Bayesian estimation approach based on modified SCAM algorithm and its application in structural damage identification

Abstract

The single-component adaptive Metropolis (SCAM) algorithm, as one of the Markov chain Monte Carlo (MCMC) sampling methods, is very effective at solving high-dimensional posterior joint probability distributions. However, studies show that the SCAM algorithm is prone to generating duplicate samples, thus lowering the sampling efficiency and causing large calculation errors. To solve this problem, a modified SCAM algorithm is proposed in the present study. In the modified algorithm, the expression of the variance of the proposal distribution is redefined so that the Markov chain formed by the sample sequence is relatively stable. With the obtained structural response, the posterior joint probability distribution of the physical parameters of the structure is achieved using Bayesian theory, which is then combined with the modified SCAM algorithm to solve the posterior marginal probability distribution and the optimal estimates. Hence, the structural damage is identified. The validity, reliability, and practicability of the modified SCAM algorithm are verified through theoretical analysis, a numerical simulation of the structural example, and a shaking table test. The results show that the modified SCAM algorithm not only enhances the accuracy of the calculation results but also increases the sampling efficiency. This method can be used as a reference for physical parameter identification and damage assessment of the engineering structures.

Bayesian RC-Frame Finite Element Model Updating and Damage Estimation Using Nested Sampling with Nonlinear Time History

“…where e is the error between the real data y, which is collected from the structure and simulated acceleration; y(θ |M ), which is outputted from the numerical model. Generally, the error vector is assumed as a normal distribution whose Mean = 0 and Variance = σ [26]. Therefore, likelihood can be derived as below:…”

“…Evidence is used to perform model selection [33,34]. This paper proposes another approach to performing model selection, where it is generally treated as a constant [26].…”

“…In previous studies, in order to solve high-dimensional and complex equation problems in model updating based on Bayesian methods, they were more likely to use highefficiency sampling methods immediately or use complex methods to simplify numerical models, such as model selection methods [26], individually. Different from other sampling methods already been used in model updating based on Bayesian methods.…”

System-reliability based multi-ensemble of GAN and one-class joint Gaussian distributions for unsupervised real-time structural health monitoring

“…Moreover, missing a novelty is probable if the model's physics cannot capture the effect of a novelty [4]. Some improvements are achieved by assuming probabilistic model parameters [3,5]; however, the proposed methods are mostly validated versus numerical simulations and laboratory testings and need further field experiments to prove their validity [5].…”

Efficient Bayesian model class selection of vector autoregressive models for system identification

“…Samples are generated according to the posterior PDF, and they are used to approximate the posterior PDF and the evidence of a model class. Two types of MCMC methods, namely, Metropolis-Hastings (MH)-based methods [10][11][12][13] and Gibbs sampling methods, 14,15 have been successfully used for Bayesian inference. Despite some successful applications of MCMC for Bayesian model class selection, difficulties still remain to be solved for high-dimensional problems in practice.…”