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| Kernel Principal Component Analysis(KPCA) | ||
| === | ||
| --------------------------------------------------------- | ||
| Updates on 18 Apr 2019 | ||
| 1. Fixed some errors | ||
| 2. Added Dynamic KPCA(DKPCA) | ||
| --------------------------------------------------------- | ||
|
|
||
| four demos are provided: | ||
| demo1: dimensionality reduction or feature extraction | ||
| demo2: fault detection for a numerical example | ||
| demo3: fault detection and fault diagnosis for TE process using KPCA | ||
| demo4: fault detection and fault diagnosis for TE process using Dynamic KPCA(DKPCA) | ||
|
|
||
| demo1: dimensionality reduction, feature extraction | ||
| = | ||
| load circledata | ||
| X = circledata; | ||
| figure | ||
| for i = 1:4 | ||
| scatter(X(1+250*(i-1):250*i,1),X(1+250*(i-1):250*i,2)) | ||
| hold on | ||
| end | ||
|
|
||
| % Train KPCA model | ||
| model = kpca_train(X,'type',0,'sigma',5,'dims',2); | ||
|
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||
| % Visualize the result of dimensionality reduction | ||
| figure | ||
| for i = 1:4 | ||
| scatter(model.mappedX(1+250*(i-1):250*i,1), ... | ||
| model.mappedX(1+250*(i-1):250*i,2)) | ||
| hold on | ||
| end | ||
|  | ||
| # Kernel Principal Component Analysis(KPCA) | ||
|
|
||
| --------------------------------------------------------------- | ||
| Updated on 16 Nov 2019 | ||
| 1. Used OOP to rewrite some modules. | ||
| 2. Added support for multiple kernel function. | ||
| 3. Fixed some bugs. | ||
| 4. Accelerated the running speed of the fault diagnosis module | ||
| --------------------------------------------------------------- | ||
|
|
||
| Notice | ||
| 1. For a brief introduction to this code, please read 'contents.m' file. | ||
| 2. Fault diagnosis module only supports gaussian kernel function at this version. | ||
| 3. The fault diagnosis module calls the precompiled file '.mexw64' to accelerate the running speed. | ||
| 4. Class is defined using 'Classdef...End', so this code can only be applied to MATLAB after the R2008a release. | ||
| 5. The original version (v1.0) is also provided. | ||
|
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||
| ### Demo for dimensionality reduction (helix data) | ||
|
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||
| ``` | ||
| clc | ||
| clear all | ||
| close all | ||
| addpath(genpath(pwd)) | ||
| % load the training data | ||
| load('.\data\helix.mat') | ||
| traindata = helix; | ||
| % create a parameter structure for the KPCA application | ||
| application = struct('type','dimensionalityreduction',... | ||
| 'dimensionality', 2); | ||
| % create an object for kernel function | ||
| kernel = Kernel('type', 'gauss', 'width', 24); | ||
| % create an object for kpca model | ||
| kpca = KpcaModel('application', application,... | ||
| 'kernel', kernel); | ||
| % train KPCA model | ||
| model = kpca.train(traindata); | ||
| % get the mapping data | ||
| mappingdata = model.mappingdata; | ||
| % plot the mapping data (only support for 2D or 3D data) | ||
| plotMappingData(traindata, mappingdata); | ||
| ``` | ||
|  | ||
|
|
||
| demo2: fault detection (Improve the performance of fault detection by adjusting parameters) | ||
| = | ||
| % Training data and Test data | ||
| X = rand(200,10); | ||
| Y = rand(100,10); | ||
| Y(20:40,:) = rand(21,10)+3; | ||
| Y(60:80,:) = rand(21,10)*3; | ||
|
|
||
| % Train KPCA model | ||
| model = kpca_train(X,'type',1,'sigma',60); | ||
|
|
||
| % Test a new sample Y (vector of matrix) | ||
| model = kpca_test(model,Y); | ||
|
|
||
| % Plot the result | ||
| plotResult(model.SPE_limit,model.SPE_test); | ||
| plotResult(model.T2_limit,model.T2_test); | ||
|  | ||
| ### Demo for dimensionality reduction (circle data) | ||
|
|
||
| ``` | ||
| clc | ||
| clear all | ||
| close all | ||
| addpath(genpath(pwd)) | ||
| % load the training data | ||
| load('.\data\circledata.mat') | ||
| traindata = circledata; | ||
| % create a parameter structure for the KPCA application | ||
| application = struct('type','dimensionalityreduction',... | ||
| 'dimensionality', 2); | ||
| % create an object for kernel function | ||
| kernel = Kernel('type', 'gauss', 'width', 6); | ||
| % create an object for kpca model | ||
| kpca = KpcaModel('application', application,... | ||
| 'kernel', kernel); | ||
| % train KPCA model | ||
| model = kpca.train(traindata); | ||
| % get the mapping data | ||
| mappingdata = model.mappingdata; | ||
| % plot the mapping data (only support for 2D or 3D data) | ||
| plotMappingData(traindata, mappingdata, label); | ||
| ``` | ||
|  | ||
|
|
||
| ### Demo for dimensionality reduction (banana data) | ||
|  | ||
|
|
||
| ### Demo for Fault Dection (using TE process data) | ||
|
|
||
| ``` | ||
| clc | ||
| clear all | ||
