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International Workshop on Machine Learning, Optimization and Big Data

MOD 2015: Machine Learning, Optimization, and Big Data pp 93–104Cite as

Advanced Metamodeling Techniques Applied to Multidimensional Applications with Piecewise Responses

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Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9432))

Abstract

Due to digital changes in the solution properties of many engineering applications, the model response is described by a piecewise continuous function. Generating continuous metamodels for such responses can provide very poor fits due to the discontinuity in the response. In this paper, a new smart sampling approach is proposed to generate high quality metamodels for such piecewise responses. The proposed approach extends the Sequential Approximate Optimization (SAO) procedure, which uses the Radial Basis Function Network (RBFN). It basically generates accurate metamodels iteratively by adding new sampling points, to approximate responses with discrete changes. The new sampling points are added in the sparse region of the feasible (continuous) domain to achieve a high quality metamodel and also next to the discontinuity to refine the uncertainty area between the feasible and non-feasible domain. The performance of the approach is investigated through two numerical examples, a two- dimensional analytical function and a laser epoxy cutting simulation model.

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Acknowledgements

The authors would like to thank the German Research Association DFG for the kind support within the Cluster of Excellence “Integrative Production Technology for High-Wage Countries” of RWTH Aachen University.

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Authors and Affiliations

  1. Department for Nonlinear Dynamics of Laser Processing (NLD), RWTH Aachen University, Aachen, Germany

    Toufik Al Khawli & Urs Eppelt

  2. Fraunhofer Institute for Laser Technology ILT, Aachen, Germany

    Wolfgang Schulz

Authors
  1. Toufik Al Khawli
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  2. Urs Eppelt
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  3. Wolfgang Schulz
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Corresponding author

Correspondence to Toufik Al Khawli .

Editor information

Editors and Affiliations

  1. University of Florida, Gainsville, Florida, USA

    Panos Pardalos

  2. University of Catania, Catania, Italy

    Mario Pavone

  3. University of Catania, Catania, Italy

    Giovanni Maria Farinella

  4. University of Catania, Catania, Italy

    Vincenzo Cutello

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© 2015 Springer International Publishing Switzerland

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Al Khawli, T., Eppelt, U., Schulz, W. (2015). Advanced Metamodeling Techniques Applied to Multidimensional Applications with Piecewise Responses. In: Pardalos, P., Pavone, M., Farinella, G., Cutello, V. (eds) Machine Learning, Optimization, and Big Data. MOD 2015. Lecture Notes in Computer Science(), vol 9432. Springer, Cham. https://doi.org/10.1007/978-3-319-27926-8_9

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  • DOI: https://doi.org/10.1007/978-3-319-27926-8_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-27925-1

  • Online ISBN: 978-3-319-27926-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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