Smart Structures and Systems

  • 제32권1호
  • /
  • Pages.61-81
  • /
  • 2023
  • /
  • 1738-1584(pISSN)
  • /
  • 1738-1991(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

An ensemble learning based Bayesian model updating approach for structural damage identification

  • Guangwei Lin (Key Laboratory of Earthquake Engineering and Engineering Vibration, Institute of Engineering Mechanics, China Earthquake Administration) ;
  • Yi Zhang (Key Laboratory of Earthquake Engineering and Engineering Vibration, Institute of Engineering Mechanics, China Earthquake Administration) ;
  • Enjian Cai (Key Laboratory of Earthquake Engineering and Engineering Vibration, Institute of Engineering Mechanics, China Earthquake Administration) ;
  • Taisen Zhao (Key Laboratory of Earthquake Engineering and Engineering Vibration, Institute of Engineering Mechanics, China Earthquake Administration) ;
  • Zhaoyan Li (Key Laboratory of Earthquake Engineering and Engineering Vibration, Institute of Engineering Mechanics, China Earthquake Administration)
  • 투고 : 2022.12.24
  • 심사 : 2023.07.24
  • 발행 : 2023.07.25
⟨ 이전 논문 다음 논문 ⟩

초록

This study presents an ensemble learning based Bayesian model updating approach for structural damage diagnosis. In the developed framework, the structure is initially decomposed into a set of substructures. The autoregressive moving average (ARMAX) model is established first for structural damage localization based structural motion equation. The wavelet packet decomposition is utilized to extract the damage-sensitive node energy in different frequency bands for constructing structural surrogate models. Four methods, including Kriging predictor (KRG), radial basis function neural network (RBFNN), support vector regression (SVR), and multivariate adaptive regression splines (MARS), are selected as candidate structural surrogate models. These models are then resampled by bootstrapping and combined to obtain an ensemble model by probabilistic ensemble. Meanwhile, the maximum entropy principal is adopted to search for new design points for sample space updating, yielding a more robust ensemble model. Through the iterations, a framework of surrogate ensemble learning based model updating with high model construction efficiency and accuracy is proposed. The specificities of the method are discussed and investigated in a case study.

키워드

과제정보

The authors gratefully acknowledge the financial support from the Scientific Research Fund of the Institute of Engineering Mechanics, China Earthquake Administration (Grant No. 2021D18), Visiting Researcher Fund Program of State Key Laboratory of Water Resources and Hydropower Engineering Science (2021SGG01), and Scientific Research Fund of Multi-Functional Shaking Tables Laboratory of Beijing University of Civil Engineering and Architecture.

참고문헌

  1. Abbasnia, R., Mirzaee, A. and Shayanfar, M. (2018), "Simultaneous identification of damage in bridge under moving mass by Adjoint variable method", Smart Struct. Syst., Int. J., 21(4), 449-467. https://doi.org/10.12989/sss.2018.21.4.449
  2. Adnan, R.M., Liang, Z.M., Heddam, S., Zounemat-Kermani, M., Kisi, O. and Li, B.Q. (2020), "Least square support vector machine and multivariate adaptive regression splines for streamflow prediction in mountainous basin using hydro-meteorological data as inputs", J. Hydrol., 586, 124371. https://doi.org/10.1016/j.jhydrol.2019.124371.
  3. Alabi, S.A., Hu, Q., Lam, H.F. and Zhu, H.P. (2018), "Bayesian ballast damage detection utilizing a modified evolutionary algorithm", Smart Struct. Syst., Int. J., 21(4), 435-448. https://doi.org/10.12989/sss.2018.21.4.435
  4. Alexander, I., Andras, S. and Andy, J. (2008), Engineering design via surrogate modelling, University Southampton, Southampton, UK.
