## 留言板

 引用本文: 颜王吉, 曹诗泽, 任伟新. 结构系统识别不确定性分析的Bayes方法及其进展[J]. 应用数学和力学, 2017, 38(1): 44-59.
YAN Wang-ji, CAO Shi-ze, REN Wei-xin.. Uncertainty Quantification for System Identification Utilizing the Bayesian Theory and Its Recent Advances[J]. Applied Mathematics and Mechanics, 2017, 38(1): 44-59. doi: 10.21656/1000-0887.370571
 Citation: YAN Wang-ji, CAO Shi-ze, REN Wei-xin.. Uncertainty Quantification for System Identification Utilizing the Bayesian Theory and Its Recent Advances[J]. Applied Mathematics and Mechanics, 2017, 38(1): 44-59.

• 中图分类号: O32

## Uncertainty Quantification for System Identification Utilizing the Bayesian Theory and Its Recent Advances

Funds: The National Natural Science Foundation of China（51408176；51278163）; The National Key Research and Development Project of China(2016YFE0113400)
• 摘要: 受测试误差、建模误差、数值离散化以及环境变异等因素的影响，结构系统识别过程不可避免地存在不确定性，因此有必要引入概率统计方法来提高其鲁棒性，为工程结构安全监测提供更为可靠的结果.近年来，Bayes(贝叶斯)方法因为其诸多优势在系统识别领域受到了广泛关注.该文梳理了Bayes系统识别的历史脉络和研究进展.从Bayes系统识别的理论框架出发，分析了量化系统识别不确定性两类方法的适用条件与局限性.此外，文章综述了Bayes方法在模态参数识别、有限元模型修正以及结构损伤识别方面进行不确定性分析的理论、实现及其应用.最后对基于Bayes方法进行系统识别研究的发展趋势做出了展望.
•  [1] 禹丹江. 土木工程结构模态参数识别——理论、 实现与应用[D]. 博士学位论文. 福州: 福州大学, 2006.(YU Dan-jiang. Modal parameter identification of civil engineering structures—theory, implementation and application[D]. PhD Thesis. Fuzhou: Fuzhou University, 2006.(in Chinese)) [2] 李炜明, 董莪, 朱宏平. 土木工程系统辨识统计方法的现状与展望[J]. 振动与冲击, 2012,31(11): 42-47.(LI Wei-ming, DONG E, ZHU Hong-ping. Progress of system identification with statistical methods in civil engineering[J]. Journal of Vibration and Shock,2012,31(11): 42-47.(in Chinese)) [3] Beck J L, Katafygiotis L S. Updating models and their uncertainties—I: Bayesian statistical framework[J]. Journal of Engineering Mechanics,1998,124(4): 455-461. [4] Katafygiotis L S, Beck J L. Updating models and their uncertainties—II: model identifiability[J]. Journal of Engineering Mechanics, 1998,124(4):463-467. [5] YAN Wang-ji. Wireless sensor network based structural health monitoring accommodating multiple uncertainties[D]. PhD Thesis. Hong Kong: Hong Kong University of Science and Technology, 2013. [6] Housner G W, Bergman L A, Caughey T K,et al. Structural control: past, present, and future[J]. Journal of Engineering Mechanics,1997,123(9): 897-971. [7] Beck J L. Bayesian system identification based on probability logic[J]. Structural Control and Health Monitoring,2010,17(7): 825-847. [8] 茆诗松. 贝叶斯统计[M]. 北京： 中国统计出版社, 1999.(MAO Shi-song. Bayesian Statistics [M]. Beijing: China Statistics Press, 1999.(in Chinese)) [9] Bayes T. An essay towards solving a problem in the doctrine of chances[J]. Resonance,2003,8(4): 80-88. [10] CHEUNG Sai-hung. Stochastic analysis, model and reliability updating of complex systems with applications to structural dynamics[D]. PhD Thesis. Pasadena, CA: California Institute of Technology, 2009. [11] CHING Jian-ye, CHEN Yi-chu. Transitional Markov chain Monte Carlo method for Bayesian model updating, model class selection, and model averaging[J]. Journal of Engineering Mechanics,2007,133(7): 816-832. [12] Katafygiotis L S, LAM Heung-fai. Tangential-projection algorithm for manifold representation in unidentifiable model updating problems[J]. Earthquake Engineering & Structural Dynamics,2002,31(4): 791-812. [13] YUEN Ka-veng. Structural modal identification using ambient dynamic data[D]. Master Thesis. Hong Kong: Hong Kong University of Science and Technology, 1999. [14] YUEN Ka-veng, Katafygiotis L S. Bayesian fast Fourier transform approach for modal updating using ambient data[J]. Advances in Structural Engineering,2003,6(2): 81-95. [15] YUEN Ka-veng, Katafygiotis L S, Beck J L. Spectral density estimation of stochastic vector processes[J]. Probabilistic Engineering Mechanics,2002,17(3):265-272. [16] Katafygiotis