Sensor FDD Using PLS and CVSS Models

Two variants of a technique which relies on input-output models developed from operation data are presented the first uses PLS and the second CVSS models. PLS regression based on the zero lag covariance of the process measurements was introduced in Section 4.3. A Multipass PLS algorith-m is developed for detecting simultaneous multiple sensor abnormalities. This algorithm is only suitable for process measurements where the successive measurements are not correlated. The negligible autocorrelation assumption is justified for a continuous process operating at steady-state and having only random noise on measurements. 

CVSS models introduced in Section 4.5 for process data with strong autocorrelation and crosscorrelation. One-step ahead residuals generated from the CVSS model will be used for sensor audit. A multipass version of the technique is developed to identify submodels by eliminating successively the corrupted measurements from both the calibration and test data sets and fitting a different CV state-space model. 

Assume that p sensors are monitored. The calibration data set is collected for n time steps and the measurements are stored in the block matrix X after being scaled to unit-variance and zero-mean columns. x(A ) is the p X 1 vector of observations at the fcth sampling time. The transpose of x k) is the fcth row of X. 

Denote by X,j the fth n x 1 column vector which contains the predicted values of the fth i = 1,. ..,p) sensor from the X block excluding itself (the fth column of X) given as 

The p — 1 nonzero elements of the regressor vector / j for each variable i are computed by using PLS algorithm where the predicted variable block Y contains the measurements of the fth sensor taken from X, and the predictor block denoted by X contains the observations from the remaining p —1 sensors. Equations 8.1 and 8.2 are defined such that the nxp matrix X which contains the measurements from all the p sensors is utilized directly. These PLS regressions are repeated for i = 1, iP- For the fth sensor, the p — 1 elements of the regressor vector /3j are [329] 

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