Online probabilistic model class selection and joint estimation of structures for post-disaster monitoring

Abstract

Online selection of the appropriate model and identifying its parameters based on measured vibrational data are among the challenging issues in dynamic system identification. After a severe earthquake, quick monitoring and assessment of structural health status play a crucial role in effective critical risk management for the building owners and decision-makers. The Bayesian multiple modeling approach is a suitable tool for optimal model class selection, which is used in this article mainly for improving data fitting precision, decreasing dimensions of structural unknown vector through removing unnecessary parameters, detecting the occurrence and type of predominant phenomenon related to degradation and pinching, and finally increasing stability and convergence rate of the used identification algorithm. In this study, a reliable and effective time-domain method is proposed for online probabilistic model class selection and joint estimation of structures using the central difference Kalman filter and Bayesian multiple modeling approach. Also, in contrast to existing studies, the performance and efficiency of the proposed algorithm are investigated in nonlinear system identification with a large number of unknowns. The proposed algorithm is implemented on three moment-frame buildings with 8, 54, and 60 unknowns. In addition, a numerical example is provided to analyze the case in which the exact model is not among the plausible models. To verify the performance of the hybrid identification method, robust simulations with synthetic measurement noises and modeling errors were generated using the Monte Carlo random simulation method. The result shows the method can be used to simultaneously select the optimal model class and identify its unknown states and parameters in an online manner.

Keywords

Online model class selection central difference Kalman filter Bayesian multiple modeling degradation pinching Monte Carlo random simulation

Get full access to this article

View all access options for this article.

References

Al-Hussein

Haldar

(2018) Condition assessment of civil structures under earthquake excitation. Journal of Aerospace Engineering 32(1): 1–12.

Asgarieh

Moaveni

Nozari

, et al. (2014) Nonlinear identification of a seven-story shear wall building based on numerically simulated seismic data. In: 32nd IMAC conference on structural dynamics (ed Catbas

), Brescia, Italy, 1–5 July 2014, pp. 245–254. Cham: Springer International Publishing, Vol. 4.

Astroza

Alessandri

Conte

(2019a) A dual adaptive filtering approach for nonlinear finite element model updating accounting for modeling uncertainty. Mechanical Systems and Signal Processing 115: 782–800.

Astroza

Barrientos

, et al. (2019b) Bayesian updating of complex nonlinear finite element models with high-dimensional parameter space using heterogeneous measurements and a batch-recursive approach. Engineering Structures 201: 1–21.

Astroza

Ebrahimian

Conte

(2019c) Performance comparison of Kalman-based filters for nonlinear structural finite element model updating. Journal of Sound and Vibration 438: 520–542.

Astroza

Ebrahimian

, et al. (2017) Bayesian nonlinear structural finite element model and seismic input identification for damage assessment of civil structures. Mechanical Systems and Signal Processing 93: 661–687.

Baber

Noori

(1985) Random vibration of degrading, pinching systems. Journal of Engineering Mechanics 111(8): 1010–1026.

Brynjarsdóttir

O’Hagan

(2007) Learning about physical parameters: the importance of model discrepancy. Inverse Problems 30: 1–23.

Cao

Wang

(2013) Bayesian approach for probabilistic site characterization using cone penetration tests. Journal of Geotechnical and Geoenvironmental Engineering 139(2): 267–276.

10.

Chatzis

Chatzi

(2017) Online Bayesian identification of non-smooth systems. Procedia Engineering 199: 918–923.

11.

Cheung

Beck

(2009) Bayesian model updating using hybrid Monte Carlo simulation with application to structural dynamic models with many uncertain parameters. Journal of Engineering Mechanics 135(4): 243–255.

12.

Ebrahimian

Astroza

Conte

(2015) Extended Kalman filter for material parameter estimation in nonlinear structural finite element models using direct differentiation method. Earthquake Engineering & Structural Dynamics 44(10): 1495–1522.

13.

Ghanem

Ferro

(2006) Health monitoring for strongly non-linear systems using the ensemble Kalman filter. Structural Control and Health Monitoring 13(1): 245–259.

14.

Ghorbani

Cha

(2018) An iterated cubature unscented Kalman filter for large-degree of freedom systems identification with noisy data. Journal of Sound and Vibration 420: 21–34.

15.

