on Finite Element Method (FEM) combined with level sets have been widely used for damage detection and characterization in structural analysis. The FEM provides a powerful numerical tool for simulating the behavior of structures and predicting their response to external loads (Abbas et al. 2023). When combined with level set methods, which represent and track the evolution of boundaries, FEM can effectively capture and analyze damage propagation and evolution in structures (Sussman et al. 1994).
The FEM-based approaches with level sets allow for the identification and tracking of damage boundaries, such as cracks or delamination, by representing them as level set functions. These functions evolve over time, reflecting the growth or shrinkage of the damaged regions. By integrating the FEM simulations with level set techniques, it becomes possible to capture the complex interactions between the structure, external loads, and evolving damage patterns.
These approaches offer several advantages, including the ability to handle complex geometries, the consideration of material heterogeneity, and the capability to model progressive damage. They have been successfully applied in various areas, such as fracture mechanics, fatigue analysis, and composite material damage assessment (Tavakkolizadeh et al. 2023). By utilizing the FEM-based approach with level sets, researchers can accurately predict and track the initiation, propagation, and severity of damage in structures.
Several research papers have explored the application of FEM combined with level set methods for damage detection. For example, Chen et al. (2018a) developed a computational framework integrating FEM and level set for crack detection in structures subjected to dynamic loading. Wu and Law (2007) proposed a FEM-level set-based approach for identifying and tracking delamination in composite laminates. These studies demonstrate the effectiveness and potential of using FEM combined with level sets for damage detection and characterization.
2.2 Inverse analysis and theoretical issues
Inverse analysis plays a vital role in damage detection and characterization by estimating the location, extent, and severity of damage based on measured response data. However, the inverse problem associated with damage detection is often ill-posed, leading to challenges in obtaining accurate and unique solutions (Tarantola 2005). The ill-posedness of the inverse problem stems from several factors, including limited measurement data, noise, and the nonlinear relationship between the measured response and the damage parameters (Emrouznejad et al. 2023).
The ill-posed nature of the inverse problem in damage detection gives rise to several theoretical issues. One key challenge is the non-uniqueness of solutions, where multiple damage scenarios can yield similar responses. This makes it difficult to uniquely identify the true damage configuration solely based on the measured data (Kaipio et al. 2005). Additionally, the inverse problem may be sensitive to measurement noise, resulting in instabilities and errors in the estimated damage parameters. Moreover, the presence of model uncertainties, such as material properties or boundary conditions, further complicates the inverse analysis and introduces additional sources of error (Beck 2014).
To address these theoretical issues, various strategies have been proposed. Regularization techniques, such as Tikhonov regularization, are commonly employed to stabilize the inverse problem and reduce the sensitivity to noise (Engl et al. 1996). These techniques introduce additional constraints or penalties to promote smooth or sparse solutions, aiding in obtaining more reliable damage estimates. Bayesian approaches, which incorporate prior knowledge or assumptions about the damage, can also improve the accuracy of the inverse analysis by providing a probabilistic framework for damage quantification (Yousaf et al. 2022).
Recent research has focused on advancing inverse analysis methods for damage detection, considering the theoretical challenges and limitations. For example, Zhao et al. (2021) investigated the application of compressed sensing techniques for sparse damage detection, addressing the non-uniqueness issue. Eltouny and Xiao (2021) proposed a Bayesian framework for robust damage detection considering uncertainties in both the measured data and the structural model. These studies highlight the ongoing efforts to address the theoretical issues related to the ill-posedness of the inverse problem in damage detection.
2.3 Modal parameter-based methods
In most vibration-based methods, the frequency domain is used. In addition to natural frequencies, mode shapes and variants have all been used as modal parameters. Using natural frequencies as damage indices has fallen out of favor due to their insensitivity to local damage, and their limited number (generally less than ten) of available frequencies.
2.3.1 Mode shapes
Yoon et al. (2010) used the mode shape of a damaged structure to identify damage in 2D plate-like structures using their previously published global fitting method (Yoon et al. 2009). In contrast to the gapped smoothing method, which uses a localized mode shape curve (MSC), global fitting uses a generic mode shape form to fit modes globally, which eliminates smearing effects and reduces false detections. A passing vehicle with a sinusoidal tapping force was used by Zhang et al. (2012) to approximate mode shapes. A comparison of the damaged and intact mode shape squares allowed the damage location to be determined. Despite requiring baseline data, the proposed method does not require the installation of an excessive number of sensors or the solution of eigenvector or singular value problems. From vehicle- induced displacement responses, Feng and Feng (2016) calculated a damage index that can be used to estimate damage location and quantify bridge damage progression.
Discrete wavelet transform is a useful means for crack identification of beam structures. However, its accuracy is severely dependent on the selecting mother wavelet and vanishing moments, which raises a significant challenge in practical structural crack identification. Saadatmorad et al. (2022) presented a novel approach is introduced for structural health monitoring of beams to fix this challenge. The approach is based on the combination of statistical characteristics of vibrational mode shapes of the beam structures and their discrete wavelet transforms. The FEM is applied to calculate the intact and damaged mode shapes of beam structure for the numerical investigation. As indicated in Fig. 2, the beam is divided into 40 elements (81 nodes). Findings show that the proposed approach has several advantages compared with the conventional mode shape signal processing by the discrete wavelet transforms and significantly improves damage detection’s accuracy.
The considered beam in numerical investigation (Saadatmorad et al. 2022)
2.3.2 Natural frequencies plus mode shapes
Natural frequencies with mode shapes have been combined by some researchers to detect damage. According to Sun et al. (2013), beam-like structures can be identified as damaged if their normalised uniform load surface curvature is determined from their modal flexibility. The proposed method outperforms the uniform load surface curvature and the multiple damage location methods for identifying single and multiple damage locations. Although this method is limited to beam-like structures based on Bernoulli–Euler theory. To quantify and locate damage, Zhao and Zhang (2012) used changes in natural frequencies and mode shapes. In mode shapes with high damage sensitivities were utilized to calculate the damage index, and modal assurance criteria (MACs) were used to evaluate mode shape sensitivity across order types.
Radizie et al. (2011) compared the modal parameter-based damage detection methods of MSC, coordinate MAC, strain energy damage index, gapped smoothing, fractal dimension (FD), and wavelet transformation (WT). In the presence of measurement noise, only the generalised FD and WT damage indicators were able to accurately determine damage location and the authors propose a new damage indicator which is based on natural frequency changes and any simple mode shape (measured or modeled). A combination of natural frequencies, mode shapes, and MSCs was employed by Javd et al. (2023) to detect damage in a parabolic arch.
Many researchers have investigated how to find single cracks using modal parameters. Only a few studies, however, have attempted to identify multicracks. Based on their previous work (Caddemi and Caliò 2013), Caddemi and Cali (2009) derived a closed-form representation of the dynamic stiffness matrix for multi-cracked Euler–Bernoulli beams. In order to determine damage, the Wittrick–Williams algorithm was used to compute the natural frequencies and mode shapes of the undamaged and damaged frames. A simplified closed-form solution to the vibration modes of multiple cracked beams was then provided by Khiem and Tran (2014). The crack locations and magnitudes were used to express shifts in natural frequencies and mode shapes. It was developed an iterative procedure to locate cracks, assess their severity and quantify their number. Khiem and Toan (2014) formulated the natural frequencies to be borne by multiple cracked beams in terms of crack positions and sizes. This method had a nonlinear relationship with crack magnitude as opposed to the previous one. By including nonlinear terms, the non-uniqueness problem in damage detection under symmetrical boundary conditions has been solved.
2.3.3 Damping phenomena-based methods
Due to the obvious sensitivity of its measurement and operation, damping has been utilized for damage identification less frequently than natural frequencies and mode shapes. A nonlinear damping method using ambient vibration responses was used by Frizzarin et al. (2010) to identify concrete damage without using a nondamaged baseline. In order to determine the localization of damage, Abbas et al. (2022) proposed a method based on energy. Ay et al. (2019) used a statistical framework to model damages-induced changes in the overall damping behavior of free-vibration dynamics.
For damping-based approaches, the damping model utilized for damping estimates is significant (Kong et al. 2017). For its mathematical simplicity, the Rayleigh damping model has been utilized in the majority of studies. For most civil buildings, however, classical Rayleigh damping may be an inaccurate assumption (Adhikari 2014). To assess the damage to such structures, Liu et al. (2019) developed a method for detecting it. To identify complicated modal parameters from vibration signals under periodic excitations, a unique modal identification technique was proposed. Through sensitivity-based model update, the positions and magnitudes of damage linked to stiffness reduction and damping defects were discovered simultaneously.
Modal parameters have the advantage of enabling for instant physical interpretation in damage detection strategies. Modal identification, on the other hand, is sensitive to noise level, particularly for high modes that are easily damaged. This procedure may involve inevitable inaccuracies, making the results of damage identification incorrect. In this example, several researchers identified damage using directly recorded values, for example the frequency response function (FRF). Damage index approaches can be classed as the aforementioned damage investigative techniques, which are presented in Table 1. The following section goes over several damage detection signal processing techniques.
2.4 Signal processing-based techniques
Signal processing techniques are crucial for unearthing concealed information that can enhance damage sensitivity in dynamic reactions. Among these, the Wavelet Transform (WT), Hilbert-Huang Transform (HHT), and Fractal Dimension (FD) have been significant in structural damage identification.
Yang and Nagarajaiah (2014) integrated the independent component method with WT to emphasize damage details in wavelet-domain signals. The application of B-spline wavelets in signal analysis became widespread after their introduction by Chui and Wang (1992). High-order B-spline wavelets further refined this approach, with Katunin (2011a) developing the mathematical foundation. Using these wavelets, Katunin (2011a, b) detected damages in beams and composite plates, both experimentally and computationally. Detecting multiple damages poses greater challenges than detecting a single one. Cao et al. (2014a, b) harnessed the WT to amplify local singularities in curvature mode forms and highlighted potential fracture sites. Shahsavari et al. (2017) adopted a probabilistic approach, using continuous WT on the initial mode shape followed by Principal Component Analysis (PCA) and a logistic regression test to pinpoint damage.
HHT is used for irregular and stochastic signal processing. Dong et al. (2010) innovatively combined a vector AR moving average (ARMA) model with standard HHT to create a damage index. Enhanced versions of HHT, as proposed by Bao et al. (2013), have showcased better noise resistance and more efficient data deconstruction capabilities. Han et al. (2013) employed HHT with other techniques, such as random decrement (RD), for improved modal identification and fault diagnosis. Ensemble Empirical Mode Decomposition (EMD) was harnessed by Aied et al. (2016) to discern swift stiffness variations in bridge acceleration responses to moving loads, even amid noisy signals and variable profiles. The Mandelbrot FD (Xue et al. 2023a), effective in detecting irregularities in nonlinear systems, doesn't require extensive spatial resolution. Li et al. (2011a) used FD to inspect the deviation in angles between two successive displacement mode spots, leveraging this insight to uncover damage. Bai et al. (2012) employed affine transformation to modify the FD-based approach (Cao et al. 2013) for higher mode shapes, preserving original damage information and reducing misleading local extremes.
Addressing the measurement inaccuracies inherent in FD research, Bai et al. (2014) and Bai and Radzie et al. (2015) separated damage information from noise using WT before conducting FD analyses. An and Ou (2012) directly applied FD to acceleration data, pinpointing damage sites by contrasting FD curvatures pre and post-damage. Similarly, Li et al. (2013) combined time–frequency study with FD to uncover damage-induced non-linearity in shear-type structures. In analyzing non-stationary dynamic systems, such as bridges under dynamic loading, the interaction of stresses with structural elements offers damage insights. Hester and González (2012) employed WT to simulate a bridge's acceleration response, with wavelet energy content serving as the damage metric. Roveri and Carcaterra (2012) used HHT to detect bridge damage under moving loads by analyzing single point reactions. Kunwar et al. (2013) employed HHT to identify damage zones in bridges, determining damage extents through joint time–frequency patterns.
In summary, while most signal processing techniques are nonparametric and reliant on experimental results, they often only provide Level 2 damage detection (identifying damage location). A tangible link between signal data and the extent of damage remains elusive. A comparative analysis of the techniques discussed is provided in Table 2.
2.5 Optimization algorithms
Several scholars have employed optimization methods for damage diagnosis, and they might be considered a more efficient alternative to the sensitivity-based FE model update strategy in solving inverse problems. Conventional optimization algorithms are gradient-based as well as require a better starting value, which limits their usefulness. A variety of optimization methods have been devised as a result of the growth of computer intelligence, like GA, ANN, particle swarm optimization (PSO), and artificial bee colony (ABC). These techniques bypass the aforementioned problems by not depending on specific formulas during optimization. Furthermore, these algorithms perform well in the situation of ambiguity and limited data, which are both significant issues in the recognition of structural deterioration. In Sect. 2.7, an essential ML technique called artificial neural networks (ANN) will be explained.
A new robust flexibility index for structural damage identification and quantification has been introduced by Khatir et al. (2021). The authors introduce an innovative approach for structural damage assessment and localization using a flexibility index. Through Finite Element Method (FEM) modeling, the authors evaluate the method's performance on diverse complex structures, including trusses and a high-rise tower. The study encompasses both single and multiple damage scenarios, demonstrating the effectiveness of the proposed damage indicator in accurately locating damage. Furthermore, the authors employ Atom Search Optimization (ASO) and Salp Swarm Optimizer (SSA) to quantify the extent of damage, highlighting ASO's superior convergence and computational efficiency. Overall, this paper provides a valuable contribution to the field of structural damage identification, showcasing a robust and accurate methodology applicable to a range of complex structures.
GA was created in the 1970s (Holland 1975) and it has been utilized for damage assessment since 1990s. It is founded on the idea of biological evolution. The fundamental drawback of GAs is the significant computing effort imposed by the enormous search space size. Meruane and Heylen (2011) employed a hybrid real-coded GA including five parameters to find and characterize structural loss: frequency, modal displacement, MAC, MSE, and modal flexibility. Conventional optimization approaches may yield a better precise result than the suggested technique. To assess plate damage, Umar et al. (2022a) employed a pattern analysis and GA. The GA improved the pattern analysis in certain circumstances, based on the numerical study. Guo and Li (2014) integrated evidence theory with PSO to discover numerous damages. By merging damage localization from MSE and natural frequencies, a data fusion method was employed to determine damage sites. The amount of the damage was determined using an enhanced PSO. To optimize the probability in Bayesian inference developed utilizing natural frequencies and mode shapes, Chen and Yu (2017) merged the PSO algorithm with an enhanced Nelder–Mead technique. The PSO-based approach gave more consistent and precise identification outcomes than scanning the small area all around the PSO-identified optimal solutions.
Minh et al. (2023a) presented a damage assessment technique for a high-rise concrete structure. Structure has the appearance of shear wall and core wall elements, which has not yet investigated in the literature. For this purpose, a new Finite Element (FE) model updating technique is proposed based on the development of a successful program, which makes a link between SAP2000 commercial software and MATLAB program. The process of structural damage assessment is then secured by inverse methods. This method will be handled by a bio-inspired meta-heuristic optimization algorithm, namely Termite Life Cycle Optimizer (TLCO), which is proposed by the authors recently. To compare with TLCO, 50 benchmark functions and seven well-known algorithms are used. The results obtained in this study show a significant improvement in the damage identification of large-scale structures.
Minh et al. (2022) also research on the development of a novel metaheuristic optimization algorithm known as K-Mean Optimizer (KO) and its application to a diverse set of optimization problems, including benchmark functions, engineering challenges, and structural damage identification. The paper outlines the methodology behind KO, compares its performance with other existing algorithms, and highlights its effectiveness in addressing optimization problems. The conclusion section suggests potential avenues for future research, including exploring the algorithm's parameters and its application in topology optimization using MATLAB and SAP2000.