L S, YUEN Ka-veng. Bayesian spectral density approach for modal updating using ambient data[J]. Earthquake Engineering & Structural Dynamics,2001,30(8): 1103-1123. [17] YUEN Ka-veng, Katafygiotis L S. Bayesian time-domain approach for modal updating using ambient data[J]. Probabilistic Engineering Mechanics,2001,16(3): 219-231. [18] YUEN Ka-veng, Beck J L, Katafygiotis L S. Probabilistic approach for modal identification using non-stationary noisy response measurements only[J]. Earthquake Engineering & Structural Dynamics,2002,31(4): 1007-1023. [19] YUEN Ka-veng. Bayesian Methods for Structural Dynamics and Civil Engineering [M]. New York: John Wiley & Sons Ltd, 2010. [20] AU Siu-kui. Fast Bayesian FFT method for ambient modal identification with separated modes[J]. Journal of Engineering Mechanics,2011,137(3): 214-226. [21] AU Siu-kui. Fast Bayesian ambient modal identification in the frequency domain, part I: posterior most probable value[J]. Mechanical Systems and Signal Processing,2012,26: 60-75. [22] AU Siu-kui. Fast Bayesian ambient modal identification in the frequency domain, part II: posterior uncertainty[J]. Mechanical Systems and Signal Processing,2012,26: 76-90. [23] AU Siu-kui, ZHANG Feng-liang. On assessing the posterior mode shape uncertainty in ambient modal identification[J]. Probabilistic Engineering Mechanics,2011,26(3): 427-434. [24] AU Siu-kui. Uncertainty law in ambient modal identification—part I: theory[J]. Mechanical Systems and Signal Processing,2014,48(1/2): 15-33. [25] AU Siu-kui. Uncertainty law in ambient modal identification—part II: implication and field verification[J]. Mechanical Systems and Signal Processing,2014,48(1/2): 34-48. [26] AU Siu-kui. Connecting Bayesian and frequentist quantification of parameter uncertainty in system identification[J]. Mechanical Systems and Signal Processing,2012,29:328-342. [27] AU Siu-kui, ZHANG Feng-liang, NI Yan-chun. Bayesian operational modal analysis: theory, computation, practice[J]. Computers & Structures,2013,126: 3-14. [28] AU Siu-kui, NI Yan-chun. Fast Bayesian modal identification of structures using known single-input forced vibration data[J]. Structural Control and Health Monitoring,2014,21: 381-402. [29] ZHANG Feng-liang, NI Yan-chun, AU Siu-kui, et al. Fast Bayesian approach for modal identification using free vibration data, part I: most probable value[J]. Mechanical Systems and Signal Processing,2016,70/71: 209-220. [30] NI Yan-chun, ZHANG Feng-liang, LAM Heung-fai, et al. Fast Bayesian approach for modal identification using free vibration data, part II: posterior uncertainty and application[J]. Mechanical Systems and Signal Processing,2016,70/71: 221-244. [31] AU Siu-kui. Assembling mode shapes by least squares[J]. Mechanical Systems and Signal Processing,2011,25(1): 163-179. [32] AU Siu-kui, ZHANG Feng-liang. Fast Bayesian ambient modal identification incorporating multiple setups[J]. Journal of Engineering Mechanics,2012,138(7): 800-815. [33] ZHANG Feng-liang, AU Siu-kui, LAM Heung-fai. Assessing uncertainty in operational modal analysis incorporating multiple setups using a Bayesian approach[J]. Structural Control and Health Monitoring,2015,22(3): 395-416. [34] AU Siu-kui, ZHANG Feng-liang. Ambient modal identification of a primary-secondary structure by fast Bayesian FFT method[J]. Mechanical Systems & Signal Processing,2012,28: 280-296. [35] AU Siu-kui, NI Yan-chun, ZHANG Feng-liang, et al. Full-scale dynamic testing and modal identification of a coupled floor slab system[J]. Engineering Structures,2012,37(4): 167-178. [36] AU Siu-kui, ZHANG Feng-liang, TO Ping. Field observations on modal properties of two tall buildings under strong wind[J]. Journal of Wind Engineering and Industrial Aerodynamics,2012,101: 12-23. [37] YAN Wang-ji, Katafygiotis L S. A two-stage fast Bayesian spectral density approach for ambient modal analysis. Part I: posterior most probable value and uncertainty[J]. Mechanical Systems & Signal Processing,2014,54/55: 139-155. [38] YAN Wang-ji, Katafygiotis L S. A two-stage fast Bayesian spectral density approach for ambient modal analysis. Part II: mode shape assembly and case studies[J]. Mechanical Systems & Signal Processing,2015,54/55: 156-171. [39] 万华平. 