# Support vector machine for determining the compressive strength of brick-mortar masonry using NDT data fusion (case study: Kharagpur, India)

- 69 Downloads

**Part of the following topical collections:**

## Abstract

The accurate prediction of compressive strength of brick-mortar masonry walls is crucial for the damage assessment of load-bearing masonry constructions. Direct tests conducted to estimate compressive strength involve core drilling and are expensive. To estimate compressive strength, several indirect test parameters can be used as empirical predictors. Nondestructive tests can be rapidly executed, can significantly reduce repair costs, and can increase the knowledge level of buildings by indirectly estimating compressive strength. This study aimed to determine the compressive strength of masonry construction by using support vector machines (SVMs). Input variables of the model are test data obtained from the nondestructive and destructive testing of 44 masonry wallettes cast in a laboratory for evaluating the compressive strength of brick (\(f_b\)), rebound hammer number, and ultrasonic pulse velocity, while the compressive strength of the wall (\(f_c\)) is output. The final results obtained using an SVM model are validated for a masonry building in Kharagpur, India through experimental testing, and these results are compared with other established empirical relationships. The results indicate that the SVM can be efficiently used to predict the compressive strength of brick-mortar masonry.

## Keywords

Machine learning Intelligent algorithms Nondestructive testing Structural health monitoring## 1 Introduction

An increase in the global population resulted in the construction of new structures to accommodate the continually increasing populace. People are living in old masonry buildings, which must be evaluated for their remaining service life by monitoring and using test strategies. A typical masonry building has load-bearing walls made using brick-mortar units, which supports a complete superstructure. This typology of buildings were widely constructed in India until the mid-1900s for building smaller residential structures. Apart from residential structures, this topology is commonly used for the construction of domes, roofs, and chimneys. If the conservative estimate of the remaining life of buildings is known, the buildings can be repaired before time. On the other hand, inaccurate estimation of the service life may cause severe damages, which results in the loss of life, rehabilitation, and major repairs, thus increasing the cost. Therefore, an accurate prediction of the service life is necessary to avoid such extreme circumstances and minimise damage progression in terms of repair costs.

Among various health monitoring indicators of masonry buildings, compressive strength is considered most crucial. Masonry buildings are subjected to compressive loads throughout their service life [1, 2], thus assessing their behaviour in compression is crucial. Although compressive strength can be estimated by extracting core samples from the building, this approach is not preferred because tests are costly and intrusive. Therefore, the prediction of the compressive strength of the masonry structures joined using mortar without causing damage is a global concern to safeguard buildings and prolong their use. With time, the compressive strength of brick walls of buildings decreases because of factors, such as ageing and material degradation caused by weathering. Therefore, empirical relations developed using various experimental studies [3, 4, 5, 6, 7, 8, 9, 10, 11] and design codes [12, 13] inaccurately estimate compressive strength. Moreover, the empirical relations are site-specific and based on old data for their calibration, and the training data must be updated with the new test data obtained from sites. The compressive strength of masonry depends on the strength of individual components (brick and mortar) and construction processes, which deteriorate estimation capacity. Various destructive and nondestructive methods are available that can be used to estimate the strength of the building.

Damage assessment in masonry structures for service life prediction is performed using multiple nondestructive techniques. The NDT data collected using various techniques and sensors are heterogeneous and are crucial for structural health monitoring. McCann and Forde [14] in their review paper summarised several ND techniques used for masonry constructions. Several researchers have developed empirical correlations between compressive strength with data from NDTs. Several studies have used regression analyses to obtain the correlations between compressive strength and mechanical parameters to quantify the strength of buildings. For example, Ramos et al. [15] fused ultrasonic, sonic, and direct core tests to determine the elastic modulus of masonry materials used in a church, which is an indicator for material degradation. Mishra et al. [16] used natural frequencies obtained through experimental modal analysis as a NDT technique to capture the extent and location of damages on the cantilever beam. Moreover, other ND techniques, such as rebound hammer (RH) [17], ultrasonic pulse velocity (UPV) [18], flat-jack method [19], impact-echo method [20], ground-penetrating radar [21], ferroscan testing [22], infrared thermography [23], and laser scanning [24], are commonly employed by various researchers. The integration of diverse sources of data to predict structural damages is a challenging task. This study integrates various ND techniques to estimate the compressive strength of brick-mortar masonry. The integration of various ND techniques reduces uncertainty in the estimation of required parameters [25, 26, 27].

