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Space partitioning in engineering design via metamodel acceptance score distribution

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Abstract

Metamodels for simulators are used to reduce computational costs in engineering system design. In general, metamodels have different fit accuracy levels over different regions in the design variables space, especially for highly nonlinear responses over wide spaces. A metamodeling strategy should place less emphasis on sub regions in the design variables space requiring relatively less complex metamodels. In this paper, we present a graphically based methodology that can be used to partition the space for piecewise metamodel building. The method is based on analyzing an initial global metamodel for acceptability in terms of prediction accuracy over the whole space; then generating acceptance score distribution (ASD) plots. Visual inspection of the ASD plots is used as a guidance to partition the design variables space, leading to a metamodel with fair prediction accuracy on a piece-by-piece basis, not just globally on average. The proposed methodology is general and can be applied to various metamodel types. It is tested on a number of problems, including some of the most highly nonlinear test problems used in the literature.

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Notes

  1. It may be appropriate to suggest here the use of a shift transformation on data points having an unacceptable number of data points with zero response if it is planned to use ASD plots. The shift transformation is achieved by adding a constant to each response value, such that all responses in the validation sample become positive.

  2. Note that if each of the six variables is varied using three levels for each for a second-order polynomial metamodel then a uniform design with 36 =  729 design points is obtained.

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Authors and Affiliations

  1. Electronic Engineering Department, Hijjawi College of Engineering Technology, Yarmouk University, Irbid, Jordan

    Husam Hamad & Adnan Al-Smadi

  2. Prince-Hussein Bin Abdullah College for Information Technology, Al Al-Bayt University, Al-Mafraq, Jordan

    Adnan Al-Smadi

Authors
  1. Husam Hamad
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  2. Adnan Al-Smadi
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Correspondence to Adnan Al-Smadi.

Additional information

Professor Adnan Al-Smadi is currently on sabbatical leave.

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Hamad, H., Al-Smadi, A. Space partitioning in engineering design via metamodel acceptance score distribution. Engineering with Computers 23, 175–185 (2007). https://doi.org/10.1007/s00366-007-0056-z

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