1 Introduction

A rough road gives poor ride quality, increases vehicle fuel consumption and affects vehicle handling. According to a report in Britain, potholes caused more than £1 million damages to vehicles every day in 2010 [1]. Road roughness measurement is vital for transport authorities in the quest to maintain adequate ride quality for vehicles. Knowledge of road profiles also provides information for adjusting control parameters to improve ride comfort and ride handling, given the development of suspension system from passive to semi-active and active control in the automotive technology.

Generally speaking, road estimation algorithms [2] can be divided into three distinct types, namely contact measurement, non-contact measurement, and system response-based estimation. Conventional contact and non-contact measurements have been used worldwide as major pavement profiling methods. The primary contact measurement includes two categories: manual profilograph such as rods and levels, straight edges, walking profilers, and trailer-towed devices such as the Longitudinal Profile Analyser (LPA). Non-contact measurement includes inertial profilers such as the GM profilometer developed by General Motors (GM), and the Automated Pavement Profiler (APP). The advantages and disadvantages of these contact and non-contact measurements are discussed in [3,4,5,6]. In recent years, road surface monitoring instruments have transcended from dedicated vehicles with special sensors to dedicated sensors mounted on public transport vehicles, and general-purpose sensors on privately-owned vehicles, and most recently, smartphone-enabled automated monitoring of road infrastructure [7]. This development is driven by response-based methods to indirectly assess road roughness condition using measurements of displacements, velocities, and accelerations of vehicle components, resulting in cost reduction for labour and equipment as compared with direct contact/non-contact profiling [8]. This has led to the emergence of Probe Data Performance Management (PDPM) or Vehicle Probe-based Pavement Management (PBPM) for assessing pavement quality through probe data [9]. There are three system structures by way of connected vehicle approach, fleet vehicle approach and smartphone approach. Basically, road excitation can be estimated using onboard sensors (accelerometers, gyroscopes) for individual or a combination of three key functions as follows (see Fig. 1):

  1. 1)

    Road Profile Reconstruction/estimation or road roughness classification - PR (e.g. Power Spectral Density – PSD), in which fast computation (e.g. in second) adapts vehicle parameters to road roughness levels;

  2. 2)

    Potholes Detection – PD, which detects potholes, manholes, road defects where the precise localisation is of importance; and

  3. 3)

    Roughness Index Estimation – RE (e.g. International roughness index – IRI or new index) for pavement maintenance where roughness data is often aggregated for a certain segment length.

Fig. 1
figure 1

Three temporal-spatial functions using response-based methods

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A brief overview of approaches using dedicated sensors and smartphone sensors can be found in [10, 11], yet a comprehensive review is lacking. Herein, in this literature review paper, around 130 articles have been reviewed focusing on the methodologies but not on theories, empirical insights or conceptual model [12]. The objectives and contribution of this review are threefold. Firstly, an examination of the state-of-the-art response-based methods is conducted to provide an overview of their developments within the last 10 years. This provides a comprehensive understanding of the diversity of on-going and dominant methodologies being used. Secondly, the key pros and cons of different methods, e.g. signal processing, data-driven, threshold-based, transfer function, are highlighted. Lastly, key focus areas on the estimation of road surface irregularity are proposed as opportunities for further studies such as the inclusion of air-suspension system, improvement of current machine learning algorithms or further development of the fleet vehicle approach. The results of this review serve to shed light and provide orientation for the research community on system response-based estimation.

Figure 2 illustrates a topology of approaches to measure road surface irregularity focusing on system response-based methods with detailed applications for vehicle dynamics control (VDC) in dealing with PR for adjusting vehicle parameters to improve ride comfort and ride handling; and PBPM utilising portable onboard sensors and smartphones for PD and RE in citywide network.

Fig. 2
figure 2

Classification of different approaches to measure road surface irregularity under three main functions

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The methodology for gathering “response-based methods literature database” is presented in the next section. PR algorithms for VDC are then described, followed by PD and RE algorithms for PBPM. The discussion, conclusion and outlook section reports the main results of this review study and proposes research and development gaps deserving of further study.

