Recursive generalised-least-squares procedure for online identification of process parameters

Hastings-James, R.; Sage, M.W.

doi:10.1049/piee.1969.0378

Cited by 72 publications

(10 citation statements)

References 2 publications

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“…Generalized least-squares (Clarke, 1967;Hastings-James and Sage, 1969) Maximum likelihood (Astrom and Bohlin, 1966)…”

Section: Black Box Modelsmentioning

confidence: 99%

Model Structure Identification From Experimental Data

Beck¹

1979

Theoretical Systems Ecology

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PREFACEIn recent years there has been considerable interest in the development of models for river and lake ecological systems. Much of this interest has been directed toward the development of progressively larger and more complex simulation models. In contrast, relatively little attention has been devoted to the problems of uncertainty and errors in the field data, of inadequate numbers of field data, of uncertainty in the relationships between the important system variables, and of uncertainty in the model parameter estimates. The International Institute for Applied Systems Analysis Resources and Environment Area's Task on Models for Environmental Quality Control and Management addresses problems such as these.The subject of this paper is model calibration. But rather than solving the customary problem of model parameter estimation, given an established structure for the model, the paper attempts to answer the prior question of identifying the dominant relationships between the system inputs, state variables, and output responses. That, then, is the problem that needs to be solved before one can consider how to estimate the model parameter values accurately. And it is a problem because, despite very many laboratory-scale experiments and a number of major field studies, our knowledge of the relationships between the mineral, organic, and microbiological components of an aquatic ecosystem is still quite uncertain.iii SUMMARY This paper is reprinted from the book Theoretical Systems Ecology: Advances and Case Studies, edited by E. Halfon of the Canada Centre for Inland Waters and published by Academic Press, New York. Acknowledging that systems ecology has had a large impact on all aspects of environmental research, the book aims to bridge the gap in communication between theoreticians, modelers, and field ecologists. Three classes of problems are treated in the book. They separate approximately into (a) how the model should be developed and analyzed prior to the collection and use of field data, (b) how the model should be developed or modified when it is evaluated against field data, and (c) the desired properties of the models for control and management purposes. The objective of this paper is to emphasize the fact that the second of these three problem categories is not simply a matter of straightforward model parameter estimation.The basic problem of model calibration -or system identification -is that information about the "externally" observed behavior of a system is required to be translated into information about the model-based description of the system's "internal" mechanisms of behavior. The measured input and output variables represent the system's external description, whereas state variables and parameter values refer to the system's internal description. In other words, during model calibration, and especially in the process of identifying the model's structure, we seek improved understanding of those physical, chemical, and biological phenomena that are thought to govern the system's observed be...

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“…Generalized least-squares (Clarke, 1967;Hastings-James and Sage, 1969) Maximum likelihood (Astrom and Bohlin, 1966)…”

Section: Black Box Modelsmentioning

confidence: 99%

Model Structure Identification From Experimental Data

Beck¹

1979

Theoretical Systems Ecology

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“…Die Ergebnisse von Gl. (7) sind daher durch Errechnen von Korrekturen Aat mit dem Ziel des genaueren Modellierens des wirklichen nichtlinearen Zusammenhangs (10) in einer Reihe entwickelt, so ergibt sich :…”

Section: B) Rekursive Algorithmen Zur On-line-verbesserung Der Geschäunclassified

“…und H ac AV) = ffau(K) + Q [e^neu ~ H,.,(10] ; (14), (15) und (16) stellen verallgemeinerte rekursive Algorithmen für die angepaßte und iterativ verbesserte Parameterschätzung dar.Die Bilder 4 und 5 zeigen Blockschaltpläne der rekursiv arbeitenden Trendfilterung und -Schätzung.In manchen Fällen sind die Variablen x¡ deterministische Funktionen (ζ. B. Polynome, harmonische Schwingungen oder Kombinationen von diesen), die in einem jeweils gleich langen, zuletzt vergangenen Zeitbereich fest definiert werden[7].…”

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Standardisierte Analyse und Führung komplexer Systeme mit Prozeßrechner, Teil 1

Shahata¹

1973

at - Automatisierungstechnik

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Für die On-Iine-Analyse und -Führung industrieller Prozesse wird eine hierarchisch aufgebaute Konzeption entwickelt, die auf mehrfacher Zerlegung des Gesamtsystems beruht. Es werden dabei drei charakteristische Teilsysteme festgelegt, die ihrerseits durch die Definition von Teilmodellen schrittweise beschrieben und analysiert werden. Die Teilmodellanalyse erfolgt auj einheitliche verallgemeinerte Weise durch statistisch-adaptiv arbeitende Trendalgorithmen. Mit der Konzeption ist eine standardisierte Programmierung möglich, so daß der Einsatz beider Analyse und Führung verschiedenartiger industrieller Prozesse gegeben ist. Anhand eines Beispiels aus der Praxis (Stahlerzeugung nach dem Sauerstoffaufblasverfahren) wird im zweiten Teil dieser Arbeit die Anwendung der Konzeption erläutert. For the on-line analysis and open-loop control of industriai processes a hierachical structured concept is derived which is based on multiple decomposition of the overall system.Three characteristic partial systems are defined which are themselves described and analyzed step by step by definition of partial mode/Is. The analysis of the partial modells is realized in generalized form by trend algorithms which work in a statistical adaptive way. With this concept a standardized programming is possible such that it can be applied for the analysis and open-loop control of different industrial processes.By use of a practical example (steel production by oxygen blasting procedure) the application of the concept is demonstrated in the second part of the paper.

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“…But its disadvantage is that estimated parameters have asymptotic bias when input and output data are contaminated by noises. In Xu (1986), Hasting-James and Sage (1969), Hsia (1977), Chen and Wang (2003), the generalized least squares method was introduced to overcome this disadvantage, but its result can not guarantee an estimation with no asymptotic bias (Lu and Fisher, 1989;Ding and Yang, 1999a;Ding and Yang, 1999b). Lagrange equation, which meets the system input and output, is established in this paper.…”

Section: Introductionmentioning

confidence: 99%

Parameter estimation with constraints based on variational method

Shi

2010

J. Marine. Sci. Appl.

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The accuracy of parameter estimation is critical when digitally modeling a ship. A parameter estimation method with constraints was developed, based on the variational method. Performance functions and constraint equations in the variational method are constructed by analyzing input and output equations of the system. The problem of parameter estimation was transformed into a problem of least squares estimation. The parameter estimation equation was analyzed in order to get an optimized estimation of parameters based on the Lagrange multiplication operator. Simulation results showed that this method is better than the traditional least squares estimation, producing a higher precision when identifying parameters. It has very important practical value in areas of application such as system identification and parameter estimation.

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Recursive generalised-least-squares procedure for online identification of process parameters

Cited by 72 publications

References 2 publications

Model Structure Identification From Experimental Data

Model Structure Identification From Experimental Data

Standardisierte Analyse und Führung komplexer Systeme mit Prozeßrechner, Teil 1

Parameter estimation with constraints based on variational method

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