Bayesian Updating Method Under Random and Interval Hybrid Uncertainties

Bayesian updating is an effective method for refining the random distribution model of the system when new observational information is gathered. To deal with the problem with multisource uncertainty, a Bayesian updating method under random and interval hybrid uncertainties is originally established in this paper. In the proposed method, the likelihood function is firstly built by considering the error of the observation and the hybrid uncertainties of the model prediction. Then, the posterior information of the random model inputs can be refined based on the defined likelihood function and the prior information. Finally, to efficiently obtain the posterior information of the random model inputs, an adaptive kriging method is developed. In this method, different learning functions are employed to accurately predict the extrema and classify the candidate samples, respectively. The significant novelty of the proposed adaptive kriging method is to design a posterior statistical information-oriented stop criterion. Four computational examples are used to illustrate the feasibility and rationality of the proposed Bayesian updating method.