Localizing structural damage based on auto-regressive with exogenous input model parameters and residuals using a support vector machine based learning approach

doi:10.1007/s11709-024-1107-x

2024, Vol. 18

Issue (10) : 1492-1506 https://doi.org/10.1007/s11709-024-1107-x

Localizing structural damage based on auto-regressive with exogenous input model parameters and residuals using a support vector machine based learning approach

Burcu GUNES(

)

Department of Civil Engineering, Istanbul Technical University, Istanbul 34467, Turkey

Download: PDF(2796 KB) HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

Machine learning algorithms operating in an unsupervised fashion has emerged as promising tools for detecting structural damage in an automated fashion. Its essence relies on selecting appropriate features to train the model using the reference data set collected from the healthy structure and employing the trained model to identify outlier conditions representing the damaged state. In this paper, the coefficients and the residuals of the autoregressive model with exogenous input created using only the measured output signals are extracted as damage features. These features obtained at the baseline state for each sensor cluster are then utilized to train the one class support vector machine, an unsupervised classifier generating a decision function using only patterns belonging to this baseline state. Structural damage, once detected by the trained machine, a damage index based on comparison of the residuals between the trained class and the outlier state is implemented for localizing damage. The two-step damage assessment framework is first implemented on an eight degree-of-freedom numerical model with the effects of measurement noise integrated. Subsequently, vibration data collected from a one-story one-bay reinforced concrete frame inflicted with progressive levels of damage have been utilized to verify the accuracy and robustness of the proposed methodology.

Keywords structural health monitoring damage localization auto-regressive with exogenous input models one-class support vector machine reinforced concrete frame

Corresponding Author(s): Burcu GUNES

Just Accepted Date: 17 July 2024 Online First Date: 25 September 2024 Issue Date: 29 October 2024

Cite this article:

Burcu GUNES. Localizing structural damage based on auto-regressive with exogenous input model parameters and residuals using a support vector machine based learning approach[J]. Front. Struct. Civ. Eng., 2024, 18(10): 1492-1506.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-024-1107-x
https://academic.hep.com.cn/fsce/EN/Y2024/V18/I10/1492

Fig.1 Unsupervised damage detection methodology employed in this study.

Tab.1 Structural parameters of the numerical model

Fig.2 Arrangement of input and output vectors for the ARX models with the reference sensor at: (a) the first floor; (b) an intermediate floor; (c) the top floor.

Fig.3 Sample acceleration response data (cm/s²) for: (a) floors 1 and 2 with impact at floor 1; (b) floors 6, 7, and 8 with impact at floor 7.

Tab.2 The natural frequencies of the system for the baseline state and the damage scenarios

Tab.3 Accuracy of the one-class SVM for classifying the health state of the structure

Fig.4 Damage localization using damage index, RCV for ‘single floor’ damage scenarios.

Fig.5 Experimental set-up: (a) loading frame; (b) impact testing; (c) test specimen during push-over; (d) accelerometer arrangement and impact locations.

Fig.6 Arrangement of input and output vectors for the ARX models with a rowing reference sensor.

Tab.4 The push-over load test cases and the associated damage states

Fig.7 Progression of damage in the tested frame for the selected drift ratios.

Fig.8 Damage localization results.

