Efficient Bayesian Reliability Analysis and Design with a User-Defined Confidence Level

Abstract

The capability to deal with both aleatory and epistemic uncertainties is of vital importance in practical engineering applications which are usually constrained by limited resources. To tackle this challenge, Bayesian Reliability Based Design Optimization (BRBDO) methodology has been developed to deal with engineering design problems involving both aleatory and epistemic uncertainties. Despite the success of BRBDO, however, the defined Bayesian reliability is somehow arbitrary and conservative for practical engineering design problems. Besides, although advanced numerical methods can substantially improve the computational efficiency, Bayesian RBDO itself is still computationally expensive when the sample size of epistemic uncertainties is relative large, since evaluation of both reliability and sensitivity at each epistemic sample points is needed for all design iterations. Thus, this paper proposes two improvements for the efficient Bayesian reliability analysis and design: (1) improving the flexibility of Bayesian reliability selection with user-defined reliability confidence levels and (2) improving the computational efficiency of Bayesian reliability analysis and design methodology by applying the statistical modeling technique on data samples of epistemic uncertainties. With the user-defined confidence level and the sample size for epistemic uncertainties, the Bayesian reliability can be flexibly defined. By applying the statistical modeling technique, the computational efficiency of BRBDO is substantially improved, and meanwhile it maintains the accuracy and capabilities of BRBDO methodology. These two improvements will substantially enhance the capability of the Bayesian RBDO and broaden it applicable area, and the improved methodology is referred as the efficient Bayesian Reliability Based Design Optimization (eBRBDO). Two examples are used to demonstrate the proposed approach.