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satisfy constraints. This technique is applied to the design of double-deck car body and was compared with conventional space-filling sampling. Fong et al. [99] developed a response surface as a surrogate for the thermal-hydraulic code for the selection of an ultimate heat sink for a passive secondary auxiliary cooling system. The reliability of the chosen design during the bounding transient, a station blackout was calculated. The uncertainty introduced by the use of the response surface itself was explored. Moller et al. [100] addressed an approach to performance based design in the context of earthquake engineering. The objective is the optimization of the total structural cost, under constraints related to minimum target reliabilities specified for the different limit states or performance requirements. The approach uses a neural network representation of the responses. Moller et al. [101] presented a comparison between three methods for the implementation of response surfaces: a global approximation of the deterministic database, local interpolation of that database, or using artificial neural networks. The comparison uses, an example, a 5 storey reinforced concrete building. The results showed good agreement between the methods and the paper discussed their corresponding advantages and limitations. RECOMMENDATIONS, GUIDELINES AND CHALLENGES In this paper, we have discussed the concept of metamodeling and survey the advancements in the metamodel based analysis within design optimization and reliability based design application in the past thirty years. Most metamodeling applications are based on low order polynomials using CCD and least square regression (RSM technique). The main limitation of the RSM is the use of single low order polynomial to represent the function. Many systems cannot be described well using a single low order polynomial. In order to accurately define the real system, use of more piecewise low order polynomials or Splines can be made. These piecewise continuous polynomials allow more complex system behavior to be redefined in small areas. Neural Networks (NN) is also another perspective to the above criteria. The weighting function which is the basis of the network, are very flexible and can adapt to any kind system behavior. Therefore, NN has no limits on shape, dimension and type of function. Kriging, an interpolation method capable of handling deterministic data which is extremely flexible due to the wide range of correlation functions may be chosen. However, the method is more complex than RSM. The opinion on the appropriate experimental design for computer analyses vary; the only consensus reached thus far is that design for non-random, deterministic computer experiments should be space filling designs [3]. Though intensive research on metamodeling has been carried out some research challenges remain to be overcome. It was recognized that when the number of design variables is large, the total computation expense for metamodel based analysis makes the approaches less attractive or even infeasible. For eg, if CCD and a second order polynomial function are 30 ACTA TECHNICA CORVINIENSIS – Bulletin of Engineering used for metamodeling, the minimum number of sample points required is 2 n + 2n + 1 , where n is the number of design variables. There seems to be a lack of research on large-scale problems. New metamodeling techniques for large-scale problems, or simple yet robust strategies to decompose a large scale problem, are needed. In summary, the following conclusions can be made: Space filling designs are the best experimental design than classical designs If the problem involves more number of design variables, neural networks and radial basis functions may be the best choice despite computationally expensive to create If the problem to be modeled is highly nonlinear and with the number of design variables less than 50, then kriging may be the best Application with few variables and the behavior is smooth with less nonlinearity, and then response surface methodology may be used. REFERENCES [1.] Simpson.T.W, Toropov.V, Balabanov. V, Viana FAC, Design and analysis of computer experiments in multidisciplinary design optimization: a <strong>review</strong> of how we have come— or not.In:12 th AIAA/ISSMO multi disciplinary analysis and optimization conference, Victoria, British Colombia, 10–12 September, 2008. [2.] Wang, G. G. and Shan, S., "Review of Metamodeling Techniques in Support of Engineering Design Optimization," ASME Journal of Mechanical Design, Vol. 129, No. 4, 2007, pp. 370-380. [3.] Simpson, T.W.; Peplinski, J.; Koch, P.N.; Allen, J.K., 2001, Metamodels for computer-based engineering design: Survey and recommendations. Engineering with Computers 17(2), 129–150 [4.] Simpson, T. W., Booker, A. J., Ghosh, D., Giunta, A. A., Koch, P. N. and Yang, R. J., 2004, "Approximation Methods in Multidisciplinary Analysis and Optimization: A Panel Discussion," Structural and Multidisciplinary Optimization, 27, 302-313. [5.] Forrester. A.I.J., Keane. A.J., 2009, “Recent advances in surrogate-based optimization”, Progress in Aerospace Sciences, Vol. 45, 50–79. [6.] Ullman, D. G., 2002, "Toward the Ideal Mechanical Engineering Design Support System," Research in Engineering Design, 13, 55-64. [7.] Sacks, J., Welch, W. J., Mitchell, T. J. and Wynn, H. P., 1989, "Design and Analysis of Computer Experiments," Statistical Science, 4(4), 409-435. [8.] Jin, R., Chen, W. and Simpson, T. W., 2001, "Comparative Studies of Metamodeling Techniques Under Multiple Modeling Criteria," Structural and Multidisciplinary Optimization, 23(1), 1-13. [9.] Tang, 1994, "A Theorem for Selecting OA-Based Latin Hypercubes Using a Distance Criterion," Communications in Statistics, Theory and Methods, Vol. 23, No. 7, pp. 2047-2058. 2013. Fascicule 2 [April–June]
