基于异方差高斯间距回归的产品设计时间预测模型  

Forecast model for product design time based on heteroscedastic Gaussian margin regression

作　　者：商志根[1,2] 严洪森[1,3] 

机构地区：[1]东南大学自动化学院,江苏南京210096 [2]盐城工学院自动化系,江苏盐城224003 [3]东南大学复杂工程系统测量与控制教育部重点实验室,江苏南京210096

出　　处：《系统工程学报》2013年第4期437-445,共9页Journal of Systems Engineering

基　　金：国家自然科学基金资助项目(50875046;60934008)

摘　　要：为了使产品设计时间预测模型既克服小样本和异方差噪音问题,又提供除预测值以外的其它有用信息,建立一种基于异方差高斯间距回归(heteroscedastic Gaussian margin regression,HGMR)的预测模型.首先,假定基于核函数的回归模型的权重向量服从高斯分布,以最小化相对熵为优化目标,利用预测值的置信区间设置约束条件,构造可同时给出预测值和预测区间的HGMR模型;然后,利用样本的独立性和异方差性对优化问题进行转化,证明HGMR模型具有较好的推广性能,并设计求解相应优化问题的迭代方法;最后,以注塑模具设计的实例进行分析,结果表明基于HGMR的时间预测模型是可行有效的.A forecast model based on heteroscedastic Gaussian margin regression is proposed to overcome the problems of small samples and heteroscedastic noise in design time forecast and to provide useful information in addition to the forecast value.Firstly,under the assumption that the weight vector of kernel based regression model is subject to Gaussian distribution,minimizing relative entropy minimization is used as the optimization objective,the constraints are formulated based on the confidence intervals of the forecast values,and HGMR model is presented,which can simultaneously provide the forecast value and the forecast interval.Then,the optimization problem is transformed by considering the independence and heteroscedasticity of the samples,and good generalization performance of HGMR model is proved.An iteration procedure is developed to solve the corresponding optimization problem.Finally,the application in injection mold designs is analyzed,and the results demonstrate that the time forecast model based on HGMR is both of feasibility and validity.

关 键 词：设计时间预测 核函数 相对熵 异方差 

分 类 号：TP391[自动化与计算机技术—计算机应用技术] TH12[自动化与计算机技术—计算机科学与技术]