Ding et al. (2017a) created an improved ABC method that uses modal parameters to improve the objective function. Two modifications were done to the ABC algorithm to enhance its convergence rate as well as local search capacity. Damage detection results from the suggested approach were found better than those from existing evolutionary algorithms such as GA and PSO in a numerical investigation. They eventually employed solely natural frequencies to locate defects in beams using the updated ABC algorithm (Ding et al. 2017b).
The study by Sang-To et al. (2023) introduces an innovative optimization method, the Shrimp and Goby Association Search algorithm (SGA), which draws inspiration from the behaviors of marine creatures. The paper's findings reveal that SGA exhibits remarkable efficiency in addressing complex optimization problems, particularly in terms of exploration and exploitation. Through rigorous testing on high-dimensional functions and real-world engineering applications, including damage identification in truss-like structures and structural health monitoring, SGA demonstrates its versatility and effectiveness. Notably, it outperforms several other metaheuristic algorithms, making it a valuable addition to the field of optimization techniques. This paper provides a notable contribution to the ever-evolving landscape of optimization algorithms, offering promising applications for challenging real-world problems.
Al Thobiani et al. (2022) introduces a novel approach for crack identification in two-dimensional structures using the eXtend Finite Element Method (XFEM) in conjunction with an original Grey Wolf Optimization (GWO) and an enhanced GWO integrated with Particle Swarm Optimization (PSO) known as IGWO. The research investigates the effectiveness of IGWO in comparison to GWO for solving inverse problems associated with crack identification. Through both static and dynamic analyses of cracked plates, the accuracy of IGWO is examined for inverse problem solving and improved Artificial Neural Network (ANN) parameter optimization. Level sets method is used to detect enriched nodes (central crack and edge crack) with small deformation, six reading sensors are employed to compute the strains, as shown in Fig. 3a. Results demonstrate that IGWO provides more accurate outcomes in terms of convergence and exact crack configuration, with notable improvements in ANN parameter selection for crack length prediction. This research highlights the potential of IGWO as a promising approach for enhanced crack identification and parameter optimization in structural engineering applications.
XFEM of cracked plate, sensor positions and BC (Thobiani et al. 2022)
2.6 Discussion on questions raised for modern optimization algorithm
2.6.1 "Why is the new algorithm better?" or "Why does a given modification make the algorithm better?"
When proposing a new metaheuristic algorithm or modification to an existing one, it is essential to provide justifications for its superiority or improvement. This can be achieved through empirical studies that compare the performance of the new algorithm against existing state-of-the-art algorithms on benchmark problems. The comparison should consider various performance metrics, such as convergence speed, solution quality, robustness, and scalability.
For example, a recent study by Mirjalili et al. introduced the Grey Wolf Optimizer (GWO), a new metaheuristic algorithm inspired by the social hierarchy and hunting behavior of grey wolves (Mirjalili et al. 2014). The authors compared GWO with other popular metaheuristic algorithms, including Particle Swarm Optimization (PSO), Genetic Algorithm (GA), and Differential Evolution (DE), on a set of well-known benchmark functions. The results demonstrated that GWO outperformed the other algorithms in terms of convergence speed and solution quality.
Similarly, modifications made to existing algorithms should be justified by empirical evidence. For instance, Li et al. (2016) proposed a modified version of the Firefly Algorithm (FA) called Opposition-Based Firefly Algorithm (OFA). They compared OFA with the original FA and other variants on a set of optimization problems. The results showed that OFA achieved better solution quality and faster convergence due to the integration of opposition-based learning.
2.6.2 Most algorithms involve random changes or motions of particles and act more or less like black boxes
The inherent randomness in many metaheuristic algorithms, where particles or solutions undergo random changes or motions, can make them appear like black boxes. However, researchers can still provide insights into their functioning and behavior by analyzing their key components, operators, and underlying principles.
For example, Ant Colony Optimization (ACO) (Dorigo et al. 2006) is a metaheuristic algorithm inspired by the foraging behavior of ants. Although it involves probabilistic decision-making and randomness, researchers have investigated and explained its behavior based on the pheromone trail updating mechanism and the exploitation-exploration trade-off. Studies have shown how the balance between pheromone trail reinforcement and evaporation affects the convergence speed and solution quality of the algorithm.
Similarly, Particle Swarm Optimization (PSO) (Kennedy et al. 2010a) is another metaheuristic algorithm that relies on the motion of particles in search space. While it involves random velocity updates and position adjustments, researchers have analyzed its convergence behavior and explored the impact of various parameters, such as inertia weight and acceleration coefficients. Understanding these parameters and their effects helps researchers fine-tune the algorithm for improved performance.
2.6.3 Theoretical aspects: no-free-lunch theorems, NP-hardness, and NP-completeness
The no-free-lunch theorems in optimization highlight the absence of a universally superior algorithm that can outperform others on all problems. These theorems imply that any algorithm's performance advantages are specific to certain problem classes or instances. When proposing a new algorithm or modification, researchers should identify the specific problem domains or characteristics where the algorithm excels and provide empirical evidence to support their claims.
Regarding the theoretical complexity of optimization problems, nonconvex optimization problems are known to be NP-hard or NP-complete. This theoretical complexity poses challenges in finding optimal solutions within a reasonable computational effort. In such cases, metaheuristic algorithms offer valuable alternatives by providing near-optimal solutions.
For example, in the field of combinatorial optimization, the Traveling Salesman Problem (TSP) is a well-known NP-hard problem. Researchers have developed various metaheuristic algorithms to tackle TSP, such as Genetic Algorithms (GA) (Yang et al. 2023a), ACO, and Simulated Annealing (SA). These algorithms aim to find good approximate solutions for TSP instances, as finding the optimal solution is computationally infeasible for large-scale problems. Empirical studies comparing the performance of these algorithms on TSP instances of different sizes and characteristics demonstrate their effectiveness in providing high-quality solutions.
Gradient-based methods, on the other hand, are widely used in convex optimization problems, where the objective function is smooth and differentiable. These methods utilize gradient information to iteratively update the solution towards the optimal point. They often offer faster convergence and efficiency guarantees compared to metaheuristic algorithms in convex optimization scenarios.
However, it's important to note that gradient-based methods have limitations in handling non-convex optimization problems, which are prevalent in many real-world applications. The presence of multiple local optima and complex search landscapes make non-convex problems challenging to solve optimally. In such cases, metaheuristic algorithms can explore the search space more extensively and provide near-optimal solutions.
Including a discussion that acknowledges the trade-offs between metaheuristic algorithms and gradient-based methods adds depth to the analysis. It highlights the benefits and limitations of each approach and helps researchers make informed decisions on which method to choose based on the problem's characteristics and requirements.
2.7 Machine learning methods
Data collection, feature selection, and feature categorization are all part of the structural damage detection problem (Farrar et al. 1778). Using statistical or signal processing approaches, feature extraction seeks to adapt a data-driven or physics-based framework to recorded structure response data. These models' design residuals, or parameters, are selected as damage vulnerable variables. Finally, the classification algorithm assesses the existence, position, and degree of damage using the selected features. Machine learning (ML) systems for structural damage identification have been explored and refined in recent decade (Farrar and Worden 2013b). Machine learning algorithms can be classed as supervised, unsupervised, or semi-supervised. Many vibration-based SDD approaches rely on machine learning algorithms, which have grown in popularity. The two types of ML-based SDD approaches are parametric and nonparametric SDD methods. Feature extraction as well as training are the two most typical steps performed by parametric and nonparametric ML-based SDD methods. This trained machine learning algorithm is then used to classify structural damage and estimate its location. Based on this introduction, the five subsections that follow give a review of the existing examples of machine learning algorithms in vibration-based SDD approaches, including supervised, unsupervised, semi-supervised, parametric, and nonparametric approaches. It's worth noting that the SDD operation's feature extraction as well as feature categorization procedures get a lot of attention. A comprehensive structure for damage assessment procedures is depicted in Fig. 4.
Classification of structural damage detection methods
2.7.1 Supervised learning
Most of machine learning algorithms adopt supervised learning, which constructs the statistical model using characteristics from both undamaged as well as damaged aspects of the structure, and also their labels, during training phase (Bishop 2006). This article will explain the benefits and drawbacks of three regularly used categorization methods: artificial neural networks (ANN), support vector machines (SVM), and random forest (RF). The ANN approach has been utilized in civil engineering like a well machine learning model since the 1980s (Adeli and Yeh 1989). Due to their pattern recognition and error tolerance in forming a nonlinear connection among the inputs and outputs, ANNs have gained a lot of interest in SHM and damage diagnosis. The ANN is employed to develop a model that reflects the link across structural vibration data characteristics and structural model properties for structural damage diagnosis through a training procedure. This trained ANN model has ability to recognize damage premised on measurement data (Bakhary et al. 2010a). Artificial neural networks (ANNs) learning techniques can be supervised or unsupervised, however most of these are supervised, particularly in damage detection scenarios.
By merging fuzzy NNs with data fusion approaches, Jiang et al. (2011a) developed a two-stage methodology. In this strategy, structural modal variables were used as inputs to fuzzy NNs. The outputs from several fuzzy NNs were integrated using the data fusion method, providing a consistent and trustworthy damage assessment outcome. In a frame construction, Dackermann et al. (2013) employed ANNs to determine component connection and mass changes. Individual networks were initially trained employing FRF data gathered at several study sites. The findings of every network were integrated to establish final damage circumstances using a network composition. The proposed system ensembles technique to surpassed the ANN's training data strategy by just adding FRF data. Using dynamic displacement reactions and excitation data, Xu et al. (2011) developed NNs to find and quantify joint deterioration.
Hakim and Razak (2013a) applied natural frequencies to train the ANN, that was subsequently used to estimate damage level in a steel girder bridge model. Using same experiment scenario, Hakim and Razak (2013b) compared the ANN to an adaptive neuro-fuzzy inference framework. Artificial neural networks with fuzzy logic systems were merged into a unified architecture that profited from both approaches. The suggested framework's damage diagnosis outcomes were more effective than the ANN's, as per experimental findings. However, ANN algorithms need a great amount of computational work, especially when large DOFs are concerned. As a consequence, damage monitoring based on ANNs is best fit to compact structures to few degrees of freedom.
PCA (principal component analysis) is a statistical technique for reducing dimensionality and extracting characteristics. This method employs orthogonal transformation to condense a significant number of associated variables into a small set of measurements while retaining the most significant data. For reduced-order models, modal analysis, and parameter determination, PCA has been frequently employed on recorded structure vibration responses. The PCA was originally used in structural damage identification by Worden et al. (2000). Some researchers (Dackermann et al. 2013; Li et al. 2011b; Samali et al. 2012; Bandara et al. 2014b) employed PCA to lower the dimensions of the FRF datasets prior to training it by an ANN for damage identification.
Bandara et al. (Bandara et al. 2014b) noticed the number of hidden layers and the number of neurons per hidden layer in process of designing an ideal ANN architecture with the least training and testing errors. Deep learning techniques developed from ANNs, like convolutional NNs (CNNs), have been significantly evolved as processing capability and network architecture have grown in recent years. Adaptive 1D CNNs were proposed by Abdeljaber et al. (2017a), and they combined feature selection and categorization into a single, compact learning unit. As a consequence, such neural networks (NNs) were able to learn directly from data gathered from defined random excitations. It can be executed in near-real-time and utilized for online SHM because modal verification was not necessary. To detect defects in bridge hangers, Duan et al. (2019) employed a CNN technique with the Fourier amplitude spectra of the acceleration effects as the input. The time series signals were converted into picture data by Bao et al. (2019b). By using greedy layer-wise training technique, the deep NNs were programmed to find anomalies in a cable-stayed bridge employing randomly picked and individually tagged image data.
SVM is a supervised learning model for distinguishing among two categories of information. It is recommended to increase the margin and reduce the misclassification while calculating the boundary among two groups (Vapnik 1998). Due to its superior capacity to address nonlinear, high-dimensional, and small sample challenges, SVM has gained favor in recent years for damage assessment (Cortes et al. 1995). SVM resolves the challenges of local reduction and poor statistical skills in compared to conventional NNs (Ghiasi et al. 2016a). To train the SVM, Kourehli (2016) employed the first two partial mode shapes and natural frequencies as input datasets. The kernel function under this approach was selected to be a radical basis function (RBF). The kernel function variables were determined using simulated annealing and the usual simplex approach. Akbar Ali et al. (2022) employed GA to improve SVM parameters to identify bridge deterioration using same input information and kernel function. Numerical investigations have shown that the GA-SVM approach is practical and superior than RBF networks and GA-optimized reverse propagation NNs on a simple supported bridge (BPNNs). To increase the learning ability of SVM, Ghiasi et al. (2016a) designed the thin plate spline Littlewood–Paley wavelet kernel function. The wavelet packet breakdown approach was utilized to generate feature vectors from the acceleration signals, which were then employed as input to SVM. The variables of the SVM were set via social harmony search strategy. The suggested kernel excelled SVMs relying on other combinational plus conventional kernels for multiple damage assessment.
To improve the penalty factors and RBF kernel parameters, Gui et al. (2017a) assessed SVM to three optimization techniques: grid search, PSO, and GA. The time series datasets yielded two sorts of characteristics: AR model parameters and residue errors of statistical variables. The classic SVM's sensitivity, reliability, and efficiency were greatly improved by the optimisation-based approaches. The reliability of residual errors was much higher than the accuracy of AR types. RF is just a decision tree classifier that uses a huge amount of decision trees in an assembly (Breiman 2004). The model forecast is calculated by utilizing majority voting to combine the predictions of every individual tree. Damage diagnosis by RFs and data fusion was suggested by Zhou et al. (2012). Wavelet packet breakdown was used to divide acceleration data into energy data, that were combined via data fusion to produce new energy characteristics. On the basis of the collected features, RFs were used to evaluate structural failure. In tests, the suggested technique outperformed RF alone, SVM alone, and SVM and data fusion in terms of reliability and consistency.
2.7.2 Unsupervised learning
The uniqueness of detection category includes unsupervised learning methods that use only information from a structure's intact state for training. To train a model with unmodified data, machine learning methods are applied. Whenever new measuring data become accessible, the trained model is utilized to assess the structural state. Whenever the discrepancy between observed and anticipated information from the model surpasses a particular level, the structure is regarded out of stable level and is probably damaged.
For online early damage assessment, Santos et al. (2016a) used two statistical learning approaches. The structural reactions were quantitatively modelled using multi-layer convolution NNs. The prediction errors of the NNs were classified using the unsupervised K-means clustering approach. To ensure continued on-line damage diagnosis, these approaches were performed successively in successive time periods. For bridge damage identification, Neves et al. (2017) proposed a model-free ANN-based technique. Accelerations gathered on the normal bridge were used to train ANNs utilizing an unsupervised learning strategy. A Gaussian process was utilized to mathematically describe each network's forecast mistakes in order to calculate a fault diagnostic threshold. As an outcome, the structural status, i.e., if it was normal or affected, was evaluated by relating damage indices to the set threshold.
Rafiei and Adeli (2018) retrieved characteristics from the frequency domain of ambient vibrations using an unsupervised restricted Boltzmann machine. For every structural component, a structural fitness index was computed using a probability density function (PDF) that correlated the present state of the system to the ambient vibrations of a normal one. The greater the discrepancy, the greater the danger. To diagnose and localize structural degradation, Cha and Wang (2018) switched from a density peaks-based rapid clustering methodology to an unsupervised machine learning technique. The training values from every sensor in the structure's original phase were employed to develop a statistical model that was whole. The sensor that related to the novelty feature was found to be damaged. Avci and Abdeljaber (2016) proposed an unsupervised self-organizing map-based damage detection algorithm relying on ANNs. To obtain damage indices from the observed structure's random acceleration reactions, their method employed self- organizing maps. The result of the total of the indices denoted the overall soundness of the structure, and it could be used to estimate the degree of the damage.
