J1ngs/Kernel-Principal-Component-Analysis-KPCA

KPCA for dimensionality reduction, feature extraction , fault detection, and fault diagnosis

Kernel Principal Component Analysis(KPCA)

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Updates on 18 Apr 2019

1. Fixed some errors
2. Added Dynamic KPCA(DKPCA)

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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);

% 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

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);

demo3: fault detection and fault diagnosis for TE process

% load TE process data
load train
load test

% Normalization 
[X, Y] = normalize(train,test);

% Train KPCA model
model = kpca_train(X,'type',1,'sigma',800,'fd',1);

% 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);

% Fault diagnosis
[CPs_T2_test_s, CPs_SPE_test_s] = CPsKPCA(X,Y,model, ... 
    'start_time',300,'end_time',500,'theta',0.7);

% Plot Contribution Plots
plotCPs(CPs_SPE_test_s)
plotCPs(CPs_T2_test_s)