基于变量选择的尖点突变模型的两步构建方法  

A two-step method for cusp catastrophe model construction based on the selection of important variables

作　　者：张明 付冬梅 程学群[4,5] 杨丙坤[6] 郝文魁 陈云[6] 邵立珍 ZHANG Ming;FU Dong-mei;CHENG Xue-qun;YANG Bing-kun;HAO Wen-kui;CHEN Yun;SHAO Li-zhen(Shunde Graduate School,University of Science and Technology Beijing,Foshan 528399,China;School of Automation and Electrical Engineering,University of Science and Technology Beijing,Beijing 100083,China;Beijing Engineering Research Center of Industrial Spectrum Imaging,University of Science and Technology Beijing,Beijing 100083,China;Institution for Advanced Materials and Technology,University of Science and Technology Beijing,Beijing 100083,China;National Materials Corrosion and Protection Scientific Data Center,University of Science and Technology Beijing,Beijing 100083,China;State Key Laboratory of Advanced Transmission Technology,Global Energy Interconnection Research Institute Limited Company,Beijing 102209,China)

机构地区：[1]北京科技大学顺德研究生院,佛山528300 [2]北京科技大学自动化学院,北京100083 [3]北京科技大学北京市工业波谱成像工程技术研究中心,北京100083 [4]北京科技大学新材料技术研究院,北京100083 [5]北京科技大学国家材料腐蚀与防护科学数据中心,北京100083 [6]全球能源互联网研究院有限公司先进输电技术国家重点实验室,北京102209

出　　处：《工程科学学报》2023年第1期128-136,共9页Chinese Journal of Engineering

基　　金：科技部科技基础资源调查专项资助项目(2019FY101404);国家电网公司总部科技资助项目(5200-202058470A-0-0-00);北京科技大学顺德研究生院科技创新基金资助项目(BK20AE004)。

摘　　要：突变是工程实践过程中广泛存在的现象.当系统的状态发生跳跃性变化时,基于微积分的传统数学建模方法精度较低,人工神经网络等机器学习算法无法对突变现象作出合理的解释.基于突变理论的尖点突变模型可以用来解释系统状态的不连续变化,然而在输入变量维度较大的情况下,传统的尖点突变模型复杂度高且精度较差.为了解决这一问题,提出了一种基于变量选择的尖点突变模型的两步构建方法.第一步,利用多模型集成重要变量选择算法(MEIVS)量化待选变量的重要性并提取重要变量;第二步,基于极大似然法(MLE)利用所提取的重要变量构建尖点突变模型.仿真结果表明,在具有突变特征的数据集上,通过MEIVS降维后的尖点突变模型在评价指标上优于线性模型、Logistic模型和通过其他方法降维的尖点突变模型,并且可以用来解释研究对象的不连续变化.Sudden transition is a widely existing phenomenon in engineering practice.When the state of the system experiences sudden abrupt transition,calculus-based traditional mathematical modeling methods has low accuracy.Although theoretically,machine learning algorithms,such as artificial neural networks,can approximate any nonlinear function,this type of black-box method makes no reasonable explanation for the sudden transition phenomenon.The cusp catastrophe model based on the catastrophe theory can be applied to explain the discontinuous changes in the system’s state.However,the construction of traditional cusp catastrophe models is often based on large amounts of prior knowledge to select the input variables for modeling.On the condition that there is a lack of prior knowledge and comparatively large dimensions of input variables,the model has high complexity and poor accuracy.In this paper we have put forward a two-step method for constructing a cusp catastrophe model based on the selection of variables to solve the abovementioned problems.The first step was to apply multimodel ensemble important variable selection(MEIVS)to quantify the importance of the variables to be selected and extract important variables.The second step was to use the extracted important variables to construct a cusp catastrophe model based on the framework of maximum likelihood estimation(MLE).Results indicate that on a dataset with characteristics of catastrophe,the cusp catastrophe model is simple in form using the MEIVS dimensionality reduction algorithm and outperforms the unreduced cusp catastrophe model and reduced cusp catastrophe model using other dimensionality reduction algorithms in terms of evaluation indicators.This shows that the algorithm proposed in this paper have improved the accuracy and reduced the complexity of the cusp catastrophe model.At the same time,the cusp catastrophe model exhibits higher accuracy compared with the linear and logistic models.Thus,it can be used to explain the discontinuous changes of the resea

关 键 词：突变理论 突变特征 尖点突变模型 变量选择 模型集成 

分 类 号：O192[理学—数学] TP181[理学—基础数学]