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The usability of Cerchar abrasivity index for the prediction of UCS and E of Misis Fault Breccia: Regression and artificial neural networks analysis
Expert Systems with Applications 37 (2010) 8750–8756
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The usability of Cerchar abrasivity index for the prediction of UCS and E of Misis Fault Breccia: Regression and artificial neural networks analysis S. Kahraman a,*, M. Alber b, M. Fener c, O. Gunaydin c a
Nigde University, Mining Engineering Department, Nigde, Turkey Ruhr University-Bochum, Applied Geology Department, Bochum, Germany c Nigde University, Geological Engineering Department, Nigde, Turkey b
a r t i c l e
i n f o
Keywords: Fault breccia Uniaxial compressive strength Elastic modulus Physical and textural properties Cerchar abrasivity index Artificial neural networks
a b s t r a c t The derivation of some predictive models for the geomechanical properties of fault breccias will be useful due to the fact that the preparation of smooth specimens from the fault breccias is usually difficult and expensive. To develop some predictive models for the uniaxial compressive strength (UCS) and elastic modulus (E) from the indirect methods including the Cerchar abrasivity index (CAI), regression and artificial neural networks (ANNs) analysis were applied on the data pertaining to Misis Fault Breccia. The CAI was included to the best regression model for the prediction of UCS. However, the CAI was not included to the best regression model for the prediction of E. The developed ANNs model was also compared with the regression model. It was concluded that the CAI is a useful property for the prediction of UCS of Misis Fault Breccia. Another conclusion is that ANNs model is more reliable than the regression models. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Artificial neural networks (ANNs) are being used commonly in science and engineering applications in recent years, since they have some important features such as self-learning, adaptive recognition, and non-linear dynamic processing comparing to the traditional expert systems. In recent years, numerous geoscientists (Kahraman, Altun, Tezekici, & Fener, 2005; Singh, Singh, & Singh, 2001; Sonmez, Gokceoglu, Nefeslioglu, & Kayabasi, 2006; Yang & Zhang, 1998; Yuanyou, Yanming, & Ruigeng, 1997; Zorlu, Gokceoglu, Ocakoglu, Nefeslioglu, & Acikalin, 2008) have applied the ANNs to many studies in geosciences since ANNs models show a good performance in the solving of non-linear multivariable problems. Knowing the geomechanical properties of fault breccias is very important in rock engineering because the fault breccias usually cause problems in geo-engineering applications. However, the fault breccias are usually not suitable for preparing smooth specimens or the preparation of such specimens is tedious, time consuming and expensive for the standard tests. So, the derivation of some predictive models for the geomechanical properties of fault breccias will be useful. The characteristics of geologically complex rocks such as melanges, sheared serpentinites, coarse pyroclastic rocks and fault rocks have been investigated by some researchers (Buergi, Parriaux, Franciosi, & Rey, 1999; Chester & Logan, 1986; Ehrbar & * Corresponding author. Tel.: +90 388 2252264; fax: +90 388 2250112. E-mail address: [email protected] (S. Kahraman). 0957-4174/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2010.06.039
Pfenniger, 1999; Goodman & Ahlgren, 2000; Habimana, Labiouse, & Descoeudres, 2002; Laws, Eberhardt, Loew, & Descoeudres, 2003; Lindquist & Goodman, 1994; Medley, 1994, 2001, 2002; Medley & Goodman, 1994; Sonmez, Gokceoglu, Medley, Tuncay, & Nefeslioglu, 2006; Sonmez, Gokceoglu, Tuncay, Medley, & Nefeslioglu, 2004). The reviews of these studies were presented by Kahraman and Alber (2006) and will not be repeated here. There are no apparent predictive models except the authors’ models in the literature for the geomechanical properties of fault breccias. Kahraman and Alber (2006) and Alber and Kahraman (2009) correlated the uniaxial compressive strength (UCS) and elastic modulus (E) values of Ahauser fault breccia (Germany) having blocks weaker than the matrix with volumetric block proportion (VBP) and texture coefficient (TC) and found strong correlations between UCS and both VBP and TC. In addition, Kahraman, Alber, Fener, and Gunaydin (2008) investigated the geomechanical properties of the Misis Fault Breccia from Turkey. As a result of multiple regression analysis, they found some significant alternative models including density, P- and S-wave velocity and textural properties for the prediction of UCS and deviator stress. Recently, Kahraman, Gunaydin, Alber, and Fener (2009) investigated the predictability of UCS and E values of Misis Fault Breccia from some indirect methods using ANNs and the results were compared with the regression models. They derived very good models for both UCS and E estimation from ANNs analysis comparing to the regression models. VBP, density, S-wave velocity, the roundness of blocks, and the average block diameter factor were included to the models.
