From d84eda70733513a365f9cfc5306e1b4584ce5864 Mon Sep 17 00:00:00 2001 From: Dhammika Widanalage Date: Tue, 16 Nov 2021 18:22:00 +0000 Subject: [PATCH] Added some dependendcy files in TECMD parameter estimation example --- .../parameterEstimation_TECMD/EstECMPara.m | 3 +- Examples/parameterEstimation_TECMD/Lls.m | 110 ++++++++++++++++++ .../TECMD_OptimisationTemplate.slx | Bin 301185 -> 301182 bytes .../TECMD_Prototype.slx | Bin 68685 -> 68920 bytes Examples/parameterEstimation_TECMD/modelFit.m | 15 +++ .../optParameters_TECMD_LGM50.mat | Bin 1225 -> 1225 bytes .../paraOptim_ThreeStep_V.mlx | Bin 676502 -> 12435 bytes 7 files changed, 126 insertions(+), 2 deletions(-) create mode 100644 Examples/parameterEstimation_TECMD/Lls.m create mode 100644 Examples/parameterEstimation_TECMD/modelFit.m diff --git a/Examples/parameterEstimation_TECMD/EstECMPara.m b/Examples/parameterEstimation_TECMD/EstECMPara.m index 35dfb47..bf3d893 100644 --- a/Examples/parameterEstimation_TECMD/EstECMPara.m +++ b/Examples/parameterEstimation_TECMD/EstECMPara.m @@ -2,8 +2,7 @@ % Estimate the parameters of an ECM. Postive current is assumed as % discharge % -% W.D. Widanage 07/01/2016 (Fade to Black) -% W.D. Widanage 21/12/2018 (Aint my ****) +% W.D. Widanage 21/12/2018 p = inputParser; % Create an input parse object to handle positional and property-value arguments diff --git a/Examples/parameterEstimation_TECMD/Lls.m b/Examples/parameterEstimation_TECMD/Lls.m new file mode 100644 index 0000000..0e49955 --- /dev/null +++ b/Examples/parameterEstimation_TECMD/Lls.m @@ -0,0 +1,110 @@ +function [theta,results] = Lls(K,Z,varargin) +% +% Computes a numerically stable (weighted) linear leaast squares estimate +% and returns the optimal estimate, its variance and an estimate of the +% noise variance. Parameters will be non-unique if K is rank deficient. +% +% Inputs (mandatory): +% K: Regresor matrix, size n x m +% Z: Output vector, size n x 1 +% +% Inputs (optional): +% ny: Output noise vector, std of output noise for weighted least +% squares, size n x 1. default ny = ones(n,1); +% plotFit: Set plot as 1 or zero to look at the fitted vs data +% +% Outputs: +% theta: Optimum parameter estimate, size m x 1 +% results: Structure variable with following fields +% - paraVar: Variance estimate of theta, size m x 1 +% - paraCov: Parameter covariance matrix size m x m +% - noiseVar: Estimate of noise variance, size 1 x 1 +% - resVec: Residual vector, size n x 1 +% - resNorm: 2 norm of residual vector, size 1 x 1 +% - regMsg: Message stating rank of regressor +% - regRankFull: A flag with value 0 or 1 if regressor is rank deficient or not. +% +% Copyright (C) W. D. Widanage - WMG, University of Warwick, U.K. 11-02-2012-12/01/2016 (Through the never) +% All Rights Reserved +% Software may be used freely for non-comercial purposes only + +Z = Z(:); % Vectorise +parObj = inputParser; % Create an input parse object to handle positional and property-value arguments + +% Create variable names and assign default values after checking the value +addRequired(parObj,'K', @isnumeric); +addRequired(parObj,'Z', @isnumeric); + +% Optional parameters +addOptional(parObj,'ny',ones(size(Z)),@isnumeric); +addOptional(parObj,'plotFit',0,@isnumeric); + + + +% Re-parse parObj +parse(parObj,K,Z,varargin{:}) + + +K = parObj.Results.K; +Z = parObj.Results.Z; +ny = parObj.Results.ny; +plotFit = parObj.Results.plotFit; + +% Weight matrix +W = spdiags(1./ny,0,length(ny),length(ny)); + +%Multiply by weights +Z = W*Z; +K = W*K; + +%Normalise K with the 1/norm of each column +Knorm = sqrt(sum(abs(K).