Reliability Based Multidisciplinary Design Optimization And Its Application In Mechanism Design

With the development of science and technology, modern engineering systems are becoming more complex. There are many coupled disciplines in these engineering systems. Traditional optimization methods cannot solve the design problems of complex engineering systems effectively. Thus the Multidisciplinary Design Optimization(MDO) method is proposed to solve this problem. MDO can consider the consistency between the coupled disciplines and solve the problems from a global perspective. It will improve the comprehensive performance of system, shorten the development cycles and reduce the production costs.Uncertainties exist in practical engineering objectively and widely. Especially in the complex engineering systems, uncertainties will be accumulated because of the transportation of coupled information. It will have an impact on the overall performance of engineering systems ultimately and bring hidden dangers to the reliability, stability and security of engineering systems. To solve this problem, the Reliability based Multidisciplinary Design Optimization(RBMDO) has been one of the focuses in engineering design.So far, the RBMDO methods using the classical probability theory have obtained more developments to consider random uncertainties. Meanwhile, the utilization of Sequential Optimization and Reliability Assessment(SORA) can improve the computational efficiency, which decouples the RBMDO into series of the design optimization and the reliability analysis. Based on the SORA strategy, the researches of this thesis focus on three aspects:(1) the improvement and innovation of deterministic MDO methods in RBMDO,(2) the introduction and application of reliability analysis methods into RBMDO, and(3) the application of RBMDO to the structure design optimization problems. Specifically, we use the hierarchical control theory and methods of large systems to improve the deterministic MDO methods; use the Saddlepoint Approximation(SPA) method to improve the assessment accuracy of First Order Reliability Method(FORM); use the Subset Simulation Reliability Analysis(SSRA) to improve the assessment efficiency for the small probability failure events. The theoretical researches can expand and improve the existing RBMDO theoretical system. Finally, we study the mechanical design optimization problem of a flip driving mechanism. We analysis the coupled information and the uncertainties in the problem, and finish it’s RBMDO. We also compare the optimized solutions with the original solutions and give the reasons of improvements.The contributions of this dissertation are summarized as follows:(1) Interaction Prediction Optimization(IPO) and Interaction Balance Optimization(IBO). We combine the interaction prediction method and the interaction balance method which are the hierarchical control methods of large systems with the distributed parallel optimization strategy of Collaborative Optimization(CO), and propose two new MDO methods which can be utilized in RBMDO. The proposed methods abandon the compatibility constraints in CO and thus do not increase the nonlinearity degree in optimization problems. Compared with the CO method, the proposed methods enjoy simpler coordination strategies. It will be helpful to improve the computational efficiency and accuracy. We give examples to show the effectiveness of proposed methods.(2) First Order Saddlepoint Approximation based MDO(FOSPA-MDO). Within the framework of SORA, First Order Saddlepoint Approximation(FOSPA) can be used for the reliability analysis of the solutions of deterministic MDO. In FOSPA, the random variables do not need to be transformed into the standard normal random variables. It will be helpful to avoid the problem that the FORM or the Second Order Reliability Method(SORM) brings the nonlinearity to the optimization problems. After obtained the Most Likelihood Point(MLP), the shifted vectors are used to re-construct the deterministic optimization model. Compared with FORM, the proposed method enjoys higher computational accuracy. We give examples to show the effectiveness of proposed method.(3) Subset Simulation Reliability Analysis based MDO(SSRA-MDO). When assess the probability of small probability failure events, the Subset Simulation Reliability Analysis(SSRA) method can be used for the high computational efficiency. This method changes the original failure probability assessment problem into a series of conditional failure probability assessment problems. The Markov Chain Monte Carlo Simulation is also used to solve each conditional failure probability assessment problem. After obtained the Simulation Most Probable Point(SMPP), the shifted vectors are used to re-construct the deterministic optimization model. Compared with MCS based RBMDO, the proposed method enjoys higher computational efficiency. We give examples to show the effectiveness of proposed method.(4) The RBMDO of flip driving mechanism considering random uncertainties. According to the mechanical movement principle, we decompose the flip driving mechanism system into the power input discipline and the power transport discipline respectively. Based on the finite element analysis and dynamic analysis, we obtain the response samples and use them to construct the response surface. The RBMDO model is established after the analysis of uncertainty sources and the RBMDO is solved using SSRA-MDO method. The optimized solutions are compared with the original solutions to show the reasonableness in detail.