1	H Sohn, C R Farrar. Damage diagnosis using time series analysis of vibration signals. Smart Materials and Structures, 2001, 10(3): 446–451 https://doi.org/10.1088/0964-1726/10/3/304
2	S D Fassois, J S Sakellariou. Time-series methods for fault detection and identification in vibrating structures. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2007, 365(1851): 411–448
3	L D Avendaño-Valencia, E N Chatzi, K Y Koo, J M Brownjohn. Gaussian process time-series models for structures under operational variability. Frontiers in Built Environment, 2017, 3: 69 https://doi.org/10.3389/fbuil.2017.00069
4	S D FassoisF P Kopsaftopoulos. Statistical Time Series Methods for Vibration Based Structural Health Monitoring. Vienna: Springer Vienna, 2013, 209–264
5	K K Nair, A S Kiremidjian, K H Law. Time series-based damage detection and localization algorithm with application to the ASCE benchmark structure. Journal of Sound and Vibration, 2006, 291(1–2): 349–368 https://doi.org/10.1016/j.jsv.2005.06.016
6	H Zheng, A Mita. Localized damage detection of structures subject to multiple ambient excitations using two distance measures for autoregressive models. Structural Health Monitoring, 2009, 8(3): 207–222 https://doi.org/10.1177/1475921708102145
7	M Gul, F N Catbas. Structural health monitoring and damage assessment using a novel time series analysis methodology with sensor clustering. Journal of Sound and Vibration, 2011, 330(6): 1196–1210 https://doi.org/10.1016/j.jsv.2010.09.024
8	R Yao, S N Pakzad. Damage and noise sensitivity evaluation of autoregressive features extracted from structure vibration. Smart Materials and Structures, 2014, 23(2): 025007 https://doi.org/10.1088/0964-1726/23/2/025007
9	D Bernal, D Zonta, M Pozzi. ARX residuals in damage detection. Structural Control and Health Monitoring, 2012, 19(4): 535–547 https://doi.org/10.1002/stc.452
10	K Roy, B Bhattacharya, S Ray-Chaudhuri. ARX model-based damage sensitive features for structural damage localization using output-only measurements. Journal of Sound and Vibration, 2015, 349: 99–122 https://doi.org/10.1016/j.jsv.2015.03.038
11	Y LeiA S KiremidjianK K NairJ P LynchK H Law T W KennyE CarryerA Kottapalli. Statistical damage detection using time series analysis on a structural health monitoring benchmark problem. In: Proceedings of the 9th International Conference on Applications of Statistics and Probability in Civil Engineering. San Francisco, CA: A.A. Balkema, 2003: 6–9
12	S D Silva, Júnior M Dias, V Junior Lopes. Damage detection in a benchmark structure using AR-ARX models and statistical pattern recognition. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2007, 29(2): 174–184 https://doi.org/10.1590/S1678-58782007000200007
13	Y Lu, F Gao. A novel time-domain auto-regressive model for structural damage diagnosis. Journal of Sound and Vibration, 2005, 283(3–5): 1031–1049 https://doi.org/10.1016/j.jsv.2004.06.030
14	M Flah, I Nunez, W Ben Chaabene, M L Nehdi. Machine learning algorithms in civil structural health monitoring: A systematic review. Archives of Computational Methods in Engineering, 2021, 28(4): 2621–2643 https://doi.org/10.1007/s11831-020-09471-9
15	O Avci, O Abdeljaber, S Kiranyaz, M Hussein, M Gabbouj, D J Inman. A review of vibration-based damage detection in civil structures: From traditional methods to machine learning and deep learning applications. Mechanical Systems and Signal Processing, 2021, 147: 107077 https://doi.org/10.1016/j.ymssp.2020.107077
16	B Z Cunha, C Droz, A M Zine, S Foulard, M Ichchou. A review of machine learning methods applied to structural dynamics and vibroacoustic. Mechanical Systems and Signal Processing, 2023, 200: 110535 https://doi.org/10.1016/j.ymssp.2023.110535
17	E Figueiredo, G Park, C R Farrar, K Worden, J Figueiras. Machine learning algorithms for damage detection under operational and environmental variability. Structural Health Monitoring, 2011, 10(6): 559–572 https://doi.org/10.1177/1475921710388971
18	A Entezami, H Shariatmadar. An unsupervised learning approach by novel damage indices in structural health monitoring for damage localization and quantification. Structural Health Monitoring, 2018, 17(2): 325–345 https://doi.org/10.1177/1475921717693572