  5. Alizadeh, R., Jia, L.Y., Nellippallil, A.B., Wang, G.X., Hao, J., Allen, J.K. and Mistree, F. (2019), "Ensemble of surrogates and cross-validation for rapid and accurate predictions using small data sets", Ai Edam-Artificial Intelligence for Engineering Design Analysis and Manufacturing, 33(4), 484-501. https://doi.org/10.1017/S089006041900026X
  6. Alkayem, N.F., Cao, M.S., Zhang, Y.F., Bayat, M. and Su, Z.Q. (2018), "Structural damage detection using finite element model updating with evolutionary algorithms: a survey", Neural Comput. Applicat., 30(2), 389-411. http://doi.org/10.1007/s00521-017-3284-1
  7. Azim, M.R., Zhang, H.Y. and Gul, M. (2020), "Damage detection of railway bridges using operational vibration data: theory and experimental verifications", Struct. Monitor. Maint., Int. J., 7(2), 149-166. http://doi.org/10.12989/smm.2020.7.2.149
  8. Barazanchy, D., Martinez, M., Rocha, B. and Yanishevsky, M. (2014), "A hybrid structural health monitoring system for the detection and localization of damage in composite structures", J. Sensors, 2014, 1-10. https://doi.org/10.1155/2014/109403
  9. Beck, J.L. and Katafygiotis, L.S. (1998), "Updating models and their uncertainties. I: Bayesian statistical framework", J. Eng. Mech., 124(4), 455-461. http://doi.org/Doi 10.1061/(Asce)0733-9399(1998)124:4(455)
  10. Beniddir, M.A., Kang, K.B., Genta-Jouve, G., Huber, F., Rogers, S. and van der Hooft, J.J.J. (2021), "Advances in decomposing complex metabolite mixtures using substructure- and network-based computational metabolomics approaches", Natural Product Reports, 38(11), 1967-1993. http://doi.org/10.1039/d1np00023c
  11. Berk, J., Nguyen, V., Gupta, S., Rana, S. and Venkatesh, S. (2018), "Exploration enhanced expected improvement for bayesian optimization", Proceedings of the Joint European Conference on Machine Learning and Knowledge Discovery in Databases. 
  12. Bisbo, M.K. and Hammer, B. (2020), "Efficient global structure optimization with a machine-learned surrogate model", Phys. Rev. Lett., 124(8), 086102. http://doi.org/10.1103/PhysRevLett.124.086102
  13. Cai, E.J. and Zhang, Y. (2022), "Gaussian mixture model based phase prior learning for video motion estimation", Mech. Syst. Signal Process., 175. https://doi.org/10.1016/j.ymssp.2022.109103.
  14. Candy, J.V. (2005), Model-based signal processing, John Wiley & Sons.
  15. Chen, Y.-T., Shi, J., Ye, Z., Mertz, C., Ramanan, D. and Kong, S. (2022), "Multimodal object detection via probabilistic ensembling", Proceedings of the Computer Vision-ECCV 2022: 17th European Conference, Tel Aviv, Israel, October.
  16. Cheng, K. and Lu, Z.Z. (2020), "Structural reliability analysis based on ensemble learning of surrogate models", Struct. Safety, 83, 101905. https://doi.org/10.1016/j.strusafe.2019.101905
  17. Cheung, S.H. and Beck, J.L. (2009), "Bayesian model updating using hybrid Monte Carlo simulation with application to structural dynamic models with many uncertain parameters", J. Eng. Mech., 135(4), 243-255. http://doi.org/10.1061/(Asce)0733-9399(2009)135:4(243)
  18. Ching, J. and Beck, J.L. (2003), Two-Stage Bayesian Structural Health Monitoring Approach for Phase II ASCE Experimental Benchmark Studies.
  19. Ching, J.Y. and Chen, Y.C. (2007), "Transitional markov chain monte carlo method for Bayesian model updating, model class selection, and model averaging", J. Eng. Mech., 133(7), 816-832. http://doi.org/10.1061/(Asce)0733-9399(2007)133:7(816)
  20. Christelis, V., Kopsiaftis, G. and Mantoglou, A. (2019), "Performance comparison of multiple and single surrogate models for pumping optimization of coastal aquifers", Hydrol. Sci. J., 64(3), 336-349. https://doi.org/10.1080/02626667.2019.1584400
  21. Collins, J.D., Hart, G.C., Hasselman, T.K. and Kennedy, B. (1974), "Statistical Identification of Structures", AIAA J., 12(2), 185-190. http://doi.org/Doi 10.2514/3.49190