| close all | ||
| addpath(genpath(pwd)) | ||
| % load the original process data of the TE process | ||
| load('.\data\teprocess.mat') | ||
| % normalization (in general, this step is important for fault detection) | ||
| [traindata, testdata] = normalize(traindata, testdata); | ||
| % create a parameter structure for the KPCA application | ||
| application = struct('type','faultdetection',... | ||
| 'cumulativepercentage', 0.75,... | ||
| 'significancelevel', 0.95); | ||
| % create an object for kernel function | ||
| kernel = Kernel('type', 'gauss', 'width', 800); | ||
| % create an object for kpca model | ||
| kpca = KpcaModel('application', application,... | ||
| 'kernel', kernel); | ||
| % train kpca model | ||
| model = kpca.train(traindata); | ||
| % test KPCA model | ||
| testresult = kpca.test(model, testdata); | ||
| % visualize the testing results | ||
| plotTestResult(model.spelimit, testresult.spe, 'SPE'); | ||
| plotTestResult(model.t2limit, testresult.t2, 'T2'); | ||
| ``` | ||
| ``` | ||
| *** Detection finished *** | ||
| Testing samples number: 960 | ||
| T2 alarm number : 799 | ||
| SPE alarm number : 859 | ||
| ``` | ||
|  | ||
|
|
||
| demo3: fault detection and fault diagnosis for TE process | ||
| = | ||
| % load TE process data | ||
| load train | ||
| load test | ||
|
|
||
| % Normalization | ||
| [X, Y] = normalize(train,test); | ||
| ### Demo for Fault Diagnosis (using TE process data) | ||
|
|
||
| ``` | ||
| clc | ||
| clear all | ||
| close all | ||
| addpath(genpath(pwd)) | ||
| % load the original process data of the TE process | ||
| load('.\data\teprocess.mat') | ||
| % normalization (in general, this step is important for fault detection) | ||
| [traindata, testdata] = normalize(traindata, testdata); | ||
| % create a parameter structure for the KPCA application | ||
| application = struct('type','faultdetection',... | ||
| 'cumulativepercentage', 0.75,... | ||
| 'significancelevel', 0.95,... | ||
| 'faultdiagnosis','on',... | ||
| 'diagnosisparameter', 0.7); | ||
| % create an object for kernel function | ||
| kernel = Kernel('type', 'gauss', 'width', 800); | ||
| % create an object for kpca model | ||
| kpca = KpcaModel('application', application,... | ||
| 'kernel', kernel); | ||
| % train kpca model | ||
| model = kpca.train(traindata); | ||
| % test KPCA model | ||
| testresult = kpca.test(model, testdata); | ||
| % visualize the testing results | ||
| plotTestResult(model.spelimit, testresult.spe, 'SPE'); | ||
| plotTestResult(model.t2limit, testresult.t2, 'T2'); | ||
| % create a parameter structure for the fault diagnosis | ||
| contribution = diagnoseFault(testresult, ... | ||
| 'startingtime', 301,... | ||
| 'endingtime', 500,... | ||
| 'theta', 0.7); | ||
| % | ||
| % % visualize the results of fault diagnosis | ||
| plotContribution(contribution, 'SPE') | ||
| plotContribution(contribution, 'T2') | ||
| ``` | ||
|  | ||
|
|
||
| ### Demo for Dynamic KPCA (DKPCA) (using TE process data) | ||
|
|
||
| ``` | ||
| clc | ||
| clear all | ||
| close all | ||
| addpath(genpath(pwd)) | ||
| % load the original process data of the TE process | ||
| load('.\data\teprocess.mat') | ||
| % normalization (in general, this step is important for fault detection) | ||
| [traindata, testdata] = normalize(traindata, testdata); | ||
| % create a parameter structure for the KPCA application | ||
| application = struct('type','faultdetection',... | ||
| 'cumulativepercentage', 0.75,... | ||
| 'significancelevel', 0.95,... | ||
| 'timelag', 60); | ||
| % create an object for kernel function | ||
| kernel = Kernel('type', 'gauss', 'width', 800); | ||
| % Train KPCA model | ||
| model = kpca_train(X,'type',1,'sigma',800,'fd',1); | ||
| % create an object for kpca model | ||
| kpca = KpcaModel('application', application,... | ||
| 'kernel', kernel); | ||
| % train kpca model | ||
| model = kpca.train(traindata); | ||
| % Test a new sample Y (vector of matrix) | ||
| model = kpca_test(model,Y); | ||
| % test KPCA model | ||
| testresult = kpca.test(model, testdata); | ||
| % Plot the result | ||
| plotResult(model.SPE_limit,model.SPE_test); | ||
| plotResult(model.T2_limit,model.T2_test); | ||
| % visualize the testing results | ||
| plotTestResult(model.spelimit, testresult.spe, 'SPE'); | ||
| plotTestResult(model.t2limit, testresult.t2, 'T2'); | ||
| ``` | ||
|
|
||
| % Fault diagnosis | ||
| [CPs_T2_test_s, CPs_SPE_test_s] = CPsKPCA(X,Y,model, ... | ||
| 'start_time',300,'end_time',500,'theta',0.7); | ||
| ``` | ||
| *** Detection finished *** | ||
| Testing samples number: 960 | ||
| T2 alarm number : 768 | ||
| SPE alarm number : 777 | ||
| ``` | ||
|  | ||
|
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||
| % Plot Contribution Plots | ||
| plotCPs(CPs_SPE_test_s) | ||
| plotCPs(CPs_T2_test_s) | ||
|  |