S. Kahraman et al. / Expert Systems with Applications 37 (2010) 8750–8756
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In this study, the usability of Cerchar abrasivity test for the determination of UCS and E of Misis Fault Breccia using ANNs analysis was investigated. The Cerchar abrasivity test which is a nondestructive method is one of the most common testing methods used for the assessment of hard rock abrasivity. Although it is developed for abrasivity, some researchers (Al-Ameen & Waller, 1994; Evenden & Edwards, 1985) showed that there are some correlations between rock strength and Cerchar abrasivity index (CAI). Since the device has a small testing pin and the scratching distance is 10 mm, it can be used for scratching on matrix area of a breccia core sample. Average CAI values obtained from the scratching procedures on the different matrix surface of a core sample may be an indirect measure of the matrix strength. 2. The rock tested and sampling Fig. 2. Prepared core samples.
The rock tested in this study pertains to the Misis Fault Breccia (Ceyhan–Adana–Turkey). A view of crust crop in the fault zone is shown in Fig. 1. Block samples were collected from the site and transported to the laboratory. Misis Fault Breccia is composed of dolomitic limestone blocks embedded in fine-grained matrix of red-coloured claystone containing Fe-rich clay. For the laboratory tests, a total of 125 core samples having different volumetric block proportion were prepared (Fig. 2). 3. Determination of textural properties The circumferential surface of the each core was scanned by the DMT (Deutsche Montan Technologie GmbH) CoreScan II-Digital Core Imaging System. The estimation of VBP, and the calculation of the average block diameter factor (ABDF), aspect ratio and roundness of blocks were performed on the scanned images of cores using a computer package (Image Pro-Plus 5.0). Fig. 3 shows the original and processed images of a sample. 3.1. Estimation of volumetric block proportion Volumetric block proportion (VBP) is defined as the total volume of blocks divided by the total volume of the rock mass. Some researchers (Goodman & Ahlgren, 2000; Haneberg, 2004; Medley, 1997, 2002; Medley & Goodman, 1994) have explained the estimation or determination methods of VBP and discussed the uncertainties in estimating three-dimensional block size distributions from one- or two-dimensional measurements. Although the sieve analysis is the best method, the separation of blocks from the matrix is very difficult in most situations. For this reason, the estimation
Fig. 3. Original (a) and processed (b) images of a sample.
of VBP from one- or two-dimensional methods such as using the drill core/block intersection lengths or scanlines, geological mapping, and image analysis is commonly applied. In this study, the scanned images of the circumferential surfaces of the cores were processed and used for the estimation of VBP.
3.2. Average block diameter factor (ABDF) The two-dimensional diameter (assumed to be the same as three-dimensional diameter) was estimated by measuring the length of the line passing through the 2° centroid of each block. Then these lines were averaged. Since the core samples prepared for the UCS and E test had different diameters, these values were converted to ABDF using the following formula:
ABDF ¼
Fig. 1. A view of crust crop in the Misis fault zone.
Dblock 100 Dsample
ð1Þ
where ABDF is the average block diameter factor (%), Dblock is the average block diameter (mm), Dsample is the core sample diameter (mm).
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several calliper readings. The weights of the specimens were determined by a balance, capable of weighing to an accuracy of 0.1 of the sample weight. The density values were obtained from the ratio of the specimen weight to the specimen volume. 4.2. Ultrasonic test The ultrasonic generator USG 40, manufactured by Geotron GmbH in Pirna, Germany, was used to evaluate the elastic properties of the samples (Fig. 4). Ultrasonic transducers of 20–250 kHz were used depending on the geometry of specimen. 4.3. Cerchar abrasivity test
Aspect ratio describes the elongation of blocks, and is the ratio of the length of the major axis and minor axis of the ellipse with an area equivalent to that of the block.
The Cerchar abrasivity index (CAI) tests were performed using the original Cerchar apparatus by scratching pins of HRC 54-56 loaded with 70 N in 1 s over a distance of 10 mm. The tests were carried out on the blocks and the matrix areas of each core sample before the UCS and deformability tests. After performing the tests on 10 limestone blocks, it was seen that the CAI values of limestone blocks were approximately same, i.e. 1.22 ± 0.12. However, the CAI values of matrix ranges from 0.00 to 0.83.