  22. Daubechies, I. (1992), Ten lectures on wavelets: SIAM.
  23. DeVore, C., Jiang, Z.S., Christenson, R.E., Stromquist-LeVoir, G. and Johnson, E.A. (2016), "Experimental verification of substructure identification for damage detection in shear buildings", J. Eng. Mech., 142(1), 04015060. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000929
  24. Dhamotharan, V., Jadhav, P.D., Ramu, P. and Prakash, A.K. (2018), "Optimal design of savonius wind turbines using ensemble of surrogates and CFD analysis", Struct. Multidiscipl. Optimiz., 58(6), 2711-2726. http://doi.org/10.1007/s00158-018-2052-x
  25. Ding, Y., Ren, P., Zhao, H. and Miao, C. (2018), "Structural health monitoring of a high-speed railway bridge: five years review and lessons learned", Smart Struct. Syst., Int. J., 21(5), 695-703. https://doi.org/10.12989/sss.2018.21.5.695
  26. Do, N.T., Mei, Q.P. and Gul, M. (2019), "Damage assessment of shear-type structures under varying mass effects", Struct. Monitor. Maint., Int. J., 6(3), 237-254. http://doi.org/10.12989/smm.2019.6.3.237
  27. Effendi, M.R., Mengko, T.L.R., Gunawan, A.H. and Munir, A. (2019), "Performance evaluation of wavelet packet modulation for wireless digital communications", Proceedings of the International Symposium on Networks, Computers and Communications (ISNCC), Istanbul, Turkey.
  28. Elias, I., Rubio, J.D., Martinez, D.I., Vargas, T.M., Garcia, V., Mujica-Vargas, D., Meda-Campana, J.A., Pacheco, J., Gutierrez, G.J. and Zacarias, A. (2020), "Genetic algorithm with radial basis mapping network for the electricity consumption modeling", Appl. Sci.-Basel, 10(12), 4239. https://doi.org/10.3390/app10124239.
  29. Erazo, K. and Hernandez, E.M. (2016), "Bayesian model-data fusion for mechanistic postearthquake damage assessment of building structures", J. Eng. Mech., 142(9), 04016062. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001114
  30. Fei, J. and Wang, T. (2019), "Adaptive fuzzy-neural-network based on RBFNN control for active power filter", Int. J. Mach. Learn. Cybernet., 10, 1139-1150. https://doi.org/10.1007/s13042-018-0792-y
  31. Flah, M., Nunez, I., Ben Chaabene, W. and Nehdi, M.L. (2021), "Machine learning algorithms in civil structural health monitoring: a systematic review", Arch. Computat. Methods Eng., 28(4), 2621-2643. https://doi.org/10.1007/s11831-020-09471-9
  32. Friedman, J.H. (1991), "Multivariate adaptive regression splines", The Annals of Statistics, 19(1), 1-67. https://doi.org/10.1214/aos/1176347963
  33. Goel, T., Haftka, R.T., Shyy, W. and Queipo, N.V. (2007), "Ensemble of surrogates", Struct. Multidiscipl. Optimiz., 33(3), 199-216. http://doi.org/10.1007/s00158-006-0051-9
  34. Guemes, A., Fernandez-Lopez, A., Pozo, A.R. and Sierra-Perez, J. (2020), "Structural health monitoring for advanced composite structures: a review", J. Compos. Sci., 4(1), 13. https://doi.org/10.3390/jcs4010013
  35. He, W.Y., Zhu, S. and Ren, W.X. (2018), "Progressive damage detection of thin plate structures using wavelet finite element model updating", Smart Struct. Syst., Int. J., 22(3), 277-290. https://doi.org/10.12989/sss.2018.22.3.277
  36. Hoa, T.N., Khatir, S., Roeck, G.D., Long, N.N., Thanh, B.T. and Wahab, M.A. (2020), "An efficient approach for model updating of a large-scale cable-stayed bridge using ambient vibration measurements combined with a hybrid metaheuristic search algorithm", Smart Struct. Syst., Int. J., 25(4), 487-499. https://doi.org/10.12989/sss.2020.25.4.487
  37. Hou, R. and Xia, Y. (2020), "Review on the new development of vibration-based damage identification for civil engineering structures: 2010-2019", J. Sound Vib., 491(9). https://doi.org/10.1016/j.jsv.2020.115741
  38. Houret, T., Besnier, P., Vauchamp, S. and Pouliguen, P. (2019), "Controlled stratification based on kriging surrogate model: An algorithm for determining extreme quantiles in electromagnetic compatibility risk analysis", IEEE Access, 8, 3837-3847. https://doi.org/10.1109/ACCESS.2019.2961851
  39. Hu, J. and Yang, J.H. (2018), "Operational modal analysis and Bayesian model updating of a coupled building", Int. J. Struct. Stabil. Dyn., 19(01), p. 1940012. https://doi.org/10.1142/S0219455419400121
  40. Huang, M.S., Cheng, X.H. and Lei, Y.Z. (2021), "Structural damage identification based on substructure method and improved whale optimization algorithm", J. Civil Struct. Health Monitor., 11(2), 351-380. http://doi.org/10.1007/s13349-020-00456-7
  41. Jiang, S.H., Papaioannou, I. and Straub, D. (2018), "Bayesian updating of slope reliability in spatially variable soils with in-situ measurements", Eng. Geol., 239, 310-320. http://doi.org/10.1016/j.enggeo.2018.03.021