Numerous novel artificial intelligence techniques have been used for various engineering applications. Advancement in soft computing techniques has enabled the effective use of data and clear interpretation by engineers. The SVM has been used to solve various problems involving predicting the compressive strength of different types of concrete [28, 29, 30, 31] and jet-grouted material [32]. Apart from estimating compressive strength, the SVM is used for several applications in engineering, such as traffic sign detection [33], modelling soil pollution [34], predicting daily flow of river [35] predicting elastic modulus of concrete [36], modelling landslide susceptibility [37], air balancing for ventilation systems [38] and predicting shear force for base isolation device [39, 40]. Its other successful applications include for example, classifying building information modelling elements [41], system reliability analysis of slopes [42], estimation of concrete expansion caused by alkali-aggregate reaction [43], damage detection in a three-story frame structure [44], prediction of lateral load capacity of piles [45], crack inspection for aircraft skin [46] and assessing liquefaction potential [47].

## 2 Data collection

Boundary range of the input and output variables

Parameter | Category | Min. | Max. | Mean | SD |
---|---|---|---|---|---|

Rebound number RH | Input | 24.60 | 41.70 | 34.01 | 4.51 |

Ultrasonic pulse velocity UPV (m/s) | Input | 1458 | 2870 | 2191 | 461 |

Compressive strength of brick \(f_b\) (kN) | Input | 10.15 | 20.60 | 15.45 | 4.80 |

Compressive strength \(f_c\) (MPa) | Output | 1.09 | 6.07 | 3.24 | 1.46 |

Failure load \(F_u\) (kN) | Output | 68.05 | 365.27 | 205.05 | 89.20 |

Table 1 reports the statistical data obtained with their range, mean, and standard deviations. Furthermore, the mechanical properties of individual units, namely bricks and mortars, are obtained through compressive tests. According to IS 1077:1992 [49] code for wall bricks, the compressive strength of type I, II, and III bricks are 20.6, 10.15, and 12.2 MPa, respectively. Moreover, cubes of mortar units comprising one part of cement and four parts of sand are cast based on the standards of IS 2116: 1980 [50]. Compression tests are performed under the same condition. The average value of compressive strength for mortar cubes is 14.3 MPa.

## 3 Support vector machine

*x*) into high-dimensional output data through nonlinear transformation. The transformation allows the identification of nonlinear separating features that cannot be recognised in a low-dimensional space. The SVR method involves structural risk minimisation rather than the minimisation of the mean square error over the data set. SVM is used in this study to predict the compressive strength of brick-mortar masonry, which is modelled as a regression problem. The mathematical formulation of SVR is as follows.

*i*= 1,...,

*N*, where \(x_i\) is the D-dimensional input vector and \(y_i\) is the scalar output or target value for

*N*number of datasets. In this study, \(f_b\), RH, and UPV are used as the input parameters (x = \(f_b\), RH, UPV) to determine the best-fit function

*f*(

*x*). The nonlinear relationship between the input and target values can be formulated using the regression function as follows:

*f*(

*x*) and \(\phi (x)\) denote the forecasting values and nonlinear mapping function in high-dimensional space;

*w*denotes the matrix representing the orientation of hyperplane separating the datasets, and b represents the bias coefficient to be adjusted. These coefficients are computed by minimising the regularised risk function.

*R*(

*C*) and \(R_{emp}\) denote the regression and empirical risks, respectively. The first term in Eq. (2) is the regularisation term, and the second term in Eq. (2) is estimated from the \(\varepsilon\)-insensitive loss function in Eq. (3). The constant

*C*(\(0<C<\infty\)) denotes the trade-off between the maximisation of the margin (Fig. 3a) and the training error. The parameter \(\varepsilon\) denotes the insensitive loss function for the radius around the training data (Fig. 3b).