结构动力不确定性及其随机模型修正方法研究[D]. 博士学位论文. 长沙: 中南大学, 2014.(WAN Hua-ping. Research on structural dynamic uncertainty and its stochastic model updating method[D]. PhD Thesis. Changsha: Central South University.(in Chinese)) [40] Beck J L, AU Siu-kui, Vanik M W. Monitoring structural health using a probabilistic measure[J]. Computer-Aided Civil and Infrastructure Engineering,2001,16(1): 1-11. [41] Vanik M W, Beck J L, Au S K. Bayesian probabilistic approach to structural health monitoring[J]. Journal of Engineering Mechanics,2000,126(7): 738-745. [42] CHING Jian-ye, Muto M, Beck J L. Structural model updating and health monitoring with incomplete modal data using Gibbs sampler[J]. Computer-Aided Civil and Infrastructure Engineering,2006,21(4): 242-257. [43] CHING Jian-ye, Beck J L. Bayesian analysis of the phase II IASC-ASCE structural health monitoring experimental benchmark data[J]. Journal of Engineering Mechanics,2004,130(10): 1233-1244. [44] CHING Jian-ye, Beck J L. New Bayesian model updating algorithm applied to a structural health monitoring benchmark[J]. Structural Health Monitoring,2004,3(4): 313-332. [45] YUEN Ka-veng, Beck J L, Katafygiotis L S. Efficient model updating and health monitoring methodology using incomplete modal data without mode matching[J]. Structural Control & Health Monitoring,2006,13(1): 91-107. [46] YAN Wang-ji, Katafygiotis L S. A novel Bayesian approach for structural model updating utilizing statistical modal information from multiple setups[J]. Structural Safety,2015,52: 260-271. [47] Papadimitriou C, Papadioti D C. Component mode synthesis techniques for finite element model updating[J]. Computers & Structures,2013,126(1):15-28. [48] Jensen H A, Millas E, Kusanovic D, et al. Model-reduction techniques for Bayesian finite element model updating using dynamic response data[J]. Computer Methods in Applied Mechanics and Engineering,2014,279: 301-324. [49] Papadimitriou C, Papadioti D C. Fast Computing Techniques for Bayesian Uncertainty Quantification in Structural Dynamics [M]//Simmermacher T, Cogan S, Moaveni B, et al, ed. Topics in Model Validation and Uncertainty Quantification.Vol5. New York: Springer, 2013: 25-31. [50] Craig Jr R R. Structural Dynamics: An Introduction to Computer Methods [M]. New York: John Wiley and Sons, 1981. [51] Wan H P, Ren W X. Stochastic model updating utilizing Bayesian approach and Gaussian process model[J]. Mechanical Systems and Signal Processing,2016,70: 245-268. [52] Behmanesh I, Moaveni B, Lombaert G, et al. Hierarchical Bayesian model updating for structural identification[J]. Mechanical Systems & Signal Processing,2015,64: 360-376. [53] Gamerman D, Lopes H F. Markov Chain Monte Carlo: Stochastic Simulation for Bayesian Inference [M]. Boca Raton: Chapman & Hall, 2006. [54] AU Siu-kui, Beck J L. A new adaptive importance sampling scheme for reliability analysis[J]. Structural Safety,1999,21(2): 135-158. [55] Kirkpatrick S, Gelatt C D, Vecchi M P. Optimization by simulated annealing[J]. Science,1983,220(4598): 671-680. [56] Beck J L, AU Siu-kui. Bayesian updating of structural models and reliability using Markov chainMonte Carlo simulation[J]. Journal of Engineering Mechanics,2002,128(4): 380-391. [57] Goller B, Schuller G I. Investigation of model uncertainties in Bayesian structural model updating[J]. Journal of