lolimotDemo5 Demo 5: Dynamic process of first order with 2 inputs and 2 outputs
LoLiMoT - Nonlinear System Identification Toolbox
Torsten Fischer, 20-October-2011
Institute of Mechanics & Automatic Control, University of Siegen, Germany
Copyright (c) 2012 by Prof. Dr.-Ing. Oliver Nelles
LMN= lolimot;
u1 = randn(300,1);
u2 = sin(linspace(0,2*pi,300))';
y1 = zeros(300,1);
y2 = zeros(300,1);
for k = 2:300
y1(k) = atan(u1(k-1)) + atan(u2(k-1)) + 0.9*y1(k-1);
y2(k) = u1(k-1).^2 + u1(k-1)*u2(k-1) + 0.7*y1(k-1) + 0.8*y2(k-1);
end
LMN.input = [u1 u2];
LMN.output = [y1 y2];
LMN.xInputDelay{1} = [1]; LMN.xInputDelay{2} = [1];
LMN.xOutputDelay{1} = [1]; LMN.xOutputDelay{2} = [1];
LMN.zInputDelay{1} = [1]; LMN.zInputDelay{2} = [1];
LMN.zOutputDelay{1} = [1]; LMN.zOutputDelay{2} = [1];
LMN.maxNumberOfLM = 10;
LMN.minError = 0.02;
LMN.kStepPrediction = inf;
LMN.history.displayMode = true;
LMN = LMN.train;
u1G = randn(270,1);
u2G = sin(linspace(0,2*pi,length(u1G)))';
y1G = zeros(length(u1G),1);
y2G = zeros(length(u1G),1);
for k = 2:length(y1G)
y1G(k) = atan(u1G(k-1)) + atan(u2G(k-1)) + 0.9*y1G(k-1);
y2G(k) = u1G(k-1).^2 + u1G(k-1)*u2G(k-1) + 0.7*y1G(k-1) + 0.8*y2G(k-1);
end
uG = [u1G u2G];
yG = [y1G y2G];
yGModel = calculateModelOutput(LMN, uG, yG);
JG = calcGlobalLossFunction(LMN ,yG, yGModel);
figure
subplot(1,2,1)
LMN.plotModel([],1)
subplot(1,2,2)
LMN.plotModel([],2)
Initial net has 1 local linear model(s): J = 0.104233.
1. Iteration. Number of local linear models = 1. Checking for split of model 1 ...
Testing split in dimension 1 with ratio 0.50: J = 0.073329.
Testing split in dimension 2 with ratio 0.50: J = 0.080388.
Testing split in dimension 3 with ratio 0.50: J = 0.088554.
Testing split in dimension 4 with ratio 0.50: J = 0.088307.
-> Splitting in dimension 1 with ratio 0.50: J = 0.073329 and penalty = 0.075400.
2. Iteration. Number of local linear models = 2. Checking for split of model 2 ...
Testing split in dimension 1 with ratio 0.50: J = 0.061569.
Testing split in dimension 2 with ratio 0.50: J = 0.060225.
Testing split in dimension 3 with ratio 0.50: J = 0.066203.
Testing split in dimension 4 with ratio 0.50: J = 0.065393.
-> Splitting in dimension 2 with ratio 0.50: J = 0.060225 and penalty = 0.062457.
3. Iteration. Number of local linear models = 3. Checking for split of model 3 ...
Testing split in dimension 1 with ratio 0.50: J = 0.056366.
Testing split in dimension 2 with ratio 0.50: J = 0.054148.
Testing split in dimension 3 with ratio 0.50: J = 0.056575.
Testing split in dimension 4 with ratio 0.50: J = 0.056377.
-> Splitting in dimension 2 with ratio 0.50: J = 0.054148 and penalty = 0.056579.
4. Iteration. Number of local linear models = 4. Checking for split of model 4 ...
Testing split in dimension 1 with ratio 0.50: J = 0.046467.
Testing split in dimension 2 with ratio 0.50: J = 0.044515.
Testing split in dimension 3 with ratio 0.50: J = 0.051451.
Testing split in dimension 4 with ratio 0.50: J = 0.051450.
-> Splitting in dimension 2 with ratio 0.50: J = 0.044515 and penalty = 0.046912.
5. Iteration. Number of local linear models = 5. Checking for split of model 7 ...
Testing split in dimension 1 with ratio 0.50: J = 0.043700.
Testing split in dimension 2 with ratio 0.50: J = 0.042060.
Testing split in dimension 3 with ratio 0.50: J = 0.043298.
Testing split in dimension 4 with ratio 0.50: J = 0.042997.
-> Splitting in dimension 2 with ratio 0.50: J = 0.042060 and penalty = 0.044637.
6. Iteration. Number of local linear models = 6. Checking for split of model 8 ...
Testing split in dimension 1 with ratio 0.50: J = 0.039049.
Testing split in dimension 2 with ratio 0.50: J = 0.041475.
Split in dimension 3 with ratio 0.50 is forbidden!
Split in dimension 4 with ratio 0.50 is forbidden!
-> Splitting in dimension 1 with ratio 0.50: J = 0.039049 and penalty = 0.041853.
7. Iteration. Number of local linear models = 7. Checking for split of model 5 ...
Testing split in dimension 1 with ratio 0.50: J = 0.036524.
Testing split in dimension 2 with ratio 0.50: J = 0.036195.
Testing split in dimension 3 with ratio 0.50: J = 0.037480.
Testing split in dimension 4 with ratio 0.50: J = 0.037357.
-> Splitting in dimension 2 with ratio 0.50: J = 0.036195 and penalty = 0.039142.
8. Iteration. Number of local linear models = 8. Checking for split of model 6 ...
Testing split in dimension 1 with ratio 0.50: J = 0.031300.
Testing split in dimension 2 with ratio 0.50: J = 0.034120.
Testing split in dimension 3 with ratio 0.50: J = 0.035770.
Testing split in dimension 4 with ratio 0.50: J = 0.035936.
-> Splitting in dimension 1 with ratio 0.50: J = 0.031300 and penalty = 0.034182.
9. Iteration. Number of local linear models = 9. Checking for split of model 15 ...
Testing split in dimension 1 with ratio 0.50: J = 0.028970.
Testing split in dimension 2 with ratio 0.50: J = 0.031549.
Split in dimension 3 with ratio 0.50 is forbidden!
Split in dimension 4 with ratio 0.50 is forbidden!
-> Splitting in dimension 1 with ratio 0.50: J = 0.028970 and penalty = 0.031911.
Maximum number of local models reached.
Final net has 10 local models and 100 parameters: J = 0.028970
Net 10 with 10 LMs and 100 parameters is suggested as the model with the best complexity trade-off.