^2)); +idxZeros = Knorm<1E-14; +Knorm(idxZeros) = 1; +N = diag(1./Knorm); +Kn = K*N; + +%Compute Lls via economic SVD decompostion +[U, S, V] = svd(Kn,0); % Perform SVD +ss = diag(S); % Singular values +idxZeros = ss < 1E-14; % Replace any small singular value with inf +nCol = size(Kn,2); +if sum(idxZeros)>0 % If there are zero singular values sum(idxZeros) > 0 and regressor is rank deficient + results.regMsg = sprintf('Estimated parameters are NON-UNIQUE.\n Lls regressor is rank defficient. Rank = %d instead of %d. \nParameters estimated from a subspace.',nCol-sum(idxZeros),nCol); + fprintf('\nEstimated parameters are NON-UNIQUE.\nRegressor rank defficient. Rank = %d instead of %d. \nParameters estimated from a subspace.\n\n',nCol-sum(idxZeros),nCol) + results.regRankFull = 0; +else + results.regMsg = sprintf('Estimated parameters are unique.\nRegressor preserves full rank. Rank = %d.',nCol); + results.regRankFull = 1; +end +ss(idxZeros) = inf; +Sv = diag(1./ss); %Inverse singular value matrix + +% Least squares solution +theta = N*V*Sv*U'*Z; +% cond(N*V*Sv*U') + +%Projection matrix and residuals +P = (eye(length(Z))-U*(U')); % Projection matrix +R = P*Z; % Residuals + +%Estimate of noise and parameter variance +if ismember('ny',parObj.UsingDefaults) % If measurement variance is not provided estiamte via residuals + results.noiseVar = ((R')*R)/real(trace(P)); % Noise variance + results.paraCov = (N')*V*Sv*Sv*(V')*N*results.noiseVar; % Parameter covariance +else % Else no need to estimate noise variance + results.noiseVar = []; % Noise variance + results.paraCov = (N')*V*Sv*Sv*(V')*N; % Parameter covariance +end + +if plotFit + figure + Zm = K*theta; + plot([1:length(Z)]',Zm,'. -',[1:length(Z)]',Z,'o-'); + xlabel('Index (-)'); ylabel('Model and Measured') + legend('Model','Data') +end +results.paraVar = diag(results.paraCov); % Parameter variance 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Copyright (C) W. D. Widanage - WMG, University of Warwick, U.K. 08/11/2019 (Mama Said) +% All Rights Reserved +% Software may be used freely for non-comercial purposes only + +x = x(:); +y = y(:); +error = x-y; +results.RMSE = sqrt(mean(error.^2,'omitnan')); +results.PkErr = max(abs(x-y)); +results.gof = max([0, 1 - (results.RMSE^2/var(y,'omitnan'))]); +end \ No newline at end of file diff --git a/Examples/parameterEstimation_TECMD/optParameters_TECMD_LGM50.mat b/Examples/parameterEstimation_TECMD/optParameters_TECMD_LGM50.mat index b3e7c62b3139e3781acf950f79feecf08de39f45..13fb87cf92e675b85d8b84e910e2a3440b57cb97 100644 GIT binary patch delta 41 wcmX@fd6IL2i9|?gs)ApBnS!C2f}w?#fq|8YiGq=Vk>SKZ<%tQb8%si20RLnQtN;K2 delta 41 wcmX@fd6IL2i9~Q|of}yFEk(rgLv4W9-k>SKZ<%tQb8%si20RPepu>b%7 diff --git a/Examples/parameterEstimation_TECMD/paraOptim_ThreeStep_V.mlx b/Examples/parameterEstimation_TECMD/paraOptim_ThreeStep_V.mlx index e8017bf58fa283585fc4f269e1d2d9c289ff20fe..4116aed774d617541808b9634d22dfb9978aab37 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