19	H Sarmadi, A Karamodin. A novel anomaly detection method based on adaptive Mahalanobis-squared distance and one-class kNN rule for structural health monitoring under environmental effects. Mechanical Systems and Signal Processing, 2020, 140: 106495 https://doi.org/10.1016/j.ymssp.2019.106495
20	A Diez, N L D Khoa, M Makki Alamdari, Y Wang, F Chen, P Runcie. A clustering approach for structural health monitoring on bridges. Journal of Civil Structural Health Monitoring, 2016, 6(3): 429–445 https://doi.org/10.1007/s13349-016-0160-0
21	L Yu, J H Zhu, L L Yu. Structural damage detection in a truss bridge model using fuzzy clustering and measured FRF data reduced by principal component projection. Advances in Structural Engineering, 2013, 16(1): 207–217 https://doi.org/10.1260/1369-4332.16.1.207
22	Y L Zhou, N M Maia, R P Sampaio, M A Wahab. Structural damage detection using transmissibility together with hierarchical clustering analysis and similarity measure. Structural Health Monitoring, 2017, 16(6): 711–731 https://doi.org/10.1177/1475921716680849
23	Y J Cha, Z Wang. Unsupervised novelty detection-based structural damage localization using a density peaks-based fast clustering algorithm. Structural Health Monitoring, 2018, 17(2): 313–324 https://doi.org/10.1177/1475921717691260
24	R Langone, E Reynders, S Mehrkanoon, J A Suykens. Automated structural health monitoring based on adaptive kernel spectral clustering. Mechanical Systems and Signal Processing, 2017, 90: 64–78 https://doi.org/10.1016/j.ymssp.2016.12.002
25	M Silva, A Santos, R Santos, E Figueiredo, C Sales, J C Costa. Agglomerative concentric hypersphere clustering applied to structural damage detection. Mechanical Systems and Signal Processing, 2017, 92: 196–212 https://doi.org/10.1016/j.ymssp.2017.01.024
26	H Sarmadi, A Entezami, M Salar, C De Michele. Bridge health monitoring in environmental variability by new clustering and threshold estimation methods. Journal of Civil Structural Health Monitoring, 2021, 11(3): 629–644 https://doi.org/10.1007/s13349-021-00472-1
27	H Sarmadi. Investigation of machine learning methods for structural safety assessment under variability in data: Comparative studies and new approaches. Journal of Performance of Constructed Facilities, 2021, 35(6): 04021090 https://doi.org/10.1061/(ASCE)CF.1943-5509.0001664
28	J P Santos, C Crémona, L Calado, P Silveira, A D Orcesi. On-line unsupervised detection of early damage. Structural Control and Health Monitoring, 2016, 23(7): 1047–1069 https://doi.org/10.1002/stc.1825
29	L Qiu, F Fang, S Yuan. Improved density peak clustering-based adaptive Gaussian mixture model for damage monitoring in aircraft structures under time-varying conditions. Mechanical Systems and Signal Processing, 2019, 126: 281–304 https://doi.org/10.1016/j.ymssp.2019.01.034
30	A AnaissiN L D KhoaS MustaphaM M AlamdariA Braytee Y WangF Chen. Adaptive one-class support vector machine for damage detection in structural health monitoring. In: Proceedings of Pacific-Asia Conference on Knowledge Discovery and Data Mining. Cham: Springer International Publishing, 2017, 42–57
31	Z Wang, Y J Cha. Unsupervised deep learning approach using a deep auto-encoder with a one-class support vector machine to detect damage. Structural Health Monitoring, 2021, 20(1): 406–425 https://doi.org/10.1177/1475921720934051
32	B Gunes. One-class machine learning approach for localized damage detection. Journal of Civil Structural Health Monitoring, 2022, 12(5): 1115–1131 https://doi.org/10.1007/s13349-022-00599-9
33	M H Rafiei, H Adeli. A novel unsupervised deep learning model for global and local health condition assessment of structures. Engineering Structures, 2018, 156: 598–607 https://doi.org/10.1016/j.engstruct.2017.10.070
34	L Sun, Z Shang, Y Xia, S Bhowmick, S Nagarajaiah. Review of bridge structural health monitoring aided by big data and artificial intelligence: From condition assessment to damage detection. Journal of Structural Engineering, 2020, 146(5): 04020073 https://doi.org/10.1061/(ASCE)ST.1943-541X.0002535