Huang

Beck

(2018) Full Gibbs sampling procedure for Bayesian system identification incorporating sparse Bayesian learning with automatic relevance determination. Computer-Aided Civil and Infrastructure Engineering 33(9): 712–730.

16.

Huang

Yang

Zhou

(2009) Adaptive quadratic sum-squares error with unknown inputs for damage identification of structures. Structural Control and Health Monitoring 17(4): 404–426.

17.

Kontoroupi

Smyth

(2017) Online Bayesian model assessment using nonlinear filters. Structural Control and Health Monitoring 24(3): 1–15.

18.

Kuok

Yuen

(2016) Investigation of modal identification and modal identifiability of a cable-stayed bridge with Bayesian framework. Smart Structures and Systems 17(3): 445–470.

19.

Lei

(2012) Identification of non-linear structural parameters under limited input and output measurements. International Journal of Non-Linear Mechanics 47(10): 1141–1146.

20.

Wong

(2014) Theory of Nonlinear Structural Analysis: The Force Analogy Method for Earthquake Engineering. Singapore: John Wiley and Sons.

21.

Ren

, et al. (2014) Reviews on innovations and applications in structural health monitoring for infrastructures. Structural Monitoring and Maintenance 1(1): 1–45.

22.

Muto

Beck

(2008) Bayesian updating and model class selection for hysteretic structural models using stochastic simulation. Journal of Vibration and Control 14(1–2): 7–34.

23.

Noël

Kerschen

(2017) Nonlinear system identification in structural dynamics: 10 more years of progress. Mechanical Systems and Signal Processing 83: 2–35.

24.

Simon

(2006) Optimal State Estimation: Kalman, H Infinity, and Nonlinear Approaches Hoboken, NJ: John Wiley & Sons Publishing.

25.

Sivaselvan

Reinhorn

(2000) Hysteretic models for deteriorating inelastic structures. American Society of Civil Engineers/Journal of Engineering Mechanics 126(6): 633–640.

26.

Song

Behmanesh

Moaveni

, et al. (2019) Modeling error estimation and response prediction of a 10-story building model through a hierarchical Bayesian model updating framework. Frontiers in Built Environment 5: 1–15.

27.

Van der Merwe

(2004) Sigma-Point Kalman Filters for Probabilistic Inference in Dynamic State-Space Models. PhD Thesis, Oregon Health & Science University, USA.

28.

Wan

Wang

, et al. (2018) A modified particle filter for parameter identification with unknown inputs. Structural Control and Health Monitoring 25(12): 1–14.

29.

Worden

Hensman

(2012) Parameter estimation and model selection for a class of hysteretic systems using Bayesian inference. Mechanical Systems and Signal Processing 32: 153–169.

30.

Smyth

(2008) Real-time parameter estimation for degrading and pinching hysteretic models. International Journal of Non-Linear Mechanics 43(9): 822–833.

31.

Jahanshahi

(2018) Data fusion approaches for structural health monitoring and system identification: past, present, and future. Structural Health Monitoring 19(2): 552–586.

32.

Yang

Huang

(2007) Sequential non-linear least-square estimation for damage identification of structures with unknown inputs and unknown outputs. International Journal of Non-Linear Mechanics 42(5): 789–801.

33.

Yang

Huang

Lin

(2006) Sequential non-linear least-square estimation for damage identification of structures. International Journal of Non-Linear Mechanics 41(1): 124–140.

34.

Yang

Xia

Loh

(2012) Damage detection of hysteretic structures with a pinching effect. Journal of Engineering Mechanics 140(3): 462–472.

35.

Yang

(2003) Constrained Kalman filter for nonlinear structural identification. Journal of Vibration and Control 9(12): 1343–1357.

36.

Yuen

Kuok

(2016) Online updating and uncertainty quantification using nonstationary output-only measurement. Mechanical Systems and Signal Processing 66-67: 62–77.

37.

Yuen

Kuok

Dong

(2019) Self‐calibrating Bayesian real‐time system identification. Computer-Aided Civil and Infrastructure Engineering 34(9): 806–821.

38.

Yuen

(2015) Real-time system identification: an algorithm for simultaneous model class selection and parametric identification. Computer-Aided Civil and Infrastructure Engineering 30(10): 785–801.

39.

Yuen

Ortiz

Huang

(2016) Novel nonparametric modeling of seismic attenuation and directivity relationship. Computer Methods in Applied Mechanics and Engineering 311: 537–555.