  42. Jiang, P., Zhou, Q. and Shao, X. (2020), Surrogate model-based engineering design and optimization, Springer.
  43. Khatir, S., Wahab, M.A., Boutchicha, D. and Khatir, T. (2019), "Structural health monitoring using modal strain energy damage indicator coupled with teaching-learning-based optimization algorithm and isogoemetric analysis", J. Sound Vib., 448, 230-246. http://doi.org/10.1016/j.jsv.2019.02.017
  44. Kirschner, J., Mutny, M., Hiller, N., Ischebeck, R. and Krause, A. (2019), "Adaptive and safe Bayesian optimization in high dimensions via one-dimensional subspaces", Proceedings of the International Conference on Machine Learning.
  45. Krige, D.G. (1951), "A statistical approach to some basic mine valuation problems on the Witwatersrand", J. Southern African Inst. Min. Metall., 52(6), 119-139. https://hdl.handle.net/10520/AJA0038223X_4792 10520/AJA0038223X_4792
  46. Krishansamy, L. and Arumulla, R. (2018), "A hybrid structural health monitoring technique for detection of subtle structural damage", Smart Struct. Syst., Int. J., 22(5), 587-609. https://doi.org/10.12989/sss.2018.22.5.587
  47. Kwag, S. and Gupta, A. (2018), "Computationally efficient fragility assessment using equivalent elastic limit state and Bayesian updating", Comput. Struct., 197, 1-11. http://doi.org/10.1016/j.compstruc.2017.11.011
  48. Li, J. and Hao, H. (2014), "Substructure damage identification based on wavelet-domain response reconstruction", Struct. Health Monitor., Int. J., 13(4), 389-405. http://doi.org/10.1177/1475921714532991
  49. Li, X., Gong, C.L., Gu, L.X., Gao, W.K., Jing, Z. and Su, H. (2018), "A sequential surrogate method for reliability analysis based on radial basis function", Struct. Safety, 73, 42-53. http://doi.org/10.1016/j.strusafe.2018.02.005
  50. Li, C., Li, H. and Chen, X. (2021), "A framework for fast estimation of structural seismic responses using ensemble machine learning model", Smart Struct. Syst., Int. J., 28(3), 425-441. https://doi.org/10.12989/sss.2021.28.3.425
  51. Liao, X., Sun, J., Wang, Y. and Li, M. (2021), "Damage detection based on multi-wavelet basis and multi-scale feature fusion", Proceedings of 2021 International Conference on Machine Learning and Intelligent Systems Engineering (MLISE), pp. 210-213. http://doi.org/10.1109/mlise54096.2021.00044
  52. Lin, G.W., Zhang, Y. and Liao, Q.Z. (2021), "Developing efficient model updating approaches for different structural complexity-an ensemble learning and uncertainty quantifications", Smart Struct. Syst., Int. J., 29(2), 321-336. http://doi.org/10.12989/sss.2022.29.2.321
  53. Liu, L., Mi, J., Zhang, Y. and Lei, Y. (2021), "Damage detection of bridge structures under unknown seismic excitations using support vector machine based on transmissibility function and wavelet packet energy", Smart Struct. Syst., Int. J., 27(2), 257-266. https://doi.org/10.12989/sss.2021.27.2.257
  54. Lo, M.K. and Leung, Y.F. (2019), "Bayesian updating of subsurface spatial variability for improved prediction of braced excavation response", Can. Geotech. J., 56(8), 1169-1183. http://doi.org/10.1139/cgj-2018-0409
  55. Mao, J.X., Wang, H. and Spencer, B.F. (2019), "Gaussian mixture model for automated tracking of modal parameters of long-span bridge", Smart Struct. Syst., Int. J., 24(2), 243-256. https://doi.org/10.12989/sss.2019.24.2.243
  56. Mao, J.X., Wang, H. and Li, J. (2020), "Bayesian Finite Element Model Updating of a Long-Span Suspension Bridge Utilizing Hybrid Monte Carlo Simulation and Kriging Predictor", KSCE J. Civil Eng., 24(2), 569-579. http://doi.org/10.1007/s12205-020-0983-4
