Research On Reliability-based Design Optimization Based On Response Surface Methods

With the continuously increasing demand for quality improvement of modern electromechanical products,the calculating resources consumed in the design process also increase as the structure of the products becomes more and more complex.At the same time,uncertain factors derived from many sources,including the lack of knowledge,the defects in design and manufacture,the evironmental intererence and other effects,are widely exist in the process of product design and manufacture.All kinds of uncertainties could affect the core performance indicators,and even could lead to failures and faults,which pose a great threat to the reliability and robustness of the product.In order to cope with the challenges,the uncertainty-based design has been developed rapidly.Rich research results have been achieved in the related uncertainty methods,including uncertainty quantification,uncertainty analysis,and applications based on response surface technology.To solve the problems of the current difficulties in the reliability-based design optimization(RBDO)process with high nonlinear and black box constraint function,this paper focuses on the response surface methods based RBDO process,which includes the following aspects:1)The study of RBDO method based on adaptive local search region sampling method.When the problem contains complex nonlinear and black box constraint functions,building the global accurate response surface model will cause a lot of expensive valuation,which will lead to huge consumption of computing resources.In order to solve this problem,the RBDO process is divided into two stages,including rough search stage and fine search stage.In the first stage,with the response surface is updated,a local range that contains the optimal solution of the RBDO problem is determined.In the second stage,the Kriging models are improved in the local range only,and then the RBDO optimal design point can be obtained.By quickly finding the local range that contains the optimal solution and update this local range adaptively,we can avoid the sampling and expensive estimation in other irrelevant regions.Thus,the calculation cost is saved and the efficiency of solving the RBDO problem is improved.2)The study of adaptive Kriging model based RBDO method.When the RBDO problem constains nonliear and black box constraint functions,complex constraints may lead to the optimization results fall into the local optimal.In order to save expensive valuations and avoid the local optimum,two new sampling criterions are constructed,and are added to the RBDO process.The first sampling criterion can update the response surfaces and guide the optimization to the global optimum.The second sampling criterion add new samples in the local range that has the most influence on the accuracy of the optimization result,Kriging models can be updated locally.So it can help to avoid sampling and expensive valuations in other unrelated areas,and improve the efficiency of solving the RBDO problem.3)The study of support vector matching method based double models RBDO method.In the RBDO process,a large number of estimations based on the response surfaces are required.The valuation process of Kriging model needs all the samples for buliding the response surface.The estimation time will increase when the dimension of the problem rises,which will affects the efficiency of the RBDO problem.Based on the accurate Kriging model,the SVM model can be built by using the adaptive support vector metching method,to save the valuation time and keep the precision.4)The study of mixed uncertainty oriented RBDO method.When the uncertainty exists both in the design variables and the parameters of the model,the assessment of the reliability will be very difficult.In this study,the Johnson distribution is used to construct a unified quantitative expression of mixed uncertainty to make an associative treatment.After that,a calculation method of reliability index for mixed uncertainty is proposed based on the stress-strength interference model.And the joint probability integral method is used to calculate the reliability of the design point under mixed uncertainty.By using the proposed methods,the RBDO process based on the Kriging model is built.Finally,the main achievements and innovations of this paper are summarized,and the studies and the development direction of the reliability-based design optimization based on response surface are discussed.In general,this paper aims to solve the shortcomings of the current response surface based RBDO process.This paper combines the Kriging model and the SVM model,generates adaptive sampling and modeling methods,efforts to improve the solving efficiency of the RBDO problem which contains complex nonlinear and black-box constraint functions;saves the estimation time of the response surface model;proposes new reliability index calculation method for mixed uncertainty when uncertainties exist in design variables and model parameters in the same time;and provides solutions to specific problems for building corresponding RBDO process.The researches in this paper has formed a series of tools and methods,which provide rich contents for improving the response surface based RBDO method.