基于特征子空间回归的软传感器精简化建模
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摘要
目前使用的软传感器模型辅助变量较多,各变量之间往往存在多重相关性,致使模型的预测精度不高,泛化性能和稳定性较差。针对此问题,本文在系统探讨各种特征提取方法的基础上,利用特征子空间思想去除这种相关性,形成基于特征子空间回归的软传感器精简化建模方法,主要包括PCA+NN,PCA+SVR,KPCA+NN,KPCA+SVR,KPLS(KCCA+LS)。同时,该类方法可解决先验知识很少的对象的建模问题。
该方法首先针对辅助变量间的线性/非线性相关问题,分别利用各种特征提取方法去除冗余信息,提高样本数据的质量。主要包括线性主成分分析PCA(Principal Component Analysis)、核主成分分析KPCA(Kernel PCA)、核典型相关分析KCCA(Kernel Canonical Correlation Analysis)方法。然后,在信息充分且不相关的样本数据的基础上,可利用信息融合方法对软传感器对象进行建模和预测。主要包括基于结构风险最小化的支持向量回归机SVR(Support Vector Regression)和基于经验风险最小化的神经网络NN(Neural Network)、最小二乘LS(Least Squares)方法。最后,用AIC信息准则(Akaike Information Criterion)为评价函数,综合评价出具有较高模型精度、较好泛化能力和较低复杂度的最佳模型。
为了验证该类方法的可行性及有效性,分别针对线性动态软传感器模型、非线性静态软传感器模型、非线性动态软传感器模型,进行了仿真对比研究。结果表明:①针对相关的样本数据,采用特征提取结合信息融合的建模方法比单独使用信息融合更为有效;②PCA+SVR在解决线性软传感器建模时精度和泛化能力较佳;③KPCA+SVR在解决非线性静态/动态软传感器建模时具有较佳的精度和泛化能力。
最后,本文针对一种新型的睡眠躁动软传感器,利用上述五种精简化建模方法进行了实例对比研究。结果表明:在综合考虑软传感器模型复杂度、精度和泛化能力的情况下,利用AIC准则评价的PCA+NN方法在解决该问题时具有最佳的效果。
Nowadays, there are many correlated secondary variables of soft sensor for complex objects, which make poor performance, low generalization and bad stability. Aiming at the problem, after the discussion of some feature extraction and regression methodology several parsimoniously modeling methodology are presented based on Feature Subspace Regression, such as PCA+NN, PCA+SVR, KPCA+NN, KPCA+SVR, KPLS (KCCA+LS), etc. Meanwhile, the methodology can solve the modeling problem of soft sensor with seldom prior knowledge.
It firstly uses feature extraction method, as PCA (Principal Component Analysis) CCA (Canonical Correlation Analysis) or KPCA (Kernel PCA) or KCCA (Kernel CCA) to extract the input matrix of second variable, obtaining the linear/nonlinear uncorrelated sample data. On the basis, the SVR (Support Vector Regression) with SRM (Structure Risk Minimization) or NN (Neural Network) or LS (Least Squares) with ERM (Empirical Risk Minimization) are utilized to realize the structure identification of information fusion part. In this way, performance, stability and generalization of soft sensor are improved.
Furthermore, the accuracy and the complexity of the modeled plant are estimated by AIC (Akaike Information Criterion). The smaller AIC value is, the better modeling structure is. In order to verify the effectivity, three types of soft sensor with linear dynamic plant, nonlinear static plant and nonlinear dynamic plant are studied with different parsimonious methods. Simulation results show that KPLS is good for its high accuracy, PCA+SVR method is most effective when solving soft sensor modeling with linear plant, and to nonlinear plant soft sensing problem, KPCA+SVR method is more excellent.
On the basis, a new type of sleeping fidget soft sensor is presented and also studied as the modeling problem. Compared with some parsimonious modeling methods, PCA+NN is evaluated best with AIC criterion of high accuracy, good generalization and low complexity to this problem.