*w*(Eq. 1) can be computed from the Lagrange multiplier by using the following equation:

*C*, \(\gamma\), \(\varepsilon\)) by comparing the accuracy of predicted and actual values of compressive strength of brick-mortar masonry. The values of SVM parameters are found out to be 500, 250 and 0.001 for

*C*, \(\gamma\), \(\varepsilon\) respectively. The tuning parameters of the SVM model can also be optimised by utilising metaheuristic optimisation algorithms which minimise the objective function in terms of mean square error formulated as the difference between predicted and actual values. Yu et al. [40] optimised SVR parameters using fruit fly optimisation algorithm to characterise an elastomer base isolator for controlling structural vibrations. In another study, SVM-based model parameters were optimised by particle swarm optimisation algorithm to predict the concrete expansion due to alkali-aggregate reactivity [43].

## 4 Case study (Kharagpur, India)

Experimental readings for old building brick specimens

Specimen nos. | Dimensions (in cm) \(\hbox {L} \times \hbox {B}\) | RH | UPV (m/s) | Failure load (kN) | Compressive strength (\(\hbox {N/mm}^2\)) |
---|---|---|---|---|---|

B-1 | \(25.2 \times 12.7\) | 33.8 | 940 | 382.13 | 11.94 |

B-2 | \(25.0 \times 11.6\) | 38 | 1280 | 279.27 | 9.63 |

B-3 | \(25.5 \times 12.7\) | 31.8 | 1190 | 340.04 | 10.5 |

B-4 | \(25.3 \times 12.8\) | 34.7 | 1260 | 268.79 | 8.3 |

B-5 | \(24.5 \times 12.7\) | 33.65 | 1160 | 289.06 | 9.29 |

B-6 | \(26.0 \times 13.0\) | 30.7 | 790 | 275.81 | 8.16 |

B-7 | \(25.0 \times 11.9\) | 41.65 | 1620 | 366.82 | 12.33 |

B-8 | \(25.0 \times 12.8\) | 32.65 | 1360 | 320.96 | 10.03 |

Average | 34.65 | 1200 | 315.36 | 10.02 | |

SD | 3.58 | 253 | 43.87 | 1.53 |

Experimental readings for old building mortar specimens

Specimen nos. | Dimensions (in cm) \(\hbox {L} \times \hbox {B}\) | RH | UPV (m/s) | Failure load (kN) | Compressive strength (\(\hbox {N/mm}^2\)) |
---|---|---|---|---|---|

M-1 | \(15.0 \times 15.0\) | 15.1 | 3020 | 145.64 | 6.47 |

M-2 | \(15.1 \times 15.0\) | 15.7 | 2950 | 138.78 | 6.16 |

M-3 | \(14.9 \times 15.1\) | 16.15 | 3020 | 146.59 | 6.51 |

M-4 | \(15.0 \times 15.1\) | 15.9 | 2990 | 156.52 | 6.95 |

M-5 | \(15.0 \times 15.0\) | 15.55 | 3020 | 157.01 | 6.97 |

Average | 15.68 | 3000 | 148.89 | 6.61 | |

SD | 0.39 | 31 | 7.79 | 0.35 |

NDT readings obtained from masonry blocks extracted from the old building

Specimen nos. | Dimensions (in cm) \(\hbox {L} \times \hbox {B} \times \hbox {H}\) | RH | UPV (m/s) |
---|---|---|---|

MB-1 | \(57.5 \times 26.5 \times 20.5\) | 31.9 | 2065 |

MB-2 | \(80.5 \times 28.0 \times 21.5\) | 33.7 | 2112 |

MB-3 | \(59.5 \times 26.0 \times 18.6\) | 34.4 | 2215 |

MB-4 | \(65.0 \times 26.5 \times 19.0\) | 36.7 | 2315 |

MB-5 | \(43.5 \times 23.2 \times 18.8\) | 25.7 | 1773 |

Average | 32.5 | 2096 | |

SD | 4.2 | 205 |

Average prism strength of demolished blocks

Specimen nos. | Dimensions (in cm) \(\hbox {L} \times \hbox {B} \times \hbox {H}\) | Failure load (kN) | Compressive strength (\(\hbox {N/mm}^2\)) |
---|---|---|---|