3.4. Roundness of blocks
4.4. Uniaxial compressive strength test
Roundness can also be described as a form factor. Roundness is 1 for a perfect circle. When the shape deviates from circularity, the roundness decreases.
Uniaxial compression tests were performed on trimmed core samples, which had height to diameter ratios of 2 to 2.5. The tests were performed using an electro-hydraulic servo-controlled stiff testing machine (MTS). The samples were loaded in axial strain control at a rate of 105 mm/mm/s beyond peak strength according to ISRM suggested method (Fairhurst & Hudson, 1999).
Fig. 4. Ultrasonic testing device.
3.3. Aspect ratio of blocks
4. Laboratory studies Density test, ultrasonic test and Cerchar abrasivity index test were first carried out on the each core sample, and then uniaxial compressive strength and deformability tests were performed. 4.1. Density test Trimmed core samples were used in the determination of density. The specimen volume was calculated from an average of Table 1 The textural properties. Statistical parameter
Number of samples Minimum Maximum Average Standard deviation Skewness
4.5. Deformability test During the uniaxial compressive strength tests, deformation measurements were also carried out using two high resolution LVDTs (linear variable differential transformer). Elastic modulus (E) values were obtained from stress–strain curves at a stress level equal to 50% of the ultimate uniaxial compressive strength.
5. Evaluation of the test results Volumetric block proportion (%)
Average block diameter factor (%)
Aspect ratio of blocks
Roundness of blocks
125 4.0 75.9 36.9 ±15.3 0.20
125 3.1 22.7 8.8 ±3.5 0.96
125 1.7 2.2 1.9 ±0.1 0.53
125 0.62 0.84 0.75 ±0.05 0.02
Textural properties together with statistical evaluation are given in Table 1. The VBP and ABDF values are highly scattered. The VBP values range from 4.0% to 75.9%. The ABDF values range from 3.1% to 22.7%. The aspect ratio and roundness of blocks are not scattered. Statistical evaluation of the physico-mechanical tests results are given in Table 2. The results are generally scattered. For example, the UCS values range from 9.1 to 108.1 MPa and E values range from 4.3 to 39.4 GPa.
Table 2 The physico-mechanical properties of the fault breccia. Statistical parameter
Uniaxial compressive strength (MPa)
Static elastic modulus (GPa)
Dynamic elastic modulus (GPa)
Static Poisson’s ratio
Dynamic Poisson’s ratio
Dynamic rigidity modulus (GPa)
P-wave velocity (km/s)
S-wave velocity (km/s)
Density (g/cm3)
Cerchar abrasivity index for matrix
Number of samples Minimum Maximum Average Standard deviation Skewness
125 9.1 108.1 44.7 ±17.7 1.04
125 4.3 39.4 20.0 ±7.3 0.21
125 14.5 74.6 39.2 ±10.1 0.05
125 0.04 0.65 0.23 ±0.11 1.02
125 0.20 0.44 0.33 ±0.04 0.12
125 5.2 27.7 14.9 ±4.1 0.03
125 3.49 6.66 4.82 ±0.49 0.22
125 1.44 3.24 2.41 ±0.34 0.54
125 2.36 2.64 2.50 ±0.05 0.07
125 0.00 0.83 0.26 ±0.20 0.63
Table 3 Correlation matrix for the data.
