ABSTRACT
A reliability analysis procedure is proposed based on a Bayesian framework, which can address the uncertainty in the input variables and the metamodel uncertainty of the response function in an integrated manner. The input uncertainty includes the statistical uncertainty due to the lack of knowledge or insufficient data, which is often the case in the design practice. A method of posterior prediction is used to evaluate the influence of this uncertainty. The metamodel uncertainty is accounted for, which arises due to the surrogate approximation to reduce the costly computation of the response function. Gaussian process model, also known as Kriging model, is employed to assess the associated uncertainty in the form of prediction band. Posterior distributions are obtained by Markov Chain Monte Carlo (MCMC) method, which is an efficient simulation method to draw random sequence of parameters that samples the given distribution. Mathematical and engineering examples are used to demonstrate the proposed method.
Keywords: Reliability analysis, Epistemic uncertainty, Statistical uncertainty, Metamodel uncertainty, Bayesian approach.