2.7.3 Semi-supervised learning
Obtaining entirely labelled data for training, is practically hard in reality, albeit a modest quantity of labelled data may be accessible. In these instances, semi-supervised learning, which really is intermediate among unsupervised and supervised learning and employs both labeled and unlabeled datasets to train classifiers, might be quite effective. Machine learning algorithms could be considerably improved by integrating unlabeled data with a little quantity of labelled data, according to many studies (Farrar and Worden 2013b). Semi-supervised learning can discover and measure structural degradation instead of merely recognizing novelty. Damage identification utilizing semi-supervised machine learning techniques, on the other hand, has a lack of research.
Chen et al. (2014b) employed a mix of multi-resolution categorisation and semi-supervised learning to identify bridge degradation. Localized time–frequency sub-bands were used to extract the characteristics. Unlabeled data was classified using previously tagged signals using the adaptive graph filter algorithm. In order to make a global conclusion, a weighting algorithm was designed to incorporate information by both labelled and unlabelled signals. The adaptable network filtration was capable of managing both incorrectly labeled and unobserved signals as well as, to unlabelled data. To identify and describe linear/nonlinear structural failure, Lai and Nagarajaiah (2019) devised a semi-supervised system. The sparse identification method learning—based on input–output time history data was used to generate the foundation (undamaged) model. Damage was considered as a variant of the restoring force, with the damaged system turned into a linear equivalent exposed to exterior disruption forces and pseudo-forces. As a result, nonlinearity was expressed by pseudo-forces, which were identified unsupervised with no need of design distinct damage cases.
For online damage identification premised on high frequency domain characteristics, Rogers et al. (2019) used clustering models. Without going through a training phase, the system learned online-data clusters and then gave tags to additional clusters in a semi-supervised manner. As new data was collected, the model with established structural states was regularly updated. The method's robustness enhanced as it acquired additional states over time. Recently, machine learning techniques have attracted a lot of attention in the field of damage recognition. However, several hurdles and limitations remain, needing additional research. To be effective, machine learning algorithms require a big training dataset. As a consequence, picking data, cleaning data, compressing data, fusing data, normalizing data, and labeling data are all necessary procedures in constructing the best datasets. The procedures are time-consuming and require a substantial level of work. A shortage of training data in structural damage identification can lead to over-fitting difficulties, like the removal of unnecessary characteristics like measurement noise (Ye et al. 2019). For ML algorithms, the problem of generalization is crucial. A model that has been properly trained as well as verified may only be effective for a given structure and damage sequence. Some of the machine learning approaches presented in this section are compared and summarized in Table 3.
2.7.4 ML approaches for SDD relying on parametric and non-parametric vibrations
Machine learning (ML) is increasingly applied to detect vibration-induced structural damage. Traditional ML algorithms don't identify modal information from structural systems. This information is extracted using input–output or output-only modal analysis methods. Extracted modal parameters are crucial for Structural Damage Detection (SDD) and localization. Non-parametric ML-based SDD has seen exploration of various feature/classifier combinations. The integrity of structures is gauged by analyzing these parameters with a trained ML algorithm. Commonly, the ML techniques employed utilize Artificial Neural Networks (ANNs), also known as Multi-layer Perceptrons (MLPs), as classifiers. These focus on modal features like natural frequencies and mode shapes.
Pawar et al. (2006) combined Spatial Fourier Analysis with ANNs to detect damage in fixed–fixed beams via Fourier coefficients as damage indexes. They used spatial Fourier analysis to discern mode shapes from the beam's free acceleration response. Similarly, Zar et al. (2022) introduced a vibration-based technique for arch dam damage detection. They utilized least-square support vector regression to link dynamic elastic modulus with modal parameters, while salp swarm algorithms (SSAs) identified dynamic parameters by analyzing vibration data. Using a hyperbolic concrete arch dam as an example, Fig. 5 displays mode shape predictions under noisy conditions. The approach effectively detects minor damages in such data but needs real-world validation, especially for online SDD applications.
Zar et al. (2022) compare calculated and measured values of third-order mode shape at arch ring
Mehrjoo et al. (2008) employed an ANN-based SDD technique to compute damage-sensitive attributes from a truss bridge's acceleration response. A MLP with a hidden layer was devised for damage detection. Truss member stiffness was reduced to simulate damage, with the network trained over 75k epochs using a back-propagation algorithm, indicating potential for real-time SDD application. YiFei et al. (2023) introduced an innovative structural damage identification approach, utilizing a surrogate modelling strategy combined with a K-means clustering optimizer and genetic algorithm (HKOGA). This method optimizes the surrogate for finite element models, enhancing efficiency in determining the best objective function value. HKOGA outperformed seven other algorithms in 23 benchmarks. The method proves highly efficient for large structural damage identification. The experimental setup and frequency response function (FRF) of a small-scaled laboratory dam are depicted in Fig. 6, highlighting the first eight peak frequencies.
Experimental setup and results for modal analysis of the small-scaled dam model. Left: required experimental devices. Right: frequency response function based on hammer test
Yuen and Lam (2006) explored ANNs in Structural Damage Detection (SDD) using the modal parameters of a five-story building model, an MLP, and five input neurons. The importance of the number of hidden layers and neurons is often overlooked in favor of the Bayesian probabilistic method for choosing an appropriately complex ANN model. The authors introduced a two-phase damage detection and a Bayesian ANN design. They used 32 input-target pairs for training and started by simplifying ANNs to one hidden layer, focusing on the number of hidden neurons. The optimal ANN structure was found to have six hidden neurons, chosen using a Bayesian approach. To replicate damage, the interstory stiffness was cut by 20%-80% at different points in the model. The proposed method successfully identified both singular and multiple damage scenarios. The use of an ANN with multiple hidden layers requires real-structure validation. Using an extended Bayesian approach (Ng 2014) for SDD and damage localization, ANNs were trained on a simulated benchmark. This research compared a reference model's modal features against varied structural damage states, discovering that tangent sigmoid functions with 17 hidden neurons were most effective. The method adequately assessed SDD's efficiency on the benchmark structure, noting minor modal parameter changes with damage presence.
To improve damage detection accuracy, Akbar et al. (2021) suggested using multiple ANNs as opposed to one ANN. Using a machine–learning-based parametric approach, the authors identified seismic damage in steel moment frames representing a five-story office building. Next, the final stiffness and mass of the structure after a severe earthquake are determined after calibration of the structure's initial stiffness and mass. Using modal parameters (i.e. damage features) and outputs from ANNs, the modal mass and stiffness of structural members were computed. ANNs are trained from results of FE models. The algorithm evaluates damage predictions made using unseen data as fairly accurate. It is, however, sensitive to modal parameter errors. To test its ability to predict stiffness and mass changes in a real building, this method must be tested on a real building first.
Bakhary et al. (2010b) introduced a two-stage ANN classifier for efficient SDD and SHM in large structures. Their study featured a two-span reinforced concrete slab measuring 6.4 by 0.86 m with a 10 cm thickness. The ANN analyzed performance at 33 centerline points over the slab's length across four damage scenarios. They used FE models, considering the first three modal frequencies. The neural network determined substructure local frequencies using these modal frequencies. By contrasting damaged and undamaged model distributions, they derived the probability of damage existence (PDE). Assuming uncertainties in all data and Gaussian distribution errors, a second ANN processed the first's output to pinpoint structural damage. Ultimately, their FE findings mirrored laboratory-tested slab results. This method excelled in detecting minor damage areas, corroborating Trendafilova et al. (1998) who emphasized probabilistic over deterministic interpretations for SDD. Given its validation on a sizable structure, the approach shows broader applicability.
Lee and Kim (2007) verified ANN-based damage detection through analytical and experimental means. They trained an ANN by contrasting mode shape alterations to an undamaged state, utilizing Seoul's Hannam Grand Bridge. With ambient vibration testing, the ANN was assessed under three damage situations, showing strain signals' superiority over acceleration responses. Injury magnitude correlated inversely with misclassification, but significant FRF alterations led to higher misclassification rates. Various networks, including BPNNs and PNNs, were explored for damage localization. While traditional BPNN struggled with multi-damage detection, leading to potential false alarms, PNNs using sequential estimation excelled. Despite the method's potential in Lee and Kim (2007), the cited false alarms caution against broad generalizations.
Minh et al. (2023b) introduced a novel variable velocity strategy particle swarm optimization (VVS-PSO) (Minh et al. 2023b) that enhances optimization solutions from numerical functions to real-world applications. By adding a term governed by a reduction linear function to the velocity update at each iteration, VVS-PSO attains faster convergence and higher accuracy. Compared to the original PSO, VVS-PSO offers greater flexibility in position updating and broadens the search space around particles. Its efficacy is demonstrated against the original PSO and four other optimization algorithms using 23 benchmark functions, an engineering design problem, and a test on a four-story steel frame by Columbia University (Fig. 7a, b). VVS-PSO showcased remarkable accuracy and reliability in structural damage identification. Hakim et al. (2015) examined an ANN-based SDD using an I-beam where slots of varying depths were made on the beam flange. They measured the beam's acceleration with a shaker and identified five natural frequencies for both undamaged and damaged cases. The neural network (ANN) was trained to detect frequency changes linked to damage location and severity. While ANN struggles to identify very-light double damages due to unaltered modal curvature, its predictions on damage severity remain accurate. Even amidst noisy data, the ANN ensemble predictions are reliable, but generalizing this method requires testing on larger structures.
Experimental setup of: a healthy structure, b geometry dimensions and c damaged structure (Minh et al. 2023b)
Betti et al. (2014) combined ANNs and genetic algorithms for an SHM problem based on field measurements from Johnson et al. (2004). Flange deterioration results in increased structural damage. They utilized input-only modal identification for recognizing modal characteristics from ambient vibrations. FFBP, having two hidden layers, was employed for damage categorization. The network comprised of four neurons in the input layer processing a frequency-dependent index. The following neuron layers processed linear output combinations. Using a genetic algorithm, they enhanced the FE model to better reflect the actual structure. The combination of ANNs and GAs proved potent for SDD, as evidenced by the benchmark structure data, suggesting potential for wider application.
Tiachacht et al. (2021) utilized modal strain energy change ratio (MSEcr) for damage identification and introduced a slime mould algorithm (SMA) for optimization. Their study focused on a laboratory beam and a bar planar truss, examining both single and multiple damage scenarios against different mode numbers. Experimental validation, illustrated in Fig. 8, used a four-story steel frame from Columbia University, New York, with sensor positions also shown in Fig. 8. The method was tested on this damaged 3D frame. Their approach, integrating MSEcr and SMA, yielded impressive results, even when challenged with white Gaussian noise at 2% and 4%. It effectively pinpointed damage location and intensity, maintaining high precision even post-noise introduction.
Tiachacht et al. (2021) exhibit the four-story shear-type steel frame
Several techniques have been employed for feature extraction from modal identification. Rucka and Wilde (2010) combined modal testing and wavelet transformations to detect damage, primarily focusing on determining mode shapes from ambient responses. After applying CWT to the computed modes, the MLP was trained using SDD and damage localization via CWT layers (100 neurons in the first hidden layer and 20 in the second). They tested this on small plate, beam, and shell structures, achieving an average error of 3.17% for all damage states. However, they noted that damage regions were minimal, contributing only 0.2% to the shell's total area. This method's applicability to larger structures remains to be validated.
Lam and Ng (2008) presented a parametric ML-based study leveraging Ritz vectors and modal parameters. By adopting a Bayesian approach, they optimized hidden neuron numbers and their activation function, subsequently implementing an MLP classifier. This method was evaluated using an analytical benchmark model (Johnson et al. 2004), highlighting its efficiency and simplicity. Tansig emerged as a preferable activation function over Satlin for SDD. Additionally, MLPs trained using modal parameters outperformed those with Ritz vectors. Other ML-based parametric approaches utilized ANNs and MLPs for feature classification. Jiang et al. introduced models merging rough set processing, PNNs, and SDD, which showcased potential in SDD. However, their real-world applicability still needs confirmation. Similarly, Lee and Lam (2011) combined GRNNTA with a fuzzy ART model, effectively training GRNNFA on modal parameter changes due to structural damage. While promising, especially in noisy environments, it awaits real-structure validation for broader application.
Jiang et al. (2011b) combined ANNs with fuzzy neural networks (FNN) and data fusion, showcasing their superiority over other SDD methods. Initially, FNN-based SDD assesses the data, followed by refinement using data fusion and FNN models. The integration of a fusion decision-making model was pivotal, enhancing accuracy and reducing uncertainty. Notably, these outcomes were simulation-based, suggesting the need for real-structure validation before wider application. Wen et al. (2007) introduced an unsupervised fuzzy neural network (UFN) for SDD. Damage location, based on reduced stiffness, is termed as damage localization (DLF). Upon detecting damage, a DLF is computed, and UFN determines the damage site. This was tested on a five-story model under various damage scenarios. Despite the model's effectiveness, real-structure validation remains a recommendation.
Khatir et al. (2020) proposed a method for crack identification by refining the training of Artificial Neural Networks (ANN) parameters using the Jaya algorithm. The eXtended IsoGeometric Analysis (XIGA) introduces dynamic and static datasets, elevating accuracy based on frequency and strain measures. Leveraging XIGA's precision in fracture mechanics, datasets from cracked plates enhanced the ANN technique. An objective function, the difference between measured and predicted frequencies, calibrates the XIGA model. The crack's dimension is adaptively predicted without prior information, using data from a numerical model. The Jaya algorithm optimizes crucial ANN parameters. Figure 9 displays the experimental setup, and Fig. 10 presents the updated XIGA cracked plate model results. Validated using experimental cracked plate data, the method reliably and accurately identifies crack lengths.
Set-up of Free-Free vibration of cracked plate and XIGA model (a) and Frequency Response Function (FRF) of healthy plate from measurements (b) (Khatir et al. 2020)
Model updating set-up (a) and updated parameters (b) (Khatir et al. 2020)
Structural health patterns can be discerned using parametric ML techniques drawing from algorithms and symbolic data. Cury and Crémona (2012) conducted a comparative study, focusing on feedforward ANNs, SVMs, and Bayesian Decision Trees (BDT). Utilizing Symbolic Data Analysis (SDA), they analyzed ambient conditions and acceleration recordings to quantify structural reinforcement on a French steel railway bridge (Fig. 11). This bridge featured specialized bearings (Fig. 11) that adjusted the first natural frequency away from the passing train frequencies. While traditional analyses were ineffective for SDD, the SDA-SVM method reached a 100% accuracy when training with 30% of tests. Meanwhile, the SDA-BDT's detection rate peaked at 90%. Both SDA-NN and SDA-SVM demonstrated superior performance, categorizing 100% of cases after 10,000 simulations, especially in mode shapes comparison.
In Cury and Cremona (2012), unique bearings (right) were used to support a railway bridge in France (left)
In another study, Yeung and Smith (2005) employed ANNs to detect vibration signatures from a FE model of a suspension bridge to analyze SDD. This FE model simulated a 40 kN vehicle's impact and the subsequent damage from interrupted riveted girder connections. ANNs' sensitivity was gauged by modifying thresholds and noise levels. Two unsupervised ANNs, the PRAN (Roberts and Tarassenko 1994) and the DIGNET (Thomopoulos et al. 1995; Wann and Thomopoulos 1997), were trained using these vibration signatures. The SDD recognized 70% of structures with moderate noise. Yet, this method requires real-structure validation before broader application.