2 Literature data retrieval method

Available articles regarding response-based methods to measure road surface condition were collected mainly from “Scopus” database [13] and partially from “Google Scholar” [14]. Articles of focus are those published by international journals and high-quality conferences. The first round of online search was conducted using the following keywords: ((“road roughness” OR “road profile” OR “pothole”) AND (accelerometer OR response) AND (estimation OR classification OR detection)) AND PUBYEAR > 2005, using Scopus’ default search settings: article titles, abstracts and/or keywords. The search period is limited to the recent 15 years since an initial investigation found that studies on the topics mostly started at around 2006, with predominant numbers in the past 10 years (see Fig. 3b).

Fig. 3
figure 3

Reviewed documents from (a) retrieval of 130 articles, and (b) development by years

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A total of 161 documents were obtained from the various field of studies, of which 86 are published journal articles, 3 are articles in press, 1 is a book chapter and 71 are conference papers. All retrieved documents were further analysed in which 87 documents were removed as being insufficiently related to the main scope of VDC or PBPM nor the main functionalities of system response-based estimation (PR, PD or RE); these rejected documents are mostly related to bridge-vehicle interaction. Relevant references (56) were retrieved and included in the analysis (see Fig. 3a). The additional literature that was missed in the direct search is due to various technical terms being used in these documents such as road anomaly, abnormal section, impact, defect, bump, irregularity, failure, damage (instead of ‘pothole’) or sensing, measurement (instead of estimation, classification, detection). Among the 130 reviewed documents, 37% are for road profile reconstruction, 39% for pothole detection and the remaining 24% for roughness index estimation.

3 Results

3.1 Road profile reconstruction/estimation for vehicles dynamics control

Profile reconstruction/estimation (PR) is essential for vehicle dynamics control (VDC). However, control algorithms are dependent on vehicle suspension types, be it passive, semi-active or active, to formulate the corrective dynamics behaviours [15]. PR algorithms for VDC can be classified into three main approaches: 1) model-based methods or observers/estimators, 2) data-driven methods/machine-learning techniques, and 3) frequency response functions/transfer functions and others. These are described in the following sections.

3.1.1 Model-based methods (observers/estimators)

Kalman filter/estimator (KF) and sliding mode observer (SM) are the most commonly-used methods since a long time. Three standard KFs are the linear KF for linear cases, the extended KF for a non-linear relationship, and the unscented KF for strong nonlinearities. Initially in 2011, the linear quarter-car model was developed to implement the KF method [16] that needed measurements of the suspension deflections, the body position and acceleration. In [17], an improved KF was developed to include the vehicle sprung mass change, and in [18] an augmented KF was developed to make use of all the available sensors. The PR is implemented with the modified KF framework in [19] for the non-linear spring-damper system to localise autonomous vehicle position. Unfortunately, for all KF methods, the tuning of the covariance matrix is usually done heuristically which effects the estimation results caused by the deterioration and loss of information. To overcome this drawback, an algebraic estimator was developed in [20], by updating the covariance matrix according to the change of road roughness [21], or by applying the adaptive KF and adaptive super-twisting observer (AKF-ASTO) algorithm in a new estimator [22].

Regarding other observer approaches, the most common method is the sliding mode observer (SM) considering the road profile as unknown inputs to be estimated. A 16-DOF full-car model was firstly used to develop the SM based on the vertical motion of the vehicle [5]. A researcher [23] then developed a second-order SM to avoid the assumption of constant velocity, while another model-based observer was developed to compensate for the chassis dynamics for minimising its interaction effect [6]. The higher-order SMs using adaptive super-twisting observer based on a nonlinear quarter-car model were also developed in [24] for PR, and in [25] for PR and tyre friction estimation simultaneously. The combination of sliding mode observer and adaptive Kalman filter for PR related to tyre dynamics can be found for active suspension control in [26]. Other methods of control theory using an adaptive observer with the Q-parameterisation method have shown their validity and feasibility [27] and the extensions in [28, 29] with detailed synthesis and experimental validation. Compared to other methods such as KF, the Q-parametrization method provides better performance and is suitable for real-time implementation due to less computing cost and implementation complexity.

Another state observer can be found in [30] to use the overall response of the preceding vehicle(s) to generate preview controller information for follower vehicles. An H∞ observer was adopted and found to be feasible for real-time implementation but required knowledge of many vehicle parameters [31], while a jump-diffusion process estimator can perform PD and PR simultaneously [32]. Although these types of estimators can work effectively for active suspension system control, extensive modelling is required as the main drawback as well as the problem of speed variation.

