The Research Of Ridge Path Construction For Multiple Response Surfaces

This thesis mainly studies the construction of ridge path for multiple response surfaces.The loss function-based ridge analysis method for multiple response problems and multiple response mixture experiments is proposed.By considering the correlations between responses,the proposed method can achieve the optimization of multi-responses and determine the optimal experimental level.The thesis introduces some basic theories and research development of ridge analysis and mixture experiment.Through the analysis and contrast of multi-response optimization methods and intelligent optimization algorithm,both of the above methods used in this thesis are determined.Traditional ridge analysis mainly deals with single response problem,only one method for multi-response ridge analysis exists,but it did not consider the correlations between responses and there is not any research about ridge analysis for multi-response mixture experiment.By improving the existing shortcomings,the loss function-based ridge analysis method for multiple response problems and multiple response mixture experiments is proposed in this thesis.The improved method seriously considers the correlations between responses,firstly applies ridge analysis to multi-response mixture experiment and proposes the steps and algorithm basis of ridge analysis.Firstly,deal with the experimental data and fit the models for responses.Secondly,select loss function method for multi-response optimization and calculate the variance covariance matrix.Finally,construct the ridge path model,solve nonlinear constrained optimization problem by genetic algorithm and plot the ridge path curve & optimal input variables curves.The selection of polynomial model and the transformation of pseudocomponent need to be considered when conducting ridge analysis for mixture experiment.Case study shows that when there exists correlation among responses,the proposed method is more effective.