Artificial Neural Networks (ANNs) were explored by Goh et al. (2013) for their ability to classify structural damage. The authors highlighted that while it's challenging to add sensors, increasing measurement points enhances the reliability of ANNs. Their study contrasted ANNs and cubic spline interpolation for predicting mode shapes with limited sensors. The findings revealed that ANNs, working in two stages—predicting mode shapes and executing Structural Damage Detection (SDD)—outperformed cubic splines in measurement point reliability. Using a Finite Element (FE) model of two-span concrete slabs, ANNs effectively predicted mode shapes and damage locations. However, real-world validation remains essential before broad application. Zara et al. (2023) focused on damage identification in composite structures crafted from glass fibre reinforced polymer (GFRP). The study introduces an enhanced ANN, harnessing optimization algorithms to pinpoint exact crack lengths. The material's characteristics were ascertained via static bending, tensile, and modal analysis tests. Further numerical validations used ABAQUS, referencing Fig. 12 for geometry and Fig. 13 for three-point bending tests. Conclusively, the E-Jaya optimization proved superior in accuracy, affirming this ANN's potential for assessing composite structures' integrity.
Left: The flexural test geometry and dimensions, Right: a specimens before the test, b three-point bending test machine and c the specimens after testing by Zara et al. (2023)
Left: Tensile test with specimen dimensions, Right: specimens before test (a), test machine (b) and the specimens after testing (c) by Zara et al. (2023)
Artificial Neural Network (ANN)-augmented Finite Element (FE) models for bridge analysis were presented by Lee et al. (2014). Their research involved analyzing a beam model, simulating a lab structure via FE, and evaluating field data from an actual bridge. Their ANN-based Structural Damage Detection (SDD) method factored in FE model errors by focusing on modal properties. By using mode shape variations before and after damage as inputs, ANNs could efficiently forecast bridge SDD even amidst traffic. Although SDD effectively pinpointed damage locations on a real bridge, a few minor inaccuracies were observed. Before wider implementation, validation on a large scale is essential. Meanwhile, Zhou et al. (2014) explored wind data from two notable bridges in Hong Kong to perform an SDD analysis on cable-supported structures, using modal frequency and Probabilistic Neural Networks (PNN). Their three-layer PNN, trained solely on modal frequency details, excelled in locating SDD, especially when noise was under 0.2. This PNN method, leveraging Bayesian inference to interpret measurements, appears promising. However, for a broader acceptance, its methodology must be corroborated using real structural data.
Ho et al. (2022), presents a novel method for pinpointing and evaluating damage in plate structures using a unique damage index named "mode shape derivative based damage identification (MSDBDI)". This research introduces ALOANN, a fusion of an artificial neural network (ANN) and an antlion optimizer (ALO), which refines ANN's starting parameters via mean squared error (MSE). This effectively overcomes MSDBDI's constraints. Two numerical applications were showcased: damage detection in plate-like structures and modeling a composite structure with various damage scenarios. One significant case features a steel cantilever plate (1.5 × 1 × 0.01 m3) shown in Fig. 14, where the damage index evaluates changes in modal properties. ALOANN outshines traditional ANN, even with modal property noise. This advancement greatly benefits plate structure damage identification.
Geometry, measurement points and damaged areas of the observed structure. by Ho et al. (2022)
The study of structural damage has evolved to consider operational and environmental factors beyond just physical damage. Traditional metrics, such as maximum and variance values, are no longer sufficient on their own. There's a shift towards using time-series models for feature extraction in machine learning (ML) nonparametric methods. Chun et al. (2015) and Figueiredo et al. (2011) simulated vibrations on a model three-story building using a random shaker, introducing various structural conditions. Damage was identified using AR models. An AANN trained on this data outperformed other classifiers in discerning between environmental and operational changes (Chun et al. 2015; Figueiredo et al. 2011). However, its broader use requires training on diverse datasets. Santos et al. (2016b) focused on kernel-based methods for Structural Damage Detection (SDD). They tested AR coefficients with several classifiers on a shaken three-story steel structure. The study found that SVDDs and SVMs reduced false negatives while KPCA and GKPCA minimized overall errors, but localization was not explored. Gui et al. (2017b) utilized SVM alongside optimization techniques like PSO, Grid Search (GS), and GAs for SDD through vibration data analysis. Sixteen damage-sensitive features were pinpointed. Their results revealed that specific combinations, including GS + RE and PSO + AR, achieved the highest accuracy in classification. Specifically, SVMs with RE were notably sensitive to damage-induced nonlinearity, with GS showing superior classification due to its parameters. Lautour and Omenzetter (2010) analyzed vibration responses of a benchmark structure. They implemented AR models to evaluate acceleration responses and used an ANN based on AR model coefficients. After using PCA for dimension reduction, they trained an MLP. One ANN design with a single hidden layer yielded a low error rate of 3.4% over 88 data points, illustrating the efficacy of combining AR models and ANNs for SDD.
In (Bandara et al. 2014c), a ten-story building's accelerometers captured vibration responses. These PCA-based damage indices informed the training of a multilayer feedforward Artificial Neural Network (ANN) designed for damage assessment. The ANN was divided into training (50%), validation (25%), and testing (25%) to enhance its accuracy. It dealt with 240 datasets involving various damage cases and noise levels. To pinpoint damage locations, 13 ANNs, inclusive of some for FRFs, were employed. Each had a distinct layering pattern. Laboratory setup used in Bandara et al. (2014c) has been shown in Fig. 15. The results verified the method's proficiency in translating FRFs to damage indicators using ANNs. The approach in Dackermann et al. (2010) mirrored that of the lab structure, where ANNs were trained to recognize varying damage degrees. ANNs trained with FRF aggregation proved more precise than those using just a single FRF. Although the technique from Bandara et al. (2014c) and (Dackermann et al. 2010) is promising, its application to larger structures remains to be tested.
Bandara et al. (2014c) show a laboratory setup (left) and an example FRF analysis for SDD (right)
Dackermann et al. (2010) used PCA on raw vibration signals without AR models in an ML-based nonparametric SDD research. Using PCA and ANN, they tackled challenges like noisy and incomplete data. They analyzed the beam's noise-filtering efficiency using PCA through numerical and experimental tests. Numerical data was examined using a Gaussian noise model. Accurate predictions were observed for noise levels of 1%, 2%, and 5%. However, samples with 10% noise were less accurate, especially in minor damage states. Testing on larger structures might offer more comprehensive insights.
Many ML-based nonparametric SDD studies utilize AR modeling and PCA. Liu et al. (2011) applied wavelet decomposition for acceleration signal feature extraction. SDD used wavelet packet transforms (WPTs), multisensor feature fusions, and ANN classification (Johnson et al. 2004). By breaking down accelerations using orthogonal wavelets, each frequency band's relative energy was noted. Wavelet packets depicted sensors' energy, serving as ANN classifier inputs. The integration of WPT, multisensor fusion, and ANN for SDD looks promising, but it needs further validation on real-world structures.
Ghiasi et al. (2016b) presented a machine learning approach combining Wavelet Packet Decomposition with SVM classification, utilizing benchmark data from Johnson et al. (2004). This method integrated a modified Littlewood–Paley function into a wavelet kernel. When compared to other SVM-based models, our model, optimized using a harmony search algorithm, showed that Wavelet kernels with the Thin Plate Spline Littlewood-Paley spline performed better. Tests on lab data and an FE model indicated its potential for broader SDD applications. A future direction is applying this to real-time structures to further validate its adaptability. Zhu et al. (2014) also relied on benchmark data from Johnson et al. (2004) for their machine learning system that identifies and predicts responses. Their approach employed interval modeling for feature extraction and the Adaptive Neuro-Fuzzy Inference System (ANFIS) for SDD and damage classification. Damage in their FE model, created with Abaqus software, was simulated as element removals. Using hammer excitation and data contaminated with noise, their method detected damage in 0.02–0.03 s. After training, ANFIS simulations generated a displacement vector. Training in 10% noise yielded reliable SDD outcomes with the ANFIS model. However, testing on an actual structure is needed before generalizing its use.
A nonparametric ML-based method was proposed by Abduljaber and Avci (2016). Self-Organizing Map (SOM) class unsupervised classifiers measure vibration response of a structure to randomly generated excitations (Abdeljaber and Avci 2016; Avci et al. 2019a). MLPs were used to process the damage indices to perform SDD and determine the severity of structural damage. Finite element simulations for stiffness loss and boundary condition changes were required to validate this method. A similar approach was used to achieve successful SDDs and localizations in another study by using DL and ANN (Abdeljaber et al. 2016a; Krizhevsky et al. 2012; Hinton and Salakhutdinov 2006; Mohamed et al. 2018; Patterson and Gibson 2017; Fallahian et al. 2017, 2018). Despite the algorithm performing well in analytical models with noisy signals, it needs to be tested on a real structure before it can be applied to other applications. Bandara et al. (2014c) and Dackermann et al. (2010) introduced a method for damage detection using Principal Component Analysis (PCA) of frequency response functions (FRFs). They utilized a Finite Element (FE) model for simulating stiffness reduction (Ghiasi et al. 2016b) and studied a three-story lab frame with specific features (Zhu and Wu 2014).
Addressing the complexities in engineering structures necessitates methodologies for early defect detection to ensure longevity and cost-effective safety. Discrepancies exist between experimental and numerical modal data due to unknown structural parameters and uncertainties. Finite element (FE) model updating techniques aim to rectify these by adjusting these unknowns, being pivotal for establishing baseline models and accurate damage identifications. Ghannadi et al. (2023) utilize the semi-rigidly connected frame element (S-RCFE) for creating a high-fidelity numerical model, demonstrating better performance over the standard Euler–Bernoulli beam element. Although GWO-MTMAC and IGWO-MTMAC have comparable FE model updating efficiency, IGWO offers more reliable damage identification results but demands more computation time. Figure 16 displays the test steel beam used, and Fig. 17 depicts the lowered natural frequencies post-crack introduction.
Experimental set-up and simulated model of the free-free beam (Ghannadi et al. 2023)
The experimental FRF of the cracked free-free beam—double notches (8 mm) (Ghannadi et al. 2023)
Nguyen and Magd (2023a) presented a method for slab structure damage detection using 2D curvature mode shapes, Convolutional Neural Networks (CNN), and Faster Region-based Convolutional Networks (faster R-CNN). The curvature of damaged and intact slabs were contrasted and visualized as images. A Finite Element model simulated 400 damage scenarios, training both CNN and faster R-CNN on damage types. Figure 18 demonstrates a steel slab test (2.5 m × 0.35 m × 0.01 m), revealing the method's high accuracy and significant overlap in damage predictions, suggesting its real-world applicability.
Nguyen and Magd (2023a) provide an outline of the SDD framework
Shirazi et al. (2023) introduced a hybrid YUKI-ANN for Structural Health Monitoring (SHM) of laminated composite plates. They used a finite element model to detect damage in five elements of the plate. The identification involved two steps: damage localization using a Modal Strain Energy change ratio (MSEcr) indicator and quantification using an ANN optimized with four algorithms. Figure 19 illustrates the model and element setup. YUKI-ANN outperformed PSO and BCMO algorithms in accuracy and computational time. Though AOA occasionally had better accuracy, it took eight times longer than YUKI-ANN.
By Shirazi et al. (2023), Simply supported three-ply [0° 90° 0°] square laminated plate modelled with a grid of 9 × 9
Dang, Bao-Loi, Hung Nguyen-Xuan, and Magd Abdel Wahab's paper (Dang et al. 2023a) introduces a method to calibrate 2D VARANS-VOF models for studying wave interactions with perforated breakwaters. Using a data-driven approach and gradient boosting decision tree algorithms, they optimally determine empirical coefficients for drag force. The model effectively predicts hydrodynamic traits with high accuracy, as validated by experimental data, especially in wave propagation contexts shown in Fig. 20. Despite a limited sample size, the study highlights the potential of GBDT in recognizing non-linear parameter impacts, enhancing the ocean engineering field. Tran-Ngoc et al. (2020) present a method combining machine learning (ML) and the Cuckoo Search (CS) technique to improve accuracy in structural damage detection. They also use a vectorization technique to lessen computational effort. Comparing ML, CS, and combined methods (MLCS1 and MLCS2) on different damage scenarios, they found the MLCS2 method excelled in accuracy and efficiency. This research highlights the potential of merging ML and search techniques in structural health monitoring.
Dang et al. (2023a) show a Empty numerical wave tank (NWT) to test the numerical model. b NWT with structure
2.7.5 Drawbacks and limitations in machine learning
Machine Learning (ML) methods are emerging as promising tools for vibration-based Structural Damage Detection (SDD) applications. A primary focus within this domain has been on feature extraction and categorization. Based on a comprehensive literature review, it's clear that these techniques involve the derivation of specific properties, often hand-crafted by the user, from vibration data. The choice of features and the classifier determines the efficacy of ML-based SDD systems. Correctly identifying these features is vital to maintain the signal's intrinsic data, and an apt classifier is crucial for accurate damage detection.
Researchers in both parametric and nonparametric vibration-based SDD fields have experimented with various feature/classifier combinations. The aim is to find an optimal pairing that can effectively characterize structural failures. Yet, current ML-based SDD methods have certain challenges:
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Supervised learning requires data from both undamaged and damaged structures. Often, real-world data for varied damages is scarce, leading researchers to rely on lab tests or Finite Element (FE) simulations. The accuracy of these models impacts the efficiency of supervised learning, making unsupervised algorithm design an attractive solution.
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While unsupervised learning is favoured for genuine damage detection, many of these methods only provide initial damage identification without further details on the damage's location or severity.
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A feature/classifier combination, optimal for one structure might not be ideal for another.
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Similarly, there's no assurance that a specific set of features will be universally effective for detecting all types of structural damage. For instance, features ideal for detecting stiffness loss might not detect changes in boundary conditions effectively.
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The use of ill-suited features or classifiers will likely result in subpar SDD performance.
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Methods like modal prediction, AR modeling, and PCA, while effective, are analytically intricate and time-intensive. This makes them less suitable for real-time Structural Health Monitoring (SHM).
Most current ML-based methods are centralized, meaning all signals must first be collected and processed in a single system before damage detection can commence. Such centralized approaches come with strict requirements. For instance, a majority of the network's sensors must be operational for effective damage detection. Centralized systems also pose challenges in Wireless Sensor Network (WSN) applications.
2.8 Vibration-based structural damage detection by deep-learning
Artificial neural networks (ANNs) generally include an input, hidden layers, and an output layer. When there are more than three layers, it falls under deep learning (DL). Deep Learning, a pinnacle of Machine Learning advancements, addresses challenges previously deemed highly complex. While AlexNet emerged in 2006, the DL epoch truly started with Hinton and Salakhutdinov's paper (Hinton and Salakhutdinov 2006). ANNs, irrespective of their depth, can learn effectively with ML. DL expands on this by adding depth and increasing hidden layers, enabling the system to scrutinize vast datasets for intricate patterns. Traditional ML methods heavily lean on handcrafted features; when these features aren't ideal, the resulting classifier can perform poorly, leading to unreliable results as indicated in Mohamed et al. (2018). In contrast, DL methods, such as deep convolutional networks, derive "optimized" features directly from raw data, enhancing classification performance—a boon for engineering applications confronting intricate classification issues.
DL facilitates communication between various abstract layers. Thus, through DL, multi-layered computation models can grasp data representations at different abstraction levels. DL algorithms not only learn correlations between features and outputs but can also oversee the entire extraction process. This means a well-trained DL system can directly map raw inputs to final outputs, sidestepping preliminary feature extraction, making them adept at decomposing complex tasks into simpler segments.
Marafini et al. (2023) examine the role of machine learning in Structural Health Monitoring (SHM), introducing a new classification system centered on vibration-based monitoring. Their research showcases how machine learning is versatile in SHM stages, from data processing to damage identification. Notably, they highlight the significance of these methods in preserving historic buildings, drawing from recent studies on cultural heritage structures. On the other hand, Patterson and Gibson (2017) detail four deep learning architectures: unsupervised pretrained networks (UPNs), convolutional neural networks (CNNs), recurrent and recursive neural networks. Figure 21 illustrates that UPNs encompass Deep Autoencoders, Deep Belief Networks (DBNs), and Generative Adversarial Networks (GANs). This review focuses on UPNs (Autoencoders) and CNNs as they are mainly applied in vibration-based SDD applications.
