Research On Reliability-based Design Optimization Using Approximate Model

Reliability based design optimization(RBDO)is an optimization design approach which considers the influence of parameter uncertainties or model uncertainties.The probabilistic constraints are used to ensure the reliability of the design product during the optimization procedure.Existing RBDO methods mainly include directly simulation method,double-loop method,single-loop method,and decoupled method,etc.The sequential optimization and reliability assessment(SORA)method is a decoupled method,which converts the original RBDO problem into a sequential optimization of the deterministic optimization and the reliability analysis,based on which a high computational efficiency is achieved.The idea of SORA has become a general solution framework for most RBDO algorithms.In this paper,a RBDO method is proposed base on the SORA and surrogate models,based on which a higher computational efficiency is obtained.The proposed method is further app lied in the multidisciplinary optimization(MDO)problems.The thesis contains three main parts:1.In engineering designs,RBDO problem is used to obtain an optimal design that satisfies the reliable requirements.The solution of a RBDO problem generally behaves as a two-layer nested optimization,where a deterministic optimization of the design variables is performed in the outer loop and a reliability analysis of the performance function is performed in the inner loop.The nested optimization problem general results in expensive computational cost.Furthermore,the performance function is often very complicated and needs to be calculated using time-consuming simulation methods such as finite element method(FEM),which further increases the computational cost.Aiming at the issue,a tipical solution is to establish surrogate models based on the first order reliable method(FORM)using HL-RF algorithm.Here,the RBF function is used to construct the approximate model.The truncated singular value decomposition(TSVD)method is adopted to avoid the ill-posed problem of radial basic matrix(Hassian matrix),based on which the accuracy of the constructed metamodel is guaranteed.The efficients of the RBF function are calculated using the genetic algorithm(GA)and the samples to consctruct the RBF function are generated by Latin Hypercube method.The results of numerical examples have demonstrated that the number of performance function analyses can be dramatically reduced using the proposed method.2.To improve the computational efficiency of RBDO problems,an approach based on surrogate models is developed.It reduces the number of calls of time-consuming numerical models,based on which a high computational efficiency is achieved.Besides,the computational efficiency of the proposed method is further enhanced by transforming the nested RBDO problem into a sequential optimization problem.The metamodels are constructed by combining the RBF function,Latin Hypercube simulation,TSVD method and genetic algorit hm.A deterministic optimization procedure is performed after the construction of the RBF approximate models which are then used to substitute the natural probability constraints in RBDO problem.Severa numerical examples have demonstrated that the proposed method can significantly reduce the number of performance function evaluations.3.An efficient reliability-based multidisciplinaty design optimization approach is developed in this thesis.First,the RBMDO problem is transformed into a regular RBDO problem by the single-discipline feasible(IDF)method.In the IDF method,the coupling variables are optimized to search for the feasible and optimal solutions among multidisciplines,while the auxiliary variables are solved to s atisfy the individual discipline state equations.Second,the RBDO problem is later converted to a sequential optimization problem composed of the deterministic optimization and the reliability analysis.Furthermore,the explicite RBF approximate model is established to substitute the actual limit-state function.Several numerical examples have been used to demonstrate the effectiveness of the proposed method.