Sound & Vibration,2011,330(25): 6122-6136. [58] ZHENG Wei, YU Yi. Bayesian probabilistic framework for damage identification of steel truss bridges under joint uncertainties[J]. Advances in Civil Engineering,2013,2013: 307171. doi: 10.1155/2013/307171. [59] WANG Jia, Katafygiotis L S. Reliability-based optimal design of linear structures subjected to stochastic excitations[J]. Structural Safety,2014,47(2): 29-38. [60] Beck J L, Zuev K M. Asymptotically independent Markov sampling: a new Markov chain Monte Carlo scheme for Bayesian inference[J]. International Journal for Uncertainty Quantification,2013,3(5): 445-474. [61] CHEUNG Sai-hung, Beck J L. Bayesian model updating using hybrid Monte Carlo simulation with application to structural dynamic models with many uncertain parameters[J]. Journal of Engineering Mechanics,2009,135(4): 243-255. [62] Green P L. Bayesian system identification of a nonlinear dynamical system using a novel variant of simulated annealing[J]. Mechanical Systems & Signal Processing,2015,52/53: 133-146. [63] Green P L, Cross E J, Worden K. Bayesian system identification of dynamical systems using highly informative training data[J].Mechanical Systems & Signal Processing,2015,56/57: 109-122. [64] Marin J M, Pudlo P, Robert C P, et al. Approximate Bayesian computational methods[J]. Statistics & Computing,2012,22(6): 1167-1180. [65] Chiachio M, Beck J L, Chiachio J, et al. Approximate Bayesian computation by subset simulation[J]. SIAM Journal on Scientific Computing,2014,36(3): A1339-A1338. [66] Vakilzadeh M K, Huang Y, Beck J L, et al. Approximate Bayesian computation by subset simulation using hierarchical state-space models[J]. Mechanical Systems & Signal Processing,2017,84(B): 2-20. [67] AU Siu-kui, Beck J L. Estimation of small failure probabilities in high dimensions by subset simulation[J]. Probabilistic Engineering Mechanics,2001,16(4): 263-277. [68] Straub D, Papaioannou I. Bayesian updating with structural reliability methods[J]. Journal of Engineering Mechanics,2014,141(3): 04014134. [69] DiazDelaO F A, Garbuno-Inigo A, Au S K, et al. Bayesian updating and model class selection with subset simulation[Z]. arXiv preprint arXiv: 1510.06989, 2015. [70] LAM Heung-fai, YANG Jia-hua, AU Siu-kui. 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. [71] SUN Hao, Büyükztürk O. Probabilistic updating of building models using incomplete modal data[J]. Mechanical Systems and Signal Processing,2016,75: 27-40. [72] ZHANG Jian, WAN Chun-feng, Sato T. Advanced Markov chain Monte Carlo approach for finite element calibration under uncertainty[J]. Computer-Aided Civil and Infrastructure Engineering,2013,28(7): 522-530. [73] Simoen E, De Roeck G, Lombaert G. Dealing with uncertainty in model updating for damage assessment: a review[J]. Mechanical Systems and Signal Processing,2015,56/57: 123-149. [74] Collins J D, Hart G C, Haselman T K, et al. Statistical identification of structures[J]. Aiaa Journal,1973,12(2): 185-190. [75] Sohn H, Law K H. A Bayesian probabilistic damage detection using load-dependent Ritz vectors[C]// Proceedings of the 16th International Modal Analysis Conference.Santa Barbara, California : Society for Experimental Mechanics, Inc,1998: 374-380． [76] Sohn H, Law K H. Bayesian probabilistic damage detection of a reinforced-concrete bridge column[J]. Earthquake Engineering & Structural Dynamics,2000,29(8): 1131-1152. [77] Vanik M W. A Bayesian probabilistic approach to structural health monitoring: technical report EERL 97-07[R]. Earthquake Engineering Research Laboratory, California Institute of Technology, Pasadena, CA, 1997. [78] YUEN Ka-veng, AU Siu-kui, Beck J L. Two-stage structural health monitoring approach for phase I benchmark studies[J]. Journal of Engineering