Research On Multi-Response Optimization Of Functional Parameters Based On LS-SVR

In modern manufacturing and processing process,facing a class of multi-response simultaneous existence of parameter optimization problems.There are often conflicting relationships between multiple responses,it is difficult to reach the optimal state at the same time,and the overall relationship is more complex than the single-response process,showing multi-polarity nonlinearities and other characteristics.Such a problem is the key issue to be solved in practice.In particular,with the continuous progress of processing level,a class of process parameters with functional data characteristics,functional parameters have emerged.Unlike the traditional parameter types,the level values of functional parameters change continuously during the machining process,exerting a dynamic influence on the quality characteristics and posing new challenges to the optimization work.For the multi-response optimization of functional parameters,there is no applicable theoretical method guiding the current quality improvement.Therefore,a multi-response optimization method for functional parameters based on improved Least squares support vector regression(LS-SVR)is proposed as follows.First,before the experimental design and modeling optimization work begins,it is necessary to determine the way to reconstruct the functional parameters from scalar to function to realize the design features of functional parameters.Taking the flexibility of the basis function system in functional data analysis as a reference,the design method of using B-sample curves similar to the basis function expansion as functional parameters is proposed,and the curve definition points are used as the representatives of functional parameters,which are used as design variables together with scalar parameters.In this way,not only the data form can be unified with the scalar parameters,but also a random variety of curve forms can be obtained by a proper sampling of the coordinate values.Afterward the experimental design is carried out by Latin hypercube sampling,which has the characteristics of uniform stratification of sample points and is more efficient and representative than ordinary random sampling,and is suitable for complex action relationship problems.Secondly,for experimental design modeling,it is necessary to determine the appropriate approximate models for the action relations between functional parameters,scalar parameters,and multiple responses.The small-sample general learning theory LS-SVR is used as the overall action relationship modeling method,which can also achieve better modeling results in the face of complex action relationship processes.On this basis,LS-SVR based on Fréchet distance improved Gaussian kernel function is used to model the action relations between parameters and each response,and functional parameters are involved in model learning while retaining function characteristics.With a limited and small sample size of the experimental design,LSSVR better fits the complex action relationship between functional parameters,scalar parameters and multiple responses together.Finally,a set of Pareto solutions is obtained by the optimization search of the proposed model by the Non-dominated Sorting Genetic Algorithm Ⅱ(NSGA-Ⅱ),and the optimal parameter combinations are determined by a comprehensive evaluation of the Pareto solutions using the entropy-technique for order preference by similarity to an ideal solution(TOPSIS)method.The optimal multi-response values obtained by combining the optimal parameter combinations and predictions are used to provide guidance for the specific optimization work,so as to realize the multi-response parameter optimization of functional parameters.The study of injection molding simulation experiments and FDM empirical experiments shows that compared with existing multi-response parameter optimization methods,the proposed method has a better optimization effect and higher prediction accuracy when the sample size is small,and can better realize the optimization of multiple responses.