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  4. Compensating data shortages in manufacturing with monotonicity knowledge
 
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2021
Journal Article
Title

Compensating data shortages in manufacturing with monotonicity knowledge

Abstract
Systematic decision making in engineering requires appropriate models. In this article, we introduce a regression method for enhancing the predictive power of a model by exploiting expert knowledge in the form of shape constraints, or more specifically, monotonicity constraints. Incorporating such information is particularly useful when the available datasets are small or do not cover the entire input space, as is often the case in manufacturing applications. We set up the regression subject to the considered monotonicity constraints as a semi-infinite optimization problem, and propose an adaptive solution algorithm. The method is applicable in multiple dimensions and can be extended to more general shape constraints. It was tested and validated on two real-world manufacturing processes, namely, laser glass bending and press hardening of sheet metal. It was found that the resulting models both complied well with the experts monotonicity knowledge and predicted the training data accurately. The suggested approach led to lower root-mean-squared errors than comparative methods from the literature for the sparse datasets considered in this work.
Author(s)
Kurnatowski, M. von
Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM  
Schmid, J.
Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM  
Link, P.
Fraunhofer-Institut für Werkzeugmaschinen und Umformtechnik IWU  
Zache, R.
Fraunhofer-Institut für Werkzeugmaschinen und Umformtechnik IWU  
Morand, L.
Fraunhofer-Institut für Werkstoffmechanik IWM  
Kraft, T.
Fraunhofer-Institut für Werkstoffmechanik IWM  
Schmidt, I.
Fraunhofer-Institut für Werkstoffmechanik IWM  
Schwientek, J.
Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM  
Stoll, A.
Fraunhofer-Institut für Werkzeugmaschinen und Umformtechnik IWU  
Journal
Algorithms  
Project(s)
MLAP
Funder
Fraunhofer-Gesellschaft FhG
Open Access
DOI
10.3390/a14120345
Language
English
Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWM  
Fraunhofer-Institut für Werkstoffmechanik IWM  
Fraunhofer-Institut für Werkzeugmaschinen und Umformtechnik IWU  
Keyword(s)
  • monotonic regression

  • manufacturing

  • informed machine learning

  • expert knowledge

  • semi-infinite optimization

  • shape constraints

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