GM(1,N)模型的病态性研究及其在生态创新中的应用  

Research on the Illness of GM (1, N ) Model andIts Application in Ecological Innovation

作　　者：熊萍萍[1,2,3] 李田田 檀成伟 武彧睿 XIONG Pingping;LI Tiantian;TAN Chengwei;WU Yurui(Research Institute for Risk Governance and Emergency Decision-making,Nanjing University of Information Science and Technology,Nanjing 210044,China;Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters,Nanjing University of Information Science and Technology,Nanjing 210044,China;School of Management Science and Engineering,Nanjing University of Information Science and Technology,Nanjing 210044,China;School of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing 210044,China)

机构地区：[1]南京信息工程大学风险治理与应急决策研究院,江苏南京210044 [2]南京信息工程大学气象灾害预报预警与评估协同创新中心,江苏南京210044 [3]南京信息工程大学管理工程学院,江苏南京210044 [4]南京信息工程大学数学与统计学院,江苏南京210044

出　　处：《运筹与管理》2023年第4期134-139,共6页Operations Research and Management Science

基　　金：教育部人文社科规划基金项目(22YJA630098);江苏省社会科学基金一般项目(22GLB022);国家自然科学基金项目(71701105);国家社会科学基金重大项目(17ZDA092)。

摘　　要：本文以中国工业企业为研究对象,深入探究适用于多因素、少数据的生态创新相关指标特征的灰色模型预测技术。针对传统灰色预测模型在进行参数估计时可能存在的病态性问题展开研究,通过引入L2正则项的最小二乘法,利用粒子群算法求解最优值。将该模型应用于生态创新,与其他模型进行结果对比。结果表明,引入L2正则项的最小二乘法解决了模型的病态性问题,具有良好的预测性能,验证了该模型的有效性。The rapid economic growth model has led to the excessive consumption of resources,and a series of ecological problems are increasingly prominent.Ecological innovation not only solves the pressure caused by the bottleneck of resources and environment,but also promotes the sustainable development of national economy.However,the amount of data related to eco-innovation indicators that can be collected is limited.The structure of the corporate eco-innovation system is complex,with certain grey characteristics such as uncertainty and small samples.Therefore,this paper takes Chinese industrial enterprises as the research object,and explores the grey model forecasting technology applicable to the characteristics of ecological innovation-related indicators with multiple variables and few data.The possible pathology of traditional grey prediction in parameter estimation is studied.In the actual data,there may be more influencing factor sequences than the number of samples,or there may be a strong grey correlation between influencing factors.When using the ordinary least squares method,pathological features may occur when the covariance matrix is close to singular.Therefore,the model parameters are estimated based on L 2 regular terms,and the relative optimal value of the regular term coefficients is found by combining with particle swarm arithmetic,so as to solve the morbidity problem and improve the prediction accuracy of the grey model.In addition,one of the reasons for the poor prediction effect of the traditional GM(1,N)model is the non-homology of parameter application,so this paper directly obtains the time response and parameter estimation from the difference equation to solve the non-homology problem.The GM(1,N)model of the optimization algorithm is applied to the prediction of the number of patents of industrial enterprises in Jiangsu province and the north of China,and the results show that the number of patents of industrial enterprises in Jiangsu province and the north of China shows an increasing trend every

关 键 词：GM(1 N)模型 病态性 粒子群算法 生态创新 

分 类 号：N941.5[自然科学总论—系统科学]