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A Weighted Sequential Sampling Method Considering Influences of Sample Qualities in Input and Output Parameter Spaces for Global Optimization

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Abstract

A new sampling method, namely weighted sequential sampling method, is introduced in this research to improve accuracy and efficiency of adaptive metamodeling considering influences of sample quality measures in both input and output parameter spaces. In this method, sample quality measures in input and output parameter spaces are associated with weighting factors. Values of these weighting factors are changed in sequential sampling considering the different levels of contributions of these sample quality measures in the input and output parameter spaces during the adaptive metamodeling process. Since quality of the metamodel developed through weighted sequential sampling is good in the whole design space, quality of global optimization can be improved through adaptive metamodeling based on weighted sequential sampling.

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References

  1. Simpson, T.W., Peplinski, J., Koch, P.N., Allen, J.K.: Metamodels for computer-based engineering design: survey and recommendations. Eng. Comput. 17(2), 129–150 (2001)

    Article  MATH  Google Scholar 

  2. McKay, M.D., Beckman, R.J., Conover, W.J.: Comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21(2), 239–245 (1979)

    MATH  MathSciNet  Google Scholar 

  3. Fang, K.T.: Experimental design by uniform distribution. Acta Math. Appl. Sin. 3, 363–372 (1980)

    MATH  Google Scholar 

  4. Jin, R., Chen, W., Sudjianto, A.: On sequential sampling for global metamodeling in engineering design. In: Proceedings of the ASME 2002 Design Engineering Technical Conferences and Computer and Information in Engineering Conference, Montreal, Quebec, Canada (2002).

  5. Xiong, Y., Chen, W., Tsui, K.L.: A new variable fidelity optimization framework based on model fusion and objective-oriented sequential sampling. In: Proceedings of the ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Las Vegas, Nevada, USA (2007).

  6. Yao, W., Chen, X., Luo, W.: A gradient-based sequential radial basis function neural network modeling method. Neural Comput. Appl. 18(5), 477–484 (2009)

    Article  Google Scholar 

  7. Gramacy, R.B., Lee, H.K.H.: Adaptive design and analysis of supercomputer experiments. Technometrics 51(2), 130–145 (2009)

    Article  MathSciNet  Google Scholar 

  8. Wei, X., Wu, Y., Chen, L.: A new sequential optimal sampling method for radial basis functions. Appl. Math. Comput. 218(19), 9635–9646 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  9. Wang, G.G., Shan, S.: Review of metamodeling techniques in support of engineering design optimization. J. Mech. Des., ASME Trans. 129(4), 370–380 (2007)

    Article  MathSciNet  Google Scholar 

  10. Matheron, G.: Principals of geostatistics. Econ. Geol. 58(8), 1246–1266 (1963)

    Article  Google Scholar 

  11. Sacks, J., Welch, W.J., Mitchell, T.J., Wynn, H.P.: Design and analysis of computer experiments. Stat. Sci. 4(4), 409–435 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  12. Lophaven, S.N., Nielsen, H.B., Søndergaard, J.: DACE: A Matlab Kriging Toolbox, Version 2.0. Technical Report IMMREP-2002-12. Technical University of Denmark, Kongens Lyngby, Denmark (2002).

  13. Fang, K.T., Li, R., Sudjianto, A.: Design and Modeling for Computer Experiments. Chapman & Hall/CRC, London (2006)

    MATH  Google Scholar 

  14. Zhao, D., Xue, D.: A comparative study of metamodeling methods considering sample quality merits. Struct. Multidiscip. Optim. 42(6), 923–938 (2010)

    Article  Google Scholar 

  15. Hickernell, F.J.: A generalized discrepancy and quadrature error bound. Math. Comput. 67(221), 299–322 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  16. Yang, Q., Kianimanesh, A., Park, S.S., Freiheit, T., Xue, D.: A semi-empirical model considering the influence of operating parameters on performance for a direct methanol fuel cell. J. Power Sources 196(24), 10640–10651 (2011)

    Article  Google Scholar 

Download references

Acknowledgments

The authors would like to acknowledge the support from the Natural Sciences and Engineering Research Council (NSERC) of Canada through its Discovery Grant.

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Authors and Affiliations

  1. Department of Mechanical and Manufacturing Engineering, University of Calgary, Calgary, Alberta , T2N 1N4, Canada

    Qinwen Yang & Deyi Xue

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  1. Qinwen Yang
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  2. Deyi Xue
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Correspondence to Deyi Xue.

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Yang, Q., Xue, D. A Weighted Sequential Sampling Method Considering Influences of Sample Qualities in Input and Output Parameter Spaces for Global Optimization. J Optim Theory Appl 164, 644–665 (2015). https://doi.org/10.1007/s10957-014-0576-9

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  • DOI: https://doi.org/10.1007/s10957-014-0576-9

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