Research On RBDO Method Based On Probability Theory And Evidence Theory

As uncertainties widely exist in engineering product design field, and affect product quality seriously, Reliability-Based Design Optimization(RBDO) is becoming the research hotspot in recent years. In general, uncertainty can be classified into two main categories: random uncertainty and epistemic uncertainty. Random uncertainty, such as manufacturing tolerance, is irreducible and can be disposed by probability theory. On the contrary, epistemic uncertainty, such as changes of operation conditions, is reducible and can be reduced by evidence theory.This paper is mainly focus on RBDO problems that contain epistemic uncertainty and mixed uncertainties. For RBDO problems that contain epistemic uncertainty, evidence theory is used to deal with epistemic uncertainty, and then an effective reliability analysis method and an effective design optimization method are proposed. For RBDO problems that contain random uncertainty and epistemic uncertainty simultaneously, probability theory and evidence theory are used to deal with random uncertainty and epistemic uncertainty respectively, and then an effective solving method, which is based on probability theory and evidence theory, is proposed. Numerical examples and engineering cases are used to test the efficiency of proposed methods, and the results show the excellent application effect.Firstly, in the reliability analysis of evidence theory, a large amount of calculations exist in calculating belief function and plausibility function because extreme value analysis of limit-state functions should be done on each focal element. To overcome this disadvantage, an effective reliability analysis method based on Most Probable Focal Element(MPFE) is proposed in this paper. Through solving the MPFE, a portion of focal elements that exist in safety and failure area are judged, and the analysis of extreme values on these focal elements can be avoided. This method reduces the number of focal elements that should conduct extreme value analyses, thus the efficiency of reliability analysis can be improved.Secondly, for RBDO problems that only contain epistemic uncertainty, the deterministic design optimization in sequential optimization and reliability assessment(SORA) method cannot be updated. This will lead to the failure of decoupling. To solve this problem, we propose a SORA combined with Evidence-Based Design Optimization(SORA-EBDO) method, in which MPFE vertex and adjacent points are approximately considered as the Most Probable Point based on Evidence theory(MPP-E) instead of MPP point in SORA. Through modifying the constraints and updating deterministic design optimization, decoupling is completed successfully.Thirdly, for RBDO problems that contain mixed uncertainty, it is hardly to solve because random variables and evidence variables are mutual coupled. To overcome this difficulty, we propose a Reliability- and Evidence-Based Design Optimization(SORA-REBDO) method, in which a sequential method is proposed to decoupling random variables and evidence variables, and probability theory is utilized to deal with random uncertainty meanwhile evidence theory is utilized to deal with epistemic uncertainty. Then, this method is combined with SORA to realize the solving of RBDO problems that contain mixed uncertainty.