Fault Isolation for Desalting Processes Using Near-Infrared Measurements

Algorithm 1

The proposed algorithm.

(1)	Set and the beginning active set . Start with .
(2)	Get the correlation vector and find the greatest absolute correlation value , where is the -th element in . Then, update the active set as .
(3)	Calculate the equiangular vector , where for , is the -th column in the matrix , , and is ones vector.
(4)	Get the step size as , where is the complementary set of with and , is the -th element in for , and indicates that the minimum is taken over only positive components within each .
(5)	Let and update for .
(6)	Return to Step 2 until which also means that the monitoring statistics fall within the corresponding control limit in Section 2.
(7)	Finally, the variables in the active set are isolated as the spectral region affected by the fault. Besides, due to the steps, the spectral region affected by the fault can be isolated from the most to the less.