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Computationally efficient Bayesian inference for probabilistic model updating with polynomial chaos and Gibbs sampling
Bayesian inference methods usually require numerous forward model simulations to generate converged samples. When the forward model is expensive to evaluate, it becomes a challenging problem to estimate the posterior distribution function from Bayesian inference. We propose a computationally efficient Bayesian inference method with a combination of polynomial chaos and Gibbs sampling for structural damage detection and condition assessment. The likelihood function is approximated with the polynomial chaos expansion, and the Gibbs sampling method is performed to generate the samples for the posterior distribution. In the Gibbs sampling, the forward model is not required, which reduces the computation time for Bayesian inference. The proposed Bayesian inference method is conducted to update the probability distributions of unknown structural parameters for structural condition assessment, and the observer data comprise the correlation function of the acceleration responses. The analytical formula for the correlation function of the acceleration response is also derived in this study. Both numerical studies and experimental studies were conducted to verify the accuracy and efficiency of the proposed method. The results show that the posterior distribution of unknown parameters can be successfully estimated by using the proposed method. In addition, the proposed improved Bayesian inference is robust to measurement noise. Comparison studies with the original Gibbs sampling method are presented. The results indicate that the proposed improved Bayesian inference method is about 100 times faster than the original Gibbs sampling method.
Computationally efficient Bayesian inference for probabilistic model updating with polynomial chaos and Gibbs sampling
Bayesian inference methods usually require numerous forward model simulations to generate converged samples. When the forward model is expensive to evaluate, it becomes a challenging problem to estimate the posterior distribution function from Bayesian inference. We propose a computationally efficient Bayesian inference method with a combination of polynomial chaos and Gibbs sampling for structural damage detection and condition assessment. The likelihood function is approximated with the polynomial chaos expansion, and the Gibbs sampling method is performed to generate the samples for the posterior distribution. In the Gibbs sampling, the forward model is not required, which reduces the computation time for Bayesian inference. The proposed Bayesian inference method is conducted to update the probability distributions of unknown structural parameters for structural condition assessment, and the observer data comprise the correlation function of the acceleration responses. The analytical formula for the correlation function of the acceleration response is also derived in this study. Both numerical studies and experimental studies were conducted to verify the accuracy and efficiency of the proposed method. The results show that the posterior distribution of unknown parameters can be successfully estimated by using the proposed method. In addition, the proposed improved Bayesian inference is robust to measurement noise. Comparison studies with the original Gibbs sampling method are presented. The results indicate that the proposed improved Bayesian inference method is about 100 times faster than the original Gibbs sampling method.
Computationally efficient Bayesian inference for probabilistic model updating with polynomial chaos and Gibbs sampling
Han, Qiang (author) / Ni, Pinghe (author) / Du, Xiuli (author) / Zhou, Hongyuan (author) / Cheng, Xiaowei (author)
2022-06-01
27 pages
Article (Journal)
Electronic Resource
English
| British Library Online Contents | 2014
A Hybrid Optimization Algorithm with Bayesian Inference for Probabilistic Model Updating
| Online Contents | 2015