Frameworks for deep-learning
2.8.1 Autoencoders and unsupervised pre-trained networks (UPNs)
The idea of UPN architectures (GANs) can be exemplified by autoencoders, Deep Belief Networks (DBNs), and Generative Adversarial Networks (GANs). In this paper, we discuss autoencoders as they are the only UPN architecture that can be used in vibration-based SDD systems. According to Hinton and Salakhutdinov (2006), autoencoders are more efficient than ANNs. Using an autoencoder, the fundamental features of the input images are determined. A "Deep Autoencoder" has many hidden layers between the input and output as opposed to a simple autoencoder, which has one. "Deep Autoencoder" is commonly called "Autoencoder" in DL terminology. Because autoencoders learn from the original data, they are excellent for classification. Until Fallahian and colleagues introduced ensemble classification based on weight majority voting (Fallahian et al. 2017) and subsequent work (Fallahian et al. 2018) SDD did not use autoencoders. They were named Deep Neural Networks (DNNs) after the Autoencoder method by Hinton and Salakhutdinov (2006). Fallahian et al.'s work is mentioned under the category of Autoencoders, as classified by Patterson and Gibson.
In Lado-Roigé et al.'s study (2023), a novel method called Learning-based video motion magnification (LB-VMM) is introduced for detecting damage in civil structures. Utilizing deep learning, LB-VMM identifies structural vibrational characteristics more effectively than traditional techniques. The method's validation on a lab-tested, three-story benchmark (Fig. 22) highlights its efficiency for structural health monitoring across various damage scenarios. Despite certain constraints like the requirement for a fixed camera and uniform lighting, LB-VMM's cost-effectiveness is notable, enabling monitoring at multiple points with a single camera. This paper sets a new direction in vibration-based structural monitoring.
Three-story building benchmark setup for validation test (Lado-Roigé et al. 2023)
Singh and Kaloni (2023) focus on improving Structural Health Monitoring (SHM) by incorporating deep learning (DL) for damage detection. Unlike traditional manual inspections that have limitations, DL offers the advantage of removing the need for predefined feature engineering, leading to stronger data-driven models. Their approach has a remarkable 98% accuracy on new datasets.
Fallahian et al. (2017) have indicated that modal properties serve as reliable damage indicators in vibration-based SDD methodologies. Their innovative SDD algorithm factors in variables like temperature and noise to assess a structure's health. This algorithm uses both automatic encoding and couple sparse coding (CSC) in its pattern recognition, while also applying PCA to distill the measured FRF data into distinct patterns. It assumes the materials' elastic modulus to be temperature-dependent, with temperature as an input. Validated using data from the I-40 bridge and a truss bridge, their method emphasizes the importance of recording temperatures from different locations due to its impact on result accuracy. In a subsequent study, Fallahian et al. (2018) expanded their methodology, using autoencoding and CSCs on data from aluminum beams. They studied two damage cases for beams and applied pattern recognition-based SDD through FRF. Their approach, validated using a 3D FE truss bridge model, was then compared in effectiveness against other methods under various conditions.
Lastly, Chen et al. (2023a) introduced an advanced method for structural damage detection. They blended one-dimensional and two-dimensional deep convolutional neural networks and used domain adaptation techniques to address challenges such as limited labeled data. This method efficiently extracts detailed spatiotemporal features from vibration data, performing excellently even with limited data. The proposed model's architecture can be seen in Fig. 23, showcasing the advantages of DL in real-world engineering scenarios.
Architecture of the proposed model (Chen et al. 2023a)
Zhang et al. (2023b) explored the potential of convolutional autoencoders (CAE) in identifying damage in seismic-isolated structures using vibration data. Their findings, verified by an analytical finite element model, indicate the CAE's consistent performance in pinpointing both broad and specific damages in the isolation layer. Figure 24 outlines the CAE-aided assessment process for the Structural Health Monitoring (SHM) system. This method aids building managers in making informed decisions. In a related study, Cao et al. (2023) proposed a method for seismic damage detection in high arch dams. Their denoising contractual sparse deep auto-encoder (DCS-DAE) model, illustrated in Fig. 25, combines various autoencoder strengths. Paired with a reconstruction error framework and a WKNN algorithm, the model provides reliable damage identification using only undamaged structure vibration data, making it especially useful in noise-filled surroundings.
Procedure of the distributed CAE-aided vibration assessment (Zhang et al. 2023b)
Auto-encoder neural network architecture (Cao et al. 2023)
Sawant et al. (2023) presented a novel vibration-based method for structural damage detection using transfer learning from a convolutional autoencoder (TL-CAE). This method improves damage detection accuracy, especially considering environmental factors like temperature. Notably, the TL-CAE utilizes raw time-domain signals, negating the need for pre-processing or knowing material properties. Figure 26 illustrates this. The technique is adaptable across various materials, structures, damages, and temperature ranges, hinting at scalability with more data. In a related study by Abbas et al. (2023), deep learning, specifically a deep auto-encoder (DAE), is employed for assessing the health of underground metro shield tunnels. By analyzing raw vibration data from a metro tunnel model under moving load, the DAE identifies structural damage effectively, confirmed using the root mean square (RMS) for pinpointing damage. This DAE method also works for simply supported beams, highlighting its versatility in underground structural health monitoring.
Illustration of the proposed TL-CAE based temperature-compensated damage identification and localization method (Sawant et al. 2023)
Pathirage et al. (2018) introduced a deep learning technique for SDD using autoencoders focused on dimensionality reduction. This method identifies modal and structural stiffness via pattern recognition. While reducing the input vector's dimensions, essential information is preserved. The study learned stiffness parameters through relationship learning and analyzed outputs like natural frequencies. Compared to conventional ANN models, this new approach yielded better results. However, the methodology will be expanded to include modal features, like FRFs, for detecting minute damages in noisy data. As of now, it's not fully adaptable to other applications.
Avci et al. (2021) explore deep learning's application to vibration-based damage detection in civil structures. They emphasize the shift in detection methods due to improved sensing and artificial neural networks, notably Convolutional Neural Networks (CNNs) and Unsupervised Pretrained Networks (UPNs). Such tools efficiently identify and locate damage in infrastructure by processing raw data. Guo et al. (2022) offer a unique vibration damage detection method, utilizing unsupervised learning with Convolutional Autoencoders (CAE). Their technique distinguishes between damage states in benchmark models and real-world structures, such as gymnasiums. By learning undamaged vibrations, the CAE method can interpret new data and detect ground motions, highlighting its capability for dynamic response analysis.
Parziale et al. (2022) present a groundbreaking technique for structural damage detection using deep learning. Incorporating CNNs and autoencoders (AEs), they discern damage-related details from complex transmissibility function (TF) spectra, considering temperature variations. Merging CNN with an unsupervised anomaly detection algorithm via AEs, they enhance damage diagnosis precision. Their findings address temperature fluctuations in vibration-based health monitoring, suggesting future advancements. Shang et al. (2021) propose an innovative vibration damage detection approach using a deep convolutional denoising autoencoder. After determining cross-correlation functions as base features and using the autoencoder to rectify noisy data, they extract crucial damage information. Their method is validated with numerical and experimental models, showing real-world application potential and advancing the field.
Rastin et al. (2021a) propose an innovative approach for structural damage detection in civil engineering structures. Their method, presented in the paper, leverages Convolutional Autoencoders (CAEs) to address the challenge of data collection from damaged states in large structures. Unlike traditional supervised methods, this approach requires only vibration data from the structure's healthy state for training. By harnessing the feature extraction capabilities of convolutional layers and the self-supervised nature of autoencoders, it efficiently identifies and quantifies structural damage. Applications on various structures, including the Tianjin Yonghe Bridge, validate its effectiveness in assessing the overall health state of civil engineering structures.
2.8.2 Supervised networks (SNs)
Supervised learning has emerged as a powerful approach in the domain of vibration-based structural damage detection. In this section, we delve into the use of supervised networks, particularly deep learning techniques, to address the challenges associated with evaluating the health status of civil engineering structures based on vibration data. Unlike traditional methods that require extensive labeled data for training, supervised networks leverage the advantages of deep neural networks. This section explores various applications and methodologies within supervised networks, shedding light on their successes and potential for future advancements in this critical field of civil engineering.
In their recent work, Dang et al. (2023b) introduce a semi-supervised structural damage detection (semi-SDD) method within the domain of vibration-based structural damage detection by deep learning. Their approach combines deep graph neural networks and contrastive learning to efficiently evaluate structural health based on vibration data. It outperforms traditional methods, even with limited labeled data. Figure 27 describe the Architecture of Encoder using 1DCNN and Graph Transformer. The paper also suggests flexible components and highlights avenues for future research.
Architecture of Encoder using 1DCNN and Graph Transformer (Dang et al. 2023b)
Yang et al. (2023b) explored the use of deep learning for structural damage identification in strain-based structural health monitoring, addressing challenges like complexities and delayed evaluations in traditional methods. Using a subway bolster as the reference, shown in Fig. 28, they introduced a deep learning model with a unique residual module, BolRes_Att, enhancing damage detection. This method identified damage with a minuscule error rate of 0.016% in elements, processing data in just 0.014 s. This research highlights deep learning's potential for swift and accurate damage detection in civil engineering structures, emphasizing its significance in vibration-based damage detection.
Schematic illustration for the bolster of a subway vehicle (Yang et al. 2023b)
Alves and Cury (2023) have developed an automated technique for locating structural damage by analyzing raw vibration data. Using unsupervised filtering and feature selection, this method is tailored for different structural forms. Tested on a steel beam at COPPE/UFRJ laboratory (Fig. 29), it determines damage by assessing outliers, proving effective in real scenarios, such as bridges. This highlights the potential of supervised machine learning in automated damage detection. Luleci et al. (2023) in 2023 addressed the issue of data scarcity in structural health monitoring (SHM) of civil structures. They utilized 1-D Wasserstein Deep Convolutional Generative Adversarial Networks with Gradient Penalty (1-D WDCGAN-GP) to produce synthetic acceleration data. This data enhanced the training set of a 1-D deep convolutional neural network (1-D DCNN) for detecting damage. The results underscored 1-D WDCGAN-GP's efficacy in overcoming data scarcity in vibration-based damage detection, offering a solution when real data collection for SHM is costly and prolonged. Piniotis and Gikas (2022) innovatively detected damage in steel bridges using Ground-Based Radar Interferometry. By converting vibration readings into Continuous Wavelet Transform scalogram images and using pre-trained Convolutional Neural Networks with Transfer Learning, they achieved an impressive 90% classification accuracy, underscoring its significant role in structural health monitoring.
Instrumented simply supported beam (Alves and Cury 2023)
Dang and Pham (2023) present the CLG-BHM framework for vibration-based building health monitoring using a unique blend of a 1D convolutional neural network, Long-Short Term Memory, and a graph attention network. This combination efficiently manages signal dimensionality reduction, temporal patterns, and spatial information. Tested on various structures, the framework effectively deals with noisy and missing data, as depicted in Fig. 30, highlighting its potential for remote, automated monitoring. Similarly, Ritzy et al. (2023) investigate damage detection in civil structures through artificial neural networks (ANNs). By monitoring stiffness attributes and modal parameters, they found strain energy combined with natural frequency to be a potent predictor of damage location and intensity. Their research utilized ANSYS 2021 R1 for modal evaluations and MATLAB for ANN creation, contributing significantly to supervised machine learning in structural damage detection.
Working flow of the proposed CLG-BHM approach, fusing 1D-CNN for local dynamic feature extraction, LSTM for temporal relationships, and GAT for spatial correlation (Dang and Pham 2023)
Kuo and Lee (2023) developed a new technique for effective structural damage detection using one-dimensional convolutional neural networks (1D-CNN). Their method optimizes sensor placement, thus reducing detection time by focusing on areas with notable displacements. This resulted in a 16.67% decrease in sensor usage and the need for only four CNN models for a structure with 30 connections. The technique's effectiveness is confirmed with a damage detection accuracy of 96.62%. This research uses supervised deep learning and is classified under "2.8.2 Supervised Networks". On a related note, Babu et al. (2023) presented the COAFCM-VDD method, which merges the Chimp Optimization Algorithm with a Fuzzy Cognitive Map to decipher damage features from vibration data, considering disturbances like noise. Their approach, detailed in Fig. 31, enhances damage detection, addressing feature sensitivity and boosting structural health monitoring system reliability.
Overall process of COAFCM-VDD system (Babu et al. 2023)
Kim et al. (2023) explored damage identification through vibration analysis using deep learning. They examined tip displacement in a 3D-printed cantilever beam using only output signals, typical in structural health monitoring. A key discovery was the significant influence of test set size on prediction accuracy. In a different study, Nick et al. (2023) proposed a two-stage damage detection technique for steel frames using artificial neural networks (ANN). This method, emphasizing modified damage indices related to modal flexibility and strain energy, first identifies damage locations and then uses ANNs for damage quantification. Simulations showed the method's efficacy in detecting single and multiple damages non-destructively. Santaniello and Russo (2023) introduced a method for bridge damage detection, combining synchrosqueezing transform (SST) and deep learning. They employed pre-trained 2D convolutional neural networks (CNNs) to analyze bridge accelerometer data, proving proficient in multiclass damage detection. The methodology's accuracy was confirmed with real data from the Z24 bridge. Figure 32 displays a proposed pipeline using image-splitting. Additionally, by integrating simple voting methods, classification accuracy was further improved.
Picture showing the pipeline of the proposed method with the addition of the image-splitting technique (Santaniello and Russo 2023)
Shi et al. (2023) developed a novel method for structural damage detection using Convolutional Neural Networks (CNN) combined with Short-Time Fourier Transform (STFT). This technique not only identifies damage patterns but also quantifies various unknown damages. The IASC-ASCE benchmark provides vibration signals of different damage scenarios, which are transformed into STFT spectrograms for CNN training. Their work introduces a unique condition-based damage function to estimate damage severity across multiple modes. In another study, Wang et al. (2023) combine digital twin (DT) technology with hierarchical deep learning for precise damage identification in cable dome structures. By creating a DT model from real data and generating a vast cable dome damage database through finite element analysis, this method precisely identifies damage type, location, and extent. Figure 33 visually represents Wang et al.'s approach. Both methods promise significant advancements in structural damage assessment.
Schematic of combined DT and Hierarchical DL approach for intelligent damage identification (Wang et al. 2023)
Cai et al. (2023) introduced the Dynamic Convolution Cross – Mix Network (DCCMN) model for structural damage detection in civil engineering, merging dynamic convolution with renowned deep learning models like ResNet and ShuffleNet. Utilizing Meta-Learning, the 'Meta + DCCMN' method displays outstanding detection of frame structure damage, even with limited data. Tests on Columbia University's floor frame structure showed a remarkable 100% accuracy in specific experiments, outperforming models like SVM and ResNet-18. Conversely, Lomazzi et al. (2023) probed the use of supervised machine learning for precise damage localization and quantification. Their research highlights the drawbacks of traditional damage indices and the potential of machine learning over standard imaging techniques. Figure 34 depicts their experimental setup. Their results, verified experimentally, show machine learning's capability to pinpoint structural damage, suggesting its potential as a robust diagnostic tool in civil engineering.
