Abstract:Structural performances will degrade with time due to the influence of loading, environmental and material factors. To assess the status of a structure in service, the structural deterioration process is usually described through physical models with uncertain model parameters. Prior distributions of model parameters are often determined by using the data collected from similar structures. To improve the accuracy of the model, Bayesian inference incorporated with available data is often used to update the distribution of the parameters. In this work, an effective Bayesian method PF-DREAM is proposed. In this approach, firstly, the mixing combination rule of the Dempster-shafer theory (DST) is utilized to get the prior distribution. Thereafter, for evaluating the complicated multidimensional integral in the Bayesian inference formula and obtaining the posterior distribution, a differential evolution adaptive Metropolis (DREAM) approach integrated with the particle filter (PF) is developed. As compared with the original PF method, the proposed PF-DREAM method can enhance the sample particles’ diversity and improve the quality of the model. To illustrate the efficiency and accuracy of the proposed method, a lithium-ion battery problem and a fatigue crack propagation problem are presented. Results demonstrated that the proposed method can provide more accurate results in parameters updating as well as response prediction. As more data is incorporated, the model’s variance becomes smaller, and the predicted mean trajectory is more reliable in terms of the actual deteriorate curves. It is pointed out that PF-DREAM method can be applied to high-dimensional problems and implicit function problems with the same algorithm presented in this paper, only accompanying more iteration numbers and greater computational load for obtaining convergent results.