Uniaxial compressive strength Static elastic modulus Static Poisson’s ratio Density P-wave velocity S-wave velocity Dynamic elastic modulus Dynamic Poisson’s ratio Dynamic rigidity modulus Cerchar abrasivity index for matrix Volumetric block proportion Average block diameter factor Aspect ratio of blocks Roundness of blocks
Static elastic modulus
Static Poisson’s ratio
Density
P-wave velocity
S-wave velocity
Dynamic elastic modulus
Dynamic Poisson’s ratio
Dynamic rigidity modulus
Cerchar abrasivity index for matrix
Volumetric block proportion
Average block diameter factor
Aspect ratio of blocks
Roundness of blocks S. Kahraman et al. / Expert Systems with Applications 37 (2010) 8750–8756
Uniaxial compressive strength 1.00
0.76
1.00
0.01
0.13
1.00
0.01 0.32 0.44 0.43
0.27 0.45 0.50 0.53
0.04 0.15 0.12 0.12
1.00 0.60 0.31 0.44
1.00 0.73 0.81
1.00 0.98
1.00
0.31
0.27
0.04
0.15
0.04
0.70
0.59
1.00
0.43
0.53
0.12
0.39
0.74
0.98
0.99
0.66
1.00
0.49
0.37
0.17
0.09
0.26
0.38
0.35
0.27
0.35
1.00
0.46
0.15
0.08
0.71
0.35
0.06
0.18
0.26
0.14
0.32
1.00
0.03
0.05
0.31
0.00
0.03
0.03
0.01
0.07
0.02
0.05
0.12
1.00
0.25
0.17
0.21
0.02
0.21
0.20
0.17
0.10
0.18
0.30
0.23
0.05
1.00
0.25
0.22
0.15
0.04
0.02
0.19
0.16
0.25
0.17
0.21
0.18
0.52
0.40
1.00
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5.1. Regression analysis
UCS ¼ 366:0 0:9VBP þ 155:8d þ 10:7V p þ 16:7CAI; r ¼ 0:75
ð2Þ
where UCS is the uniaxial compressive strength (MPa), VBP is the volumetric block proportion (%), d is the density (g/cm3), Vp is Pwave velocity (km/s), and CAI is the Cerchar abrasivity index. The best model produced for E has a comparatively low correlation coefficient. In addition, CAI was not included to this model. The equation of this model is:
E ¼ 180:2 0:3VBP þ 74:1d þ 5:4V p ;
r ¼ 0:62
ð3Þ
where E is the static elastic modulus (MPa), VBP is the volumetric block proportion (%), d is the density (g/cm3), and Vp is the P-wave velocity (km/s). 5.2. Artificial neural networks (ANNs) analysis ANNs take a different problem solving approach than that of numerical methods. In ANNs models, the activity of the human brain is simulated in a highly simplified way. These models consist of interconnected assembly of simple processing elements, neurons, which organized in a layered fashion. Each neuron in a layer is connected to the neurons in the subsequent layer and so on, as seen in Fig. 5. The interconnection between ith and jth layers is labelled as wij and is called ‘‘weights”. It is these interconnections between layers that provide a powerful tool for prediction and classification. During learning phase, these interconnections are optimized in order to minimize a predefined cost function. The weighted sum of inputs to a neuron is calculated and the output of a neuron, the activation of the neuron, is determined by an activation function, which is illustrated in Fig. 5 as f( ). The type of neural network used in this study is Multi Layered Perception (MLP). A MLP neural network is shown in Fig. 6. The MLP networks consist of an input layer, one or more hidden layers and an output layer. Each layer has a number of processing units (neurons) and each unit is fully interconnected with weighted connections to units in the subsequent layer. The MLP transforms i inputs into k outputs through non-linear mapping functions.
x1 x1 x2 xk xi
Input Layer
Weights wij
Hidden Layer
Output Layer
Weights wjk
Fig. 6. A Multilayered Perception Neural Network.
Some investigators (Altun, Bilgil, & Fidan, 2007; Kumar, 2005) indicated that ANNs models are not consistently good in estimation for highly skewed data. When the data is skewed, some transformation like power transformation can be used for reducing the skewness before performing neural network analysis. The skewness is a measure for the degree of symmetry in the normal distribution. If the skewness coefficient is 0, the distribution is symmetric (not skewed). Positive skewness indicates the distribution is skewed to the right, and negative skewness indicates the distribution is skewed to the left. As indicated in Tables 1 and 2, the skewness values of parameters are generally small. Furthermore, histograms of variables exhibited that the data of variables are generally show normal distribution. Figs. 7 and 8 are given as examples. Therefore, it can be said that the transformation or the treatment of data is not necessary. The data set is usually normalized to obtain better convergence in the ANNs analysis. The data set used in this study was scaled between 0 and 1 using the following equation (Rafiq, Bugmann, & Easterbrook, 2001):
U norm ¼
U actual U min U max U min
ð4Þ
where Unorm is the normalized value, Uactual is the actual value, Umax is the maximum value of the data set and Umin is the minimum value of the data set. The data pertaining to 125 rock sample were used in the ANNs analysis. The first group consisting of 100 data points was used to train the network and to develop ANNs models. The second group consisting of 25 data points was used to test the accuracy of the
30 25
Frequency
Firstly the correlation matrix was constructed for the all data. As shown in Table 3, CAI exhibits the highest correlation coefficient (r = 0.49) with UCS. However, CAI does not exhibit the highest correlation coefficient with E. When the correlation coefficient (r) values among the dynamic elastic parameters are checked, it was found that a high redundancy exists between these independent variables. Since the determination of P-wave velocity is easy and practical compared to the other elastic parameters, this parameter was selected for the multiple regression analysis. Multiple regression analysis was performed for the estimation of UCS and E. The independent variables used in the multiple regression analysis are density, P-wave velocity, CAI, VBP, ABDF, aspect ratio and roundness of blocks. The stepwise regression method was used to obtain the best model. The best model developed for the UCS estimation is given below:
20 15 10
x1 The output of previous layer
wij 5
x2 x3
f(Σxiwij)
xi Fig. 5. A simple block diagram of a neuron.
