Home > Codi > compute_reconstruction_correlation_matrix.m

compute_reconstruction_correlation_matrix

PURPOSE ^

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SYNOPSIS ^

function C_r_i = compute_reconstruction_correlation_matrix(Xi_i, Xi_res_i)

DESCRIPTION ^

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 C_r_i = compute_reconstruction_correlation_matrix(Xi_i, Xi_res_i)       %
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 FUNCTIONALITY:                                                          %
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 This function aim is to compute the matrix that relates the variables   %
 to use when reconstructing a faulty observation for a given fault       %
 direction (Xi_i), using the projection of that fault direction in the   %
 residual subspace (Xi_res_i).                                           %
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 INPUT PARAMETERS:                                                       %
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 Xi_i:     Column array or matrix with as many rows as variables were    %
           used to build the PCA model and as many columns as individual %
           sensor faults are involved for the multisensory fault vector. %
 Xi_res_i: Projection of xi_i in the residual subspace of a PCA model.   %
           It has the same dimensions as Xi_i.                           %
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 OUTPUT PARAMETERS:                                                      %
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 C_r_i:    Matrix that indicates the weight of each variable included to %
           build the PCA model when reconstructing using the fault       %
           direction Xi_i (and its projection in the residual subspace   %
           Xi_res_i). C_r_i is a square matrix with as many rows and     %
           columns as variables where used to build the PCA model.       %
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 We compute the the value of C_r_i for the fault direction Xi_i and its
 projection in the residual subspace Xi_res_i. The resulting value is
 subtracted from an identity matrix in order to have all variables
 affected by fault direction Xi_i have no influence on the reconstruction
 (their value are set to 0).

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0002 % C_r_i = compute_reconstruction_correlation_matrix(Xi_i, Xi_res_i)       %
0003 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0004 % FUNCTIONALITY:                                                          %
0005 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0006 % This function aim is to compute the matrix that relates the variables   %
0007 % to use when reconstructing a faulty observation for a given fault       %
0008 % direction (Xi_i), using the projection of that fault direction in the   %
0009 % residual subspace (Xi_res_i).                                           %
0010 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0011 % INPUT PARAMETERS:                                                       %
0012 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0013 % Xi_i:     Column array or matrix with as many rows as variables were    %
0014 %           used to build the PCA model and as many columns as individual %
0015 %           sensor faults are involved for the multisensory fault vector. %
0016 % Xi_res_i: Projection of xi_i in the residual subspace of a PCA model.   %
0017 %           It has the same dimensions as Xi_i.                           %
0018 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0019 % OUTPUT PARAMETERS:                                                      %
0020 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0021 % C_r_i:    Matrix that indicates the weight of each variable included to %
0022 %           build the PCA model when reconstructing using the fault       %
0023 %           direction Xi_i (and its projection in the residual subspace   %
0024 %           Xi_res_i). C_r_i is a square matrix with as many rows and     %
0025 %           columns as variables where used to build the PCA model.       %
0026 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0027 function C_r_i = compute_reconstruction_correlation_matrix(Xi_i, Xi_res_i)
0028 % We compute the the value of C_r_i for the fault direction Xi_i and its
0029 % projection in the residual subspace Xi_res_i. The resulting value is
0030 % subtracted from an identity matrix in order to have all variables
0031 % affected by fault direction Xi_i have no influence on the reconstruction
0032 % (their value are set to 0).
0033 C_r_i = eye(size(Xi_i, 1)) - Xi_i * ((Xi_res_i' * Xi_res_i)\Xi_res_i');

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