Optimum Design of a Multilayered Composite Plate Using Neural Networks

Ashida, Fumihiro; Sakata, Sei-ichiro; Horinokuchi, Naokazu

doi:10.1080/714050876

Cited by 10 publications

(1 citation statement)

References 6 publications

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“…For instance, response surface methods using a polynomial-based approximation [5], neural network [6], radial basis function method [7] or Kriging method [8][9][10][11] have been applied to an approximate optimization for an engineering problem. These methods will be usable if a set of discrete sampling results for an unknown surface is obtained.…”

Section: Introductionmentioning

confidence: 99%

Integral estimation with the ordinary Kriging method using the Gaussian semivariogram function

Sakata

Ashida

2009

Int. J. Numer. Meth. Biomed. Engng.

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SUMMARYThis paper describes a detailed procedure for integral estimation of an unknown function using the ordinary Kriging method. This method estimates the definite integral of an approximated surface generated using the ordinary Kriging method. The integral of an approximated surface can be computed directly using a set of sampling data for a function value. One of the merits of the proposed method is that the integral can be estimated without iterative summation generally used in a conventional numerical integration technique. In addition to a continuous function, the proposed method enables to estimate the integral using a set of discrete sampling data.In this paper, a basic formulation for an integral estimation using the Kriging method, especially with the Gaussian-type semivariogram model, is introduced. An explicit form of the integral of the Gaussian function is approximated by Williams' method.As test problems, definite integrals of some elementary functions are estimated using the proposed method. In addition, as an engineering example, a flow in a pipe is estimated using the proposed method with less samples of the velocity of fluid. The numerical results illustrate the accuracy and efficiency of the proposed method.

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