基于高斯过程模型的时空响应稳健参数设计  

Spatio-temporal response robust parameter design based on Gaussian process model

作　　者：翟翠红 汪建均[1] 马义中[1] 冯泽彪 杨世娟 ZHAI Cuihong;WANG Jianjun;MA Yizhong;FENG Zebiao;YANG Shijuan(School of Economics and Management,Nanjing University of Science and Technology,Nanjing 210094,China;School of Management,Nanjing University of Posts and Telecommunications,Nanjing 210003,China)

机构地区：[1]南京理工大学经济管理学院,南京210094 [2]南京邮电大学管理学院,南京210003

出　　处：《系统工程理论与实践》2023年第2期537-555,共19页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金面上项目(72171118,71771121,71931006);江苏省研究生科研与实践创新计划(KYCX21_0361)。

摘　　要：针对大规模时空数据的稳健参数设计问题,将快速不可分离高斯过程(fast nonseparable Gaussian process,FNSGP)模型与多元质量损失函数相结合,建立一个新的优化方案.首先,在考虑空间与时间相关性的条件下,使用FNSGP模型构建输入因子与质量特性之间的响应曲面,并采用前向滤波和后向平滑的快速、精确算法对模型进行估计和预测;其次,基于信噪比计算时空响应的联合损失权重,构造多元质量损失函数;然后,结合多元质量损失函数建立两阶段参数优化方案;最后,利用非线性优化算法寻找空间与时间因子的联合最优参数设计值.研究结果表明,本文所提方法可以有效地处理大规模时空数据的元建模与稳健参数设计问题,与可分离高斯过程、线性回归、随机森林等替代方法相比能够获得更为稳健的优化结果.A new spatio-temporal response optimization model,combined with multivariate quality loss function in the framework of fast nonseparable Gaussian process(FNSGP)modeling,is constructed for robust parameter design of large-scale spatio-temporal data.Firstly,considering the spatial and temporal correlation,the response surface between the input factors and quality characteristics is constructed by the FNSGP model.The fast and accurate algorithm of forward-filtering and backward-smoothing is used to estimate and predict the model.Secondly,the joint quality loss weights of the spatio-temporal responses are calculated based on the signalto-noise ratio to construct the multivariate quality loss function.Then,a two-stage parameter optimization scheme is established using the multivariate quality loss function.Finally,the nonlinear optimization algorithm is used to find the joint optimal parameter design values of spatial and temporal factors.The results show that the proposed method can effectively deal with the meta-modeling and robust parameter design problems of large-scale spatio-temporal data.Compared with alternative methods such as the separable Gaussian process,linear regression,and random forest,it can obtain more robust optimization results.

关 键 词：时空数据 不可分离高斯过程 卡尔曼滤波器 质量损失函数 稳健参数设计 

分 类 号：F273.2[经济管理—企业管理]