Structural damage identification using ABC combined with improved PMC sampling

PDF(1134 KB)

Journal of Vibration and Shock ›› 2020, Vol. 39 ›› Issue (5) : 143-149.

FANG Sheng’en1,2, CHEN Shan1

Author information +

History +

Abstract

In order to avoid sampling being immersed in low-probability areas and to raise sampling efficiency, the population Monte Carlo (PMC) sampling algorithm was improved and then combined with the approximate Bayesian calculation (ABC) and stochastic response surface (SRS) to propose a probabilistic damage identification method.Firstly, PMC algorithm was embedded in ABC, and sample variance in each iteration step was used to perturb a particle swarm, and obtain adaptive weight coefficients.An error function was constructed to measure the similarity between simulated and measured samples, and replace the likelihood function.Then the explicit expression for structural stochastic response was established using SRS to greatly improve the calculation efficiency of response statistical features.Finally, obtained statistical values of parametric posterior probability distribution were taken as damage indexes.According to indexes’ changes before and after damage, damage locations and degrees were judged.Damages of a test reinforced concrete beam under a single working condition and multiple working conditions were identified, respectively.It was shown that the proposed method can be used to effectively improve the calculation efficiency of Bayesian inference process under the condition of ensuring parametric posterior distribution’s estimation accuracy.

Key words

probabilistic damage identification / approximate Bayesian calculation (ABC) / improved population Monte Carlo (PMC) sampling / stochastic response surface (SRS) / parametric posterior probability distribution

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

FANG Sheng’en1,2, CHEN Shan1. Structural damage identification using ABC combined with improved PMC sampling[J]. Journal of Vibration and Shock, 2020, 39(5): 143-149

References

[1] 宗周红, 牛杰, 王浩. 基于模型确认的结构概率损伤识别方法研究进展[J]. 土木工程学报, 2012, 45(8):121-130.
ZONG Zhouhong, NIU Jie, WANG Hao. A review of structural damage identification methods based on the finite element model validation[J]. China Civil Engineering Journal, 2012, 45(8):121-130.
[2] 侯立群, 赵雪峰, 欧进萍, 等. 结构损伤诊断不确定性方法研究进展[J]. 振动与冲击, 2014, 33(18): 50-58.
HOU Liqun, ZHAO Xuefeng, OU Jinping, et al. A review of nondeterministic methods for structural damage diagnosis[J]. Journal of Vibration and Shock. 2014, 33(18): 50-58.
[3] SOHN H, CZARNECKI J A, FARRAR C R. Structural health monitoring using statistical process control[J]. Journal of Structural Engineering, 2000, 126(11):1356-1363.
[4] YAO R, PAKZAD S N. Autoregressive statistical pattern recognition algorithms for damage detection in civil structures[J]. Mechanical Systems & Signal Processing, 2012, 31(8):355-368.
[5] XIA Y, HAO H, BROWNJOHN J M W, et al. Damage identification of structures with uncertain frequency and mode shape data[J]. Earthquake Engineering & Structural Dynamics, 2010, 31(5):1053-1066.
[6] 陈淮, 何伟, 王博, 等. 基于频率和振型摄动的结构损伤识别方法研究[J]. 工程力学, 2010, 27(12):244-249.
CHEN Huai, HE Wei, WANG Bo, et al. Study on structure damage detection based on perturbations of frequency and mode shapes[J]. Engineering Mechanics, 2010, 27(12): 244-249.
[7] BECK J L. Statistical system identification of structures[C]. Proceedings of International Conference on Structural Safety and Reliability, San Francisco, 1989:1395-1402.
[8] BECK J L, KATAFYGIOTIS L S. Updating models and their uncertainties. I: Bayesian statistical framework[J]. Journal of Engineering Mechanics, ASCE, 1998, 124(4):455-461.
[9] ROCCHETTA R, BROGGI M, HUCHET Q, et al. On-line Bayesian model updating for structural health monitoring[J]. Mechanical Systems & Signal Processing, 2018, 103: 174-195.
[10] LAM H F, YANG J H, AU S K. Bayesian model updating of a coupled-slab system using field test data utilizing an enhanced Markov chain Monte Carlo simulation algorithm[J]. Engineering Structures, 2015, 102:144-155.
[11] 易伟建, 周云, 李浩. 基于贝叶斯统计推断的框架结构损伤诊断研究[J]. 工程力学, 2009, 26(5):121-129.
YI Weijian，ZHOU Yun，LI Hao. Damage assessment research on frame structure based on Bayesian statistical inference[J]. Engineering Mechanics, 2009, 26(5): 121-129.
[12] 李小华, 谢礼立, 公茂盛. 结构物理参数识别的贝叶斯估计马尔可夫蒙特卡罗方法[J]. 振动与冲击, 2010, 29(04): 59-63.
LI Xiaohua, XIE Lili, GONG Maosheng. Structural physical parameter identification using Bayesian estimation with Markov chain Monte Carlo method[J]. Journal of Vibration and Shock. 2010, 29(04): 59-63.
[13] 边涛, 谢寿生, 任立通, 等. 基于贝叶斯理论的拉杆转子模态特性确认[J]. 振动与冲击, 2017, 36(23): 92-98.
BIAN Tao, XIE Shousheng, REN Litong, et al. Modal characteristics confirmation of a rod-fastening rotor based on Bayesian theory. Journal of Vibration and Shock. 2017, 36(23): 92-98.
[14] HE S, NG C T. Guided wave-based identification of multiple cracks in beams using a Bayesian approach[J]. Mechanical Systems & Signal Processing, 2017, 84: 324-345.
[15] TURNER B M, ZANDT T V. A tutorial on approximate Bayesian computation[J]. Journal of Mathematical Psychology, 2012, 56(2): 69-85.
[16] WARNE D J, BAKER R E, SIMPSON M J. Multilevel rejection sampling for approximate Bayesian computation[J]. Computational Statistics & Data Analysis, 2018, 124:71-86.
[17] ISUKAPALLI S S. An uncertainty analysis of transport transformation models[D]. New Brunswick: The State University of New Jersey, 1999.
[18] 茆诗松, 汤银才. 贝叶斯统计[M]. 中国统计出版社, 2012.
MAO Shisong, TANG Yincai. Bayesian Statistics[M]. China Statistics Press, 2012.