Determination of Spatial Variability of Rock Depth of Chennai

Determination of Spatial Variability of Rock Depth of Chennai

Pijush Samui (National Institute of Technology Patna, India), Viswanathan R. (Galgotias University, India), Jagan J. (VIT University, India) and Pradeep U. Kurup (University of Massachusetts – Lowell, USA)
DOI: 10.4018/978-1-5225-2857-9.ch023
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Abstract

This study adopts four modeling techniques Ordinary Kriging(OK), Generalized Regression Neural Network (GRNN), Genetic Programming(GP) and Minimax Probability Machine Regression(MPMR) for prediction of rock depth(d) at Chennai(India). Latitude (Lx) and Longitude(Ly) have been used as inputs of the models. A semivariogram has been constructed for developing the OK model. The developed GP gives equation for prediction of d at any point in Chennai. A comparison of four modeling techniques has been carried out. The performance of MPMR is slightly better than the other models. The developed models give the spatial variability of rock depth at Chennai.
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Background

Researchers used various random field method for prediction purpose (Yaglom, 1962; Lumb, 1975; Alonso & Krizek, 1975; Vanmarcke, 1977; Tang, 1979; Wu &Wong, 1981; Tabb & Yong, 1981; Asaoka & Grivas, 1982; VanMarcke, 1998; Baecher, 1984; Baker, 1984; Kulatilake & Miller, 1987; Kulatilake, 1989; Fenton, 1998; Phoon & Kulhawy, 1999; Fenton, 1999; Uzielli et al., 2005). In random field method, the science of prediction in the presence of correlation between samples is not at all well developed. Statistical parameters contain uncertainty in random field method. In order to fill the holes of some uncertainty and also to reduce the cost, various intelligent techniques were evolved and utilized according to the requirements.

Key Terms in this Chapter

Rock Depth: Rock Depth is defined as the distance from top of the surface to the bottom of the rock.

Prediction: Prediction is defined as the action of forecasting something.

Genetic Programming: Genetic Programming (GP) is a technique whereby computer programs are encoded as a set of genes that are then modified (evolved) using an evolutionary algorithm.

Spatial Variability: Spatial variability occurs when a quantity that is measured at different spatial locations exhibits values that differ across the locations. Spatial variability can be assessed using spatial descriptive statistics such as the range.

Minimax Probability Machine Regression: Minimax Probability Machine Regression (MPMR) is defined as the process of maximizing the minimum probability of regression model for all possible distribution with known mean and covariance matrix.

Generalized Regression Neural Network: Generalized Regression Neural Network (GRNN) falls under probabilistic neural network category, which is utilized for function approximation.

Ordinary Kriging: Ordinary Kriging is the type of kriging method in which the weights of the values sum to unity. It uses an average of a subset of neighboring points to produce a particular interpolation point.

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