Reliability Based Optimization with Metaheuristic Algorithms and Latin Hypercube Sampling Based Surrogate Models
Applied and Computational Mathematics
Volume 4, Issue 6, December 2015, Pages: 462-468
Received: Nov. 20, 2015;
Accepted: Nov. 29, 2015;
Published: Dec. 18, 2015
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Liu Chu, Laboratory of Optimization and Reliability in Mechanical Structure, Department of Mechanics, National Institute of Applied Science of Rouen, France
Eduardo Souza De Cursi, Laboratory of Optimization and Reliability in Mechanical Structure, Department of Mechanics, National Institute of Applied Science of Rouen, France
Abdelkhalak El Hami, Laboratory of Optimization and Reliability in Mechanical Structure, Department of Mechanics, National Institute of Applied Science of Rouen, France
Mohamed Eid, Laboratory of Optimization and Reliability in Mechanical Structure, Department of Mechanics, National Institute of Applied Science of Rouen, France
Reliability based optimization (RBO) is one of the most appropriate methods for structural design under uncertainties. It searches for the best compromise between cost and safety while considering system uncertainties by incorporating reliability measures within the optimization. Despite the advantages of RBO, its application to practical engineering problem is still quite challenging. In this paper, we propose an effective method to decouple the loops of reliability assessment analysis and optimization by creating surrogate models. The Latin Hypercube sampling approach is applied to a structural finite element model to obtain an effective database for building surrogate models. In order to avoid premature convergence of the optimization process, the RBO problem is solved with metaheuristic methods such as genetic algorithm and simulated annealing. The relative efficiency of surrogate models and their relationship with metaheuristic search engine are discussed in the article.
Eduardo Souza De Cursi,
Abdelkhalak El Hami,
Reliability Based Optimization with Metaheuristic Algorithms and Latin Hypercube Sampling Based Surrogate Models, Applied and Computational Mathematics.
Vol. 4, No. 6,
2015, pp. 462-468.
D.L. Phillips, M. Spatial. Uncertainty analysis: propagation of interpolation errors in spatially distributed models. Ecological Modelling, Volume 91, Issues 1–3, 15 November 1996.
P Doubilet, CB Begg, MC Weinstein. Probabilistic sensitivity analysis using Monte Carlo simulation. A practical approach. Journal of the Society for Medical Decision Making [1985, 5(2): 157-177].
J. C. Helton, F. J. Davis. Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems. Reliability Engineering & System Safety, 2003.
John C. Brigham, W. Aquino. Surrogate-Model Accelerated Random Search algorithm for global optimization with applications to inverse material identification. Computer Methods in Applied Mechanics and Engineering, Volume 196.
J.-C. Jouhaud, P. Sagaut, M. Montagnac, J. Laurenceau. A surrogate-model based multidisciplinary shape optimization method with application to a 2D subsonic airfoil. Computers & Fluids, Volume 36, Issue 3, March 2007, Pages 520-529.
Jack P.C. Kleijnen. Kriging metamodeling in simulation: A review. European Journal of Operational Research, Volume 192, Issue 3, 1 February 2009, Pages 707-716.
H.N. A. Pham, E. Triantaphyllou. A metaheuristic approach for improving the accuracy in some classification algorithms. Computers & Operations Research, Volume 38, Issue 1, January 2011, Pages 174-189.
A. F. Shahraki, R. Noorossana. Reliability-based robust design optimization: A general methodology using genetic algorithm. Computers & Industrial Engineering, Volume 74, August 2014, Pages 199-207.
P. S. Laursen. Simulated annealing for the QAP — Optimal tradeoff between simulation time and solution quality. European Journal of Operational Research, Volume 69, Issue 2, 10 September 1993, Pages 238-243.
J. R. Harland, P. Salamon. Simulated annealing: A review of the thermodynamic approach. Nuclear Physics B - Proceedings Supplements, Volume 5, Issue 1, September 1988, Pages 109-115.
H. Ishigami, T. Fukuda, T. Shibata, F. Arai. Structure optimization of fuzzy neural network by genetic algorithm. Fuzzy Sets and Systems, Volume 71, Issue 3, 12 May 1995, Pages 257-264.
B.G.J. Thompson, B. Sagar. The development and application of integrated procedures for post-closure assessment, based upon Monte Carlo simulation: the probabilistic systems assessment (PSA) approach. Reliability Engineering & System Safety, Volume 42, Issues 2–3, 1993, Pages 125-160.
L. Goel, R. Billinton. Monte Carlo simulation applied to distribution feeder reliability evaluation. Electric Power Systems Research, Volume 29, Issue 3, May 1994, Pages 193-202.
R.E. Melchers. Importance sampling in structural systems. Structural Safety, Volume 6, Issue 1, July 1989, Pages 3-10.
M. Z. Miguel, G. Josselin, R. Emmanuel. An original sensitivity statistic within a new adaptive accelerated Monte-Carlo method. Procedia - Social and Behavioral Sciences, Volume 2, Issue 6, 2010, Pages 7712-7713.
Y. Liu, M. Y. Hussaini, G. Ökten. Optimization of a Monte Carlo variance reduction method based on sensitivity derivatives. Applied Numerical Mathematics, Volume 72, October 2013, Pages 160-171.
A. Florian. An efficient sampling scheme: Updated Latin Hypercube Sampling. Probabilistic Engineering Mechanics, Volume 7, Issue 2, 1992, Pages 123-130.
B. Gaspar, A.P. Teixeira, C. G. Soares. Assessment of the efficiency of Kriging surrogate models for structural reliability analysis. Probabilistic Engineering Mechanics, Volume 37, July 2014, Pages 24-34.
M. Miki, Y. Murotsu, T. Tanaka, S. Shao. Reliability-based optimization of fibrous laminated composites. Reliability Engineering & System Safety, Volume 56, Issue 3, June 1997, Pages 285-290.
A. D. Kiureghian, T. Dakessian. Multiple design points in first and second-order reliability. Structural Safety, Volume 20, Issue 1, 1998, Pages 37-49.
S. Shan, G. Wang. Reliable design space and complete single-loop reliability-based design optimization. Reliability Engineering & System Safety, Volume 93, Issue 8, August 2008, Pages 1218-1230.
G. I. Schuëller, H. A. Jensen. Computational methods in optimization considering uncertainties – An overview. Computer Methods in Applied Mechanics and Engineering, Volume 198, Issue 1, 15 November 2008, Pages 2-13.