  57. Martino, L. (2018), "A review of multiple try MCMC algorithms for signal processing", Digital Signal Process., 75, 134-152. http://doi.org/10.1016/j.dsp.2018.01.004
  58. Mei, L., Li, H., Zhou, Y., Wang, W. and Xing, F. (2019), "Substructural damage detection in shear structures via ARMAX model and optimal subpattern assignment distance", Eng. Struct., 191(JUL.15), 625-639. https://doi.org/10.1016/j.engstruct.2019.04.084
  59. Nagarajaiah, S. and Erazo, K. (2016), "Structural monitoring and identification of civil infrastructure in the United States", Struct. Monitor. Maint., Int. J., 3(1), 51-69. https://doi.org/10.12989/smm.2016.3.1.051
  60. Naser, A.H., Badr, A.H., Henedy, S.N., Ostrowski, K.A. and Imran, H. (2022), "Application of Multivariate Adaptive Regression Splines (MARS) approach in prediction of compressive strength of eco-friendly concrete", Case Studies Constr. Mater., 17, e01262. https://doi.org/10.1016/j.cscm.2022.e01262
  61. Panda, A.K. and Modak, S.V. (2022), "An FRF-based perturbation approach for stochastic updating of mass, stiffness and damping matrices", Mech. Syst. Signal Process., 166, p. 108416. https://doi.org/10.1016/j.ymssp.2021.108416
  62. Park, H.S., Kim, J. and Oh, B.K. (2019), "Model updating method for damage detection of building structures under ambient excitation using modal participation ratio", Measurement, 133, 251-261. http://doi.org/10.1016/j.measurement.2018.10.023
  63. Qasem, S.N. and Shamsuddin, S.M. (2011), "Radial basis function network based on time variant multi-objective particle swarm optimization for medical diseases diagnosis", Appl. Soft Comput., 11(1), 1427-1438. http://doi.org/10.1016/j.asoc.2010.04.014
  64. Qin, S.Q., Zhang, Y.Z., Zhou, Y.L. and Kang, J.T. (2018), "Dynamic model updating for bridge structures using the kriging model and PSO algorithm ensemble with higher vibration modes", Sensors, 18(6), 1879. https://doi.org/10.3390/s18061879
  65. Queipo, N.V. and Nava, E. (2019), "A gradient boosting approach with diversity promoting measures for the ensemble of surrogates in engineering", Struct. Multidiscipl. Optimiz., 60(4), 1289-1311. https://doi.org/10.1007/s00158-019-02325-4
  66. Ren, W.X. and Chen, H.B. (2010), "Finite element model updating in structural dynamics by using the response surface method", Eng. Struct., 32(8), 2455-2465. https://doi.org/10.1016/j.engstruct.2010.04.019
  67. Ren, X.Y., Wang, Y.M., Guo, T. and Wang, Q. (2020), "Robust Adaptive Beamforming Using Support Vector Machines", IEEE Access, 8, 137955-137965. http://doi.org/10.1109/Access.2020.3009993
  68. Roy, D.K. and Datta, B. (2019), "An ensemble meta-modelling approach using the Dempster-Shafer theory of evidence for developing saltwater intrusion management strategies in coastal aquifers", Water Resour. Manag., 33, 775-795. https://doi.org/10.1007/s11269-018-2142-y
  69. Sarmadi, H., Entezami, A., Saeedi Razavi, B. and Yuen, K.V. (2021), "Ensemble learning-based structural health monitoring by Mahalanobis distance metrics", Struct. Control Health Monitor., 28(2), e2663. https://doi.org/10.1002/stc.2663
  70. Sener, O. and Savarese, S. (2017), "Active learning for convolutional neural networks: A core-set approach", arXiv preprint arXiv:1708.00489. https://doi.org/10.48550/arXiv.1708.00489
  71. Siddiqui, Y., Valentin, J. and Niessner, M. (2020), "Viewal: Active learning with viewpoint entropy for semantic segmentation", Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition.
