Sequential Design And Modeling Methods Based On The LS-SVR

The optimization of input parameters is difficult and expensive for the complicated process featured with more than one local extremum and uneven quality characteristics.Choosing appropriate sequential design and modeling method is a critical issue for the optimization of input parameters.The existing researches mostly focus on some certain region while rarely consider the significant difference between the sample points within the region.In this thesis,we concentrate on the significance of sample points and propose respectively the corresponding sequential design and modeling methods for different types of variables.The main contents are as follows:?1?The significance test method of sample points is proposed.Firstly,LS-SVR is selected as the modeling method in this thesis,Secondly,the statistical distribution of support vectors is given,and statistical magnitude of the significance test is constructed,the P-value that representing the significance of sample points is obtained through hypothesis test,Finally,the significance test method of sample points is constructed.?2?The nested orthogonal design and nested LHS design methods are proposed respectively for quantitative variables and mixed variables.For the different variables,Firstly,this thesis makes respectively the orthogonal design and LHS design as the initial design of experiment to obtain the original sample set,then the initial LS-SVR model is established.Secondly,the P-value is acquired by the significance test of sample points,then adding the new experimental points by nesting into new orthogonal design or LHS design around the close-by region of the non-edge sample points whose P-value is less than the P₀.Finally,the nested orthogonal design and nested LHS design method are constructed.In addition,this thesis sets a relevant statistical magnitude which could assure the rationality of the established LS-SVR model and avoid the generation of"overfitting"phenomenon.?3?Two kinds of sequential design methods are studied respectively by the way of simulation and empirical.On the one hand,nested orthogonal design and nested LHS design methods are carried out respectively by introducing three simulation functions that represent complex processes.On the other hand,the traditional“path-oriented”sequential design and nested orthogonal design methods are conducted respectively by introducing the Paper helicopter experiment.Researches show that,Comparing with one-shot LHS design,the prediction mean square error and the maximum prediction deviation of nested orthogonal design and nested LHS design methods reduced respectively by more than 4.2%,6.6%and 29.2%,15.1%.Comparing with the traditional“path-oriented”sequential design,the nested orthogonal design method has significant advantages in the ability and efficiency of finding the extremum points.