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An integrated geostatistical-geomechanical approach for predicting potential risk of failure in pit walls
Published in Vladimir Litvinenko, Geomechanics and Geodynamics of Rock Masses: Selected Papers from the 2018 European Rock Mechanics Symposium, 2018
Nader Ghasempour, Kamran Esmaieli, Hesameddin Eivazy
Geostatistical techniques offer a means of mathematically approximating the spatial patterns of parameters. This is based on the regionalized variable theory which takes into consideration both the random and structured characteristics of spatially distributed variables (Journel & Huijbregts 1978). Geostatistical techniques were originally developed for ore reserve estimation; however, many researchers have applied the geostatistical interpolation and simulation methods for analysis of spatial distribution of geomechanical properties in slope stability problems (Mayer and Stead 2017; Ferrari et al., 2014; Marchesi et al., 2009). The interpolation technique is composed of kriging methods, a series of linear weighted estimators that gives exact local predictions, using semi-variograms to define weights. Kriging methods return a mean value and a variance at each node, representing a best linear unbiased estimator. However, a disadvantage of using kriging methods is in their smoothed effect. The simulation methods are based on a probability distribution function, and can simulate many equi-probable realizations of a variable, honouring the heterogeneity of the input distribution. The conditional simulation algorithms such as Sequential Gaussian Simulation (SGS) honour the samples at their locations, and ensure that the variogram/covariance is honored.
A surrogate assisted thermal optimization framework for design of pin-fin heat sink for the platform inertial navigation system
Published in Engineering Optimization, 2021
To overcome the difficulties of high-dimensional modelling, KG-HDMR, which integrates kriging and HDMR, is used to construct the approximate model of an underlying problem. Kriging, which was proposed by Krige (1951), is a method of interpolation derivation based on regionalized variable theory. It was originally used to predict the distribution of mineral resources. Some scholars extended kriging to the field of numerical approximation for interpolation analysis of data. The mathematical form of kriging is where is the global regression model of the actual response, is the regression coefficient, is the predetermined basis function vector, and is a random function of deviation that follows the normal distribution.
Multiobjective optimization study of jet impingement heat transfer through a porous passage configuration
Published in Numerical Heat Transfer, Part A: Applications, 2018
Sampath Kumar Chinige, Nikhilesh Ghanta, Arvind Pattamatta
The average Nusselt number and nondimensional pressure drop values, ΔP*, are calculated over the stagnation region which is considered to be a nondimensional distance of 1.5 W distance in the present study. With these 20 sample points, a Kriging model is developed using the DACE toolbox of MATLAB R2014 [25]. Kriging approximation involves regionalized variable theory, which assumes that the spatial variation of any variable can be expressed as a sum of three components—the first being a structural component having a constant mean or a trend, the second being a random, but spatially correlated component, known as the regionalized variable, and the third being the spatially uncorrelated random noise or the residual component.