Premium
Practical improvements to autocovariance least‐squares
Author(s) -
Zagrobelny Megan A.,
Rawlings James B.
Publication year - 2015
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.14771
Subject(s) - autocovariance , estimator , least squares function approximation , weighting , mathematics , observability , singular value decomposition , linear least squares , mathematical optimization , covariance , total least squares , variance (accounting) , observable , covariance matrix , algorithm , statistics , medicine , mathematical analysis , physics , accounting , fourier transform , quantum mechanics , business , radiology
Identifying disturbance covariances from data is a critical step in estimator design and controller performance monitoring. Here, the autocovariance least‐squares (ALS) method for this identification is examined. For large industrial models with poorly observable states, the process noise covariance is high dimensional and the optimization problem is poorly conditioned. Also, weighting the least‐squares problem with the identity matrix does not provide minimum variance estimates. Here, ALS method to resolve these two challenges is modified. Poorly observable states using the singular value decomposition (SVD) of the observability matrix is identified and removed, thus decreasing the computational time. Using a new feasible‐generalized least‐squares estimator that approximates the optimal weighting from data, the variance of the estimates is significantly reduced. The new approach on industrial data sets provided by Praxair is successfully demonstrated. The disturbance model identified by the ALS method produces an estimator that performs optimally over a year‐long period. © 2015 American Institute of Chemical Engineers AIChE J , 61: 1840–1855, 2015