3.1.2 Data-driven methods/machine-learning techniques

The emergence of machine-learning techniques (MLs) has motivated researchers to focus on various ML algorithms to measure road surface irregularity, as reported in more than half of the reviewed documents. Among them, Neural Network (NN)/Artificial Neural Network (ANN) and Support Vector Machine (SVM) are the most common methods. In 2010, a study [33] used a Bayesian-regularised nonlinear autoregressive exogenous model (NARX) for PR based on the acceleration from a linear half-vehicle model. The ANN-based methodology has been applied for road surface condition identification on mining vehicles and mining roads [34], and for the Land Rover Defender 110 [35]. Similar ANN can be found in [36] using seven vehicle acceleration variables as inputs. To improve estimation efficiency, different techniques/algorithms have been implemented along with ANN. In [8], wavelet analysis was included in similar ANN for the connected vehicle environment. In [37], ANN was used with the mean square of unsprung mass acceleration divided by vehicle speed to classify road Power Spectral Density (PSD) regardless of vehicle speed and suspension parameters.

To classify different road types/terrains (e.g. brick, gravel, grass), ANN and principal component analysis (PCA) were used in combination with image processing [38], or SVM with PCA [39]. To remove the speed dependence from terrain classification, SVM was combined with wavelet analysis of acceleration data [40], or SVM with spatial frequency component analysis by Fast Fourier Transform [41].

Apart from ANN and SVM, other sophisticated MLs were developed and often combined with other techniques for VDC. Deep Neural Networks [42] and Probabilistic Neural Network classifier [43] were proposed by using measurable system responses. The Adaptive Neuro-Fuzzy Inference System - ANFIS road classification method was proposed using wavelet analysis based solely on sprung mass acceleration [44]. ANFIS classifier was found to be better than other methods in [45], and ANFIS was combined with KF for VDC of semi-active suspension in [21, 46]. PNN classifier using wavelet analysis showed better performance than ANFIS and NARX methods. The combination with PNN classifier and AKF-ASTO [22] adaptively changes the process noise covariances Q and R for the KF, resulted in higher accuracy than existing KF method. Random forest classifier (RF) was used to combine information from both time and frequency domains for a controllable suspension system in [2], while the RF was combined with transfer function to develop a speed independent road classification strategy in [47]. Most recently, independent component analysis as a simple and fast method was developed in [48], and various MLs were compared in [49].

3.1.3 Transfer functions and other techniques

The transfer function (TF) was first used by Gonzalez in 2008 [50] to estimate road PSD based on the relationship between the road surface and vehicle acceleration via a TF as Eq. 1:

$$ H (\Omega)=PSD_{acc}(\Omega)/PSD_{road}(\Omega)$$
(1)

where PSDacc(Ω) and PSDroad(Ω) are the PSD for a frequency Ω due to vehicle accelerations and road profile, respectively.

The road can be classified according to ISO 8608 [51] based on PSDroad estimated from the PSDacc of the axle or body acceleration measurements [50]. In [52], similar results have confirmed the efficiency of the TF approach, and in [53] the TF was extended to a full-vehicle model to estimate road PSD regardless of vehicle speeds. From another point of view, dynamic tyre pressure sensor was used to estimate road profiles based on an assumption of a linear relationship between road surface profiles and tyre pressure via a TF [54].

Regarding other methods, a numerical optimisation technique can be found in [55] that employs Monte Carlo simulations to obtain the optimal PR, but it is costly for computing. The method of control-constraints was proposed [56] that focuses on tyre dynamics and requires solving differential-algebraic equations. A modulating function technique [57] can fulfil the real-time and noise suppression requirements with the focus particularly on off-road vehicles. In [58], Bayesian estimator was proposed regardless of vehicle models; but a priori information of the road is required. In addition to acceleration measurements, PR can be done by microphones to measure tyre noise [59]; however, a robustness study is needed to reduce signal contaminations.