MB-1 | \(63.0 \times 22.0 \times 28.0\) | 421.23 | 3.03 |

MB-2 | \(59.0 \times 16.0 \times 27.0\) | 256.20 | 2.70 |

MB-3 | \(60.0 \times 27.0 \times 20.5\) | 505.24 | 3.12 |

MB-4 | \(57.0 \times 21.2 \times 28.5\) | 342.23 | 2.81 |

MB-5 | \(53.5 \times 23.0 \times 23.5\) | 295.32 | 2.35 |

Average | 367.42 | 2.80 | |

SD | 100.0 | 0.30 |

The masonry blocks (Fig. 5b–c) are obtained from one of the load-bearing walls of the demolished structure. Table 4 provides various sizes of the specimens. The surface of the specimens is smoothened to eliminate any unwanted residue of building materials. After that, the samples are tested using an NDT apparatus (Fig. 5d–e). Table 4 presents different NDT parameters of these specimens. Thereafter, the samples are tested for compressive strength (Fig. 5f), and data are reported in Table 5.

## 5 Comparison with different methods

Different empirical formulas for predicting the compressive strength of masonry

S. no. | Empirical formulas | Equation | Average value |
---|---|---|---|

a | Mann [3] | \(0.83 \times f_b^{0.67} \times f_m^{0.33}\) | 7.25 |

b | Hendry and Malek [4] | \(0.317 \times f_b^{0.531} \times f_m^{0.208}\) | 1.60 |

c | Dayaratnam [5] | \(0.275 \times f_b^{0.5} \times f_m^{0.5}\) | 2.24 |

d | Benett et al. [6] | \(0.3 \times f_b\) | 3.01 |

e | Eurocode 6 [12] | \(0.5 \times f_b^{0.65} \times f_m^{0.25}\) | 3.59 |

f | ACI 1999 [13] | \(2.8 + 0.2 \times f_b\) | 4.80 |

g | MSJC [7] | (\(400 + 0.25 \times f_b\))/145 | 2.78 |

h | Kaushik et al. [8] | \(0.63 \times f_b^{0.49} \times f_m^{0.32}\) | 3.57 |

i | Dymiotis et al. [9] | \(0.3266 \times f_b \times (1-0.0027\times f_b + 0.0147\times f_m\)) | 3.50 |

j | Gumaste et al. [10] | \(0.225 \times f_b^{0.855} \times f_m^{0.146}\) | 2.13 |

k | Garzón-Roca [11] | \(0.53 \times f_b + 0.93 \times f_m - 10.32\) | 1.14 |

Table 6 summarises the values obtained by the equations suggested by various researchers. The value obtained using SVM model is 2.79 N/mm\(^2\). The lowest difference is obtained between the experimental value and the value predicted by MSJC and SVM. Hence, the current approach (SVM) can estimate the compressive strength of masonry with more accuracy than empirical equations. From the table, it is worth deducing that apart from SVM, models by MSJC [7] and Gumaste et al. [10], give realistic results which are closer to the experimental values (2.80 N/mm\(^2\)) obtained using destructive tests. Figure 7 displays a comparison between the predicted and measured values reported in Table 6. The Figure demonstrates an acceptable match between the actual and predicted values. Figure 8a and b reports the comparison between the experimental values obtained from compressive testing in the laboratory with the values predicted by SVM for both training and testing data from the case study. Again, the values closely agree with the experimental test data making the model applicable on-site conditions. Some minor errors can be attributed to incorrect estimation in failure load for masonry blocks, the difference in mortar strength used to reconstruct sample and workmanship. Although, apart from individual variations among the five samples, the average value predicted by SVM closely matches with the value obtained from experimental testing.

## 6 Conclusion and discussion

In this study, an SVM is developed for estimating the compressive strength of brick-mortar masonry at a building site in Kharagpur, India. The inputs for the model comprise ND tests. The SVM model is developed with an f_{b }, RH and ultrasonic velocity as inputs and the compressive strength of wallettes as an output for 44 laboratory samples. The model is tested for five datasets by directly obtaining samples at building sites. The compressive strength of masonry buildings is estimated through the analysis of collected data using the SVM. For performance indicators, the SVM model generated a coefficient of correlation and root mean square error of 0.980 and 0.589.

