T. W. Simpson, T. M. Mauery, J. J. Korte and F. Mistree, "Comparison of Response Surface and Kriging Models for Multidisciplinary Design Optimization". 7th AIAA/USAF/ISSMO Symposium on Multidisciplinary Analysis & Optimization, 381--391. AIAA, Institute of Aeronautics and Astronautics, September 1998.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....k = 1; N; where R is the correlation function between any two of the N samples, and R is the symmetric correlation matrix of dimension N N with values of unity along the diagonal. The form of the correlation matrix can be selected by the user, and the following form has often been used [11, 28, 78]: R(x ) exp[ i jx i j ] 12) where i are the unknown correlation parameters, x i i are the i th component of sample points x . Thus, the prediction of y(x) is a function of unknown parameters and i ; i = 1; 2; n: y = r (x)R (y I) 13) ....

....) b) y i i (23) y i ( w x i ) b) i ; i 0; i = 1; l: 25) Thus, quadratic programming techniques can be applied to solve the minimization problem. 5. 5 Comparative Remarks There are several papers that compare the performance of di erent approximation models [13, 14, 28, 78, 77, 34]. However, no clear conclusions on the advantages and disadvantages of the di erent approximation models have been drawn. This is reasonable not only because the performance may depend on the problem to be addressed, but also because more than one criterion needs to be considered. The most ....

T. Simpson, T. Mauery, J. Korte, and F. Mistree. Comparison of response surface and Kriging models for multidiscilinary design optimization. Technical Report 98-4755, AIAA, 1998.

....0.94 [10] SFC 0.96 d 1 = 1 [12] STDSFC 0.01 d 2 = 1 [13] THRUST 1052 d 3 = 1 [14] STDTHR 29 d 4 = 1 [15] Weight 1425 lbs [16] Length 7 ft [17] Fan diameter 38.4 in [18] Thegoals: WEIGHT 1350 d 5 = 1 [19] STDWGT 0. 005 d 6 = 1 [20] LENGTH 6 d 7 = 1 [21] STDLNG 0.02 d 8 = 1 [22] FANDIA 37 d 9 = 1 [23] Bounds on the control factors (Table 3) d i . d i = 0, with d i , d i 0 Minimize: The deviation function: Z = f 1 (d 1 ) f 6 (d 6 ) 24] Five design scenarios (different deviation function formulations) ....

Simpson, T.W., Comparison of Response Surface and Kriging Models in the Multidisciplinary Design of an Aerospike Nozzle, , Institute for Computer Applications in Science and Engineering, NASA Langley Research Center: Hampton, VA, February 1998.

....Multi layer Perceptrons (MLP) and Radial Basis Function Networks (RBFN) have also been employed to build approximate models for design optimization. A more comprehensive review of di erent approximation concepts is provided in [11] and a comparison of the di erent techniques can be found in [12, 13, 14]. 1 In this work, the MLP neural network is used for building an approximate model. However, it is generally dicult to get a model with sucient approximation accuracy. One of the problems is the lack of training data for the neural network, because data collection is a computationally expensive ....

T. Simpson, T. Mauery, J. Korte, and F. Mistree. Comparison of response surface and Kriging models for multidiscilinary design optimization. Technical Report 98-4755, AIAA, 1998.

....the application of one metamodeling technique or the other, typically for a specific application exist; however, our survey reveals a lack of comprehensive comparative studies of the various techniques, let al..one standard procedures for testing the relative merits of different methods. In Simpson, et al. 1998), kriging methods are compared against polynomial regression models for the multidisciplinary design optimization of an aerospike nozzle. Giunta, et al. 1998) also compare kriging models and polynomial regression models for two 5 and 10 variable test problems. In Varadarajan, et al. 2000) ....

....( b , 2) where Z(x) is assumed to be a realization of a stochastic process with mean zero and spatial correlation function given by Cov[Z(x ) Z(x ) s 2 R(x i , x j ) 3) where s 2 is the process variance and R is the correlation. A variety of correlation functions can be chosen (cf. Simpson, et al. 1998); however, the Gaussian correlation function proposed in (Sacks, et al. 1989) is the most frequently used. Furthermore, f (x) in Eqn. 2 is typically taken as a constant term. In our study, we use a constant term for f (x) and a Gaussian correlation function with p=2 and k q parameters, one q for ....

Simpson, T. W., Mauery, T. M., Korte, J. J. and Mistree, F., 1998, September 2-4, "Comparison of Response Surface and Kriging Models for Multidisciplinary Design Optimization," 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis & Optimization, St. Louis, MO, AIAA, Vol. 1, pp. 381-391. AIAA-98-4755.

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T. W. Simpson, T. M. Mauery, J. J. Korte and F. Mistree, "Comparison of Response Surface and Kriging Models for Multidisciplinary Design Optimization". 7th AIAA/USAF/ISSMO Symposium on Multidisciplinary Analysis & Optimization, 381--391. AIAA, Institute of Aeronautics and Astronautics, September 1998.

No context found.

T. W. Simpson, T. M. Mauery, J. J. Korte, and F. Mistree, "Comparison of response surface and kriging models for multidisciplinary design optimization, " in AIAA paper 98-4758. 7 th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, St. Louis, USA, 1998.

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Simpson, T. W., Mauery, T.M., Korte J.J., and Mistree, F., 1998, "Comparison of Response Surface and Kriging Models for Multidisciplinary Design Optimization," Proceedings of the 7 AIAA/USAF/NASA/ISSMO St. Louis, MO. AIAA-98-4755.

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