3.1.4 Summary of methods for road profile reconstruction/estimation

Table 1 lists the related model-based methods where most of them use a passive suspension system and quarter-vehicle model while fewer use active suspension system. Q-parameterisation has demonstrated its better performance than other methods, with less parameter information required after experimental validation using passive, semi-active and active suspension systems. The pothole detection does not gain much research interest with only 2 relevant studies. Studies on data-driven methods are listed in Table 2 and similarly most studies use a passive suspension system and quarter-vehicle model. Together with road profile reconstruction, the functions of pothole detection (2 studies), roughness index estimation (1 study) or terrain classification (4 studies in which 3 are from the same first author) can be found. Since the first ML emerging from NARX in 2010, recent research continues to improve the algorithms by increasing estimation accuracy and using less parameter information such as the ANFIS (only sprung mass). Research related to speed independence has shown the potential for large-scale application with both offline-online phase classification steps such as the speed independent road classification strategy - SIRCS. Studies on transfer function and other methods are listed in Table 3 for road profile reconstruction only without consideration of pothole detection or roughness index estimation, in which all the algorithms were developed using the passive suspension system. The sophisticated modelling of other methods has negated them from the real-time or online application.

Table 1 Summary of model-based methods for road profile reconstruction function
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Table 2 Summary of data-driven methods for road profile reconstruction function
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Table 3 Summary of TF and other methods for road profile reconstruction function
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In summary, various methods have been developed for PR (48 studies) and several include additional functions for PD (4/48 or 8.3%) and RE (1/48 or 2%), in which TF and other methods have focused on PR (9/48 or 19%) only (see Fig. 4). A high number of studies use quarter-vehicle model (29/48 or 60%) and passive suspension system (32/48 or 67%), in which TF and other methods mostly use passive system (8/9 or 89%). Starting from the first developed Kalman filter, sliding mode observer, artificial neural network and transfer function methods in the 2010s which require many vehicle parameters but fewer accuracy levels, recent methods are focusing on fast computation with fewer parameters for online and real-time application. The combination of different techniques has resulted in higher estimation performance such as machine learning and feature extraction, or machine learning and Kalman filters.

Fig. 4
figure 4

Method classification for RE, PD and PR

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3.2 Pothole detection and roughness index estimation

The three approaches in PBPM has been classified as: connected vehicle approach (uses OEM-installed accelerometers, sensor hardware and standardised onboard vehicle) fleet vehicle approach (uses semi-permanent, non-stock accelerometers in a fleet of agency-owned vehicles, supplemented by GPS units) and mobile device approach (uses accelerometer-equipped mobile devices to gather and transmit roughness information to a central database) [9]. The latter approach using smartphone sensors as the concept of “citizen as sensors” in [60] or “citizen engineer” [61] has received much research interest in recent years, followed by the connected vehicle and the fleet vehicle (which can be grouped into one dedicated sensor onboard approach). Regardless of applications, the methodology can be classified into three groups: acceleration thresholds or threshold-based methods, signal processing and machine-learning techniques.

3.2.1 Threshold-based methods

Threshold-based methods are the most straightforward approaches for PD detection by processing mainly the vertical acceleration (Z-acc) or in combination with other direction acceleration (x and y) and gyroscopes. A researcher [62] has proposed four indices in which the Z-THRESH was further modified [63] to build a cloud computing system: Z-THRESH (from vertical vibration), Z-DIFF (from the difference of consecutive Z-acc above threshold), STDEV(Z) (as the standard deviation of Z-acc above threshold in a window), and G-ZERO (whether the sensor senses a 0-G vibration). Similar STDEV(Z) can also be found in [64] and to develop a bump index in [65]. Other acceleration thresholds are used to classify three relative rough road levels [66] or severity levels of potholes [67, 68] and to characterise road bumps [69]. Thresholds of Z-acceleration and ultrasonic data were combined in [70] while the Z-jerk as the “rate of change of acceleration” is used in Cyber-physical system [71]. However, how to set up correct thresholds is challenging under the influence of vehicle speeds, suspension parameters as well as sensor location and orientation. Furthermore, only pothole detection alone is not sufficient for real application, as transport authorities care about roughness index estimation as well for road surface maintenance.

