In this paper, we apply a Bayesian model selection and parameter estimation scheme for a stochastic nonlinear dynamical system using noisy experimental data. The scheme involves three stages: 1) selection of candidate model set, 2) parameter estimation and 3) model selection. Assuming limited prior knowledge of the system dynamics, a stepwise backward elimination procedure is adopted to form a candidate set. The parameter estimation is performed using the Bayesian inference scheme, whereby a Metropolis-Hastings (M-H) Monte Carlo Markov Chain (MCMC) algorithm is employed to sample from the joint posterior distribution of the parameters and the associated state estimation problem is tackled by the Extended Kalman Filter (EKF). The experimental data obtained from the free-decay response of a nonlinear oscillator is considered for the application of the model selection scheme.

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Conference 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013
Citation
Sandhu, R. (R.), Khalil, M. (M.), Poirel, D. (D.), & Sarkar, A. (2013). Model selection method for stochastic nonlinear dynamical systems using experimental data. In Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures - Proceedings of the 11th International Conference on Structural Safety and Reliability, ICOSSAR 2013 (pp. 3657–3659).