Mechanics,2004,130(1):16-33. [79] YUEN Ka-veng, Katafygiotis L S. Model updating using response measurements without knowledge of the input spectrum[J]. Earthquake Engineering and Structural Dynamics,2005,34(2): 167-187. [80] YUEN Ka-veng, Katafygiotis L S. Substructure identification and health monitoring using response measurement only[J]. Computer-Aided Civil and Infrastructure Engineering,2006,21(4): 280-291. [81] YAN Wang-ji, Katafygiotis L S. Application of transmissibility matrix and random matrix to Bayesian system identification with response measurements only[J]. Smart Materials and Structures,2016,25(10): 105017. [82] Ebrahimian H, Astroza R, Conte J P, et al. Nonlinear finite element model updating for damage identification of civil structures using batch Bayesian estimation[J]. Mechanical Systems & Signal Processing,2017,84(B): 194-222. [83] 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 Wei-jian, ZHOU Yun, LI Hao. Damage assessment research on frame structure based on Bayesian statistical inference[J]. Engineering Mechanics,2009,26(5): 121-129.(in Chinese) ) [84] Lam H F, Yin T. Statistical detection of multiple cracks on thin plates utilizing dynamic response[J]. Engineering Structures,2010,32(10): 3145-3152. [85] Lam H F, Lee Y Y, Sun H Y, et al. Application of the spatial wavelet transform and Bayesian approach to the crack detection of a partially obstructed beam[J]. Thin-Walled Structures,2005,43(1): 1-21. [86] Lam H F, Ng C T, Veidt M. Experimental characterization of multiple cracks in a cantilever beam utilizing transient vibration data following a probabilistic approach[J]. Journal of Sound and Vibration,2007,305(1): 34-49. [87] Lam H F, Wong M T, Yang Y B. A feasibility study on railway ballast damage detection utilizing measured vibration of in situ concrete sleeper[J]. Engineering Structures,2012,45: 284-298. [88] Ng C T, Veidt M, Lam H F. Guided wave damage characterisation in beams utilising probabilistic optimisation[J]. Engineering Structures,2009,31(12): 2842-2850. [89] Flynn E B, Todd M D, Wilcox P D, et al. Maximum-likelihood estimation of damage location in guided-wave structural health monitoring[J]. Proceedings: Mathematical, Physical and Engineering Sciences,2011,467(2133): 2575-2596. [90] YUEN Ka-veng. Recent developments of Bayesian model class selection and applications in civil engineering[J]. Structural Safety,2010,32(5): 338-346. [91] Beck J L, YUEN Ka-veng. Model selection using response measurements: Bayesian probabilistic approach[J]. Journal of Engineering Mechanics,2004,130(2): 192-203. [92] CHEUNG Sai-hung, Beck J L. Calculation of posterior probabilities for Bayesian model class assessment and averaging from posterior samples based on dynamic system data[J]. Computer-Aided Civil and Infrastructure Engineering,2010,25(5): 304-321. [93] Papadimitriou C. Pareto optimal sensor locations for structural identification[J]. Computer Methods in Applied Mechanics and Engineering,2005,194(12): 1655-1673. [94] YUEN Ka-veng, KUOK Sin-chi. Efficient Bayesian sensor placement algorithm for structural identification: a general approach for multi-type sensory systems[J]. Earthquake Engineering & Structural Dynamics,2015,44(5): 757-774. [95] SUN Hao, FENG Dong-ming, LIU Yang, et al. Statistical regularization for identification of structural parameters and external loadings using state space models[J]. Computer-Aided Civil and Infrastructure Engineering,2015,30(11): 843-858. [96] Simoen E, Papadimitriou C, Lombaert G. On prediction error correlation in Bayesian model updating[J]. Journal of Sound and Vibration,2013,332(18): 4136-4152.

##### 计量
• 文章访问数:  1321
• HTML全文浏览量:  108
• PDF下载量:  965
• 被引次数: 0
##### 出版历程
• 收稿日期:  2016-10-11
• 修回日期:  2016-12-10
• 刊出日期:  2017-01-15

/

• 分享
• 用微信扫码二维码

分享至好友和朋友圈