3.2.2 Signal processing

To overcome the drawbacks of the threshold-based methods, various signal processing filters have been used. Researcher [72] further processed Z-acc by simple filters and Gaussian model-based algorithm to detect the severity of potholes and differentiate humps and potholes. A study in [73] combined Z-THRESH and G-ZERO and adopted a spatial interpolation method to obtain precisely pothole locations. Fuzzy logic was used to detect and recognise the speed bumps from vehicle speed and Z-acc variance [74]. Time-frequency analysis was used such as the Discrete Wavelet Transform to estimate gravel roads ride quality, detect the location and the severity of surface potholes [75], or the Gabor transform to estimate road roughness condition in combination with image processing for PD [76]. In [77], a greedy heuristic approach for an optimal mobile sensor placement maximises the total length of the road inspected by sensors.

Frequency filter, speed filter and small peaks filter were used to develop the vertical acceleration impulse that corresponds to a “high-energy event” on the road surface in UNIquALroad [78, 79]. Dynamic Time Warping – DTW detects pothole by using the pattern-matching technique independent of time and speed [80]. Similar to DTW, the Smartphone Probe Car system was developed using a new road anomaly indexing heuristic which is adaptive to vehicle dynamics [81].

To evaluate road roughness IRI, the well-known regression relationships between PSD with IRI was investigated in [82, 83], so do the root-mean-squared acceleration (RMS) and IRI in [84, 85]. A compact road profiler and ArcGIS to measure and evaluate road roughness condition was introduced in [86]. Filter and Fast Fourier Transform (FFT) were used to estimate IRI from smartphone data under realistic setting (e.g. inside pockets) based on the approximate proportion of spectrum magnitude and road IRI [87, 88]. The inverse pseudo-excitation method offers a new approach to estimate IRI independent of the travelling speed, road roughness grade, and vehicle type [89]. The RMS acceleration was further studied to detect potholes using speed filter and Z-axis filter in Pothole Patrol, and to develop new roughness index (IRI-proxy) depicting overall road quality [60]. Based on the relationship of PSD between road surface and vertical acceleration, parameters of road profile can be evaluated using Maximum Likelihood-based estimation [90], or using linear predictive coding by averaging the power of the prediction error [91, 92]. In [93], a recursive multiscale Correlation-Averaging algorithm was developed to deal with the uncertainty/noise such as GPS inaccuracies, driving path variation and errors from the distance-measuring devices.

Regarding new roughness index, a speed-independent road impact factor - RIF (individual vehicle) and its corresponding time-wavelength-intensity-transform – TWIT (vehicle groups) for connected vehicles were established using advanced signal processing in [94]. Further studies were conducted intensively to investigate and validate the RIF regarding sampling rate selection [95], localisation [96, 97], RIF-IRI proportionality [98], deterioration forecasts in consideration of suspension parameter variances [99], stop-and-go conditions [100], and wavelength sensitivity [101].

3.2.3 Machine learning techniques

With more data availability, machine learning techniques (MLs) have been utilised in PD and RE functions while noting that most of them were developed for the PD. The abovementioned Z-THRESH is similar but simpler than Z-peak in Pothole Patrol [102], Nericell [103] and TrafficSense [104], which used specific algorithms to filter and to cluster the collected data. Based on Pothole Patrol, further analysis to differentiate pothole and bump-road cases in [105], or to develop the PRISM platform for remote sensing [106]. For the same purpose, a supervised learning approach based on temporal classification was undertaken in [107]. Based on Pothole Patrol, P3 can infer the depth and length of the pothole by adopting a one degree-of-freedom (DOF) vibration model as well as perform a self-learning vibration recovery algorithm [108]. A clustering ML was used to cluster potholes with an adaptive detection threshold and learning rate update in CRSM [109, 110] after using pothole filters in Pothole Patrol. K-mean clustering was used in [111] and additional Random Forest (RF) classifier in [112]. Another study [113] developed an online road roughness classification system using bicycles instrumented with smartphones embedded with the K-Nearest-Neighbour and Naive Bayes algorithm.

