Robust Parameter Design With Model Uncertainty

Quality design is an important supporting technology in the continuous quality improvement activities,which mainly is used in the design stage of products or processes,so it can reduce and control the variation of products or processes at the beginning.However,in a real manufacturing process,since some factors,such as instrument,measurement,will affect the accuracy of experimental data or significant effects cannot be obtained accurately,so model uncertainty is widely exist in practical engineering problems.Ensemble of surrogates and interval estimation are the main techniques for solving robust parameter design(including response surface modeling and construction of optimization strategy)in model uncertainty,which not only assure the preciseness of modeling,but also improve the efficiency of quality design.Therefore,implementing product/process quality design under the framework of ensemble of surrogates and interval estimation has the important theoretical and practical significance.In the paper,taking the quality design under the model uncertainty as the subject of the research,we systematically study the problems of response surface modeling and optimization strategy constructing in model uncertainty based on simulation experiment and empirical research,which synthetically use ensemble of surrogates,interval estimation,Bayesian statistics,stochastic search technique and heuristic optimization approach.The thesis includes the following main contents:(1)Robust modeling techniques based on BMA(Bayesian Model Averaging)model.As to the selection of sub-modes' prior information in BMA model,this thesis incorporates effect principle(Effect Hierarchy and Heredity Principle)to construct prior information under the framework of BMA model,and combines sample information to calculate Bayesian posterior probability which conforms to the principle of experiment design.Then,the effectiveness of the proposed methodology is verified through a practical industrial example combined with a simulation example.The results reveal that the proposed method not only assures the constructed model that will not violate the principle of experiment design,but also keeps a good predictive performance even if the system variation increases.(2)Response surface modeling based on encompassing test.As to the selection of sub-models in ensemble of surrogates,encompassing tests are used to eliminate the redundant information among surrogates and the number of surrogates contained in the ensemble of surrogates is reduced,then weighted average for all models is carried out to obtain a robust ensemble model.The effectiveness of the proposed methodology is verified through a practical industrial example combined with a simulation example.The results reveal that the proposed method not only improves model prediction and the robustness of model prediction,but also reduce the computing cost for constructing models.(3)Robust parameter design based on robust loss function.In robust parameter design of multiple responses,location effect and dispersion effect are both important when we determinate the optimal input setting.As to the existing loss function methods ignore the robustness of the optimal setting,we simultaneously consider location effect and dispersion effect of squared error loss and then construct a robust loss function optimization strategy.Meanwhile,based on the research mentioned above,we further consider the effect of model uncertainty on the determination of optimal input setting based on the confidence interval of model prediction.Finally,effectiveness of the proposed methodology is verified by a real example.(4)Robust parameter design based on region analysis method.As to the construction of optimization strategy in model uncertainty.This thesis simultaneously considers the worst strategy and the best strategy to construct a robust loss function,which is based on the idea of model prediction region and robust optimization.Since the new loss function is a nested optimization problem,genetic algorithm and pattern search are combined to optimize the objective function and obtain the optimal input setting.Based on the analysis of a real example,the proposed loss function not only reduces the effect of model uncertainty on the determination of optimal input setting,but also further extends the content of quality loss function.(5)Robust parameter design considering the variation in input parameters.As to the robust parameter design of the parameter uncertainty in models and noise variables,this thesis simultaneously considers the worst and the best strategies to construct the location and dispersion effects of loss function from the perspective the interval estimation.Then,the optimal weights of the location and dispersion effects are calculated based on a data-driven approach and then the robust loss function is constructed.Finally,genetic algorithm and pattern search are combined to optimize the objective function.The comparison of the proposed optimization strategy and others strategy is made based on a real example and simulation experiments.The proposed loss function not only incorporates model parameter uncertainty into the optimization of objective function,but also considers the estimation uncertainty in the parameters of noise variables,which improve rapidly the efficiency of robust parameter design.Finally,the thesis also discusses some challenging topics which deserve further research in the future based on the above research results.