xj 0 5
15
25
35
45
55
65
75
85
95
105
Uniaxial compressive strength (MPa) Fig. 7. The histogram of uniaxial compressive strength values.
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100
35
90
Predicted UCS (MPa)
40
Frequency
30 25 20 15 10 5
80 70 60 50 40 30 20 10 0
0 2.350
2.425
2.500
2.575
0
2.650
10
20
3
30
40
50
60
70
80
90
100
Measured UCS (MPa)
Density (g/cm ) Fig. 8. The histogram of density values.
Fig. 9. Measured versus predicted UCS for the ANNs model.
developed models. The ANNs analysis was only applied for the prediction of the UCS. Since the CAI was not included to the best regression model for the prediction of E, the ANNs analysis was not applied for the prediction of this parameter.
Table 5 Correlation coefficients and standard error of estimates for the models produced from ANNs and regression analysis.
5.2.1. The development of ANN models for the prediction of UCS A four entries neural network structure is implemented in MATLAB environment for the prediction of UCS to compare with the regression model (Eq. (2)). The structure of the ANNs model, i.e. the number of input layer neurons, the number of hidden layer neurons and the number of output layer neurons, is given in Table 4. The training parameters and the algorithm which employed in the training phase are also shown Table 4. A neural network with the structure 4–6–1 as shown in Table 4 is employed. This structure is used to construct a model, which delineates the non-linear relation between the independent variables and UCS value. The model is as follows
UCS ¼ f ðVBP; d; V p ; CAIÞ
ð5Þ
where UCS is the uniaxial compressive strength (MPa), VBP is the volumetric block proportion (%), d is the density (g/cm3), Vp is Pwave velocity (km/s), and CAI is the Cerchar abrasivity index. The scatter diagrams of the observed and estimated values can be plotted to see the estimation capability of the derived model. Ideally, on a plot of observed versus estimated, the points should be scattered around the 1:1 diagonal straight line. A point lying on the line indicates an exact estimation. A systematic deviation from this line may indicate, for example, that larger errors tend to accompany larger estimations, suggesting non-linearity in one or more variables. The plot of estimated UCS versus observed UCS for the ANNs model is shown in Fig. 9. In the plot the points are scattered uniformly about the diagonal line, suggesting that the models are reasonable.
Model type
Coefficient of correlation (r)
Standard error of estimate
Regression model (Eq. (2)) ANNs model
0.75 0.86
11.89 9.91
6. The comparison of regression and ANNs models The correlation coefficients and the standard error of estimates were used for the comparison of the models produced from ANNs and regression analysis. As shown in Table 5, the correlation coefficient of regression model (Eq. (2)) for the estimation of UCS is good. However, corresponding ANNs model for the estimation of UCS have much stronger correlation coefficient that that of regression model. The values of standard error of estimates for ANNs model is lower than that of the regression model as shown in Table 5. The comparison of the model produced from ANNs and regression analysis using the correlation coefficients and the standard error of estimates shows that ANNs model for the prediction of UCS is more reliable than the regression model.
