A Reliability-Based Multidisciplinary Design Optimization Method with Evidence Theory and Probability Theory

Abstract

Uncertainties, including aleatory and epistemic uncertainties, always exist in multidisciplinary system. Due to the discontinuous nature of epistemic uncertainty and the complex coupled relation among subsystems, the computational efficiency of reliability-based multidisciplinary design optimization (RBMDO) with mixed aleatory and epistemic uncertainties is extremely low. A novel RBMDO procedure is presented in this paper based on combined probability theory and evidence theory (ET) to deal with hybrid-uncertainties and improve the computational efficiency. Firstly, based on Bayes method, a novel method to define the probability density function of the aleatory variables is proposed. Secondly, the conventional equivalent normal method (J-C method) is modified to reliability analysis with hybrid-uncertainties. Finally, a novel RBMDO procedure is suggested by integrating the modified J-C method into the frame of sequence optimization and reliability analysis (SORA). Numerical examples and engineering example are applied to demonstrate the performance of the proposed method. The examples show the excellence of the RBMDO method both in computational efficiency and accuracy. The proposed method provides a practical and effective reliability design method for multidisciplinary system.