35	D A Tibaduiza Burgos, R C Gomez Vargas, C Pedraza, D Agis, F Pozo. Damage identification in structural health monitoring: A brief review from its implementation to the use of data-driven applications. Sensors, 2020, 20(3): 733 https://doi.org/10.3390/s20030733
36	M Azimi, A D Eslamlou, G Pekcan. Data-driven structural health monitoring and damage detection through deep learning: State-of-the-art review. Sensors, 2020, 20(10): 2778 https://doi.org/10.3390/s20102778
37	Y Tian, Y Xu, D Zhang, H Li. Relationship modeling between vehicle-induced girder vertical deflection and cable tension by BiLSTM using field monitoring data of a cable-stayed bridge. Structural Control and Health Monitoring, 2021, 28(2): e2667 https://doi.org/10.1002/stc.2667
38	Y Xu, W Qian, N Li, H Li. Typical advances of artificial intelligence in civil engineering. Advances in Structural Engineering, 2022, 25(16): 3405–3424 https://doi.org/10.1177/13694332221127340
39	H Sarmadi, K V Yuen. Structural health monitoring by a novel probabilistic machine learning method based on extreme value theory and mixture quantile modeling. Mechanical Systems and Signal Processing, 2022, 173: 109049 https://doi.org/10.1016/j.ymssp.2022.109049
40	H Sarmadi, A Entezami, C De Michele. Probabilistic data self-clustering based on semi-parametric extreme value theory for structural health monitoring. Mechanical Systems and Signal Processing, 2023, 187: 109976 https://doi.org/10.1016/j.ymssp.2022.109976
41	N Dervilis, E J Cross, R J Barthorpe, K Worden. Robust methods of inclusive outlier analysis for structural health monitoring. Journal of Sound and Vibration, 2014, 333(20): 5181–5195 https://doi.org/10.1016/j.jsv.2014.05.012
42	A Entezami, H Shariatmadar, S Mariani. Early damage assessment in large-scale structures by innovative statistical pattern recognition methods based on time series modeling and novelty detection. Advances in Engineering Software, 2020, 150: 102923 https://doi.org/10.1016/j.advengsoft.2020.102923
43	A Entezami, H Sarmadi, B Behkamal. A novel double-hybrid learning method for modal frequency-based damage assessment of bridge structures under different environmental variation patterns. Mechanical Systems and Signal Processing, 2023, 201: 110676 https://doi.org/10.1016/j.ymssp.2023.110676
44	M Mousavi, A H Gandomi. Prediction error of Johansen cointegration residuals for structural health monitoring. Mechanical Systems and Signal Processing, 2021, 160: 107847 https://doi.org/10.1016/j.ymssp.2021.107847
45	F Cadini, L Lomazzi, M F Roca, C Sbarufatti, M Giglio. Neutralization of temperature effects in damage diagnosis of MDOF systems by combinations of autoencoders and particle filters. Mechanical Systems and Signal Processing, 2022, 162: 108048 https://doi.org/10.1016/j.ymssp.2021.108048
46	L D Avendaño-Valencia, E N Chatzi. Sensitivity driven robust vibration-based damage diagnosis under uncertainty through hierarchical Bayes time-series representations. Procedia Engineering, 2017, 199: 1852–1857 https://doi.org/10.1016/j.proeng.2017.09.111
47	A Entezami, H Shariatmadar, A Karamodin. Data-driven damage diagnosis under environmental and operational variability by novel statistical pattern recognition methods. Structural Health Monitoring, 2019, 18(5–6): 1416–1443 https://doi.org/10.1177/1475921718800306
48	L Ljung. System Identification: Theory for the User. 2nd Edition. Upper Saddle River: Prentice Hall PTR, 1999
49	B SchölkopfA J Smola. Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond. Cambridge, MA: MIT press, 2002
50	D Gale, H W Kuhn, A W Tucker. Linear programming and the theory of games. Activity Analysis of Production and Allocation, 1951, 13: 317–335
51	M Horner, S N Pakzad, N S Gulgec. Parameter estimation of autoregressive-exogenous and autoregressive models subject to missing data using expectation maximization. Frontiers in Built Environment, 2019, 5: 109
52	B Gunes, O Gunes. Vibration-based damage evaluation of a reinforced concrete frame subjected to cyclic pushover testing. Shock and Vibration, 2021, 2021: 1–16 https://doi.org/10.1155/2021/6666702

