Research On Reliability Based Design Optimization Based On Explicit Design Space Decomposition

Uncertainties due to inherent variability, imperfect knowledge, and errors are important in almost every step of the design. Engineers should appreciate the great importance of employing rational and systematic approaches for managing uncertainty in design. For this purpose, the critical issues about uncertainty need to be addressed and the models of uncertainty should to be proposed. Based on the different types of information, the theory of probability can be used to construct models of uncertainty. Managers and engineers should be aware of successful applications of uncertainties in product design, especially in product reliability design, which is one of the main factors to determine product quality and cost. Reliability analysis and the methodology of reliability based design optimization (RBDO) were proposed to help the engineers deal with the uncertainty and reliability in product design. However, complex product involves the complex models, high nonlinear behaviors, and implicit response, even discontinuities, which hamper the design optimization and the computational design process by the large computational time.For this purpose, a RBDO research system was proposed in this dissertation. A classification approach to construct constraints or limit-state functions (LSFs) explicitly by Support Vector Machines (SVMs), referred to as Explicit Design Space Decomposition (EDSD), and was proposed. This approach not only can solve the discontinuities, but also make the implicit problem become the explicit problem based the decision boundary which can be given explicitly. In addition, it can also solve the multi failure modes in the field of reliability assessment, and multi constraints of optimization problem. In order to limit the numbers of finite analysis, this dissertation proposed updating the explicit boundary through the adaptive sampling scheme and the parallel algorithm of EDSD. Aiming at solving double loop method of RBDO, the sequential approximate optimization approach was developed to decompose the reliability assessment and optimization. The above research system was well proved by a car full frontal crush optimization case study.Firstly, the reliability assessment based on SVM-based EDSD was proposed. The responses of design configurations were dealed with classifying not fitting, the decision boundary such as the boundary of LSFs, constraint boundary, can be constructed explicitly. In order to limit the numbers of finite analysis, updating the explicit boundary through the adaptive sampling scheme was developed. The MPP was redefined by the values of the joint probability density function (VJPDF). Based on the new definition of MPP, the relationships of VJPDF, MPP and the adaptive samples were obtained. When the decision boundary is approximated to the actual one, the adaptive samples is approached to the real MPP, then the failure of probability can be quickly estimated.Secondly, in order to limit the number of function evolution, such as Finite Element Analysis, the parallel algorithm of EDSD was proposed. The parallel algorithm can be described as:the adaptive sampling scheme is parallel implemented on several numbers of processors, and then the responses of all the adaptive samples are calculated simultaneously. An approach to investigate the optimal number of processors or the number of sampling based on the linear speedup and margin effect, in order not to "waste" all the processors for the parallel computation in the environment of the limited computation resources.Thirdly, this dissertation proposed sequential approximation optimization methodology based on EDSD. Based on the character of updating the explicit boundary through the adaptive sampling scheme and the basic idea of the sequential approximate programming strategy, the probability constraints of RBDO and the boundary of LSFs are explicitly constructed by EDSD gradually. At the same time, the original RBDO problem can be decomposed into a sequence of sub-optimization problems based on the first order Taylor expansion. And the final optimal solution can be obtained. The scheme makes the reliability analysis and optimization calculated simultaneously.Fourthly, the proposed RBDO solving approach based on Explicit Design Space Decomposition was employed in car optimization based on full frontal crash to verify the proposed theory system in this dissertation is useful and ideal.Finally, the conclusions deduced from this dissertation and prospects for future research will be suggested.