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Nonlinear system categorization for structural data mining with state space models

  • Hermann Klein

    Hermann Klein graduated at the University of Siegen in 2021 with a Master of Science in Mechanical Engineering and worked as a test engineer in industry. In 2022 he has joined Prof. Nelles’ research group for Automatic Control – Mechatronics at the Department of Mechanical Engineering at the University of Siegen. His research interests are nonlinear system identification and state space modeling.

     EMAIL logo     , Max Schüssler

    Max Schüssler was a research assistant with the working group Automatic Control – Mechatronics of Prof. Nelles until 2022 and is currently employed as Data Scientist in the industry. He received his doctor’s degree in 2022 at the University of Siegen. In his work, he focuses on machine learning perspectives for nonlinear system identification and adjacent research fields.

         and Oliver Nelles

    Oliver Nelles is Professor at the University of Siegen in the Department of Mechanical Engineering and chair of Automatic Control – Mechatronics. He received his doctor’s degree in 1999 at the Technical University of Darmstadt. His key research topics are nonlinear system identification, design of experiments, metamodeling, and local model networks.
Published/Copyright: October 10, 2025
at - Automatisierungstechnik
From the journal at - Automatisierungstechnik Volume 73 Issue 10

Abstract

Data-driven state space models allow accurate descriptions of nonlinear systems, as they represent a general and abstract modeling approach. With the help of the model structure according to the canonical controllable form, it is possible to determine the main nonlinear influences on the process and thus, carry out learning-based categorization. Within this contribution, we explain and test categorization with the help of the Local Model State Space Network and show how conclusions about the underlying process can be drawn. Especially for time-variant behavior, the method provides the possibility to categorize the process in terms of its nonlinear characteristics to enable fault diagnosis.

Zusammenfassung

Datengetriebene Zustandsraummodelle ermöglichen die präzise Beschreibung nichtlinearer Systeme, indem sie einen allgemeinen und abstrakten Modellbildungsansatz verfolgen. Mit Hilfe der Modellstruktur entsprechend der Regelungsnormalform ist die Bestimmung der nichtlinearen Haupteinflussgrößen auf den Prozess und dadurch die lernbasierte Kategorisierung möglich. Innerhalb dieses Beitrags erklären und testen wir die Kategorisierung mit Hilfe des Local Model State Space Networks und legen dar, wie Rückschlüsse über den zu Grunde liegenden Prozess gezogen werden können. Insbesondere bei zeitvariantem Verhalten bietet das Verfahren die Möglichkeit, den Prozess hinsichtlich seiner nichtlinearen Charakteristik zu kategorisieren, um eine Fehlerdiagnose zu ermöglichen.

Keywords: local model networks; nonlinear state space models; data mining; time-varying systems; fault detection and isolation
Schlagwörter: Lokale Modellnetze; nichtlineare Zustandsraummodelle; Data Mining; zeitvariante Systeme; Fehlererkennung und -isolation
Corresponding author: Hermann Klein, Department Maschinenbau, Institut für Mechanik und Regelungstechnik – Mechatronik, Universität Siegen, Paul-Bonatz-Str. 9-11, 57068 Siegen, Germany, E-mail: 

About the authors

Hermann Klein

Hermann Klein graduated at the University of Siegen in 2021 with a Master of Science in Mechanical Engineering and worked as a test engineer in industry. In 2022 he has joined Prof. Nelles’ research group for Automatic Control – Mechatronics at the Department of Mechanical Engineering at the University of Siegen. His research interests are nonlinear system identification and state space modeling.

Max Schüssler

Max Schüssler was a research assistant with the working group Automatic Control – Mechatronics of Prof. Nelles until 2022 and is currently employed as Data Scientist in the industry. He received his doctor’s degree in 2022 at the University of Siegen. In his work, he focuses on machine learning perspectives for nonlinear system identification and adjacent research fields.

Oliver Nelles

Oliver Nelles is Professor at the University of Siegen in the Department of Mechanical Engineering and chair of Automatic Control – Mechatronics. He received his doctor’s degree in 1999 at the Technical University of Darmstadt. His key research topics are nonlinear system identification, design of experiments, metamodeling, and local model networks.

  1. Research ethics: Not applicable.

  2. Informed consent: Not applicable.

  3. Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  4. Use of Large Language Models, AI and Machine Learning Tools: None declared.

  5. Conflict of interest: The authors declare no conflict of interest regarding this article.

  6. Research funding: None declared.

  7. Data availability: Not applicable.

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Received: 2025-02-16
Accepted: 2025-08-04
Published Online: 2025-10-10
Published in Print: 2025-10-27

© 2025 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Editorial
  3. Selected contributions from the workshops “Computational Intelligence” in 2023 and 2024
  4. Methods
  5. Nonlinear system categorization for structural data mining with state space models
  6. Incorporation of structural properties of the response surface into oblique model trees
  7. Takagi-Sugeno based model reference control for wind turbine systems in frequency containment scenarios
  8. On autoregressive deep learning models for day-ahead wind power forecasts with irregular shutdowns due to redispatching
  9. Applications
  10. Efficiently determining the effect of data set size on autoencoder-based metamodels for structural design optimization
  11. Kalibriermodellerstellung und Merkmalsselektion für die mikromagnetische Materialcharakterisierung mittels maschineller Lernverfahren
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  13. EAP4EMSIG – enhancing event-driven microscopy for microfluidic single-cell analysis
https://doi.org/10.1515/auto-2025-0015
Keywords for this article
local model networks; nonlinear state space models; data mining; time-varying systems; fault detection and isolation

Articles in the same Issue

  1. Frontmatter
  2. Editorial
  3. Selected contributions from the workshops “Computational Intelligence” in 2023 and 2024
  4. Methods
  5. Nonlinear system categorization for structural data mining with state space models
  6. Incorporation of structural properties of the response surface into oblique model trees
  7. Takagi-Sugeno based model reference control for wind turbine systems in frequency containment scenarios
  8. On autoregressive deep learning models for day-ahead wind power forecasts with irregular shutdowns due to redispatching
  9. Applications
  10. Efficiently determining the effect of data set size on autoencoder-based metamodels for structural design optimization
  11. Kalibriermodellerstellung und Merkmalsselektion für die mikromagnetische Materialcharakterisierung mittels maschineller Lernverfahren
  12. Investigating quality inconsistencies in the ultra-high performance concrete manufacturing process using a search-space constrained non-dominated sorting genetic algorithm II
  13. EAP4EMSIG – enhancing event-driven microscopy for microfluidic single-cell analysis
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