Adaptive Estimation of Difficult-to-Measure Process Variables

Abstract

Original scientific paperThere exist many problems regarding process control in the process industry since some of the important variables cannot be measured online. This problem can be significantly solved by estimating these difficult-tomeasure process variables. In doing so, the estimator is in fact an appropriate mathematical model of the process which, based on information about easy-to-measure process variables, estimates the current value of the difficultto-measure variable. Since processes are usually time-varying, the precision of the estimation based on the process model which is built on old data is decreasing over time. To avoid estimator accuracy degradation, model parameters should be continuously updated in order to track process behavior. There are a couple of methods available for updating model parameters depending on the type of process model. In this paper, PLSR process model is chosen as the basis of the difficult-to-measure process variable estimator while its parameters are updated in several waysby the moving window method, recursive NIPALS algorithm, recursive kernel algorithm and Just-in-Time learning algorithm. Properties of these adaptive methods are explored on a simulated example. Additionally, the methods are analyzed in terms of computational load and memory requirements.Key words: Process variable estimation, Adaptive estimator, Moving window, Recursive algorithms, JITL algorithm Adaptivna estimacija teško-mjerljivih procesnih veličina. Problemi s upravljanjem mnogih procesa u industriji vezani su s nemogućnošću on-line mjerenja nekih važnih procesnih veličina. Ovaj se problem može u značajnoj mjeri riješiti estimacijom ovih teško-mjerljivih procesnih veličina. Estimator je pri tome odgovarajući matematički model procesa koji na temelju informacije o ostalim (lako-mjerljivim) procesnim veličinama procjenjuje trenutni iznos teško-mjerljive veličine. Budući da su procesi po prirodi promjenjivi, točnost estimacije zasnovane na modelu procesa izgra enog na starim podacima u pravilu opada s vremenom. Kako bi se ovo izbjeglo, parametre modela procesa je potrebno kontinuirano prepodešavati kako bi model što bolje opisivao (trenutno) vladanje procesa. Ovisno o tipu matematičkog modela, za prepodešavanje njegovih parametara na raspolaganju je više metoda. Kao osnova estimatora teško-mjerljive veličine u radu se koristi PLSR model procesa, dok se njegovi parametri prepodešavaju na više načina -metodom pomičnog prozora, rekurzivnim NIPALS algoritmom, rekurzivnim kernel algoritmom te Just-in-Time Learning metodom. Svojstva navedenih metoda adaptacije PLSR modela procesa ispitana su na odabranom primjeru. Nadalje, metode adaptacije su analizirane i s obzirom na računalnu i memorijsku zahtjevnost.Ključne riječi: estimacija procesne veličine, adaptivni estimator, pomični prozor, rekurzivni algoritmi, JITL algoritam

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