Research On Time-dependent Reliability-based Design Optimization Based On Surrogate Model Methods

The complex structural mechanism are developing in the trend of diversification,complexity,and precision,the reliability problem has become increasingly.It is an important issue to improve the quality and reliability of complex structural mechanism in the process of manufacturing and using modern industrial products.The collected data and information usually contain time-dependent uncertainties,but it is large errors to deal with them by traditional methods because of the limitation in standardization and quantification of uncertainties.It results in the design scheme difficult to meet the engineering practice requirements for the complex structure.Surrogate model methods(eg.SVR,Kriging,RBF,PCE,GP)have the advantages of low computing cost,short design cycle,and high optimization efficiency,which is one of the best methods to solve the time-dependent reliability-based optimization design(t-RBDO)of complex structural mechanism.This article is devoted to research 'How to design the scheme to meet the reliability requirements under time-dependent uncertainties'.The realization of the goal is to reflect the responses,input variables,constraints,and model in the t-RBDO of complex structural mechanism.It also establishes the t-RBDO method and theoretical considering the effect of the time factor.The main research contents and achievements are as follows:(1)The t-RBDO method based on the SVR and covariance matrix adaptation evolution strategy(CMA-ES)was proposed to solve the difficulty in reliability design optimization while considered that responses increase monotonously with time.Firstly,the experimental design method determines the samples in the design space.Then,the SVR model is constructed by training samples,and the test samples calculate the accuracy which can be improved by increasing the training samples.Finally,the CMA-ES solves the t-RBDO model.The results show that the proposed method can support the time-dependent reliability design optimization that response monotonously with time,and the design scheme significantly improves the reliability of structural products.(2)The t-RBDO method based on the improved nested extreme response surface(NERS)was proposed to solve the difficulty in reliability design optimization while considered that responses increase non-monotonously with time.In the improved NERS method,a parallel computer mechanism is studied to constructed the extreme Kriging model,which is used to improve the efficiency of the construction limit state function.The genetic algorithms solved the t-RBDO model.The results show that the improved NERS method has a significant improvement in reliability.(3)The t-RBDO method based on the improved mixed efficient global optimization(EGO)was proposed to solve the difficulty in reliability design optimization while considered that interactive effects existing in variables.First,a parallel EGO method identified extreme samples in the proposed improved EGO method.Then,the extreme Kriging model was established to predict the extreme response.Next,the extreme Kriging model is updated by the active learning Kriging combined with the Monte Carlo simulation.Finally,The genetic algorithm solves the t-RBDO model.The proposed method can improve the reliability of the mechanical structural products while considering the interactive effects existing in the variables.(4)The t-RBDO method is based on the RBF and Subset Simulation was developed to solve the difficulty in the improvement of the time-dependent reliability.This method studied an active learning RBF model which includes identification of extreme samples,construction of active learning function,determination of convergence criteria,and updating RBF model.The Subset Simulation method analyses the small failure probability and it also solves the t-RBDO model.The results show that the proposed method can further improve the time-dependent reliability under the small failure probability.(5)The t-RBDO method was proposed to solve the low credibility of the t-RBDO design strategy based on a novel ensemble of surrogates.The weighted combination of the single surrogate model is determined by the ensemble of the surrogates method.The learning function and convergence criterion are constructed.An active learning strategy updates the ensemble of surrogates to improve prediction accuracy.In the construction stage of the objective function,the robustness index(mean and standard deviation)is considered.The double loop optimization strategy solves the t-RBDO model.The numerical examples show that the proposed method can enhance the credibility of the t-RBDO design strategy and reduce the computational cost under model uncertainty.The results were summarized.This paper points out the shortcomings and the problems worthy of further study.