The results obtained using the SVM model are considerably consistent with on-site conditions, which are validated using the experimental testing of the extracted samples. The estimated and measured values obtained using the SVM are similar, and thus, the model is satisfactory in predicting the compressive strength of the brick-mortar masonry structure. The SVM model also can take into account the noise associated with NDT measurements in the field via two slack variables \(\xi\) and \(\xi ^*\). Thus, it can decrease uncertainty in estimation of compressive strength by cancelling the effect of noise in the measurements up-to some extent, which might not be possible in other soft computing techniques such as ANN. Furthermore, empirical formulas used for comparison are primarily based on two parameters, and the sample-specific data is used to derive these formulas. Under actual site conditions, compressive strength changes with time and is influenced by various factors, such as the current damage condition of buildings. Therefore, the developed model must consider indicators that are updated with time. In addition, some sources of error may be observed because of the presence of noise and unreliable data in the data acquisition stage. The proposed approach is advantageous because the on-site NDT results are used to update the model instead of constant indicators, which may not reflect the damage conditions of buildings. The proposed approach can serve as a theoretical guidance for the inspection professionals and practitioners to evaluate structural damage in the field. This will then facilitate timely and appropriate administering of retrofitting technique.

In the future work, the SVM model can be improved by considering more parameters for the input layer for more accurate indicators of the service life of buildings. Furthermore, flat jack tests will endeavour to provide an insight into the joint characteristics of brick mortar masonry that should further assist realistic compressive strength of masonry. After the development of the model incorporating additional parameters, it can be applied to sites for compressive strength estimation. The SVM model can also be compared with commonly used soft computing techniques such as artificial neural networks (ANN) and adaptive neuro fuzzy inference system (ANFIS) to demonstrate its performance against alternative approaches. More input data can be obtained by performing additional experimental tests in the laboratory by varying the dimensions of the masonry wallet, type of bricks and different strengths of mortar. In this way, the model can avoid the problem of overfitting prevalent over limited data sets and hence will improve its accuracy. Furthermore, the parameters of the SVM model, can further be refined by using an optimisation algorithm in order to avoid choosing incorrect values by trial and error method.

## Notes

### Acknowledgements

The authors would like to thank Civil Construction and Maintenance (CCM) at Indian Institute of Technology Kharagpur for providing the support for collection of requisite samples from the demolished building.

### Compliance with ethical standards

### Conflict of interest

The authors declare that they have no conflict of interest.

