An Evidence-theory Based Mechanical Reliability Analysis Method And Optimization Design Method

The uncertainties widely exist in the whole life of engineering products process including design, manufacture and use. Generally, a single or a few uncertain factors have little affection on the system's performance, but the couple of multiple uncertainty factors may result in quiet negative influence to structural system's performance, so it is important to effectively measure and manage the uncertainty in design stage for ensuring the quality and reliability of products.Uncertainty can be viewed as the difference between the present state of knowledge and the complete knowledge.According to this standpoint, uncertainty can be calssified into aleatory and epistemic types. The probability theory is widely used to deal with the aleatory uncertainty. Currently, different kinds of theories haved been developed to handle episdemic uncertainty, which include prossibility method, fuzzy method, interval approach and evidence theory. Evidence theory is viewed as a more general method than the others, which has a larger application potential for practical engineering problems. However, it is still at its preliminary stage for the evidence-theory based reliability analysis and optimization design method. Some key technical difficulties remain, such as its low computational efficiency. As a result, the following studies are carried out in this dissertation:(1) Due to the discrete property of BPA in evidence theory, the computational efficiency of reliability analysis based evidence theory is quite low, which severely restricts its application. Here, a novel structural reliability analysis method using evidence theory based on tolerance correction strategy is proposed to solve the problem. Firstly, we obtain the samples by the design of experiment, and then the surrogate model can be easily produced based on the samples; secondly, we propose a tolerance correction strategy to correct the result of reliability analysis, so the analytical precision can be improved to meet the requirements.(2) An efficient reliability analysis method for structure has been proposed, whose inputs consist of both probable variables and evidence variables. The method greatly reduces the computation cost of reliability analysis with mixture of aleatory and epistemic uncertainty, at the same time its result has high accuracy. In the method, a uniformity approach is used to deal with evidence variables, and then the concept of most probable point (MPP) in probability theory is introduced to reliability analysis for hybrid model, which has both aleatory and epistemic uncertainty. A first order Taylor expansion is expanded at MPP, which is used for reliability analysis as approximation model instead of the original performance function.(3) The present reliability-based design optimization methods concerning epistemic uncertainty are computationally inefficient, which severely restricts its application for practical engineering probelms. Therefore the gradient approximation for reliability-based design optimization method using evidence theory is proposed. Firstly, we demonstrate a new approximate gradient for the reliability measures without gathering any excess information, and then the high-efficiency and mature gradient-based optimization algorithm can be used to solve the problem; secondly, the surrogates of constraints are always updated along the with variation of design point, which can efficiently and accurately calculate the reliability measure of the constrains.