Among MLs, support vector machine (SVM) is used most frequently, and it is often combined with feature extraction methods as multiple classifiers. In [114], SVM was used to detect road anomalies by processing the data collected from a motorcycle-mounted tri-axial accelerometer and further classify road surface condition using unsupervised ML. Recently, SVM and Dynamic Time Warping algorithm were developed in [115] to identify aggressive driving events, road bumps and potholes for cycling. Another improvement was included in [116] where the gyroscope around gravity rotation was used. SVM and wavelet analysis were also used in RoADS [117] to classify the road anomaly into three event classes: severe, mild and span, and in [118] to detect road anomaly based on driver attitudes toward the speeds and turnings. SVM and Fast Fourier Transformation were used in [119] to remove the speed dependence and to label road anomaly. Another study in [120] combined SVM and Wavelet Package Decomposition to detect potholes with low computing cost. In Wolverine [121], the smartphone accelerometer data is used to detect braking events and bumps using K-means clustering and SVM. In [122, 123], SVM was trained using extensive data set from CarSim vehicle simulation as well as experiment, applying for under-sampled vehicles sensor problems and multi-lane pothole detection. In [124], a virtual road network inspector was built based on SVMs to detect potholes using accelerometers mounted to the front and rear axles of the buses.

The comparison of different MLs was conducted in several studies to find the best ML. In [125], a data mining approach was developed to compare the performance of five algorithms for PD. By adopting the framework of this study, a study [126] used RF for its best performance to develop a cloud-based Road Anomaly Service architecture in which PCA was used for feature extraction. PCA was also used in [127, 128] after NN and RF classification were compared to develop a street defect classifier to select NN for its better performance. RMS thresholds were set as a triggering condition for data logging condition and a new street defect level (from 0 to 1) to evaluate the road segment condition. In RoadSense [129], Decision Tree (DT) was designed and compared with SVM and Naïve Bayes algorithm after feature extraction. In Pothole lab [130], a new SVM(Z) and Swarm indices were developed to compare with the four thresholds in [62], Nericell, Pothole Patrol, and PERT [119]. Backward feature elimination was used in [131] to select the optimal set of features for different classification models while in [132] the forward selection and backwards elimination process was performed showing better performance than existing approaches.

Besides CRSM system for IRI estimation, MLs were used in [133] where the authors used smartphone sensor data for training a feature-based prediction model and compared with the road condition from official IRI measurements of the road surface. Another researcher [134] applied NARX ANN to estimate IRI from the connected vehicle after investigating vehicle suspension characteristics and its speed in [8]. In [7], the mean-absolute-value of the Z-acc for every 100 m was sensed by a smartphone on a motorbike, and a fuzzy classifier from a server was used for RE.

3.2.4 Summary of methods for pothole detection and road roughness estimation

Studies on threshold-based methods are listed in Table 4. Given the simplicity of this method based on true positive and false positive of the detection rate, the threshold values may vary due to different factors which make this method not being feasible to be used in real scenarios and large-scale implementation. Table 5 lists the studies on signal processing methods, in which not only the methods of accurate PD and RE but also further concerns on GPS data noise/inaccuracy, sensor and smartphone installation/direction, data fusion/aggregation and crowdsensing system/platform were considered. Among them, the adaptive thresholds in Smartphone Probe Car and Smart patrolling, as well as the IRI-proxy, SmartRoadSense and UNIquaALroad system are found to be promising for large scale application. RIF and TWIT are also potential replacements of IRI in the context of connected vehicle environments. As for ML methods recent studies are listed in Table 6. MLs have attracted many studies resulting in high performance in which PCA plays an important role in feature extraction for the training process. CRSM [109, 110], the system in [122, 123] and another in [133] are promising systems for large scale application.

Table 4 Summary of threshold-based methods for pothole detection and roughness index estimation
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Table 5 Summary of signal processing methods for pothole detection and roughness index estimation
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Table 6 Summary of ML methods for pothole detection and roughness index estimation
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In summary, the diversity of methods and systems have been described in over 80 reviewed articles for the main functions of PD (50/80 or 63%) and RE (30/80 or 27%). Many algorithms can perform both PD and RE (20/80 or 20%). The same number of studies use MLs and signal processing (34 each or 41%) whereas threshold-based methods are used mostly for PD (8%). MLs received more research interest than other methods for PD (26/50 or 52%). In contrast, signal processing is preferred for RE (22/30 or 73%) especially for IRI estimation, in which 11/22 studies (50%) are original algorithms while others are further development or application (Fig. 4). Over the studies related to RE, 6/30 (20%) is about the relative roughness index, 14/30 (47%) for IRI estimation, 2/30 (7%) for IRI-proxy estimation and 8/30 (27%) for the new roughness index (RIF and TWIT). There are only 6 studies (7%) related to fleet vehicle approach, 23 studies for the connected vehicle (28%) and 53 studies for smartphone approach (65%). The problems of GPS accuracy, data aggregation and crowdsourcing have been considered in many studies using signal processing (9/21 studies) and ML (13/30 studies), aiming at supporting the emergence of crowdsourcing-based road surface monitoring.