## Supplementary material

## References

- 1.Hendry AW (1998) Structural masonry, 2nd edn. Macmillan, LondonGoogle Scholar
- 2.Lourenço PB, Pina-Henriques J (2006) Validation of analytical and continuum numerical methods for estimating the compressive strength of masonry. Comput Struct 84(29–30):1977–1989Google Scholar
- 3.Mann W (1982) Statistical evaluation of tests on masonry by potential functions. In: Sixth international brick masonry conferenceGoogle Scholar
- 4.Hendry AW, Malek M (1986) Characteristic compressive strength of brickwork from collected test results. Mason Int 7:15–24Google Scholar
- 5.Dayaratnam P (1987) Brick and reinforced brick structures. Oxford and IBH, New DelhiGoogle Scholar
- 6.Bennett R, Boyd K, Flanagan R (1999) Compressive properties of structural clay tile prisms. J Struct Eng 123(7):920–926Google Scholar
- 7.MSJC (2002) Masonry Standards Joint Committee, building code requirements for masonry structures, ACI 530-02/ASCE 5-02/TMS 402-02, American Concrete Institute, Structural Engineering Institute of the American Society of Civil Engineers, The Masonry Society, DetroitGoogle Scholar
- 8.Kaushik HB, Rai DC, Jain SK (2007) Stress-strain characteristics of clay brick masonry under uniaxial compression. J Mater Civ Eng 19(9):728–739Google Scholar
- 9.Dymiotis C, Gutlederer BM (2007) Allowing for uncertainties in the modeling of masonry compressive strength. Constr Build Mater 16(7):1385–1393Google Scholar
- 10.Gumaste KS, Rao KSN, Reddy BVV, Jagadish KS (2007) Strength and elasticity of brick masonry prisms and wallettes under compression. Mater Struct 40(2):241–253Google Scholar
- 11.Garzón-Roca J, Marco CO, Adam JM (2013) Compressive strength of masonry made of clay bricks and cement mortar: estimation based on neural networks and fuzzy logic. Eng Struct 48:21–27Google Scholar
- 12.ENV 1996-1-1 (1998) Eurocode no. 6, design of masonry structures, part 1-1: general rules for buildings-rules for reinforced and un-reinforced masonryGoogle Scholar
- 13.ACI Committee 530 (1999) Building code requirements for masonry structure. American Concrete Institute, Farmington HillsGoogle Scholar
- 14.McCann DM, Forde MC (2001) Review of NDT methods in the assessment of concrete and masonry structures. NDT E Int 34(2):71–84Google Scholar
- 15.Ramos LF, Miranda TF, Mishra M, Fernandes FM, Manning E (2015) A Bayesian approach for NDT data fusion: the Saint Torcato church case study. Eng Struct 84:120–129Google Scholar
- 16.Mishra M, Barman SK, Maity D, Maiti DK (2019) Ant lion optimisation algorithm for structural damage detection using vibration data. J Civ Struct Health Monit 9(1):117–136Google Scholar
- 17.Vasconcelos G, Lourenço PB, Alves CSA, Pamplona J (2007) Prediction of the mechanical properties of granites by ultrasonic pulse velocity and Schmidt hammer hardness. In: North American masonry conference, pp 981–991Google Scholar
- 18.Hobbs B (1995) Ultrasonic NDE for assessing the quality of structural brickwork. Nondestruct Test Eval 12(1):75–85Google Scholar
- 19.Schuller MP (2003) Nondestructive testing and damage assessment of masonry structures. Prog Struct Eng Mater 5:239–251Google Scholar
- 20.Hoła J, Schabowicz K (2010) State-of-the-art non-destructive methods for diagnostic testing of building structures: anticipated development trends. Arch Civ Mech Eng 10(3):5–18Google Scholar
- 21.Diamanti N, Giannopoulos A, Forde MC (2008) Numerical modelling and experimental verification of GPR to investigate ring separation in brick masonry arch bridges. NDT E Int 41(5):354–363Google Scholar
- 22.Mishra M, Grande C (2016) Probabilistic NDT data fusion of ferroscan test data using Bayesian inference. Structural analysis of historical constructions: anamnesis, diagnosis, therapy, controls. CRC Press, Boca Raton, pp 740–744Google Scholar
- 23.Li Z, Yao W, Lee S, Lee C, Yang Z (2000) Application of infrared thermography technique in building finish evaluation. J Nondestruct Eval 19(1):11–19Google Scholar
- 24.Vassallo R, Mishra M, Santarsiero G, Masi A (2016) Interaction of a railway tunnel with a deep slow landslide in clay shales. Procedia Earth Planet Sci 16:15–24Google Scholar
- 25.Gros XE (1996) NDT data fusion. Butterworth-Heinemann, London, pp 1–205. ISBN: 978-0-340-67648-6Google Scholar
- 26.Esteban J, Starr A, Willetts R, Hannah P, Bryanston-Cross P (2005) A Review of data fusion models and architectures: towards engineering guidelines. Neural Comput Appl 14(4):273–281Google Scholar
- 27.Wu RT, Jahanshahi MR (2018) Data fusion approaches for structural health monitoring and system identification: past, present, and future. Struct Health Monit. https://doi.org/10.1177/1475921718798769
- 28.Chou S, Chiu CK, Farfoura M, Al-Taharwa I (2011) Optimizing the prediction accuracy of concrete compressive strength based on a comparison of data-mining techniques. J Comput Civ Eng 25:242–253Google Scholar