[1]	Junchen YE, Zhixin ZHANG, Ke CHENG, Xuyan TAN, Bowen DU, Weizhong CHEN. Investigation on identification of structural anomalies from polluted data sets using an unsupervised learning method[J]. Front. Struct. Civ. Eng., 2024, 18(10): 1479-1491.
[2]	Jarun SRECHAI, Wongsa WARARUKSAJJA, Sutat LEELATAVIWAT, Suchart LIMKATANYU. Performance evaluation of low-rise infilled reinforced concrete frames designed by considering local effects on column shear demand[J]. Front. Struct. Civ. Eng., 2023, 17(5): 686-703.
[3]	Jiang CHEN, Zizhen ZENG, Ying LUO, Feng XIONG, Fei CHENG. Crack detection for wading-concrete structures using water irrigation and electric heating[J]. Front. Struct. Civ. Eng., 2023, 17(3): 368-377.
[4]	Yue CHEN, Rong XU, Hao WU, Tao SHENG. A multi-objective design method for seismic retrofitting of existing reinforced concrete frames using pin-supported rocking walls[J]. Front. Struct. Civ. Eng., 2022, 16(9): 1089-1103.
[5]	Yixian LI, Limin SUN, Wang ZHU, Wei ZHANG. A dynamic stiffness-based framework for harmonic input estimation and response reconstruction considering damage[J]. Front. Struct. Civ. Eng., 2022, 16(4): 448-460.
[6]	Sheng PENG, Chengxiang XU, Xiaoqiang LIU. Truss-arch model for shear strength of seismic-damaged SRC frame columns strengthened with CFRP sheets[J]. Front. Struct. Civ. Eng., 2019, 13(6): 1324-1337.
[7]	Ayaho MIYAMOTO, Risto KIVILUOMA, Akito YABE. Frontier of continuous structural health monitoring system for short & medium span bridges and condition assessment[J]. Front. Struct. Civ. Eng., 2019, 13(3): 569-604.
[8]	T. VO-DUY,N. NGUYEN-MINH,H. DANG-TRUNG,A. TRAN-VIET,T. NGUYEN-THOI. Damage assessment of laminated composite beam structures using damage locating vector (DLV) method[J]. Front. Struct. Civ. Eng., 2015, 9(4): 457-465.
[9]	Jong-Woong PARK,Sung-Han SIM,Jin-Hak YI,Hyung-Jo JUNG. Development of temperature-robust damage factor based on sensor fusion for a wind turbine structure[J]. Front. Struct. Civ. Eng., 2015, 9(1): 42-47.
[10]	João Pedro SANTOS,Christian CREMONA,André D. ORCESI,Paulo SILVEIRA,Luis CALADO. Static-based early-damage detection using symbolic data analysis and unsupervised learning methods[J]. Front. Struct. Civ. Eng., 2015, 9(1): 1-16.
[11]	Carmelo GENTILE, Antonella SAISI. Continuous dynamic monitoring of a centenary iron bridge for structural modification assessment[J]. Front. Struct. Civ. Eng., 2015, 9(1): 26-41.
[12]	Xinqun ZHU, Hong HAO. Development of an integrated structural health monitoring system for bridge structures in operational conditions[J]. Front Struc Civil Eng, 2012, 6(3): 321-333.
[13]	Michael CH HUI, Doris YAU. Major bridge development in Hong Kong, China—past, present and future[J]. Front Arch Civil Eng Chin, 2011, 5(4): 405-414.
[14]	Qi LI, You-lin XU, Yue ZHENG, An-xin GUO, Kai-yuen WONG, Yong XIA. SHM-based F-AHP bridge rating system with application to Tsing Ma Bridge[J]. Front Arch Civil Eng Chin, 2011, 5(4): 465-478.
[15]	Youliang DING, Aiqun LI. Assessment of bridge expansion joints using long-term displacement measurement under changing environmental conditions[J]. Front Arch Civil Eng Chin, 2011, 5(3): 374-380.

Viewed

Full text

Abstract

Cited

Shared

Discussed