Research On Model-Based Optimization Design Methods Under Uncertainty

Model-based optimization design under uncertainty is an important tool in the engineering design. Reliability-based design and robust design are two typical kinds of model-based optimization design under uncertainty. Reliability-based design ensures that the probability of failure should be less than an acceptable level to reduce the likelihood of catastrophic results. While the task of robust design is to reduce the effect on the performance of a product caused by input uncertainty to improve the quality without elminating the source of the input uncertainty. Since the requirement of practical engineering design becomes higher and higher, the current optimization design methods under uncertainty are yet not suitable for the practical design and display some limitations.Some research has been done in terms of the requirement of practical engineering in this dissertation. Firstly, the traditional static reliability-based design is extended to the whole product lifecycle and some dynamic reliability-based design models are built. Secondly, a reliability-based design model based on two types of uncertainty including epistemic uncertainty and aleatory uncertainty is built. Finally, a unified framework for integrated optimization design model under uncertainty is given. All these models extend the traditional optimization design under uncertainty to consummate the theoretical system of optimization design under uncertainty and to have a wider application in the engineering practices.The contributions of this dissertation are summarized as follows.(1)Dynamic reliability-based design models under uncertainty based on maintenanceThe same goal of maintenance and reliability-based design under uncertainty is to improve the reliability of a product. Actually, maintenance will affect the design. Hence some dynamic reliality-based design models based on maintenance are built according to different maintenance strategies and capacity of maintenance. After that, we propose some efficient algorithms to resolve the models. These models realize the extension from the static reliability-based design to the whole lifecycle. (2) Dynmic reliability-based optimization design models under uncertainty based on warrantyWarranty is a widely accepted commercial action in the post-sold period. From the technique's view, the main effect of warranty is also to improve the reliability and will affect the design. Two dynamic reliability-based design models are built. The first model only covers the warranty period and the second model covers both warranty and post-warranty period. And then we propose some numerical algorithms to resolve these two models. These two models can also realize the extension from the traditional static reliability-based design to dynamic reliability-based design by accounting for the warranty in the whole lifecycle of a product.(3)Reliability-based design model under two types of uncertaintyUncertainty is mainly categorized into two types:epistemic uncertainty and aleatory uncertainty. At the early design stage, there is little information to determine the distributions of some random variables or the information is fuzzy. Then it is reasonable to consider the random variables as the fuzzy random variables. Then a reliability-based design model is built based on fuzzy random variables. After that a method combining simulation and saddlepoint approximation is used to resolve the model. Since fuzzy random variables include epistemic uncertainty and aleatory uncertainty, the optimal design results will be more suitable for the engineering practices.(4) A unified framework for integrated optimization design under uncertaintyReliability and robustness are two main attributes of design under uncertainty. In the engineering design, reliability and robustness should be satisfied at the same time. Currently, some attempts have been done to integrate reliability-based design and robust design. However, there is no unified framework. This will lead to many different designs. Therefore, a unified framework for intergrated reliability-based design and robust design is proposed in this dissertation. In some senses, the unified framework realizes the genuine combination of reliability-based design and robut design to form a theorical system of design under uncertainty.