Plate considered in the case study. a Plate geometry and sensors, b experimental setup (Lomazzi et al. 2023)
Piniotis and Gikas (2022) developed a novel method for detecting structural damage in a steel bridge model using Ground-Based Radar Interferometry (GBRI). The technique involves transforming vibration data from the bridge's healthy and damaged states into Continuous Wavelet Transform (CWT) scalogram images. These images are then analyzed with Convolutional Neural Networks (CNNs) enhanced by Transfer Learning, boasting an impressive 90% accuracy. The model employed was a single-truss/single-storey Bailey type steel bridge. Similarly, Xue et al. (2023b) employed deep learning (DL) to monitor the health of cable-stayed bridges. Their approach uses sensors to pinpoint damage-induced stiffness variations and is backed by finite element analysis data. They emphasized the role of data quality, sample size, and the relevance of supervised networks in damage detection. In another study, Mahdavi and Xu (2023) utilized Supervised Networks combined with ensemble bagged trees and evolutionary optimization algorithms for detailed damage identification. They introduced artificial feature generation and a modified genetic algorithm to localize damage rapidly. Their research, validated both numerically and experimentally, underscores the value of detailed features and a data integration approach for optimizing machine learning. Figure 35 provides a schematic of their methodology. The overarching theme is the burgeoning potential of machine learning and deep learning in civil structure monitoring.
The schematic view of the proposed methodology to generate the artificial class labels and features based on the original dataset (Mahdavi and Chao 2023)
Liao et al. (2022) introduced a pioneering deep learning technique for vibration-based damage detection titled 'A channel-spatial–temporal attention-based network.' This method emphasizes refining specific features across channels, space, and time using a unique attention mechanism and a squeeze-and-excitation block. Figure 36 illustrates the CSTA architecture flowchart incorporating ResNet. When tested on real-world datasets like the three-span continuous rigid frame bridge and IASC-ASCE benchmark data, it outperformed previous methods, marking its potential for civil engineering applications. Similarly, Sony et al. (2022) highlighted a novel technique employing Long Short-Term Memory (LSTM) networks to analyze samples from acceleration responses, facilitating multiclass damage classification. This LSTM approach has shown better results compared to traditional one-dimensional convolutional neural networks (1D CNN) in some datasets, underscoring its significance in structural health monitoring. Both studies enhance the vibration-based damage detection domain through innovative methods.
Flowchart of the CSTA architecture with ResNet as the backbone. The responses are first collected and divided into samples into the CSTA block. Then the basic feature extractor and attention module are followed by to extract and refine features adaptively (Liao et al. 2022)
Hajializadeh (2022) developed a method to monitor the structural integrity of aging railway bridges using vibration-based damage identification with a deep Convolutional Neural Network optimized through Bayesian Optimization. This approach accurately detects damage using simulated acceleration data from a railway bridge under various conditions like different train speeds, damage levels, and noise. Ghiasi (2022) aims to modernize damage detection in steel railway bridges. Traditional methods can be inefficient and resource-heavy. Ghiasi introduces machine learning techniques such as Support Vector Machines (SVM), Convolutional Neural Networks (CNN), and Siamese Convolutional Neural Networks (SCNN) to enhance this process, negating the need for intricate signal processing or manual Damage Sensitive Feature extraction. This progress offers a more efficient, data-driven approach for real-world railway bridge health monitoring. Meanwhile, Seventekidis et al. (2021) use finite element models to train a deep learning neural network for structural health monitoring in a CFRP truss structure, proving its efficacy and potential limitations.
In 2022, Woo et al. (2022) presented a cutting-edge method for vibration-based structural damage detection using Convolutional Neural Networks (CNNs). By analyzing transverse vibration data, CNNs demonstrated impressive accuracy in identifying structural flaws in a composite model through vibration experiments and Finite Element Analysis (FEA) using ANSYS. The study acknowledged a need for further exploration of CNN's capacity under varying boundary conditions. Seventekidis and Giagopoulos (2022) proposed an innovative Structural Health Monitoring (SHM) technique. They utilized Finite Element (FE) models to produce SHM data, simulating deviations from the normative health of structures. Tested on a Carbon Fiber Reinforced Polymer truss under different damage scenarios, including minor damages, their approach used artificially-introduced uncertainties to replicate deviations. This data subsequently trained a Deep Learning classifier, proving its efficacy when juxtaposed with real damage data. The success of this method lies in the accurate simulation of varied model parameters. In another pivotal study by Ghiasi et al. (2022), the spotlight was on detecting structural damages in operational steel railway bridges using CNNs. Concentrating on cross-section losses primarily due to corrosion—a leading cause of bridge failures—they combined field tests with simulated scenarios. Their 1D CNN methodology, augmented with innovative data strategies, yielded an exceptional nearly 100% damage classification accuracy. Further insights were gained from visualizations using t-SNE and Grad-CAM techniques. This paper underscored the potential of supervised deep learning in enhancing vibration-based damage detection in civil infrastructure. In summary, these studies highlight the growing scientific interest and results in utilizing advanced computational methods, particularly deep learning, for effective structural health monitoring.
De et al. (2020) utilized Long short-term memory (LSTM) networks, a deep learning model, for detecting structural damage through acceleration response time history. The study, executed on Google Colaboratory with Keras and TensorFlow, validated its effectiveness using a damaged cantilever beam example. Iannelli et al. (2022) introduced a Deep Neural Networks (DNN) based method for structural health monitoring of large space antennas. Given the increased risk of damage in larger spacecraft components, this approach employed Finite Element simulations for training data, simulating diverse damage situations. The model was trained using sensor-measured responses, confirming DNN's effectiveness in this context. Alazzawi and Wang (2022) proposed a deep learning method using a deep residual network (DRN) for civil engineering structures' health monitoring. The DRN, optimized via Bayesian techniques, processes raw time-domain signals, eliminating feature engineering. Tested on various datasets, it showcased its capability to detect and quantify damage, outperforming other machine learning methods. Sands et al. (2022) harnessed LSTM and GRU models to identify anomalies in vibration signals. Trained using a 3D printed beam's time response, it achieved a more accurate structural health depiction. Their use of 'signal caricature' datasets further refined model accuracy, and traditional vibration analysis confirmed its efficacy. These studies collectively highlight the significant potential of deep learning in advanced structural health monitoring. Dizaji and Mao (2022) introduce an innovative approach to structural damage prediction using deep learning. Their method employs deep convolutional neural networks (CNNs) to analyze video data derived from vibration measurements. The uniqueness of their approach lies in the integration of attention mechanisms, which enable the model to selectively focus on dynamic frames, capturing temporal dynamics. By combining ConvLSTM and CNNs, the model takes video footage of vibrating structures and provides structural health assessments. The results demonstrate the model's efficiency, autonomy, and accuracy, with validation through laboratory experiments.
Fu and Li (2023) present a novel approach for vibration-based structural damage detection using deep learning. They combine fractal dimension analysis, data fusion, and a revised counter-propagation network (RCPN) to enhance identification accuracy. This method first extracts fractal dimensions from the signal response and performs feature-level data fusion. These fused data are then used as input for RCPN to identify initial damage. Subsequently, decision-level data fusion is applied. Their experiments on a four-storey ASCE benchmark structure demonstrate that this approach outperforms single RCPN decisions and feature-level fusion decisions, providing superior accuracy, reliability, noise resistance, and robustness in structural damage identification. ASCE benchmark structural model is shown in Fig. 37.
ASCE benchmark structural model. a Experimental model of steel frame, b analysis model (Fu and Li 2023)
Wang et al. (2021) introduced a novel approach utilizing densely connected convolutional networks (DenseNets). This technique, adapted from computer vision, effectively extracts features from acceleration-based time-domain vibration responses, addressing a fundamental challenge in damage detection. The approach not only streamlines information flow during training but also mitigates the issue of gradient vanishing while significantly reducing the number of parameters for easier network training. The proposed architecture is shown in Fig. 38. Numerical and experimental validations demonstrate exceptional performance, achieving regression values exceeding 96.0% on numerical data and over 94.9% on experimental data, even in the presence of modeling uncertainties and measurement noise. This study underscores the promise of supervised deep learning methods in advancing structural health monitoring.
The proposed SDI-DenseNet (Wang et al. 2021)
Wang (2021) introduced advanced deep learning techniques to enhance vibration-based structural damage identification, addressing challenges from high-dimensional, noisy vibration signals. Using supervised deep learning, Wang's methods significantly improved damage detection. Similarly, Teng and Chen (2021) used a convolutional neural network (CNN) for damage detection from vibration signals. Their database was built from tests on a steel frame, recording vibrations with a camera and extracting displacements through digital image correlation (DIC). Their CNN approach achieved almost perfect accuracy and outperformed back-propagation neural networks (BPNN) in computational speed. Both studies contribute significantly to the 'Supervised Networks' domain in deep learning for structural damage detection, merging advanced methods with real-world applications.
Won et al. (2021) developed a method for vibration-based structural damage detection by merging data normalization and 1-D convolutional neural networks. This approach effectively maintains excitation quality while adjusting input data, achieving accuracy rates of 99.90% and 99.20% for detecting damage in a beam model under various loadings. Wang and Shahzad (2021) improved structural damage identification accuracy using a combination of Hilbert-Huang transform (HHT) and Convolutional Neural Networks (CNNs). By analyzing IASC-ASCE SHM benchmark damage signals and using time–frequency graphs as CNN inputs, they enhanced accuracy by over 10% with an adaptive CNN model, optimized using a particle swarm optimization (PSO) algorithm. Their method, depicted in Fig. 39, is especially resilient to noise, marking significant progress in structural damage identification.
The structure model of benchmark: a actual structure; b structure model (Wang and Shahzad 2021)
Mohebian et al. (2023) tackle the underexplored area of damage detection in retaining wall structures. They propose a novel approach by utilizing a high-fidelity finite element model updating method in ABAQUS. This approach formulates damage as a decrease in the wall material's elasticity modulus and minimizes the difference between actual and computed displacement data. To optimize the computational process, they employ radial basis functions (RBF) to create a surrogate model and apply the differential evolution (DE) algorithm. Through numerical examples involving various retaining wall types, the method is demonstrated to be both efficient and accurate in detecting damage within these civil engineering structures.
Yang et al. (2021) introduced a novel method for structural damage detection by merging Convolutional Neural Networks (CNNs) and Bidirectional Gated Recurrent Units (Bi-GRUs). Their approach outperformed traditional methods on both the IASC-ASCE benchmark and the TCRF dataset. Similarly, Hakim et al. (2022) explored the capabilities of artificial neural networks (ANNs) for analyzing vibration data to detect structural impairments. They used data from I-beam-like structures and formulated five ANNs, highlighting the enhanced efficiency of an ensemble neural network. Moving in a unique direction, Rastin et al. (2021b) brought forward an unsupervised method for structural health monitoring (SHM). This two-phased strategy employs generative adversarial networks (GANs). The first stage uses a deep convolutional GAN (DCGAN) for damage detection and quantification, and the second leverages a conditional GAN (CGAN) for damage pinpointing. Importantly, only undamaged acceleration signals are required for training, proving its potential for real-world applications. On the other hand, Silionis and Anyfantis (2023) delve into the challenge of uncertainty in SHM systems. They assessed the statistical structure of model prediction errors, investigating their influence on strain-based SHM systems. Employing statistical methodologies and simulations, their findings emphasize the significance of systematic errors and correlations in practical SHM systems. In conclusion, these studies signify the growing potential of deep learning and neural networks in advancing the field of structural health monitoring. Their findings not only promise enhanced detection accuracy but also stress the importance of understanding uncertainties in real-world applications.
2.8.3 Implementations of CNNs for vibration-based SDD
Deep learning algorithms, especially convolutional neural networks (CNNs), are now the preferred method for analyzing large datasets. CNNs, which are a type of artificial neural network, have their structure inspired by cells in the mammalian brain's vision cortex (Scherer et al. 2010; Kiranyaz et al. 2016a, 2017; Ciresan et al. 2010). Historically, they showed superior performance in object identification and face recognition tasks in computer vision (Kiranyaz et al. 2016b). A recent study by Teng et al. (2023) introduced a method for vibration-based structural damage detection using a one-dimensional CNN combined with transfer learning (TL). Due to the scarcity of real-world structural damage samples, the research leveraged numerical models for training. Using TL, the study found an improvement in damage detection accuracy by up to 47% and a 50% increase in the convergence speed. Moreover, when applied to a real bridge scenario, the accuracy surged by 44.4%, illustrating TL's ability to prevent overfitting. The findings highlight the immense promise of TL for enhancing damage detection and its broad applicability, even in structures of varying sizes, emphasizing the widespread relevance of their approach.
They were later adopted by a variety of other fields. CNN's success is largely due to these advantages:
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An artificial neural network combines both classification and feature extraction stages. CNNs can learn directly from the raw input during the training phase.
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The CNN neurons are sparsely connected and have tied weights, compared to fully-connected Multi-Layer Perceptrons (MLP) networks. This allows them to efficiently process large amounts of data.
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Transposition, scaling, skewing, and distortion of minor data are not affecting CNNs.
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The size of inputs does not matter when using CNNs.
The backpropagation algorithm, also known as stochastic gradient descent, is used to train CNNs. During BP iteration, each network parameter's gradient magnitudes (or sensitivities) are computed. For example, the convolutional and fully-connected layer weights. Iteratively updating the CNN parameters can be accomplished using the parameter sensitivities. A detailed description of BP in CNNs can be found in Kiranyaz et al. (2016b), Teng et al. (2023), Abdeljaber et al. (2017b) and Kiranyaz et al. (2015).
Convolutional Neural Networks (CNNs) (Yu et al. 2019; Nguyen and Wahab 2023b; Xiang et al. 2023; Zhu and Xiang 2023; Chen et al. 2023b; Satpathy et al. 2023; Parziale et al. 2023; Fathnejat et al. 2023; Bai et al. 2023; Khodabandehlou et al. 2018; Ma et al. 2023; Ai et al. 2023; Teng et al. 2022a; Teng et al. 2023; Cofre-Martel et al. 2019; Cofré et al. 2018; Avci et al. 2017, 2018a, b, 2019b, c; Ince et al. 2016; Kiranyaz et al. 2018; Abdeljaber et al. 2018, 2017c; Eren 2017; Li et al. 2017; Zhou et al. 2022a; Brethee et al. 2023; Xiong et al. 2017; Real Time 2019; Abdeljaber et al. 2016b; Pandit et al. 2021; Shu et al. 2023; Zhang et al. 2022b; Xia et al. 2002; Dang et al. 2022; Teng et al. 2021; Bui-Ngoc et al. 2022; Song et al. 2022; Zhang et al. 2022c; Flah et al. 2022; Teng et al. 2022b; do Cabo et al. 2022; Chen et al. 2022; Hajializadeh 2023; Rautela and Gopalakrishnan 2021; He et al. 2021) show promise in structural damage detection (SDD) for civil structures. Yu et al. (2019) utilized CNNs to detect damage in a five-story building by turning 14 accelerometer signals into a 2D matrix for CNN analysis. Their ten-layer model identified damage more effectively in noisy signals than traditional machine learning. However, they suggest real-world testing, as their study was limited to numerical simulations. Xiang et al. (2023) introduced a Parallel Convolutional Neural Network (P-CNN) that combines frequency and time domain data. This method could pinpoint structural damage with less than 5% error, even with limited sensors and amid uncertainties. This fusion of information enhances the efficiency of 2D-CNNs, suggesting a cost-effective method for SDD. Another method by Zhu and Xiang (2023) employs CNNs in structural health monitoring. Focusing on uncertainties in varied measurement conditions, CNNs were used to draw a link between structural response data and damage states. Their experiment, showcased in Fig. 40, involved a simply supported bridge and demonstrated the CNN's high accuracy in damage detection under inconsistent measurement conditions. These findings underline the potential of CNNs in civil structural health assessment.
Settlement of the sensors of the experimental structure (Zhu and Xiang 2023)
In 2023, Chen et al. (2023b) unveiled a novel approach for structural health monitoring in civil engineering using the '1DCNN-BiLSTM model for structural state recognition of RC beams'. This deep learning model, illustrated in Fig. 41, integrates 1DCNNs for spatial analysis with BiLSTM for time-related data, achieving a remarkable 98.8% accuracy in detecting minor changes in reinforced concrete (RC) beams, surpassing traditional methods. Notably, the model is robust against noise and data gaps. Similarly, Satpathy et al. (2023) presented a new architecture utilizing CNNs for detecting structural damage, particularly cracks, shown in Fig. 42. This approach, refining earlier methods, showcases its significance in enhancing structural health assessments, beneficial for architectural management bodies.