  72. Sotoudehnia, E., Shahabian, F. and Sani, A.A. (2019), "An iterative method for damage identification of skeletal structures utilizing biconjugate gradient method and reduction of search space", Smart Struct. Syst., Int. J., 23(1), 45-60. https://doi.org/10.12989/sss.2019.23.1.045
  73. Sousa, H., Santos, L.O. and Chryssanthopoulos, M. (2019), "Quantifying monitoring requirements for predicting creep deformations through Bayesian updating methods", Struct. Safety, 76, 40-50. http://doi.org/10.1016/j.strusafe.2018.06.002
  74. Tran-Ngoc, H., Khatir, S., De Roeck, G., Bui-Tien, T., NguyenNgoc, L. and Wahab, M.A. (2018), "Model updating for Nam O bridge using particle swarm optimization algorithm and genetic algorithm", Sensors, 18(12), 4131. http://doi.org/ARTN 413110.3390/s18124131
  75. Vapnik, V. (1999), The Nature of Statistical Learning Theory, Springer Science & Business Media.
  76. Wang, Z. and Cha, Y.-J. (2021), "Unsupervised deep learning approach using a deep auto-encoder with a one-class support vector machine to detect damage", Struct. Health Monitor., 20(1), 406-425. https://doi.org/10.1177/1475921720934051
  77. Wang, Z.Y. and Shafieezadeh, A. (2020), "Highly efficient Bayesian updating using metamodels: An adaptive Kriging-based approach", Struct. Safety, 84, 101915. https://doi.org/10.1016/j.strusafe.2019.101915
  78. Wang, Y.H., Lv, J., Feng, Y., Dai, B.W., Wang, C., Wu, J. and Chen, Z.Y. (2021), "Implementation of online model updating with ANN method in substructure pseudo-dynamic hybrid simulation", Smart Struct. Syst., Int. J., 28(2), 261-273. https://doi.org/10.12989/sss.2021.28.2.261
  79. Weng, S., Zhu, H., Xia, Y., Li, J. and Tian, W. (2020), "A review on dynamic substructuring methods for model updating and damage detection of large-scale structures", Adv. Struct. Eng., 23(3), 584-600. https://doi.org/10.1177/1369433219872429
  80. Xing, Z.X., Qu, R.Z., Zhao, Y., Fu, Q., Ji, Y. and Lu, W.X. (2019), "Identifying the release history of a groundwater contaminant source based on an ensemble surrogate model", J. Hydrol., 572, 501-516. http://doi.org/10.1016/j.jhydrol.2019.03.020
  81. Ye, P.C., Pan, G. and Dong, Z.M. (2018), "Ensemble of surrogate based global optimization methods using hierarchical design space reduction", Struct. Multidiscipl. Optimiz., 58(2), 537-554. http://doi.org/10.1007/s00158-018-1906-6
  82. Zhang, Y., Kim, C.W., Tee, K.F., Garg, A. and Garg, A. (2018), "Long-term health monitoring for deteriorated bridge structures based on Copula theory", Smart Struct. Syst., Int. J., 21(2), 171-185. http://doi.org/10.12989/sss.2018.21.2.171
  83. Zhang, Y., Kim, C.W. and Lin, J.M. (2019), "Removing Environmental Influences in Health Monitoring for Steel Bridges Through Copula Approaches", Int. J. Steel Struct., 19(3), 888-895. http://doi.org/10.1007/s13296-018-0170-3
  84. Zhang, Y., Wei, K., Shen, Z.H., Bai, X.W., Lu, X.Z. and Soares, C.G. (2020), "Economic impact of typhoon-induced wind disasters on port operations: A case study of ports in China", Int. J. Disaster Risk Reduct., 50. https://doi.org/10.1016/j.ijdrr.2020.101719
  85. Zhu, Z., Au, S.K., Li, B. and Xie, Y.L. (2020), "Bayesian operational modal analysis with multiple setups and multiple (possibly close) modes", Mech. Syst. Signal Process., 150, 107261. https://doi.org/10.1016/j.ymssp.2020.107261
  86. Zhu, H.P., Li, J.J., Tian, W., Weng, S., Peng, Y.C., Zhang, Z.X. and Chen, Z.D. (2021), "An enhanced substructure-based response sensitivity method for finite element model updating of largescale structures", Mech. Syst. Signal Process., 154, 107359. https://doi.org/10.1016/j.ymssp.2020.107359