Modeling of tensile strength of rocks materials based on support vector machines approaches

Abstract

In the predicting of geological variables, artificial neural networks (ANNs) have some drawbacks including possibility of getting trapped in local minima, over training, subjectivity in the determining of model parameters and the components of its complex structure. Recently, support vector machines (SVM) has been found to be popular in prediction studies due to its some advantages over ANNs. Because the least squares SVM (LS-SVM) provides a computational advantage over SVM by converting quadratic optimization problem into a system of linear equations, LS-SVM method is also tried in study. The main purpose of this study is to examine the capability of these two SVM algorithms for the prediction of tensile strength of rock materials and to compare its performance with ANN and linear regression (MLR) models. Total porosity, sonic velocity, slake durability index and aggregate impact value were used as input in modeling applications. Favorite performance evaluation measures were employed to assess developed models. The results determined in study indicate that the SVM, LS-SVM and ANN methods are successful tools for prediction of tensile strength variable and can give good prediction performances than MLR model. Although these three methods are powerful artificial intelligence techniques, LS-SVM makes the running time considerably faster with the higher accuracy. In terms of accuracy, the LS-SVM model resulted in error reductions relative to that of the other models.Tensile strength was used for different geotechnical aims, and laboratory and full-scale studies were carried out to explore the possible relationship between fine production and water content of rock material [11]. Results of the laboratory work showed that the percentage of fines fraction produced by a cone crusher machine was a function of the type of rock tested and the tensile strength of individual specimens [11].There are mainly two methods for determining the tensile strength of rock materials. One of the methods is laboratory tests including direct uniaxial tensile test and indirect tensile tests (direct method) or making use of the previously derived empirical equations from literature called as indirect method. Direct uniaxial tensile test have some disadvantages and limitations. This test, which is theoretically the simplest and most effective method for the determination of tensile strength, is in fact difficult to carry out in practice for rock material and the difficulty in specimen preparation [4,9,[12][13][14][15][16]. Therefore, to determine tensile strength, indirect tensile tests are developed, for example Brazilian test, ring test, hoop test, bending test, etc. Brazilian test which is much more popular among those carried out has been proved as a satisfactory technique for determining the tensile strength of many rocks [6,[8][9][10][11][17][18][19][20]. Brazilian test measures tensile strength indirectly by developing tension across the diameter of a rock disc that is subjected to compression through a vertical load [8]. Testing proc...

Multifractal Analysis and Compressive Strength Prediction for Concrete through Acoustic Emission Parameters

“…ese statistical parameters can reflect the accuracy of predicting results. e calculation formulas of RMSE, MAPE, and R2 have been given in literature [49,50].…”

En Küçük Kareler Destek Vektör Makineleri (LS-SVM) Kullanarak Kaya Malzemesi Tanjant Elastisite Modülünün Tahmini

“…(b: bias terimi, y k : ölçülen değer; ŷ k : SVM/ LS-SVM modeli çıktı değeri, w: ağırlık vektörü, M:marj). Figure 2. a)The optimal separator canonical hyperplane having the most margin (Tolun 2008), b)insensitive band for a one-dimensional linear regression mode (Tolun, 2008), c) insensitive loss function of SVM (Ceryan et al, 2012) and d) quadratic loss function of LS-SVM (Ceryan et al, 2012 (b: …”

“…Figure 2. a)The optimal separator canonical hyperplane having the most margin (Tolun 2008), b)insensitive band for a one-dimensional linear regression mode (Tolun, 2008), c) insensitive loss function of SVM (Ceryan et al, 2012) and d) quadratic loss function of LS-SVM (Ceryan et al, 2012 (b: the bias term, y k : the parameter value measured, ŷ k : the output of SVM/LS-SVM models, w: weight vector, M: Margin).…”

“…LS-SVM modellemesinde düzenleme faktörü (γ) ve RBF'nin genişlik parametresi (σ) olmak üzere iki adet kalibre edilmesi gereken parametreye ihtiyaç duyulmaktadır. Bu çalışmada en uygun LS-SVM parametreleri hata kareler ortalamasını minimum yapacak şekilde k-kat çapraz-doğrulama tekniği (Kalra vd., 2013) (Ceryan et al, 2012).…”

Reply to the “Discussion by Haddad et al. on ‘Hydroclimatic stream flow prediction using least square-support vector regression’ by Bhagwat and Maity (2013)”

“…We also like to mention that transformation through Equation (11) is also termed as "normalization" in many studies (e.g. Ceryan et al 2013;Ismail et al 2012;Kisi 2012;Samsudin et al 2011). Thus, the word "normalization" was used in BM2013.…”