Information about the specimen and detailed drawing of the working conditions (unit: mm) (Chen et al. 2023b)
Testing image output using the CNN model
Parziale et al. (2023) recently proposed a novel method for structural damage assessment using vibration data and convolutional neural networks (CNNs). This method directly processes Transmissibility Functions (TFs) spectra, bypassing extensive preprocessing. Applied to a steel structure with bolted joints, the method proved effective. Moreover, an explainable AI technique revealed the key features the CNN used for damage characterization, underscoring its value in structural health monitoring and explainable AI research. Similarly, Fathnejat et al. (2023) developed the CNN-ATT-biGRU model, combining 1D Convolutional Neural Networks (1DCNN) and recurrent neural networks (RNN) with an attention mechanism. Specialized in analyzing raw acceleration time-history data, this model demonstrated exceptional accuracy, speed, and compactness in structural damage detection, excelling in industry tests and environmental resilience. Meanwhile, Bai et al. (2023) presented a technique for steel structure damage detection using Transmissibility Change Data (TCD) and CNNs, eliminating the need for load response measurements. By experimenting with a cantilever beam, three damage indicators were assessed: TDD, FDD, and TCD. The TCD proved most accurate and stable. Importantly, the 2D-TCD-CNN achieved a 100% accuracy rate and faster processing, highlighting the growing role of deep learning in structural damage detection.
In a study by Khodabandehlou et al. (2018), a Convolutional Neural Network (CNN)-based Structural Damage Detection (SDD) method was introduced. Utilizing a scaled lab structure, a 2D CNN was trained to identify different damages. The framework used 14 accelerometers, 48 components, and produced input images from acceleration histories. CNN's training involved 40 shake tables, with eight used for testing. The method efficiently detects minor structural changes. Another study by Ma et al. (2023) explored CNNs for damage detection in quad-rotor UAVs. They found one-dimensional (1-D) CNNs to be superior to two-dimensional (2-D) CNNs. Using vibration signals, they could diagnose propeller damage and connection problems in UAVs, showing 1-D CNNs' advantage over conventional methods in UAV and civil structure diagnostics.
Similarly, Ai et al. (2023) introduced a method for identifying damage in concrete structures using 1-D CNNs. This method directly processes raw electromechanical impedance data, avoiding tedious preprocessing. The CNN model excelled in damage severity assessment compared to traditional approaches. Their method is especially effective in spotting small damages in concrete, as illustrated in Fig. 43, where a PZT transducer is attached to the monitored structure.
EMA measuring system in 1D coupled model of PZT-adhesive-structure interaction (Ai et al. 2023)
Teng et al. (2022a) utilized a Convolutional Neural Network (CNN) for automatic structural state classification from vibration signals of a steel frame, achieving a notable 99% accuracy, an 81% reduction in training time, and outperforming traditional networks. The study emphasizes the efficiency of CNN in extracting structural information, even with incomplete data and amidst noise. In a subsequent study (Teng et al. 2023), they combined digital twin (DT) technology and transfer learning (TL) with CNNs for structural damage detection. By training the CNN on vast datasets from DTs, they achieved over 90% accuracy for numerical models and an exceptional 97.3% for real bridges, as illustrated in Fig. 44. This showcases the potential of DT and TL in improving CNN's damage detection capability.
Test layout of the experimental bridge model (Teng et al. 2023)
Cofre-Martel and colleagues (Cofre-Martel et al. 2019; Cofré et al. 2018; Avci et al. 2018a) used CNNs for transmissibility-based Structural Damage Detection (SDD) to quantify damage, observing that structural damage affected transmission functions via stiffness reduction. They trained their system using noise-contaminated mass springs data. Interestingly, they achieved good SDD performance using only raw vibrational data. Subsequently, while 2D CNNs have been traditionally used in SDD, the potential of 1D CNNs has been uncovered (Gui et al. 2017b), especially in detecting irregularities in electrocardiograms (ECGs) (Ince et al. 2016; Avci et al. 2017, 2018b; Kiranyaz et al. 2018; Abdeljaber et al. 2017c, 2018). Key differences between 1 and 2D CNNs are highlighted, with 1D CNNs using 1D arrays and convolutions. Recent studies (Ince et al. 2016; Avci et al. 2017, 2018b; Kiranyaz et al. 2018; Abdeljaber et al. 2017c, 2018; Eren 2017; Li et al. 2017) emphasize the advantages of compact 1D CNNs, especially when dealing with sparse datasets like ECGs (Kiranyaz et al. 2018), engine vibrations (Shahsavari et al. 2017), and power electronics data (Cofre-Martel et al. 2019). Deep layers in these contexts may result in “underfitting”.
Zhou et al. (2022a) proposed a groundbreaking method that fuses finite element modeling (FEM) with 1D-CNNs for real-time structural damage detection. This approach automatically extracts damage features from raw displacement data, considerably minimizing computational efforts. The 1D-CNNs have been found particularly adept at accurately detecting and pinpointing damage. The study further accentuates the value of analyzing displacement data component-wise. Brethee et al. (2023) unveiled a novel vibration-based damage detection strategy for laminated composite plates subjected to forced vibrations. By using vibration modal analysis, they introduced the Improved Curvature Damage Factor (ICDF) and the Cumulative Improved Damage Factor (CICDF) to detect and pinpoint damages, including fiber breakage and delamination. Comparative and experimental tests underscored the ICDF's heightened sensitivity to fiber breakage over delamination, presenting a promising direction for structural health monitoring in composite materials.
Utilizing the 1D CNN method, research (Xiong et al. 2017; Avci et al. 2019b, c; Real Time 2019; Abdeljaber et al. 2016b) applied to Wireless Sensor Networks (WSN) identifies damage-sensitive directions using triaxial wireless sensors. The method excellently detects and localizes structural damage from ambient vibrations. Each 1D CNN in this study comprises two CNN layers (four neurons) and two MLP layers (five neurons). Pandit et al. (2021) examined CNNs for high-rise building damage identification, contrasting 1D and 2D CNNs on an FEM software model of a G+20 storey building. Using the Probability of Damage (POD) as an indicator, they found 1D CNNs superior for structural damage diagnosis. Shu et al. (2023) proposed a novel structural damage identification approach termed model-informed deep learning (MIDL). Merging data-driven and model-based methods with vision-based displacement estimation, this method, depicted in Fig. 45, employs 1D CNN for precise damage detection. Experimental results showed 86.09% accuracy, emphasizing the value of MIDL in vibration-based damage identification.
Proposed MIDL damage identification strategy (Shu et al. 2023)
Zhang et al. (2022b) present a pioneering method for structural damage detection by merging Convolutional Neural Networks (CNNs) with phase-based motion estimation (PME). This method treats each video pixel as an individual displacement sensor, extracting millions of vibration signals from one video. Tests on a two-story steel structure confirm its ability to accurately pinpoint both the location and extent of damage with a single video, addressing limited training data concerns.
Addressing the data-intensive training needed for 1D CNNs, especially in large civil structures, Abdeljaber et al. (2018) and Xia et al. (2002) introduced a 1D CNN-based technique requiring minimal training. The CNN was constructed in C++ using Intel's OpenMP API and tested on a 32 GB PC. Twelve CNNs were trained with 37 undamaged and 112 damaged frames, achieving impressive training speeds. The CNN classifier could determine the Probability of Damage (PoDi) for a 300-s signal in just 5 ms, and the average PoD for 12 signals in 60 ms, making the method 5000 times faster than "real-time" needs. Importantly, even with limited training data from two damage cases, the classifier accurately assessed structural health in all scenarios (Abdeljaber et al. 2017c, 2018). Meanwhile, Dang et al. (2022) unveiled g-SDDL, a cutting-edge technique for structural damage detection from vibration data, eliminating the need for manual feature engineering. Using graph neural networks, g-SDDL identifies spatial correlations between sensor locations and uses convolution operations to discern vibration patterns. Achieving over 90% accuracy in multi-damage situations, its framework is depicted in Fig. 46. The approach promises a breakthrough in structural health monitoring, enabling real-time tracking without intricate pre-processing.
Working flow of the g-SDDL framework for structural damage detection (Dang et al. 2022)
Pioneering studies confirm the capability of compact 1D CNNs to differentiate complex, uncorrelated acceleration recordings. In a study (Abdeljaber et al. 2017b), CNNs were assessed on a large laboratory frame, training separate 1D CNNs for each accelerometer location. Only local data from each location was used. Teng et al. (2021) enhanced structural damage detection by using a 1-D CNN and decision-level fusion to classify damage from vibration signals, efficiently capturing dynamic response changes. Challenges like non-synchronous data were tackled using multiple sensors. Figure 47 illustrates the bridge model. Simulations and experiments show improved detection accuracy, emphasizing the method's structural damage detection efficiency.
The bridge model with 60 flat steel bars (Teng et al. 2021)
Bui-Ngoc et al. (2022) introduced a method using Convolutional Neural Networks (CNNs) for bridge damage detection by analyzing vibration signals as time–frequency images. This technique proves highly accurate, especially in civil engineering. Abdeljaber et al. (2017b) further tested this 1D CNN approach on numerous damage cases. The method detected 100% of the damages, even minor ones due to bolt loosening. A computational analysis showed that 1D CNNs could identify complex acceleration time-histories, as demonstrated in Fig. 48, processing data 45 times faster than real-time. This advancement can significantly aid analysts in damage assessment.
Abdeljaber et al. (2017b) evaluated damaged as well as undamaged vibration data at the joints
Song et al. (2022) introduced a method for detecting bridge structural damage using pre-trained convolutional neural networks (CNNs) like AlexNet and Resnet. By converting structural acceleration data into image form with wavelet scalograms, both spatial and temporal details are retained. AlexNet achieved a 98% prediction accuracy, while Resnet scored 100% in varied damage situations, showcasing deep learning's potential in advancing damage detection precision in civil engineering. Similarly, Zhang et al. (2022c) improved damage detection by fusing multiple vibration signals (acceleration, strain) as CNN inputs. This approach led to an impressive 10% boost in locating damage accuracy (85.1%) in their 3D steel bridge model experiment, as depicted in Fig. 49.
Steel bridge model
Flah et al.'s (2022) introduced BuildingNet as shown in Fig. 50, a One-Dimensional Convolutional Neural Network tailored for real-time feature extraction from raw acceleration sensor data. Their research focuses on optimizing network architecture and training data, particularly in different damage scenarios. Through mid-rise building case studies and time-domain monitoring data, including single-channel measurements and noisy datasets, their model exhibited exceptional performance in damage localization and classification.
BuildingNet design methodology
Teng et al. (2022b) explored Convolutional Neural Networks (CNNs) for structural damage detection in bridges, achieving an impressive 99.4% accuracy with acceleration signals. They showcased the capability of CNNs to detect damage in various bridge models, underscoring its potential for widespread applications. do Cabo et al. (2022) innovatively merged CNNs with Long Short-Term Memory (LSTM) networks for damage detection using vibration data. Figure 51 show the proposed CNN-LSTM flowchart. Their method enhances spatial and temporal resolution, and is validated on a lab-scale truss under varied load conditions. Both studies significantly contribute to the 'Vibration-based SDD implementations of CNNs' subsection of 'Vibration-based structural damage detection by Deep-Learning', highlighting the rising importance of deep learning in structural health monitoring.
Flowchart of CNN-LSTM structure (do Cabo et al. 2022)
Chen et al. (2022) introduced a unique method for detecting rail fastener damage in railway maintenance using vibration analysis combined with a fully convolutional network (FCN). This approach can detect even subtle damages, thus enhancing the traditional visible damage detection techniques. This innovation can significantly improve the efficiency of railway maintenance. Similarly, Hajializadeh (2023) presents a novel structural health monitoring approach highlighted in Fig. 52. By employing deep learning, she aims to detect and categorize damages in civil engineering structures, especially bridges. This system uses data from an instrumented traveling train and employs a deep convolutional neural network (CNN) for damage identification, optimized through Bayesian techniques. Both studies signify the growing influence of deep learning in structural damage detection.
Schematic demonstration of a typical convolutional neural network architecture (Hajializadeh 2023)
Rautela and Gopalakrishnan (2021) explored structural damage detection using ultrasonic waves and deep learning, employing a spectral finite element model and time-series data. They introduced noise to mimic real-world situations and used a supervised approach combining classification and regression. Their analysis showcased convolutional neural networks' (CNN) advantages over traditional machine learning techniques and their adaptability to varied conditions. Similarly, He et al. (2021) integrated deep learning with vibration-based structural damage detection. By merging fast Fourier transform (FFT) with deep convolutional neural networks (DCNN), they improved damage identification. Tested on a three-story building and ASCE benchmark, the FFT-DCNN method surpassed other algorithms like SVM and RF in accuracy.
2.9 Bayesian methods
Often, the noise in measurement and modeling errors causes incorrect damage identification in civil structures (Abdeljaber et al. 2016b; Xia et al. 2002). Measurement noise, for example, could obscure subtle structural changes associated with damage. Consequently, deterministic methods may not work on real-world civil structures. Damage can be identified in this regard using probabilistic approaches (Xia and Hao 2003; Simoen et al. 2015). With Bayesian inference (Beck and Katafygiotis 1998; Katafygiotis and Beck 1998), model uncertainties are explicitly quantified based on observations and prior information. The Bayesian method provides an adequate inverse problem solution by incorporating uncertainties in probabilistic models over input variables. A normalization concept could be added to the optimization problem (Williams 1995).
Bayesian-based approaches to structural health monitoring in bridges have been extensively explored. Figueiredo et al. (2014) introduced a Bayesian pattern recognition model, utilizing a Markov-chain Monte Carlo method, to group structural responses. The model was effectively applied to the Z-24 Bridge dataset, showcasing its real-world applicability. Arango and Beck (2012) focused on the stability of bridges amid ambient vibrations, with a particular emphasis on the Bayesian model class selection for optimal network architecture. The Bayesian Neural Network (NN) technique has been employed for damage detection, as highlighted by Arangio and Bontempi (2015), who used it to detect damages in the Tianjin Yonghe Cable-Stayed Bridge.
Ásgrímsson et al. (2022) brought forth a machine learning perspective with a Bayesian autoencoder neural network. This network adeptly reconstructs raw sensor data, keeping uncertainties in mind, and has been tested on the Z24 bridge dataset, effectively spotting structural damages. Wang (2022b) delved into vibration-based structural damage detection, emphasizing probabilistic machine learning and Bayesian inference. Wang's research addresses uncertainties in damage detection from sources like environmental changes and measurement noise. By integrating Bayesian methods, Wang accentuates data-driven detection while also introducing advanced methods for environmental adjustments. Collectively, these studies highlight the transformative potential of Bayesian-based methodologies in the realm of structural damage identification.
Pepi et al. (2023) introduced a Bayesian framework for structural health monitoring (SHM) that utilizes polynomial chaos to improve traditional Bayesian updating. This method addresses both model prediction and measurement errors. Its application on a cable-stayed footbridge showcased better damage identification and localization, enhancing data-driven SHM's accuracy. Lam et al. (2014) employed a Bayesian approach with modal parameters to identify railway ballast damage. They discovered evenly distributed concrete sleepers in stiffness regions, determined using the Bayesian model class selection. Behmanesh and Moaveni (2015) used FE model updating on structures with concrete block-covered bridge decks to simulate damage, while Behmanesh et al. (2017) explored Bayesian FE model updating, obtaining a final damage estimate through Bayesian model averaging. Yin et al. (2017) detected bolt connection damage using incomplete modal parameters, avoiding full mode shapes through specific methods (Yuen et al. 2006; Lam and Yin 2011), and estimating parameters using Gaussian distributions.