4 Discussion, conclusion and outlook

Different methods present different levels of complexity, precision and computing intensiveness. Across all the reviewed documents and methods, it is recognised that data-driven methods/MLs are increasingly being used for all the functions in PR, PD and RE (see Fig. 4), as well as the usage of the passive suspension system and quarter-vehicle model due to their modelling simplification. Recent studies have shifted towards RE as shown in the time series graphs, in which signal processing techniques have been preferred for RE given the ability to achieve advanced functionalities such as adaptive thresholds or data fusion. Regarding the function of PR for the individual suspension system, it is more comprehensive to integrate PR for suspension control with variable uncertainty, but more challenges will occur on the knowledge of vehicle dynamic characterisation. Whereas to deal with PD and RE for group of vehicles (fleet or connected vehicle) and “citizen sensor” concept in the large-scale society, the issues of GPS accuracy, data fusion (e.g. the aggregation of sensor data or vehicle suspension types) and crowdsourcing will be challenges to the development of appropriate algorithms/systems. So far, several established algorithms/systems have solved these issues successfully.

In summary, the development of response-based methods to evaluate road surface irregularity has attracted research interests from both automotive technology and pavement engineering, aiming at the three main functions of Road profile reconstruction (PR), pothole detection (PD) and roughness index estimation (RE). The review of about 130 articles on this topic has revealed the diversity of recent approaches mostly within the recent decade. At first, the present study describes the algorithms used for PR including model-based methods, data-driven methods, transfer functions and others. Then, related algorithms for PD and RE are described including the threshold-based, signal processing and machine-learning methods. Following this, all reviewed documents and discussion are summarised on their advantages and disadvantages (see Table 7) which should be beneficial for further research in this field.

Table 7 Advantages and disadvantages of response-based methods
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As for future research, it should be of strong value-add to focus on several potential topics as follows. Firstly, the air-suspension system (as an active-suspension type) has not been investigated by any research for PR whereas most existing studies are about passive suspension system (67%). The reason is probably due to the high modelling complexity of the air-suspension while it is noted that the Macpherson controllable suspension was simulated and simplified in [2]. Secondly, MLs have demonstrated their capability for multiple functions such as ANN algorithms for PR and PD in [33], PR and RE in [8, 134] in which certain limitation in the estimation accuracy, vehicle parameters or speed variance can be further studied to develop comprehensive algorithms.

Thirdly, although fleet vehicle approach seems to be less complicated to deal with, a comprehensive PBPM for PD and RE for the fleet of public transport (e.g. bus fleet) is still missing, except the general concept in [64] or smart PD in [124]. This fleet vehicle approach faces fewer challenges on data aggregation since vehicle fleets are quite identical, with lower GPS errors caused by lane-by-lane difference and without crowdsourcing platform. Such a system, once developed, will be beneficial in maintaining the road condition for public transport such as the citywide bus lane system in Singapore, London or worldwide BRT lane system, in which the road surfaces often deteriorate quickly due to heavy-loading from heavy-duty vehicles [136]. Fourthly, how to localise precise road roughness condition and potholes by lane accuracy (probably less than 0.5 m accuracy) is crucial to make the PBPM comparable to conventional Pavement management system, in which APP instruments currently measure road surface lane-by-lane. Higher GPS localisation of potholes also serves to optimise the trajectories of following vehicles in the connected platooning to avoid road defects by passing the vibration information from the leader to the followers. This can be done with the help of the future development of sensor technology. Lastly, the intensive on-going research on RIF and TWIT [95,96,97,98,99,100,101] as the alternatives for IRI in connected vehicle environment will be promising for large-scale implementation.