该方法首先针对辅助变量间的线性/非线性相关问题,分别利用各种特征提取方法去除冗余信息,提高样本数据的质量。主要包括线性主成分分析PCA(Principal Component Analysis)、核主成分分析KPCA(Kernel PCA)、核典型相关分析KCCA(Kernel Canonical Correlation Analysis)方法。然后,在信息充分且不相关的样本数据的基础上,可利用信息融合方法对软传感器对象进行建模和预测。主要包括基于结构风险最小化的支持向量回归机SVR(Support Vector Regression)和基于经验风险最小化的神经网络NN(Neural Network)、最小二乘LS(Least Squares)方法。最后,用AIC信息准则(Akaike Information Criterion)为评价函数,综合评价出具有较高模型精度、较好泛化能力和较低复杂度的最佳模型。
为了验证该类方法的可行性及有效性,分别针对线性动态软传感器模型、非线性静态软传感器模型、非线性动态软传感器模型,进行了仿真对比研究。结果表明:①针对相关的样本数据,采用特征提取结合信息融合的建模方法比单独使用信息融合更为有效;②PCA+SVR在解决线性软传感器建模时精度和泛化能力较佳;③KPCA+SVR在解决非线性静态/动态软传感器建模时具有较佳的精度和泛化能力。
最后,本文针对一种新型的睡眠躁动软传感器,利用上述五种精简化建模方法进行了实例对比研究。结果表明:在综合考虑软传感器模型复杂度、精度和泛化能力的情况下,利用AIC准则评价的PCA+NN方法在解决该问题时具有最佳的效果。
Nowadays, there are many correlated secondary variables of soft sensor for complex objects, which make poor performance, low generalization and bad stability. Aiming at the problem, after the discussion of some feature extraction and regression methodology several parsimoniously modeling methodology are presented based on Feature Subspace Regression, such as PCA+NN, PCA+SVR, KPCA+NN, KPCA+SVR, KPLS (KCCA+LS), etc. Meanwhile, the methodology can solve the modeling problem of soft sensor with seldom prior knowledge.
It firstly uses feature extraction method, as PCA (Principal Component Analysis) CCA (Canonical Correlation Analysis) or KPCA (Kernel PCA) or KCCA (Kernel CCA) to extract the input matrix of second variable, obtaining the linear/nonlinear uncorrelated sample data. On the basis, the SVR (Support Vector Regression) with SRM (Structure Risk Minimization) or NN (Neural Network) or LS (Least Squares) with ERM (Empirical Risk Minimization) are utilized to realize the structure identification of information fusion part. In this way, performance, stability and generalization of soft sensor are improved.
Furthermore, the accuracy and the complexity of the modeled plant are estimated by AIC (Akaike Information Criterion). The smaller AIC value is, the better modeling structure is. In order to verify the effectivity, three types of soft sensor with linear dynamic plant, nonlinear static plant and nonlinear dynamic plant are studied with different parsimonious methods. Simulation results show that KPLS is good for its high accuracy, PCA+SVR method is most effective when solving soft sensor modeling with linear plant, and to nonlinear plant soft sensing problem, KPCA+SVR method is more excellent.
On the basis, a new type of sleeping fidget soft sensor is presented and also studied as the modeling problem. Compared with some parsimonious modeling methods, PCA+NN is evaluated best with AIC criterion of high accuracy, good generalization and low complexity to this problem.
