Skip to main content
Log in

An accumulative error based adaptive design of experiments for offline metamodeling

  • RESEARCH PAPER
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

A popular method to reduce the computational effort in simulation-based engineering design is by way of approximation. An approximation method involves two steps: Design of Experiments (DOE) and metamodeling. In this paper, a new DOE approach is introduced. The proposed approach is adaptive and samples more design points in regions where the simulation response is expected to be highly nonlinear and multi-modal. Numerical and engineering examples are used to demonstrate the applicability of the proposed DOE approach. The results from these examples show that for the same number of simulation evaluations and according to metamodel accuracy, the proposed DOE approach performs better for majority of test examples compared to two previous methods, i.e., the maximum entropy design method and maximum scaled distance method.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Barthelemy J-FM, Haftka RT (1993) Approximation concepts for optimum structural design—a review. Struct Optim 5:129–144

    Article  Google Scholar 

  • Chen VCP, Tsui KL, Barton RR, Meckesheimer M (2006) A review on design, modeling and applications of computer experiments. IIE Trans 38:273–291

    Article  Google Scholar 

  • Clark SM, Griebsch JH, Simpson TW (2005) Analysis of support vector regression for approximation of complex engineering analyses. J Mech Des 127:1077–1087

    Article  Google Scholar 

  • Cormen TH, Leiserson CE, Rivest RL, Stein C (2001) Introduction to Algorithms, 2nd edn. MIT, Cambridge

    MATH  Google Scholar 

  • Cox DD, John S (1997) SDO: a statistical method for global optimization. In: Alexandrov N, Hussaini MY (eds) Multidisciplinary design optimization: state of the art. SIAM, Philadelphia, pp 315–329

    Google Scholar 

  • Cressie NAC (1993) Statistics for spatial data. Wiley, New York

    Google Scholar 

  • Fang K-T, Wang Y (1994) Number-theoretic methods in statistics. Chapman & Hall, New York

    MATH  Google Scholar 

  • Fang K-T, Lin DKJ, Winker P, Zhang Y (2000) Uniform design: theory and application. Technometrics 42:237–248

    Article  MATH  MathSciNet  Google Scholar 

  • Farhang-Mehr A, Azarm S (2002) A sequential information-theoretic approach to design of computer experiments. CD-ROM proceedings of the 9th AIAA/ISSMO symposium on multidisciplinary analysis and optimization, Atlanta

  • Farhang-Mehr A, Azarm S (2005) Bayesian meta-modeling of engineering design simulations: a sequential approach with adaptation to irregularities in the response behavior. Int J Numer Methods Eng 62:2104–2126

    Article  MATH  Google Scholar 

  • Farhang-Mehr A, Azarm S, Diaz A, Ravisekar A (2003) Approximation-assisted crashworithness design of front-end of a pickup truck. CD-ROM proceedings of the ASME 2003 design engineering technical conference. Chicago

  • Goldberg DE (1989) Genetic algorithms in search, optimization and machine learning. Addison-Wesley, Boston

    MATH  Google Scholar 

  • Gunawan S, Azarm S (2005) A feasibility robust optimization method using sensitivity region concept. J Mech Des 127:858–865

    Article  Google Scholar 

  • Hedar AR (2005) Test problems for unconstrained and constrained global optimization, global optimization methods and codes. System Optimization Lab, Kyoto University, Kyoto

    Google Scholar 

  • Jin R, Chen W, Sudjianto A (2002) On sequential sampling for global metamodeling in engineering design. CD-ROM proceedings of ASME IDETC, design automation conference. Montreal, Canada

  • Johnson ME, Moore LM, Ylvisaker D (1990) Minimax and maximin distance designs. J Stat Plan Inference 26(2):131–148

    Article  MathSciNet  Google Scholar 

  • Jones DR (2001) A taxonomy of global optimization methods based on response surfaces. J Glob Optim 21:345–383

    Article  MATH  Google Scholar 

  • Jones DR, Schonlau M, Welch WJ (1998) Efficient global optimization of expensive black box functions. J Glob Optim 13:455–492

