Adaptive Kriging for Simulation-based Design under Uncertainty - Development of Metamodels in Augmeted Input Space and Adaptive Tuning of Their Characteristics

Alexandros Taflanidis, Juan Camilo Medina

2014

Abstract

This investigation focuses on design-under-uncertainty problems that employ a probabilistic performance as objective function and consider its estimation through stochastic simulation. This approach puts no constraints on the computational and probability models adopted, but involves a high computational cost especially for design problems involving complex, high-fidelity numerical models. A framework relying on kriging metamodeling to approximate the system performance in an augmented input space is considered here to alleviate this cost. A sub region of the design space is defined and a kriging metamodel is built to approximate the system response (output) with respect to both the design variables and the uncertain model parameters (random variables). This metamodel is then used within a stochastic simulation setting (addressing uncertainties in the model parameters) to approximate the system performance when estimating the objective function for specific values of the design variables. This information is then used to search for a local optimum within the previously established design sub domain. Only when the optimization algorithm drives the search outside this domain, a new metamodel is generated. The process is iterated until convergence is established and an efficient sharing of information across these iterations is established to adaptively tune characteristics of the kriging metamodel.

References

  1. Dubourg, V., Sudret, B. & Bourinet, J.-M. 2011. Reliability-based design optimization using kriging surrogates and subset simulation. Structural and Multidisciplinary Optimization, 44(5), 673-690.
  2. Gasser, M. & Schueller, G. I. 1997. Reliability-based optimization of structural systems. Mathematical Methods of Operations Research, 46, 287-307.
  3. Gavin, H. P. & Yau, S. C. 2007. High-order limit state functions in the response surface method for structural reliability analysis. Structural Safety, 30(2), 162-179.
  4. Jaynes, E. T. 2003. Probability Theory: The logic of science, Cambridge, UK, Cambridge University Press.
  5. Jia, G. & Taflanidis, A. A. 2011 Relative entropy estimation through stochastic sampling and stochastic simulation techniques. Second International Conference on Soft Computing Technology in Civil, Structural and Environmental Engineering. Chania, Greece.
  6. Jia, G. & Taflanidis, A. A. 2013. Kriging metamodeling for approximation of high-dimensional wave and surge responses in real-time storm/hurricane risk assessment. Computer Methods in Applied Mechanics and Engineering, 261-262, 24-38.
  7. Jin, R., Chen, W. & Simpson, T. W. 2001. Comparative studies of metamodelling techniques under multiple modelling criteria. Structural and Multidisciplinary Optimization, 23(1), 1-13.
  8. Klee, H. & Allen, R. 2007. Simulation of dynamic systems with MATLAB and SIMULINK, Boca Raton, FL, CRC Press.
  9. Lophaven, S. N., Nielsen, H.B., and Sondergaard, J. 2002 DACE-A MATLAB Kriging Toolbox. Technical University of Denmark.
  10. Medina, J. C. & Taflanidis, A. 2014. Adaptive importance sampling for optimization under uncertainty problems. Computer Methods in Applied Mechanics and Engineering, (10.1016/j.cma.2014.06.025).
  11. Picheny, V., Ginsbourger, D., Roustant, O., Haftka, R. T. & Kim, N. H. 2010. Adaptive designs of experiments for accurate approximation of a target region. Journal of Mechanical Design, 132(7).
  12. Robert, C. P. & Casella, G. 2004. Monte Carlo statistical methods, New York, NY, Springer.
  13. Rodri´guez, J. F., Renaud, J. E., Wujek, B. A. & Tappeta, R. V. 2000. Trust region model management in multidisciplinary design optimization. Journal of Computational Applied Mathematics, 124(1), 139- 154.
  14. Royset, J. O. & Polak, E. 2004. Reliability-based optimal design using sample average approximations. Probabilistic Engineering Mechanics, 19, 331-343.
  15. Sacks, J., Welch, W.J., Mitchell, T.J., Wynn, H.P. 1989. Design and analysis of computer experiments. Statistical Science, 4(4), 409-435.
  16. Schuëller, G. I. & Jensen, H. A. 2008. Computational methods in optimization considering uncertainties - An overview. Computer Methods in Applied Mechanics and Engineering, 198(1), 2-13.
  17. Spall, J. C. 2003. Introduction to stochastic search and optimization, New York, Wiley-Interscience.
  18. Taflanidis, A. A. & Beck, J. L. 2008. An efficient framework for optimal robust stochastic system design using stochastic simulation. Computer Methods in Applied Mechanics and Engineering, 198(1), 88-101.
  19. Taflanidis, A. A. & Beck, J. L. 2010. Reliability-based design using two-stage stochastic optimization with a treatment of model prediction errors. Journal of Engineering Mechanics, 136(12), 1460-1473.
  20. Verros, C., Natsiavas, S. & Papadimitriou, C. 2005. Design optimization of quarter-car models with passive and semi-active suspensions under random road excitation. Journal of Vibration and Control, 11(5), 581-606.
  21. Wang, G. G. & Shan, S. 2007. Review of metamodeling techniques in support of engineering design optimization. Journal of Mechanical Design, 129(4), 370-380.
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Paper Citation


in Harvard Style

Taflanidis A. and Medina J. (2014). Adaptive Kriging for Simulation-based Design under Uncertainty - Development of Metamodels in Augmeted Input Space and Adaptive Tuning of Their Characteristics . In Proceedings of the 4th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SDDOM, (SIMULTECH 2014) ISBN 978-989-758-038-3, pages 785-797. DOI: 10.5220/0005134007850797


in Bibtex Style

@conference{sddom14,
author={Alexandros Taflanidis and Juan Camilo Medina},
title={Adaptive Kriging for Simulation-based Design under Uncertainty - Development of Metamodels in Augmeted Input Space and Adaptive Tuning of Their Characteristics},
booktitle={Proceedings of the 4th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SDDOM, (SIMULTECH 2014)},
year={2014},
pages={785-797},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0005134007850797},
isbn={978-989-758-038-3},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 4th International Conference on Simulation and Modeling Methodologies, Technologies and Applications - Volume 1: SDDOM, (SIMULTECH 2014)
TI - Adaptive Kriging for Simulation-based Design under Uncertainty - Development of Metamodels in Augmeted Input Space and Adaptive Tuning of Their Characteristics
SN - 978-989-758-038-3
AU - Taflanidis A.
AU - Medina J.
PY - 2014
SP - 785
EP - 797
DO - 10.5220/0005134007850797