引文
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[4] Brosilow C. B. and Martin T. The structure and dynamics of inferential control system. AICHE J, 1978, 13(3):492-500
[5] Zadeh L A. Berkeley Initiative in Softcomputing. IEEE, 1994,41(3):8-10
[6] Lofti A. Zadeh. Fuzzy logic, neural networks and soft computing. One-page course announcement of CS 294-4, Spring 1993, the University of California at Berkeley: November 1992
[7] McAvoy T. J. Contemplative stance for chemical process control: an IFAC report. automatica, 1992, 28 (2):441-442
[8] 蔡自兴. 智能控制. 北京:电子工业出版社,2004. 8
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[11] 邓乃扬,田英杰. 数据挖掘中的新方法—支持向量机. 北京:科学出版社,2004
[12] K. Person. On lines and planes of closest fit to systems of points in spance, Philosophical Magazine, 1901, 2:559-572
[13] 林海明. 因子分析的精确模型及其解. 统计与决策,2006,(14):4-5
[14] Aapo Hyvarinen , Juha Karhunen, Erkki Oja. 独立成分分析. 北京:电子工业出版社, 2007
[15] John Shawe-Taylor, Nello Cristianini. Kernel methods for pattern analysis. Beijing:China Machine Press, 2006
[16] N.Cristianini, J.Shawe-Taylor, and J.Kandola. Spectral kernel methods for clustering. In T.G. Dietterich, S.Becker, and Z. Ghahramani, editors, Advances in Neural Information Processing Systems 14. MIT Press,649-655,2002
[17] R.Herbrich. Learning Kernel Classifiers: Theory and Algorithms. MIT Press, 2001
[18] 阎平凡,张长水. 人工神经网络与模拟进化计算. 北京:清华大学出版社,2005
[19] 吴今培. 基于核函数的主成分分析及应用. 系统工程,2005,23(2):117-120
[20] 夏国恩. 基于核主成分分析特征提取的客户流失预测. 计算机应用,2008,(1):149-151
[21] 冯燕,何明,宋江红,魏江. 基于独立成分分析的高光谱图像数据降维及压缩. 电子与信息学报. 2007,29(12):2871-2875
[22] 张玉川,张作泉. 支持向量机在股票价格预测中的应用. 北京交通大学学报,2007,31(6):73-76
[23] Bailing Zhang. Off-Line signature recognition and verification by kernel principal component self-Regression. Proceedings of the 5th International Conference on Machine Learning and Applications,2006:28-33
[24] 杨辉华,王行愚,王勇,何倩. 基于 KPLS 的网络入侵特征抽取及检测方法. 控制与决策,2005,20(3):251-256
[25] 方崇智,萧德云. 过程辨识. 北京:清华大学出版社,1988
[26] 胡寿松. 自动控制原理. 北京:科学出版社,2007
[27] 冯培悌. 系统辨识. 杭州:浙江大学出版社,1999
[28] Vladimir N. Vapnik. 统计学习理论的本质. 北京:清华大学出版社,2000
[29] 克里斯特安尼等著,李国正,王猛,曾华军译. 支持向量机导论. 北京:电子工业出版社,2004
[30] 李德萍,黄明政. 用主成分回归方法制作青岛市 8 月降水预报. 山东气象,2001,21(1):11-12
[31] 韩汉鹏. 偏最小二乘法在回归设计多因变量建模中的应用及其优化. 数理统计与管理,2007,26(2):303-307
[32] 刘遵雄,况志军,刘觉夫. 核主成分回归方法在电力负荷中期预测中的应用. 计算机工程,2006,32(1):31-33
[33] 杨辉华,王行愚,王勇,何倩. 基于 KPLS 的网络入侵特征抽取及检测方法. 控制与决策,2005,20(3):251-256
[34] 焦卫东,杨世锡,吴昭同. 复合 ICA—SVM 机械状态模式分类. 中国机械工程,2004,15(1):62-65
[35] 郭辉,刘贺平. 基于核的偏最小二乘特征提取的最小二乘支持向量机回归方法. 信息与控制,2005,34(4):403-406
[36] 王华忠,俞金寿. 基于核函数主元分析的软测量建模方法及应用. 华东理工大学学报,2004,30(5):567-570
[37] 王惠文. 偏最小二乘回归的线性与非线性方法. 北京:国防工业出版社,2006
[38] 王华忠. 核函数方法及其在过程建模与故障诊断中的应用研究:[博士学位论文]. 上海:华东理工大学,2004
[39] Muller K-R, Mika S and Ratsch G., et al. An introduction to kernel-based learning algorithms. IEEE transactions on neural networks, 2001, 12(2):181-202
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