In this work a methodology is presented for the rigorous optimization of nonlinear programming problems in which the objective function and (or) some constraints are represented by noisy implicit black box functions. The special application considered is the optimization of modular process simulators in which the derivatives are not available and some units operations introduce noise preventing...

This paper describes a combination approach of a digital finite element modeling technique and the Kriging method for structural optimization. Since the digital modeling technique includes some inaccuracies in a modeling process, applicability of the Kriging method to noisy data is investigated. An estimated surface generated by the conventional Kriging method will be wavy and not appropriate t...

This paper presents the application of Exploratory Spatial Data Analysis (ESDA) and Kriging from GIS (ArcGIS8.3) in disease mapping through the analysis of hepatitis B in China. The research shows that geostatistical analysis techniques such as Kriging and ESDA have a good effect in disease mapping. Kriging methods can express properly the spatial correlation. Furthermore, unlike model-based me...

We are interested in estimating probabilities of rare events in the context of computer experiments. These rare events depend on the output of a physical model with random input variables. Since the model is only known through an expensive black box function, standard efficient Monte Carlo estimates of rare events probabilities can not be used. We then propose two strategies to deal with this d...

the aim of this study preparation of the predicted soil maps by using kriging and inverse distance weighting methods in east rangeland of semnan. sampling was done within each unit of sampling parallel transects and 1 vertical transect with 750m length. soil samples were taken from 0-20 cm in starting and ending points of each transect. there were used kriging and inverse distance weighting met...

Kriging is a spatial interpolation algorithm which provides the best unbiased linear prediction of an observed phenomena by taking a weighted average of samples within a neighbourhood. It is widely used in areas such as geo-statistics where, for example, it may be used to predict the quality of mineral deposits in a location based on previous sample measurements. Kriging has been identified as ...

In order to overcome the drawbacks of expensive function evaluation in practical reliability-based design optimization (RBDO) problem, researchers have proposed black box-based RBDO method. The algorithm flow commonly employed method for box problem consists outer construction loop surrogate model constraint and inner model-based solving loop. To improve ability this paper proposes a transforma...

We propose a new framework for the optimization of computationally expensive black box problems, where neither closed-form expressions nor derivatives of the objective functions are available. The proposed framework consists of two procedures. The first constructs a global metamodel to approximate the underlying black box function and explores an unvisited area to search for a global solution; ...

“Kriging” is the name of a parametric regression method used by hydrologists and mining engineers, among others. Features of the kriging approach are that it also provides an error estimate and that it can conveniently be employed also to estimate the integral of the regression function. In the present work, the kriging method is described and some of its statistical characteristics are explore...