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Application of Generalized Regression Neural Networks in Predicting the Unconfined Compressive Strength of Carbonate Rocks

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Abstract

Measuring unconfined compressive strength (UCS) using standard laboratory tests is a difficult, expensive, and time-consuming task, especially with highly fractured, highly porous, weak rock. This study aims to establish predictive models for the UCS of carbonate rocks formed in various facies and exposed in Tasonu Quarry, northeast Turkey. The objective is to effectively select the explanatory variables from among a subset of the dataset containing total porosity, effective porosity, slake durability index, and P-wave velocity in dry samples and in the solid part of samples. This was based on the adjusted determination coefficient and root-mean-square error values of different linear regression analysis combinations using all possible regression methods. A prediction model for UCS was prepared using generalized regression neural networks (GRNNs). GRNNs were preferred over feed-forward back-propagation algorithm-based neural networks because there is no problem of local minimums in GRNNs. In this study, as a result of all possible regression analyses, alternative combinations involving one, two, and three inputs were used. Through comparison of GRNN performance with that of feed-forward back-propagation algorithm-based neural networks, it is demonstrated that GRNN is a good potential candidate for prediction of the unconfined compressive strength of carbonate rocks. From an examination of other applications of UCS prediction models, it is apparent that the GRNN technique has not been used thus far in this field. This study provides a clear and practical summary of the possible impact of alternative neural network types in UCS prediction.

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Abbreviations

ϕ :

Porosity

AdjR 2 :

Adjusted determination coefficient

k :

Number of parameters in the model

I d (%):

Slake durability index (fourth cycle)

MSE i :

Mean of residual squares in the model with i parameters

n (%):

Total porosity

N :

Number of data

n e (%):

Effective porosity

R 2 :

Determination coefficient

S :

Smoothing parameter

S d :

Output from the denominator neuron

S j :

Output from the jth numerator neuron

u i :

Input portion of the ith training vector represented by the ith neuron in the pattern layer

V :

Volume of the sample

V fl :

Velocity in the fluid

V m :

P-wave velocity in rock samples lacking pores and fissures

V p :

P-wave velocity in the sample

W d :

Weight of the sample in the dried condition

W ij :

Weight vector between the pattern layer and summation layer

W s :

Weight of the sample in the saturated condition

X :

Input vector

y j :

Output vector

θ i :

Output from the ith neuron in the pattern layer

ρ d :

Density of solid particles

ρ s :

Dry density

ρ w :

Water density

σ 2 :

Variance of the dependent variable

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Authors and Affiliations

  1. Department of Geology Engineering, Balikesir University, Balikesir, Turkey

    Nurcihan Ceryan

  2. Department of Civil Engineering, Balikesir University, Balikesir, Turkey

    Umut Okkan

  3. Department of Mining Engineering, Karadeniz Technical University, Trabzon, Turkey

    Ayhan Kesimal

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  1. Nurcihan Ceryan
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  2. Umut Okkan
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  3. Ayhan Kesimal
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Correspondence to Nurcihan Ceryan.

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Ceryan, N., Okkan, U. & Kesimal, A. Application of Generalized Regression Neural Networks in Predicting the Unconfined Compressive Strength of Carbonate Rocks. Rock Mech Rock Eng 45, 1055–1072 (2012). https://doi.org/10.1007/s00603-012-0239-9

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