一种基于特征子空间的改进动态核主元分析方法
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摘要
针对传统的动态核主成分分析(dynamic kernel principal component analysis,DKPCA)用于大样本数据集的故障检测时,占用计算机内存大、计算复杂度高等不足,提出一种基于特征子空间的DKPCA算法(EFS-DKPCA)。该方法通过构建具有较小维数特征子空间上的正交基来简化核矩阵K,从而降低DKPCA的计算复杂性。与DKPCA方法相比,该方法具有更高的计算效率,且只需较小的计算机存储空间。将该方法应用于TE(tennessee eastman)过程,仿真结果显示,两者诊断结果大致相同,而所需时间大大减小,说明了本算法的有效性。
For large sample data sets,traditional DKPCA occupancy a lot of computer memory and large computation,in order to solve these problems,this paper proposed an improved DKPCA based on effective feature subspace( EFS-DKPCA). The new method based on a orthonormal basis of the sub-space spanned by the training samples mapped onto the smaller feature space to simplify K,thereby reducing DKPCA computational complexity. When applied to process monitoring,the EFS-DKPCA-based method was more efficient in computation and needed less computer memory than DKPCA-based methods. Computer simulation of TE process demonstrates the effectiveness and efficiency of the proposed method.
For large sample data sets,traditional DKPCA occupancy a lot of computer memory and large computation,in order to solve these problems,this paper proposed an improved DKPCA based on effective feature subspace( EFS-DKPCA). The new method based on a orthonormal basis of the sub-space spanned by the training samples mapped onto the smaller feature space to simplify K,thereby reducing DKPCA computational complexity. When applied to process monitoring,the EFS-DKPCA-based method was more efficient in computation and needed less computer memory than DKPCA-based methods. Computer simulation of TE process demonstrates the effectiveness and efficiency of the proposed method.
引文
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[15]Fan Zizhu,Wang Jinghua,Xu Baogen,et al.An efficient KPCA algorithm based on feature correlation evaluation[J].Neural Computing and Applications,2014,24(7-8):1795-1806.
[16]Zhang Zhaoyang,Tian Zheng,Duan Xifa,et al.Adaptive kernel subspace method for speeding up feature extraction[J].Neurocomputing,2013,113:58-66.
[17]穆新亮.基于混合核函数的快速KPCA人脸识别算法[J].电子科技,2015,28(2):46-50.
[18]Leea J M,Yoob C K,Lee I B.Statistical monitoring of dynamic processes based on dynamic independent component analysis[J].Chemical Engineering Science,2004,59(14):2995-3006.
[19]Xiao Yingchao,Wang Huangang,Xu Wenli.Model selection of Gaussian kernel PCA for novelty detection[J].Chemometrics and Intelligent Laboratory Systems,2014,136:164-172.
[20]Jia Mingxing,Xu Hengyuan,Liu Xiaofei,et al.The optimization of the kind and parameters of kernel function in KPCA for process monitoring[J].Computers&Chemical Engineering,2012,46:94-104.
[21]Tracy N D,Young J C,Mason R L.Multivariate control charts for individual observations[J].Journal of Quality Technology,1992,24:88-95.
[22]Tong Chudong,Song Yu,Yan Xuefeng.Distributed statistical process monitoring based on four-subspace construction and Bayesian inference[J].Industrial&Engineering Chemistry Research,2013,52(29):9897-9907.
[2]Schoblkopf B,Smola A,Miller K R.Nolinear component analysis as a kernel eigenvalue problem[J].Neural Computation,1998,10(5):1299-1319.
[3]Choi S W,Lee C,Lee J M,et al.Fault detection and identification of nonlinear processes based on kernel PCA[J].Chemometrics and Intelligent Laboratory Systems,2005,75(1):55-67.
[4]刘雅莉,许鹏飞.一种模糊核聚类的线性滤波多光谱图像增强算法[J].计算机应用研究,2015,32(5):1536-1539.
[5]刘元,吴小俊.基于核融合的多信息流形学习算法[J].计算机应用研究,2016,33(3):673-676.
[6]钟秉翔,李太福,王德彪,等.一种基于核主元分析的话务量特征提取方法[J].计算机应用研究,2010,27(6):2189-2191.
[7]Ku Wenfu,Storer R H,Georgakis C.Disturbance detection and isolation by dynamic principal component analysis[J].Chemometrics and Intelligent Laboratory Systems,1995,30(1):179-196.
[8]Choi S W,Lee I B.Nonlinear dynamic process monitoring based on dynamic kernel PCA[J].Chemical Engineering Science,2004,59(24):5897-5908.
[9]Wang Yajun,Jia Mingxing,Mao Zhizhong.Weak fault monitoring method for batch process based on multi-model SDKPCA[J].Chemometrics and Intelligent Laboratory Systems,2012,118:1-12.
[10]Schraudolph N N,Günter S,Vishwanathan S V N.Fast iterative kernel PCA[J].Journal of Machine Learning Research,2007,8:1893-1918.
[11]Gnecco G,Sanguineti M.Accuracy of suboptimal solutions to kernel principal component analysis[J].Computational Optimization and Applications,2009,42(2):265-287.
[12]Cui Peiling,Li Junhong,Wang Guizeng.Improved kernel principal component analysis for fault detection[J].Expert Systems with Applications,2008,34(2):1210-1219.
[13]赵峰,张军英.一种KPCA的快速算法[J].控制与决策,2007,22(9):1044-1048.
[14]付克昌.基于结构优化PCA的传感器故障诊断方法及其应用研究[D].杭州:浙江大学,2007.
[15]Fan Zizhu,Wang Jinghua,Xu Baogen,et al.An efficient KPCA algorithm based on feature correlation evaluation[J].Neural Computing and Applications,2014,24(7-8):1795-1806.
[16]Zhang Zhaoyang,Tian Zheng,Duan Xifa,et al.Adaptive kernel subspace method for speeding up feature extraction[J].Neurocomputing,2013,113:58-66.
[17]穆新亮.基于混合核函数的快速KPCA人脸识别算法[J].电子科技,2015,28(2):46-50.
[18]Leea J M,Yoob C K,Lee I B.Statistical monitoring of dynamic processes based on dynamic independent component analysis[J].Chemical Engineering Science,2004,59(14):2995-3006.
[19]Xiao Yingchao,Wang Huangang,Xu Wenli.Model selection of Gaussian kernel PCA for novelty detection[J].Chemometrics and Intelligent Laboratory Systems,2014,136:164-172.
[20]Jia Mingxing,Xu Hengyuan,Liu Xiaofei,et al.The optimization of the kind and parameters of kernel function in KPCA for process monitoring[J].Computers&Chemical Engineering,2012,46:94-104.
[21]Tracy N D,Young J C,Mason R L.Multivariate control charts for individual observations[J].Journal of Quality Technology,1992,24:88-95.
[22]Tong Chudong,Song Yu,Yan Xuefeng.Distributed statistical process monitoring based on four-subspace construction and Bayesian inference[J].Industrial&Engineering Chemistry Research,2013,52(29):9897-9907.