Several approximate optimization methods will be effective for a recent engineering optimization, especially more flexible methods such as neural network, radial basis function or Kriging method are applicable to complex problem, for example, a non-convex and multi-peaked solution space. These methods will generate an estimated surface which is fit well to the sampling results It is sometimes difficult, however, that these methods are applied to noisy data because of its flexibility. Especially the ordinary Kriging will give an exact interpolation [
], therefore some improvement will be required to be used for approximate optimization with noisy data.
In this study, the ordinary-type Kriging method will be originally improved to apply to both of precise and noisy data. A formulation of Kriging estimation and empirical semivariogram will be arranged from the viewpoint of dispersion of sampling results. We choose different types of semivariogram function for sampling data and estimated surface in the case of using the semivariogram model, and the Gaussian type semivariogram model is adopted in this study. The nugget effect is included in the semivariogram model to consider some noises. The nugget effect will cause discontinuity of estimated surface, but this approach enables to eliminate the discontinuity. To take a dispersion of sampling results into account, the empirical semivariogram and Cressie’s weighted least squares criterion is re-defined. The effect of changing empirical semivariogram on estimated results will be also investigated.
As a test problem, a surface is estimated with using noisy data, which are generated by giving random noises to a known mathematical function. By comparing the results obtained by the proposed Kriging system with the exact ones or the results obtained by other approximation method, estimation quality of the proposed method is investigated. Influence of noises in sampling results on estimated results is investigated. The proposed method will give a better estimation, and numerical examples illustrate validity and effectiveness of the proposed approach.