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Incremental DoE and Modeling Methodology with Gaussian Process Regression: An Industrially Applicable Approach to Incorporate Expert Knowledge

Author

Listed:
  • Tim Voigt

    (Center for Applied Data Science Gütersloh, Faculty of Engineering and Mathematics, University of Applied Sciences, 33619 Bielefeld, Germany)

  • Martin Kohlhase

    (Center for Applied Data Science Gütersloh, Faculty of Engineering and Mathematics, University of Applied Sciences, 33619 Bielefeld, Germany)

  • Oliver Nelles

    (Automatic Control—Mechatronics, University of Siegen, 57076 Siegen, Germany)

Abstract

The use of data-based models is a favorable way to optimize existing industrial processes. Estimation of these models requires data with sufficient information content. However, data from regular process operation are typically limited to single operating points, so industrially applicable design of experiments (DoE) methods are needed. This paper presents a stepwise DoE and modeling methodology, using Gaussian process regression that incorporates expert knowledge. This expert knowledge regarding an appropriate operating point and the importance of various process inputs is exploited in both the model construction and the experimental design. An incremental modeling scheme is used in which a model is additively extended by another submodel in a stepwise fashion, each estimated on a suitable experimental design. Starting with the most important process input for the first submodel, the number of considered inputs is incremented in each step. The strengths and weaknesses of the methodology are investigated, using synthetic data in different scenarios. The results show that a high overall model quality is reached, especially for processes with few interactions between the inputs and low noise levels. Furthermore, advantages in the interpretability and applicability for industrial processes are discussed and demonstrated, using a real industrial use case as an example.

Suggested Citation

  • Tim Voigt & Martin Kohlhase & Oliver Nelles, 2021. "Incremental DoE and Modeling Methodology with Gaussian Process Regression: An Industrially Applicable Approach to Incorporate Expert Knowledge," Mathematics, MDPI, vol. 9(19), pages 1-26, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2479-:d:649683
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    References listed on IDEAS

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    2. Friedman, Jerome H., 2002. "Stochastic gradient boosting," Computational Statistics & Data Analysis, Elsevier, vol. 38(4), pages 367-378, February.
    3. Jack P.C. Kleijnen, 2015. "Design and Analysis of Simulation Experiments," International Series in Operations Research and Management Science, Springer, edition 2, number 978-3-319-18087-8, January.
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    1. Paweł Fic & Adam Czornik & Piotr Rosikowski, 2023. "Anomaly Detection for Hydraulic Power Units—A Case Study," Future Internet, MDPI, vol. 15(6), pages 1-29, June.
    2. Muhammad Yousaf Arshad & Muhammad Azam Saeed & Muhammad Wasim Tahir & Halina Pawlak-Kruczek & Anam Suhail Ahmad & Lukasz Niedzwiecki, 2023. "Advancing Sustainable Decomposition of Biomass Tar Model Compound: Machine Learning, Kinetic Modeling, and Experimental Investigation in a Non-Thermal Plasma Dielectric Barrier Discharge Reactor," Energies, MDPI, vol. 16(15), pages 1-26, August.

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