Evaluation of methods for feasible parameter set estimation of Takagi-Sugeno models for nonlinear regression with bounded errors
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Felix Wittich
Felix Wittich, M. Sc., is a research associate at the Department of Measurement and Control at the University of Kassel. His research interests include system identification, data-driven modeling, and machine learning.
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Andreas Kroll
Univ.-Prof. Dr.-Ing. Andreas Kroll is head of the Department of Measurement and Control at the University of Kassel. His research areas include nonlinear identification and control methods, computational intelligence, and complex systems.
Abstract
In data-driven modeling besides the point estimate of the model parameters, an estimation of the parameter uncertainty is of great interest. For this, bounded error parameter estimation methods can be used. These are particularly interesting for problems where the stochastical properties of the random effects are unknown and cannot be determined. In this paper, different methods for obtaining a feasible parameter set are evaluated for the use with Takagi-Sugeno models. Case studies with simulated data and with measured data from a manufacturing process are presented.
Zusammenfassung
Bei der datengetriebenen Modellierung ist neben der Punktschätzung der Modellparameter eine Schätzung der Parameterunsicherheit von großem Interesse. Hierfür kann eine Parameterschätzung, basierend auf Fehlerschranken, eingesetzt werden. Diese Verfahren sind insbesondere interessant, wenn die stochastischen Eigenschaften der Zufallseffekte unbekannt sind und nicht bestimmt werden können. In diesem Beitrag werden verschiedene Verfahren untersucht, um zulässige Parametermengen bei garantierten Fehlerschranken für die Schätzung von Takagi-Sugeno-Modellen zu erhalten. Dazu werden Fallstudien mit simulierten Daten und mit gemessenen Daten aus einem Fertigungsprozess vorgestellt.
Funding source: Deutsche Forschungsgemeinschaft
Award Identifier / Grant number: KR 3795/8-1
Funding statement: The scientific work has been supported by the DFG within the research priority program SPP 2086 (KR 3795/8-1).
About the authors
Felix Wittich, M. Sc., is a research associate at the Department of Measurement and Control at the University of Kassel. His research interests include system identification, data-driven modeling, and machine learning.
Univ.-Prof. Dr.-Ing. Andreas Kroll is head of the Department of Measurement and Control at the University of Kassel. His research areas include nonlinear identification and control methods, computational intelligence, and complex systems.
Acknowledgment
The authors thank the DFG for this funding and intensive technical support. Furthermore we would like to thank the anonymous reviewers for their comments that helped to improve and clarify this manuscript. The authors would also like to thank the Institute of Machining Operations at TU Dortmund for performing the hard turning operations and the Institute for Materials Engineering at University of Kassel for conducting the residual stress measurements.
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Editorial
- Ausgewählte Beiträge aus dem GMA-Fachausschuss 5.14 „Computational Intelligence“
- Methods
- Model-based control of wind turbines for active power control
- Evaluation of methods for feasible parameter set estimation of Takagi-Sugeno models for nonlinear regression with bounded errors
- Modellheuristiken für effizientes forward model learning
- Anwendungen
- Zur approximativen Maximum-Likelihood-Schätzung dynamischer Multi-Modelle vom Typ Takagi-Sugeno: Methodik und Anwendung auf einen Servo-Pneumatikantrieb
- Identification of a potable water system
- CAD-to-real: enabling deep neural networks for 3D pose estimation of electronic control units
- Evaluierung von Merkmalen zur Abbildung von Veränderungen in ungeordneten Bilddaten
- Automating the optical identification of abrasive wear on electrical contact pins
- Forum
- Toolbox zur Identifikation von Takagi-Sugeno-Fuzzy-Modellen
- Persönliches
- Nachruf für Prof. Dr. rer. nat. Hartwig Steusloff
- Prof. Dr.-Ing. habil. Jürgen Beyerer zum 60. Geburtstag
Artikel in diesem Heft
- Frontmatter
- Editorial
- Ausgewählte Beiträge aus dem GMA-Fachausschuss 5.14 „Computational Intelligence“
- Methods
- Model-based control of wind turbines for active power control
- Evaluation of methods for feasible parameter set estimation of Takagi-Sugeno models for nonlinear regression with bounded errors
- Modellheuristiken für effizientes forward model learning
- Anwendungen
- Zur approximativen Maximum-Likelihood-Schätzung dynamischer Multi-Modelle vom Typ Takagi-Sugeno: Methodik und Anwendung auf einen Servo-Pneumatikantrieb
- Identification of a potable water system
- CAD-to-real: enabling deep neural networks for 3D pose estimation of electronic control units
- Evaluierung von Merkmalen zur Abbildung von Veränderungen in ungeordneten Bilddaten
- Automating the optical identification of abrasive wear on electrical contact pins
- Forum
- Toolbox zur Identifikation von Takagi-Sugeno-Fuzzy-Modellen
- Persönliches
- Nachruf für Prof. Dr. rer. nat. Hartwig Steusloff
- Prof. Dr.-Ing. habil. Jürgen Beyerer zum 60. Geburtstag
