PCA Q statistic (SPE) Hotelling T2
alkan alkaya
Peter Perkins
> I want to use PCA (Principle component analysis) Q and T statistics test for fault detection control process. How can I use and how can I plot the Q or T2 statistics of the measured data?
The PRINCOMP function in the Statistics Toolbox returns the T^2 statistics; the PCARES function returns residuals that are used to compute the Q statistics. Hope this helps.
alkan alkaya
> alkan alkaya wrote:
> > I want to use PCA (Principle component analysis) Q and T statistics test for fault detection control process. How can I use and how can I plot the Q or T2 statistics of the measured data?
>
> The PRINCOMP function in the Statistics Toolbox returns the T^2 statistics; the PCARES function returns residuals that are used to compute the Q statistics. Hope this helps.
Thank you peter perkins,
I could see the T2 plot by using PRINCOMP function but I couldn't plot the Q statistic. I have 1024*4 matrix 4= variables,1024= samples. When I use PCARES function I have RESIDUAL=R with same dimension (1024*4). for Q statistic as I know Q=R'*R after this calculation Q matrix occurs with 4*4 dimension but I think It should be 1*1024 dimension in order to plot Q test like T2 testing. I think I miss something. Thanks for your help.
Peter Perkins
> I could see the T2 plot by using PRINCOMP function but I couldn't plot the Q statistic. I have 1024*4 matrix 4= variables,1024= samples. When I use PCARES function I have RESIDUAL=R with same dimension (1024*4). for Q statistic as I know Q=R'*R after this calculation Q matrix occurs with 4*4 dimension but I think It should be 1*1024 dimension in order to plot Q test like T2 testing. I think I miss something. Thanks for your help.
I suspect what you want is diag(R*R'), or equivalently, sum(R.^2,2).
alkan
I can calculate the confidence limit for T^2 test in matlab with
"T2Upper=p*(n-1)/(n-p)*finv(0.98,p,n-p); here p =PCs,n= sample number"
like this how can I calculate the confidence limits for Q test?
alkan alkaya
a.m.r.pg-h...@student.lboro.ac.uk
> I want to use PCA (Principle component analysis) Q and T statistics test for fault detection control process. How can I use and how can I plot the Q or T2 statistics of the measured data?
zhou
> > I want to use PCA (Principle component analysis) Q and T statistics test for fault detection control process. How can I use and how can I plot the Q or T2 statistics of the measured data?
>
> The PRINCOMP function in the Statistics Toolbox returns the T^2 statistics; the PCARES function returns residuals that are used to compute the Q statistics. Hope this helps.
Shashank
where, P = var(Qr(:,1)), m = mean (Qr(:,1)), V=(2*(m^2))/p;
Stephen Murray
Assume x is a data matrix with rows as observations, and columns as system variables. P is a loading matrix that can be calculated usign pca.m
In order to calculate the errors (e), you can use pcares.m, or alternatively:
e = x* (eye(size(x,2)) - P(:,1:N)*P(:,1:N)' ); % (use both and check result) N is number of retained components
Q = e*e' ; % this gives an nx1 vector of q-stat corresponding to each column
To find an upper control limit for Q:
theta1 = trace(e*e'/(size(x,1)-1));
theta2 = trace((e*e'/(size(x,1)-1)).^2);
theta3 = trace((e*e'/(size(x,1)-1)).^3);
h0 = 1 - (2*theta1*theta3)/(3*theta2^2);
ca=2.57; % standard deviate for alpha=0.01
Qa = theta1*( ca*sqrt(2*theta2*h0^2)/theta1 + 1 + (theta2*h0*(h0-1))/(theta1^2))^(1/h0);
To check if this works, compare your Q vector against Qa; youll expect about 2% of your results to be greater than Qa
Source: This Paper
http://www.ans.org/pubs/journals/nt/a_3240
Kaistha & Upadhyaya: Incipient Fault Detection and Isolation of Field Devices in Nuclear Power Systems Using Principal Component Analysis
Stephen Murray
- dont use e, this is reserved by MATLAB, use something liuke err instead
- Q = e*e' ; should read Q = diag(e*e') ;
profess...@gmail.com
Rafael Lima
you've wrote that:
Thank you in advance.
