The kernel algorithm for PLS

Lindgren, Fredrik; Geladi, Paul; Wold, Svante

doi:10.1002/cem.1180070104

Cited by 303 publications

(160 citation statements)

References 17 publications

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“…The most popular algorithms for calculating directions of projection are the Nonlinear Iterative Partial Least Squares (NIPALS) algorithm [27] and kernel algorithm [28]. The general PLS algorithm is based on the decomposition of the predictor matrix X nxm (ETM variables) and the response matrix Y nxp (DTM variables) into sums of rank one component matrices [26,27]:…”

Section: Plsr Modelmentioning

confidence: 99%

“…Since the basis of this recursive algorithm is the kernel algorithm [28], covariance data matrices X T X and X T Y play a central role in the algorithm.…”

Section: Recursive Kernel Pls Algorithmmentioning

confidence: 99%

“…Since only the matrix X T Y has to be deflated, the improved kernel algorithm is 2-5 times faster than the original kernel algorithm proposed in [28].…”

Section: Recursive Kernel Pls Algorithmmentioning

confidence: 99%

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Adaptive Estimation of Difficult-to-Measure Process Variables

2013

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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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Section: Plsr Modelmentioning

confidence: 99%

“…Since the basis of this recursive algorithm is the kernel algorithm [28], covariance data matrices X T X and X T Y play a central role in the algorithm.…”

Section: Recursive Kernel Pls Algorithmmentioning

confidence: 99%

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Adaptive Estimation of Difficult-to-Measure Process Variables

2013

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“…Using the classical NIPALS algorithm or kernel algorithm [8], we can get a PLS regression model. Hoskuldsson [9] discussed the calculation method of the latent factors vector in PLSR.…”

Section: Principle and Algorithm Researchmentioning

confidence: 99%

Improved Partial Least Squares Regression Recommendation Algorithm

Liao¹,

Du²,

Jin³

et al. 2013

Advances in Intelligent Systems Research

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-This paper aims to improve the performance of partial least squares regression, and then, improve efficiency of its implementation. In this paper we provide a novel derivation based on optimization for the partial least squares (PLS) algorithm. The derivation shows that only one of either the X-or the Y-matrix needs to be deflated during the sequential process of computing latent factors. And then, based on this derivation, an improved recursive exponentially weighted PLS regression algorithm was proposed. And the improved algorithm is obviously superior to traditional PLS regression algorithm on performance.Index Terms -partial least squares (PLS), kernel algorithm, algorithms improvement, recursive exponentially weighted algorithms

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“…A recursive algorithm for partial least squares (RPLS) for time varying processes was first introduced in Helland et al [6], and it has since been enhanced by Dayal and MacGregor [4], Qin [26,27] and Wang et al [37]. For very large data sets, Lindgren et al [16] proposed transforming the large data matrix into a smaller kernel matrix, which could then be analysed with PLS (KPLS). Nomikos and MacGregor [20] presented the idea of multi-way PLS (MPLS) to apply PLS to batch processes.…”

Section: Introductionmentioning

confidence: 99%

Fault tolerant control for a dearomatisation process

Sourander¹,

Vermasvuori²,

Sauter³

et al. 2009

Journal of Process Control

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Author 's accepted manuscript, published in Journal of Process Control 19 (2009) [1091][1092][1093][1094][1095][1096][1097][1098][1099][1100][1101][1102] Fault tolerant control for a dearomatisation process AbstractIn this paper, a fault tolerant control (FTC) for a dearomatisation process in the presence of faults in online product quality analysers is presented. The FTC consists of a fault detection system (FDI) and a logic for triggering predefined FTC actions. FDI is achieved by combining several process data driven approaches for detecting faults in online quality analysers. The FTC exploits the diagnostic information in adapting a quality controller (MPC) to the faulty situation by manipulating tuning parameters of the MPC to produce both proactive and reactive strategies. The proposed FTC was implemented, tested offline and validated onsite at the Naantali oil refinery. The successful testing and plant validation results are presented and discussed.

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The kernel algorithm for PLS

Cited by 303 publications

References 17 publications

Adaptive Estimation of Difficult-to-Measure Process Variables

Adaptive Estimation of Difficult-to-Measure Process Variables

Improved Partial Least Squares Regression Recommendation Algorithm

Fault tolerant control for a dearomatisation process

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