ACTA TECHNICA CORVINIENSIS – Bulletin of Engineering [10.] Park, J.-S., 1994, "Optimal Latin-Hypercube Designs for Computer Experiments," Journal of Statistical Planning and Inference, Vol. 39, No. 1, pp. 95-111. [11.] ZHAO Min, CUI Wei-cheng, 2007, “Application of the optimal Latin Hypercube design and radial basis function network to collaborative optimization”, Journal of Marine Science and Application, Vol.6, No.3, pp. 24-32. [12.] Stein, M. Stein, 1987, Large sample properties of simulations using Latin Hypercube sampling, Technometrics, Vol. 29, No. 2, pp. 143–151. [13.] M. Vořechovský and D. Novák, “ Efficient random fields simulation for stochastic FEM analyses”, Computional fluid and solid mechanics, 2007, pp 2383-2386. [14.] Fasihul M. Alam, Ken R. McNaught and Trevor J. Ringrose, 2004, A comparison of experimental designs in the development of a neural network simulation metamodel, Simulation Modelling Practice and Theory, Volume 12, Issues 7-8, pp. 559-578. [15.] Jack P.C. Kleijnen, 2005, An overview of the design and analysis of simulation experiments for sensitivity analysis, European Journal of Operational Research, Vol.164 pp. 287–300. [16.] Benjamin Wilson, David Cappelleri, Timothy W. Simpson, and Mary Frecker, 2001, “Efficient Pareto Frontier Exploration using Surrogate Approximations”, Optimization and Engineering, Vol.2, pp.31–50. [17.] F. Jurecka, M. Ganser and K.-U. Bletzinger, 2006, Update scheme for sequential spatial correlation approximations in robust design optimization, Computers and Structures Vol. 85, pp. 606–614 [18.] H. Fang, M. Rais-Rohani, Z. Liu and M.F. Horstemeyer, 2005, A comparative study of metamodeling methods for multiobjective crashworthiness optimization, Computers & Structures Vol. 83, No. 25-26, pp. 2121-2136. [19.] Feng Pan, Ping Zhu and Yu Zhang, 2010, Metamodel-based lightweight design of B-pillar with TWB structure via support vector regression, Computers and Structures, Vol.88, pp.36–44 [20.] Z. Qian, C. Seepersad, R. Joseph, J. Allen and C. F. J. Wu, 2006, Building surrogate models with detailed and approximate simulations, ASME Journal of Mechanical Design, 128, 668- 677 [21.] M.-L. Bouazizi, S.Ghanmi, N.Bouhaddi, 2009, Multi-objective optimization in dynamics of the structures with nonlinear behavior: Contributions of the metamodels, Finite Elements in Analysis and Design, Vol.45, pp. 612-623. [22.] Wasim Raza, Kwang-Yong Kim, Shape optimization of wire-wrapped fuel assembly using Kriging metamodeling technique, Nuclear Engineering and Design, vol.238 (2008) 1332– 1341 [23.] R. Rikards, H. Abramovich, K. Kalnins, J. Auzins, 2006, Surrogate modeling in design optimization of stiffened composite shells, Composite Structures, Vol.73, pp.244-251. [24.] N. Jansson, W.D. Wakeman, J.-A.E. Manson, 2007,Optimization of hybrid thermoplastic composite structures using surrogate models and genetic algorithms, Composite Structures, Vol.80, pp.21–31. [25.] Jay D. Martin, Timothy W. Simpson, 2002, Use of adaptive metamodeling for design optimization, 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Georgia, AIAA 2002-5631. [26.] Patrick N. Koch, Brett Wujek, Oleg Golovidov, Timothy W. Simpson, 2002, Facilitating probabilistic multidisciplinary design optimization using kriging approximation models, 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Georgia, AIAA 2002- 5415. [27.] Kwang-Yong Kim, Dong-Yoon Shin, Optimization of a staggered dimpled surface in a cooling channel using Kriging model, 2008, International Journal of Thermal Sciences, Vol. 47, pp.1464–1472. [28.] Jay D. Martin, Timothy W. Simpson, 2004, On the use of kriging models to approximate deterministic computer models, International Design Engineering <strong>Technica</strong>l Conferences and Computers and Information in Engineering Conference, Utah USA, DETC2004/DAC-57300. [29.] Jay D. Martin, Timothy W. Simpson, 2005, Use of kriging models to approximate deterministic computer models, AIAA JOURNAL, Vol. 43, No. 4, pp.853-863. [30.] William E. Biles, Jack P. C. Kleijnen, Wim C. M. van Beers, Inneke van Nieuwenhuyse, 2007, Kriging metamodeling in constrained simulation optimization: an explorative study, Proceedings of the 2007 Winter Simulation Conference, pp.355-362. [31.] S. Sakata, F. Ashida, M. Zako, 2007, On applying Kriging-based approximate optimization to inaccurate data, Computational Methods in Applied Mechanical Engineering, Vol.196, pp.2055–2069. [32.] N. Logothetis and A. Haigh, Characterizing and optimizing multi-response processes by the Taguchi method. Quality and Reliability Engineering International 4 (1988), pp. 159– 169. [33.] Genichi Taguchi, Subir Chowdhury, Shin Taguchi, Robust Engineering, 1999, McGraw Hill. [34.] Sung H. Park, Robust design and analysis for quality engineering, 1996, Chapman & Hall. [35.] Bhadra, S., and Ganguli, R., “Aeroelastic Optimization of a Helicopter Rotor Using Orthogonal Array Based Metamodels” AIAA Journal, Vol. 44, No. 9, 2006, pp. 1941-1951. [36.] Hedayat, A. S., Sloane, N. J. A. and Stufken, J., 1999, Orthogonal Arrays: Theory and Applications, Springer, New York. [37.] Mateen-ud-Din Qazi, and He Linshu, 2006, Nearly-orthogonal sampling and neural network 2013. Fascicule 2 [April–June] 31
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