Huang and Schröder (2021) introduced a novel Bayesian technique for damage identification in plate structures, essential in engineering. Their method uses dynamic responses at specific vibration nodal points (NODIS) for real-time damage assessment, eliminating complex finite element models. They utilize a perturbation-based surrogate model in the Bayesian framework, which is proven accurate against finite element results. They applied this method to a carbon fiber-reinforced polymer structure, emphasizing its practicality. Ierimonti et al. (2021) employ a Bayesian approach for evaluating damage in historical structures via vibration monitoring. Their method facilitates real-time model updating, considering uncertainties, and includes a digital twin of the structure. This approach addresses the preservation needs of aging historical structures vulnerable to seismic events. Fathi et al. (2020) address the challenges of monitoring offshore jacket structures. Their Bayesian model, which uses Frequency Response Function (FRF) data without model reduction, is effective even amid uncertainties. Tests on a 2D fixed platform (Fig. 53) validate their method. Collectively, these studies highlight the significant advancements Bayesian methods offer in structural health monitoring.
Experimental steel frame model structure (Fathi et al. 2020)
Sparse Bayesian Learning (SBL) is a supervised learning framework (Tipping 2001; Wipf and Rao 2004; Ji et al. 2008) that offers sparse solutions in regression and classification contexts (Ji et al. 2008; Williams et al. 2005; Zhang and Rao 2011). Key to SBL is its distinct regularisation, steered by prior distributions. Unlike fixed priors in traditional sparse recovery, SBL uses the ARD prior, favoring discrete parameters, and determining sparse outcomes through individual parameter's hyper-parameters (Lam and Yin 2011; Wipf and Rao 2004). This obviates the challenge of selecting regularisation parameters seen in sparse recovery, as SBL auto-updates its hyperparameters.
Henikish et al. (2023) unveil a Bayesian model updating method for detecting structural damage. Diverging from norm, it harnesses complex modal data from dynamic tests, addressing both Most Probable Values (MPVs) and modal parameter uncertainties. Employing Bayesian techniques like Metropolis-within-Gibbs sampler, the model assesses structural damage likelihood, a claim backed by simulations and experiments. Zeng et al. (2023) introduce BayesFlow, an advanced Bayesian inference technique for probabilistic damage detection, addressing the challenge of complex likelihood functions to facilitate real-time monitoring. During its training, BayesFlow uses a conditional invertible neural network (cINN) to approximate structural parameter posterior distributions. Its uniqueness lies in direct posterior distribution predictions, bypassing lengthy likelihood and model evaluations. Benchmarks on building frames validate its precision and speed, outperforming methods like DREAM.
A Bayesian probabilistic technique for detecting structural damage emerged nearly twenty years ago. Yet, only recently has SBL been applied to this purpose, largely due to the nonlinear character of modal data. As a result, direct calculation of the Bayesian equation is challenging. Solutions involve mathematical tools like hierarchical modelling and Laplace's approximation, or analytical methods such as expectation–maximization techniques. Lin et al. (2013) pioneered a hierarchy-based SBL approach, transforming nonlinear problems into multiple linear regressions. Yuen et al.'s method (Cai et al. 2023) enhanced damage detection accuracy. Huang and Beck (2015) further refined the SBL algorithm, showing better efficiency in real structures, even with notable modelling errors. Vega and Todd (Vega and Todd 2022) introduced a Bayesian neural network using variational inference for structural health monitoring, adept at learning from limited, noisy data. Their method, resistant to overfitting and effectively simulates damage evolution in miter gates with real inspection data.
Multi-task learning optimizes data redundancy across various measurements. Huang et al. (2017a) introduced a multi-task SBL that fuses two FD-based damage indices, enhancing damage localization. The method hinges on a damage localization vector and two damage indices, utilizing linear regression models for modeling the likelihood function. In another study by Huang et al. (2018), multiple measurement groups were integrated into large-scale Bayesian models for multi-task SBL, highlighting a shared sparsity profile across tasks. Previous algorithms (Huang et al. 2019b; Ji et al. 2009) marginalized prediction error precision parameters to boost learning robustness. Wang et al. (2022) unveiled a groundbreaking method in structural health monitoring (SHM). Their approach, rooted in Sparse Bayesian Learning (SBL), constructs a damage index from solely healthy-state data, negating the need for structural or excitation data. This unsupervised model, verified using cable-stayed bridge data, offers a promising way for structural damage detection. Hou et al. (2019) proposed an EM-based damage detection, resolving a nonlinear eigenvalue problem iteratively. Meanwhile, Wang et al. (2020) used an analytical method to approximate a complex integral in evidence. Huang et al. (2017b) showcased the Gibbs sampling (GS) algorithms, assessing the posterior PDF of parameters using a similar SBL model. Their research validated the full GS algorithm's reliability through real-world experiments.
Nguyen (2022) introduces the 'Change in Central Position of Probability Spectrum' (C-PSD) as a new method for detecting damage in beams. Rather than using filtered data as in traditional methods, this technique optimizes the data with 'Balancing Composite Motion Optimization' (BCMO) and applies Bayesian deep learning for accurate damage assessment. The method's strength lies in its sensitivity to structural alterations. Kamariotis et al. (2022) and Straub present a Bayesian decision analysis to evaluate the worth of information from structural health monitoring (SHM) systems. By gathering sequential data from accelerometers, updating models, and computing reliability, they quantify the benefit of long-term vibrational SHM data, assessing its optimal use in decision-making. Zhou et al. (2022b) improve the accuracy of a structural FE model for a steel truss bridge (Fig. 54) using vibration-based Bayesian model updating. With the TMCMC sampling method, they analyze various damage scenarios and identify modal properties using a Bayesian FFT approach, suggesting three model categories. Their findings emphasize the importance of prior knowledge in model updating and the potential for damage detection in civil engineering. These techniques, especially those using Bayesian methods, are detailed in Table 4.
Target bridge (Zhou et al. 2022b)
2.10 Comparison research work
Over the past decade, vibration-based methods have been extensively studied for damage detection in various structures. Kosaftopoulos and Fassois (2010) analyzed several statistical time series techniques on an aluminum truss and found that parametric methods outperformed nonparametric ones. Talebinejad et al. (2011) examined four mode shape techniques for detecting damage in long-span cable-stayed bridges. MSC and damage index were the most effective, but struggled to detect multiple deck damages amidst noise. Zhia et al. (2023) proposed the use of multiple artificial neural networks (ANNs) and adaptive neurofuzzy systems to pinpoint crack dimensions in curvilinear beams, using reduced FRF data via PCA. ANNs delivered the lowest prediction errors, while adaptive neurofuzzy systems exhibited noise resilience. Ali et al. (2022) assessed nine damage detection methods using natural frequencies, MSCs, and MSEs, categorizing them based on the need for baseline data. They demonstrated that damage indexes were proficient at determining damage location and severity on an Euler–Bernoulli beam. Notably, damage detection efficacy varies with the beam's damage location. Researchers (Yan et al. 2011; Ahmed et al. 2021) recommend a blend of traditional and contemporary structural health monitoring, highlighting kernel algorithms' superior performance in scenarios with nonlinear temperature-stiffness relationships.
2.11 Classical issues in ML-based approaches
2.11.1 Overfitting and underfitting
Overfitting occurs when a machine learning model becomes overly complex and memorizes the training data, leading to poor generalization on unseen data. On the other hand, underfitting happens when a model is too simplistic and fails to capture the underlying patterns in the data. Regularization techniques, such as L1 and L2 regularization, dropout, and early stopping, can help mitigate overfitting by adding penalties or constraints to the model's parameters. Recent research has explored advanced regularization methods, such as mixup and label smoothing, which have shown promising results in improving generalization performance (Zhang et al. 2018b; Szegedy et al. 2016).
2.11.2 Local minima
Local minima are points in the parameter space where the loss function of a machine learning model reaches a relatively low value but may not correspond to the global minimum. Gradient-based optimization algorithms can sometimes get stuck in local minima and fail to converge to the best possible solution. To address this issue, techniques like stochastic gradient descent with momentum, adaptive learning rate algorithms (e.g., Adam), and randomized initialization of model parameters have been proposed. Recent research has also explored alternative optimization algorithms, such as second-order methods (e.g., L-BFGS), which can potentially avoid local minima and converge faster (Kingma et al. 2015a; Byrd 1995).
2.11.3 Gradient vanishing and exploding
Deep neural networks often encounter the vanishing or exploding gradient problem during training. The gradients can become extremely small or large, impeding learning in deep networks. To mitigate these issues, activation functions that alleviate the vanishing gradient problem, such as Rectified Linear Unit (ReLU), Leaky ReLU, and Parametric ReLU (PReLU), have gained popularity. Additionally, normalization techniques, such as batch normalization and layer normalization, have been introduced to stabilize the training process and alleviate gradient-related challenges (Nair et al. 2010b; Ioffe et al. 2015b).
2.11.4 Uncertainty in network setup
Setting up a neural network involves determining its architecture, including the number of layers, the number of neurons in each layer, and other hyperparameters such as learning rate and batch size. However, there is uncertainty about the optimal choices for these settings. Recent research has explored automated approaches, such as neural architecture search and hyperparameter optimization using methods like Bayesian optimization and evolutionary algorithms, to automate the process of network setup and hyperparameter tuning. These techniques aim to find optimal or near-optimal configurations without the need for manual exploration (Zoph et al. 2017; Bergstra et al. 2012).
2.11.5 Comparison between machine learning methods and classical methods
Machine learning methods, particularly deep learning, have shown remarkable performance in various domains. However, it is essential to consider the trade-offs between machine learning methods and classical methods, especially in terms of efficiency and accuracy. Classical methods, such as support vector machines (SVMs), decision trees, and linear regression, often have interpretable models and can perform well with limited training data. They are computationally efficient and suitable for problems with smaller datasets. Recent studies have explored hybrid approaches that combine the strengths of both classical and machine learning methods, aiming to leverage interpretability while benefiting from the representation learning capabilities of deep neural networks (Deng 2020; Chawla 2002).
2.12 Emergence of ML and DL in aerospace and mechanical engineering
Recent advancements in Machine Learning (ML) and Deep Learning (DL) have shown transformative potential in the domain of aerospace and mechanical engineering, especially concerning damage detection. Studies such as those by Amini and Rahmani (2023) and Bergmayr et al. (2023) have unveiled the efficacy of ML in monitoring the condition and health of aerospace components, such as Carbon Fiber Reinforced Polymer (CFRP) composites and sandwich structures. Meanwhile, in mechanical engineering, innovative approaches like Dong et al.'s (2023) integrated wavelet-learning have provided unprecedented insights into predicting the mechanical properties of concrete composites.
Deep learning, a subset of ML, has further expanded the horizon of possibilities. Li et al. (2023a) successfully refined existing models to enhance the detection accuracy for aeroengine blade damages. In another breakthrough, Uzun's (2023) study introduced an automated damage detection framework for aircraft engine borescope inspections, replacing traditional, subjective methods with objective, data-driven insights. Applications are not limited to aerospace. Bono et al. (2023) utilized deep learning to detect structural changes in building models, suggesting wider applications of these techniques in related engineering domains.
Recent studies underscore the transformative potential of Machine Learning (ML) and Deep Learning (DL) in aerospace and mechanical engineering. Che et al. (2023a, b) employed neural techniques to improve aircraft fatigue damage evaluation and repair decision-making. Nerlikar et al. (2023) optimized damage detection using ultrasonic waves, achieving high classification performance despite structural variabilities. Meanwhile, Dipietrangelo et al. (2023) highlighted the effectiveness of ML in pinpointing impacts on aluminium plates. These advancements are captivating because they offer enhanced accuracy and adaptability in Structural Health Monitoring (SHM). Such innovations could revolutionize diagnostics and repair processes in the industry, paving the way for safer and more efficient aerospace operations in the future.
Notably, some studies transcended traditional application boundaries. Fan et al. (2023) employed ML for the nondestructive evaluation of CFRP in aircraft structures after lightning strikes, exemplifying DL's role in safety and maintenance. Moreover, Dharmadhikari et al.'s (2023) neural network achieved remarkable accuracy in detecting micron-scale fatigue damage in aluminum alloys. The work of Li et al. (2023b), while centered on bridge damage detection, offers techniques that could be adapted for real-time monitoring in aerospace and mechanical systems. As these studies suggest, the integration of ML and DL in aerospace and mechanical engineering is not just promising but pivotal for future innovations in damage detection and system monitoring. Other conventional methods (Umar et al. 2022b; Hussain et al. 2021) that have been used as structural monitoring systems in civil engineering should be integrated with these ML and DL to enhance the capability of better crack prediction.
3 Conclusions, challenges, and future research
This paper offers a holistic literature review on vibration-based structural damage detection (SDD) methods for civil engineering structures, highlighting both traditional and cutting-edge approaches, including Machine Learning (ML) and Deep Learning (DL) techniques. Especially noteworthy is the application of Convolutional Neural Networks (CNNs), which have brought state-of-the-art performance levels, versatility, and computational benefits to the field. The efficacy of any technique, however, largely hinges on the damage type, building design, and data availability.
The pressing need for precise and reliable SDD techniques arises from the essential role that infrastructure plays in societal safety and progress. While there have been strides in the use of non-destructive methodologies, the infusion of artificial intelligence into civil engineering has revolutionized the sector. This review thus offers a synthesized overview of this evolving landscape, comparing features, methodologies, test structures, and damage scenarios, giving professionals a consolidated reference point.
From our comprehensive analysis, several key insights emerge:
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Validation principles While various validation metrics like MAC, MAE, and RMSE have been employed, each technique has limitations concerning damage indices or structural complexities. A universal validation principle could bolster confidence in these methodologies.
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Addressing nonlinearity Civil engineering structures, inherently nonlinear, encounter diverse loads. Yet, many algorithms focus on single-load situations, sidelining comprehensive nonlinear behavior. Advanced detection methods that encompass multiple load scenarios are imperative.
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Challenges with inverse analysis This approach, while crucial, grapples with the ill-posed nature arising from factors like limited data, noise, and complex relationships between measurements and damage parameters.
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Data scarcity and quality While structural damage identification remains a challenge due to factors like noise and modeling inaccuracies, the significance of continual updates in statistical methods and noise elimination is underscored.
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Advancements and challenges in ML ML techniques, especially ANNs and SVMs, have broadened SDD's horizons. However, issues like model overfitting and real-world validation persist. The vast data generated by Structural Health Monitoring (SHM) systems presents an opportunity for automated processing using AI and big data technologies.
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Modal characteristics in ML While modal properties like natural frequencies, damping ratios, and mode shapes have been popularly used as damage-sensitive features, they may not always be the best choice. Factors like temperature and moisture variations can influence them, making their sole use in ML-based damage detection questionable.
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Deep learning's role Deep learning techniques, particularly CNNs, have provided innovative pathways for direct feature extraction from raw data. But challenges remain, including data overfitting, the nuanced balance between feature extraction, classifier selection, and computational demands, especially in Wireless Sensor Networks (WSNs).
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Future directions Real-world undamaged structure data combined with simulated damage scenarios can be pivotal in training classifiers. There's a clear trend toward semi-supervised and unsupervised algorithms, showcasing the evolving nature of the field. Furthermore, there's a growing acknowledgment of the unique challenges faced when applying advanced ML and DL techniques to civil structures due to their inherent complexities.
In conclusion, the intersection of traditional SDD techniques with ML and DL presents a promising future for enhanced structural health monitoring. The swift innovations underline the importance of periodic reviews and the potential of these methodologies in ensuring safer, resilient civil infrastructures.
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Zar, A., Hussain, Z., Akbar, M. et al. Towards vibration-based damage detection of civil engineering structures: overview, challenges, and future prospects. Int J Mech Mater Des 20, 591–662 (2024). https://doi.org/10.1007/s10999-023-09692-3
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DOI: https://doi.org/10.1007/s10999-023-09692-3