Research On Reliability-Based Design Optimization Based On Response Band Methods

In practical engineering,objectively existing uncertainty may lead to the unexpected failure of the design which is based on the traditional deterministic design optimization.This problem is partially solved by the development of Reliability-Based Design Optimization(RBDO)theory.However,the capability of the traditional RBDO method to analyze and process the reliability design optimization of the static design optimization problem is insufficient in the non-linear situation.In addition,the research of the RBDO is gradually extended from the traditional static design optimization problem to the dynamic response design optimization problem and the dynamic-static hybrid design optimization problem,forming the so-called dynamic reliability design optimization method.However,the relevant methods treat the dynamic factors in the problem in a single way and the algorithm suffers from nested coupling,and the method still needs further improvement.To address the above problems,the concept of "response band" is introduced and extended in this dissertation to the static design optimization problem,dynamic response design optimization problem and dynamic-static hybrid design optimization problem in the field of reliability,and systematically carries out the research of response band-based reliability design optimization method using the surrogate modeling technique.The effectiveness of the optimization method is verified by comparing data from case tests and the cited literature.The main research content of this dissertation are as follows:(1)In the reliability analysis of the static design optimization problem,the design solution may correspond to multiple failure modes at the limit state boundary of the nonlinear constraint function.The limited capability of existing methods to identify multiple failure modes makes the reliability analysis in this case slowly or inaccurately.To address this problem,a reliability analysis method based on constraint response band is proposed.By designing a radial sampling strategy to simultaneously identify and extract subspaces for potential multiple failure failure modes,wchich are employed to improve the accuracy of the constraint response band.At the same time,a Dendritic Neural Network is introduced and a characteristic matching filling criterion is designed for the network algorithm which is used to construct the constraint response band and subspace extraction model.(2)In the reliability design optimization of the static design optimization problem,the iteration process based on the most probable point is affected by the nonlinear constraint function,which leads to difficulties in the convergence.To address this problem,a reliability design optimization method based on the reliability index response band is proposed.By generating paired samples with specific relationships to construct the reliability index response band,the target reliability index response surface is obtained indirectly,and the original problem is converted into a deterministic problem.(3)In the reliability design optimization of dynamic response design optimization problems,the time-dependent reliability constraint function is not only expensive to evaluate,but the coupling of its time-dependent and reliability factors can also lead to multiple nesting of algorithms.In addition,there is a lack of a general method if the reliability of the time-dependent constraint and the robust of the time-dependent objective are considered simultaneously.To address the above problems,a time-dependent reliability design optimization method based on response bands is proposed in this dissertation.By constructing a time-dependent response band based on dynamic modal decomposition and introducing a reliability index response band,the original problem is gradually equivalently static and equivalently deterministic.At the mean time,the time-consuming problem of multiobjective evaluation in the robust optimization is addressed by constructing the objective response band.(4)In the reliability design optimization of the dynamic-static hybrid design optimization problem,the reliability assessment of the state trajectory needs to consume huge computational resources.To address this problem,a dynamic-static hybrid reliability design optimization method based on state trajectory response band is proposed in this dissertation.By constructing the state trajectory response band with accompanying samples and solving the cross rate,the transfer vector for reliability improvement of the hybrid design solution is obtained,and the sequential optimization of hybrid design optimization and reliability design optimization is implemented.