Bayesian Approach for Structural Reliability Analysis and Optimization Using the Kriging Dimension Reduction Method

Abstract

An efficient method for a structural reliability analysis is proposed under the Bayesian framework, which can deal with the epistemic uncertainty arising from a limited amount of data. Until recently, conventional reliability analyses dealt mostly with the aleatory uncertainty, which is related to the inherent physical randomness and its statistical properties are completely known. In reality, however, epistemic uncertainties are prevalent, which makes the existing methods less useful. In the Bayesian approach, the probability itself is treated as a random variable of a beta distribution conditional on the provided data, which is determined by conducting a double loop of reliability analyses. The Kriging dimension reduction method is employed to promote efficient implementation of the reliability analysis, which can construct the PDF of the limit state function with favorable accuracy using a small number of analyses. Mathematical examples are used to demonstrate the proposed method. An engineering design problem is also addressed, which is to find an optimum design of a pigtail spring in a vehicle suspension, taking material uncertainty due to limited test data into account.