- 29.Abd AM, Abd SM (2017) Modelling the strength of lightweight foamed concrete using support vector machine (SVM). Case Stud Constr Mater 6:8–15Google Scholar
- 30.Ghanizadeh AR, Abbaslou H, Amlashi AT, Alidoust P (2019) Modeling of bentonite/sepiolite plastic concrete compressive strength using artificial neural network and support vector machine. Front Struct Civ Eng 13(1):215–239Google Scholar
- 31.Yu Y, Li w, Li J, Nguyen TN (2018) A novel optimised self-learning method for compressive strength prediction of high performance concrete. Constr Build Mater 184:229–247Google Scholar
- 32.Tinoco J, Correia AG, Cortez P (2014) Support vector machines applied to uniaxial compressive strength prediction of jet grouting columns. Comput Geotech 55:132–140Google Scholar
- 33.Madani A, Yusof R (2018) Traffic sign recognition based on color, shape, and pictogram classification using support vector machines. Neural Comput Appl 30(9):2807–2817Google Scholar
- 34.Sakizadeh M, Mirzaei R, Ghorbani H (2017) Support vector machine and artificial neural network to model soil pollution: a case study in Semnan Province, Iran. Neural Comput Appl 28(11):3229–3238Google Scholar
- 35.Shafaei M, Kisi O (2017) Predicting river daily flow using wavelet-artificial neural networks based on regression analyses in comparison with artificial neural networks and support vector machine models. Neural Comput Appl 28(Supplement 1):15–28Google Scholar
- 36.Golafshani EM, Behnood A (2018) Application of soft computing methods for predicting the elastic modulus of recycled aggregate concrete. J Clean Prod 176:1163–1176Google Scholar
- 37.Huang Y, Zhao L (2018) Review on landslide susceptibility mapping using support vector machines. CATENA 165:520–529Google Scholar
- 38.Jing G, Cai W, Chen H, Zhai D, Cui C, Yin X (2018) An air balancing method using support vector machine for a ventilation system. Build Environ 143:487–495Google Scholar
- 39.Yu Y, Li Y, Li J (2015) Forecasting hysteresis behaviours of magnetorheological elastomer base isolator utilizing a hybrid model based on support vector regression and improved particle swarm optimization. Smart Mater Struct 24(3):035025Google Scholar
- 40.Yu Y, Li Y, Li J, Gu X (2016) Self-adaptive step fruit fly algorithm optimized support vector regression model for dynamic response prediction of magnetorheological elastomer base isolator. Neurocomputing 211(41):41–52Google Scholar
- 41.Koo B, La S, Cho NW, Yu Y (2019) Using support vector machines to classify building elements for checking the semantic integrity of building information models. Autom Constr 98:183–194Google Scholar
- 42.Kang F, Li J (2015) Artificial bee colony algorithm optimized support vector regression for system reliability analysis of slopes. J Comput Civ Eng 30(3):04015040Google Scholar
- 43.Yu Y, Zhang C, Gu X, Cui Y (2018) Expansion prediction of alkali aggregate reactivity-affected concrete structures using a hybrid soft computing method. Neural Comput Appl. https://doi.org/10.1007/s00521-018-3679-7
- 44.Gui G, Pan H, Lin Z, Li Y, Yuan Z (2017) Data-driven support vector machine with optimization techniques for structural health monitoring and damage detection. KSCE J Civ Eng 21(2):523–534Google Scholar
- 45.Samui P, Kim D (2013) Least square support vector machine and multivariate adaptive regression spline for modeling lateral load capacity of piles. Neural Comput Appl 23(3–4):1123–1127Google Scholar
- 46.Wang C, Wang X, Zhou X, Li Z (2016) The aircraft skin crack inspection based on different-source sensors and support vector machines. J Nondestruct Eval 35:46Google Scholar
- 47.Karthikeyan J, Kim D, Aiyer BG, Samui P (2013) SPT-based liquefaction potential assessment by relevance vector machine approach. Eur J Environ Civ Eng 17(4):248–262Google Scholar
- 48.Bhatia AS (2018) Determination of compressive strength of the burnt clay brick mortar masonry structure (unreinforced) using non-destructive experimental techniques. M.Tech thesis, Indian Institute of Technology Kharagpur, pp 1–73Google Scholar
- 49.Bureau of Indian Standard (BIS) (1992) Common burnt clay building bricks, IS 1077Google Scholar
- 50.Bureau of Indian Standard (BIS) (1999) Specification for sand for masonry mortars IS: 2116 - 1980, 1980Google Scholar
- 51.Cortes C, Vapnik V (1995) Support-vector networks. Mach Learn 20:273–297zbMATHGoogle Scholar
- 52.Basak D, Pal S, Patranabis DC (2007) Support vector regression. Neural Inf Process Lett Rev 11(10):203–224Google Scholar
- 53.Sanchez DV (2003) Advanced support vector machines and kernel methods. Neuro Comput 55:5–20Google Scholar
- 54.MATLAB (2010) Version 7.10.0 (R2010a) Natick. The MathWorks Inc., MassachusettGoogle Scholar
- 55.IS 2250-1981 (1981) Code of practice for preparation and use of masonry mortarsGoogle Scholar