核主元分析KPCA的降维特征提取以及故障检测应用-Kernel Principal Componen

文件名称: 核主元分析KPCA的降维特征提取以及故障检测应用-Kernel Principal Component Analysis (KPCA).zip

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详细说明：核主元分析KPCA的降维特征提取以及故障检测应用-Kernel Principal Component Analysis .zip 本帖最后由 iqiukp 于 2018-11-9 15:02 编辑核主元分析（Kernel principal component analysis ，KPCA）在降维、特征提取以及故障检测中的应用。主要功能有：（1）训练数据和测试数据的非线性主元提取（降维、特征提取）（2）SPE和T2统计量及其控制限的计算（3）故障检测参考文献： Lee J M, Yoo C K, Choi S W, et al. Nonlinear process monitoring using kernel pr incipal component analysis[J]. Chemical engineering science, 2004, 59: 223-234. 1. KPCA的建模过程（故障检测）：（1）获取训练数据（工业过程数据需要进行标准化处理）（2）计算核矩阵（3）核矩阵中心化（4）特征值分解（5）特征向量的标准化处理（6）主元个数的选取（7）计算非线性主成分（即降维结果或者特征提取结果）（8）SPE和T2统计量的控制限计算 function model = kpca_train % DESCRIPTION % Kernel principal component analysis % % mappedX = kpca_train % % INPUT % X Training samples % N: number of samples % d: number of features % options Parameters setting % % OUTPUT % model KPCA model % % % Created on 9th November, 2018, by Kepeng Qiu. % number of training samples L = size; % Compute the kernel matrix K = computeKM; % Centralize the kernel matrix unit = ones/L; K_c = K-unit*K-K*unit unit*K*unit; % Solve the eigenvalue problem [V,D] = eigs; lambda = diag; % Normalize the eigenvalue V_s = V ./ sqrt; % Compute the numbers of principal component % Extract the nonlinear component if options.type == 1 % fault detection dims = find) >= 0.85,1, first); else dims = options.dims; end mappedX = K_c* V_s ; % Store the results model.mappedX = mappedX ; model.V_s = V_s; model.lambda = lambda; model.K_c = K_c; model.L = L; model.dims = dims; model.X = X; model.K = K; model.unit = unit; model.sigma = options.sigma; % Compute the threshold model.beta = options.beta;% corresponding probabilities [SPE_limit,T2_limit] = comtupeLimit; model.SPE_limit = SPE_limit; model.T2_limit = T2_limit; end复制代码2. KPCA的测试过程：（1）获取测试数据（工业过程数据需要利用训练数据的均值和标准差进行标准化处理）（2）计算核矩阵（3）核矩阵中心化（4）计算非线性主成分（即降维结果或者特征提取结果）（5）SPE和T2统计量的计算 function [SPE,T2,mappedY] = kpca_test % DESCRIPTION % Compute the T2 statistic, SPE statistic,and the nonlinear component of Y % % [SPE,T2,mappedY] = kpca_test % % INPUT % model KPCA model % Y test data % % OUTPUT % SPE the SPE statistic % T2 the T2 statistic % mappedY the nonlinear component of Y % % Created on 9th November, 2018, by Kepeng Qiu. % Compute Hotellings T2 statistic % T2 = diag)*model.mappedX); % the number of test samples L = size; % Compute the kernel matrix Kt = computeKM; % Centralize the kernel matrix unit = ones/model.L; Kt_c = Kt-unit*model.K-Kt*model.unit unit*model.K*model.unit; % Extract the nonlinear component mappedY = Kt_c*model.V_s; % Compute Hotellings T2 statistic T2 = diag)*mappedY); % Compute the squared prediction error SPE = sum.^2,2)-sum; end复制代码 3. demo1: 降维、特征提取源代码 % Demo1: dimensionality reduction or feature extraction % ---------------------------------------------------------------------% clc clear all close all addpath) % 4 circles load circledata % X = circledata; for i = 1:4 scatter:250*i,1),X:250*i,2)) hold on end % Parameters setting options.sigma = 5; % kernel width options.dims = 2; % output dimension options.type = 0; % 0:dimensionality reduction or feature extraction % 1:fault detection options.beta = 0.9; % corresponding probabilities options.cpc = 0.85; % Principal contribution rate % Train KPCA model model = kpca_train; figure for i = 1:4 scatter:250*i,1), ... model.mappedX:250*i,2)) hold on end 复制代码（2）结果（分别为原图和特征提取后的图） demo1-1.png demo1-2.png 4. demo2: 故障检测（需要调节核宽度、主元贡献率和置信度等参数来提高故障检测效果）（1）源代码 % Demo2: Fault detection % X: training samples % Y: test samples % Improve the performance of fault detection by adjusting parameters % 1. options.sigma = 16; % kernel width % 2. options.beta % corresponding probabilities % 3. options.cpc ; % principal contribution rate % ---------------------------------------------------------------------% clc clear all close all addpath) % X = rand; Y = rand; Y = rand 3; Y = rand*3; % Normalization % mu = mean; % st = std; % X = zscore; % Y = bsxfun,st); % Parameters setting options.sigma = 16; % kernel width options.dims = 2; % output dimension options.type = 1; % 0:dimensionality reduction or feature extraction % 1:fault detection options.beta = 0.9; % corresponding probabilities options.cpc = 0.85; % principal contribution rate % Train KPCA model model = kpca_train; % Test a new sample Y [SPE,T2,mappedY] = kpca_test; % Plot the result plotResult; plotResult; 复制代码（2）结果（分别是SPE统计量和T2统计量的结果图） demo2-1.png demo2-2.png 附件是基于KPCA的降维、特征提取和故障检测程序源代码。如有错误的地方请指出，谢谢。 Kernel Principal Component Analysis .zip KPCA

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