    Article  MATH  MathSciNet  Google Scholar 

  • Kalagnanam JR, Diwekar UM (1997) An efficient sampling technique for off-line quality control. Technometrics 39(3):308–319

    Article  MATH  Google Scholar 

  • Koehler JR, Owen AB (1996) Computer experiments. Handbook of statistics, vol 13. Elsevier, New York

    Google Scholar 

  • Li G (2007) Online and offline approximations for population based multi-objective optimization. Ph.D. Dissertation, University of Maryland, College Park

  • Lindley DV (1956) On a measure of the information provided by an experiment. Ann Math Stat 27:986–1005

    Article  MATH  MathSciNet  Google Scholar 

  • Lophaven SN, Nielsen HB, Søndergaard J (2002) Aspects of the matlab toolbox DACE. IMM-TR2002–13. Technical University of Denmark, Lyngby

    Google Scholar 

  • McKay MD, Beckman RJ, Conover WJ (1979) A comparison of three methods for selecting values of input variables in the analysis of response from a computer code. Technometrics 21(2):239–245

    Article  MATH  MathSciNet  Google Scholar 

  • Meckesheimer M, Booker AJ (2002) Computationally inexpensive metamodel assessment strategies. AIAA J 40(10):2053–2060

    Article  Google Scholar 

  • Myers RH, Montgomery DC (1995) Response surface methodology: process and product optimization using designed experiments. Wiley, New York

    MATH  Google Scholar 

  • Owen AB (1992) Orthogonal arrays for computer experiments, integration and visualization. Stat Sin 2:439–452

    MATH  MathSciNet  Google Scholar 

  • Roux WJ, Stander N, Haftka RT (1998) Response surface approximations for structural optimization. Int J Numer Methods Eng 42:517–534

    Article  MATH  Google Scholar 

  • Ruzika S, Wiecek MM (2003) A survey of approximation methods in multiobjective programming. J Optim Theory Appl 126(3):473–501

    Article  MathSciNet  Google Scholar 

  • Sacks J, Welch WJ, Mitchell TJ, Wynn HP (1989) Design and analysis of computer experiments. Stat Sci 4:409–435

    Article  MATH  MathSciNet  Google Scholar 

  • Sasena MJ (2002) Adaptive experimental design applied to an ergonomics testing procedure. CD-ROM proceedings of the ASME IDETC. Montreal, Canada

  • Sasena MJ, Papalambros PY, Goovaerts P (2000). Metamodeling sampling criteria in a global optimization framework. CD-ROM proceedings of the 8th AIAA/USAF/ISSMO symposium on multidisciplinary analysis and optimization. Long Beach, CA

  • Schonlau M, Welch WJ, Jones DR (1997) Global versus local search in constrained optimization of computer models. In: Flournoy N, Rosenberger WF, Wong WK (eds) New developments and applications in experimental design. Institute of Mathematical Statistics, Beachwood

    Google Scholar 

  • Shewry MC, Wynn HP (1987) Maximum entropy sampling. J Appl Stat 14:165–170

    Article  Google Scholar 

  • Simpson TW, Booker AJ, Ghosh D, Giunta AA, Koch PN, Yang R-J (2004) Approximation methods in multidisciplinary analysis and optimization: a panel discussion. Struct Multidisc Optim 27(5):302–313

    Article  Google Scholar 

  • Watson AG, Barnes RJ (1995) Infill sampling criteria to locate extremes. Math Geol 27(5):589–608

    Article  Google Scholar 

  • Weiss MA (1997) Data structures and algorithm analysis in C, 2nd edn. Addison-Wesley, Boston

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Shapour Azarm.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, G., Aute, V. & Azarm, S. An accumulative error based adaptive design of experiments for offline metamodeling. Struct Multidisc Optim 40, 137–155 (2010). https://doi.org/10.1007/s00158-009-0395-z

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-009-0395-z

Keywords

Navigation