基于B-样条曲线与嵌套LS-SVR的函数型参数优化  

Optimization for functional parameters based on B-spline curve and nested LS-SVR

作　　者：崔庆安 张亦驰 CUI Qing'an;ZHANG Yichi(School of Economics&Management,Shanghai Maritime University,Shanghai 201306,China;School of Management Engineering,Zhengzhou University,Zhengzhou 450001,China)

机构地区：[1]上海海事大学经济管理学院,上海201306 [2]郑州大学管理工程学院,郑州450001

出　　处：《系统工程理论与实践》2021年第12期3378-3392,共15页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(71571168);国家自然科学基金河南省联合基金重点项目(U1904211);科技部创新方法工作专项(2019IM020200)。

摘　　要：函数型参数在制造过程中以"曲线"形式变化,其对质量特性的影响与传统的标量型参数显著不同.提出一种适用于函数型参数的实验设计建模及优化方法.首先分析函数型参数的定义域表现形式,通过基函数展开对其进行自身建模;其次,以最小二乘支持向量回归机(LS-SVR)为基本拟合模型,构造"内-外"双层嵌套结构:内层是函数型参数的B-样条曲线基函数展开模型,外层则是函数型参数,标量型参数与质量特性之间的全局性作用关系模型.通过对LS-SVR的Gaussian核函数的距离度量改进,将内层模型嵌套入外层模型;第三,利用超拉丁方设计获取样本集,建立具体的双层嵌套LS-SVR拟合模型,而后采用遗传算法寻优,再利用基函数模型得到函数型参数的优化曲线.对注塑加工以及3D打印制成品翘曲量优化的仿真与实证研究表明,与现有将函数型参数简化为标量型参数的响应曲面优化方法相比,样本量较小时,双层嵌套模型的预测精度更高,可以得到更优的质量特性值;所给出函数型参数优化曲线也较为平滑,有利于实际制造过程的参数优化值的稳定控制.Functional parameters vary in the form of curves during the course of manufacturing process,whose influence on the quality characteristic is quite different from that of the traditional scalar parameters.This paper proposes an experimental design,modeling and optimization approach for functional parameters.Firstly,after analysing the representation of their definitional domains,the functional parameters are modeling by the basis function expansion.Secondly,by using the least squares support regression(LSSVR) as basic fitting model,a two-layers nested model is given:The inner is the basis function expansion model of the functional parameters,and the outer is the global model between the functional parameters,scalar parameters and quality characteristics.Moreover,the inner model is nested in the LS-SVR model by modifying the distance measurement of Gaussian kernel function.Thirdly,the Latin hypercube sampling is applied to get the sample set of modeling,and an empirical LS-SVR model is fitted consequently.Then the optimal settings of the basis expansion model of functional parameters are achieved by the genetic algorithm,and therefore the optimal curves of functional parameter are obtained.The simulation and case studies of decreasing the part’s warping in injection molding and 3 D printing processes show that,comparing with the traditional response surface optimization in which the functional parameters have been simplified to the scalar ones,the nested model has a relative higher accuracy of prediction and can obtain a better quality characteristics.Moreover,the optimal curves of functional parameter are more smooth,which is beneficial to the stability control of optimal parameter settings during manufacturing in practice.

关 键 词：函数型参数优化 双层嵌套模型 实验设计 最小二乘支持向量回归 

分 类 号：O212.6[理学—概率论与数理统计]