7. Conclusions The predictability of UCS and E values of Misis Fault Breccia from some indirect methods including the CAI was investigated using the regression and ANNs analysis. The CAI was included to the best regression model for the prediction of UCS. However, the CAI was not included to the best regression model for the prediction of E. The derived ANNs model was also compared with the regression model. Concluding remark is that the CAI can be used
Table 4 The structures of the ANNs model. Number of input neuron
Number of hidden neuron
Number of output neuron
Network type
Transfer function
Training parameters
Training algorithm
4
6
1
Feed-forward back propagation
logsig
Learning rate: Adaptive Momentum coeff.: 0.9 Epochs: 500
GDX (gradient descent)
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for the prediction of UCS of Misis Fault Breccia. Another conclusion is that ANNs model is more reliable than the regression model. Acknowledgement This study was supported by Alexander von Humboldt Foundation. References Al-Ameen, S. I., & Waller, M. D. (1994). The influence of rock strength and abrasive mineral content on the Cerchar Abrasive Index. Engineering Geology, 36, 293–301. Alber, M., & Kahraman, S. (2009). Predicting the uniaxial compressive strength and elastic modulus of a fault breccia from texture coefficient. Rock Mechanics and Rock Engineering, 42, 117–127. Altun, H., Bilgil, A., & Fidan, B. C. (2007). Treatment of skewed multi-dimensional training data to facilitate the task of engineering neural models. Expert System with Applications, 33, 978–983. Buergi, C., Parriaux, A., Franciosi, G., & Rey, J.-Ph. (1999). Cataclastic rocks in underground structures – Terminology and impact on the feasibility of projects (initial results). Engineering Geology, 51, 225–235. Chester, F. M., & Logan, J. M. (1986). Implications for mechanical properties of brittle faults from observations of the Punchbowl Fault Zone, California. Pure and Applied Geophysics, 124, 79–106. Ehrbar, H., & Pfenniger, I. (1999). Umsetzung der geologie in technische massnahmen im tavetscher zwischenmassive nord. In S. Loew & R. Wyss (Eds.), Vorerkundung und prognose der basistunnels am gotthard und am lötschberg (pp. 381–394). Rotterdam: Balkema. Evenden, M. P., & Edwards, J. S. (1985). Cutting theory and coal assessment techniques and their application to shearer design. Mining Science and Technology, 2, 253–270. Fairhurst, C. E., & Hudson, J. A. (1999). Draft ISRM suggested method for the complete stress–strain curve for intact rock in uniaxial compression. International Journal of Rock Mechanics and Mining Sciences, 36, 279–289. Goodman, R. E., & Ahlgren, C. S. (2000). Evaluating safety of concrete gravity dam on weak rock: Scott Dam. Journal of Geotechnical and Geoenvironmental Engineering, 126(5), 429–442. Habimana, J., Labiouse, V., & Descoeudres, F. (2002). Geomechanical characterisation of cataclastic rocks: experience from the Cleuson–Dixence project. International Journal of Rock Mechanics and Mining Sciences, 39(6), 677–693. Haneberg, WC. (2004). Simulation of 3-D block populations to characterize outcrop sampling bias in block-in-matrix rocks (bimrocks). Felsbau-Rock and Soil Engineering, 22, 19–26. Kahraman, S., & Alber, M. (2006). Estimating the unconfined compressive strength and elastic modulus of a fault breccia mixture of weak rocks and strong matrix. International Journal of Rock Mechanics and Mining Sciences, 43, 1277–1287. Kahraman, S., Alber, M., Fener, M., & Gunaydin, O. (2008). Evaluating the geomechanical properties of Misis Fault Breccia (Turkey). International Journal of Rock Mechanics and Mining Sciences, 45, 1469–1479. Kahraman, S., Altun, H., Tezekici, B. S., & Fener, M. (2005). Sawability prediction of carbonate rocks from shear strength parameters using artificial neural
networks. International Journal of Rock Mechanics and Mining Sciences, 43(1), 157–164. Kahraman, S., Gunaydin, O., Alber, M., & Fener, M. (2009). Evaluating the strength and deformability properties of Misis Fault Breccia using Artificial Neural Networks. Expert Systems with Applications, 36, 6874–6878. Kumar, U. A. (2005). Comparison of neural networks and regression analysis: A new insight. Expert System with Applications, 29, 424–430. Laws, S., Eberhardt, E., Loew, S., & Descoeudres, F. (2003). Geomechanical properties of shear zones in the Eastern Aar Massif, Switzerland and their implication on tunnelling. Rock Mechanics and Rock Engineering, 36(4), 271–303. Lindquist, E. S., & Goodman, R. E. (1994). Strength and deformation properties of a physical model melange. In P. P. Nelson & S. E. Laubach (Eds.), Proceedings of the 1st North American rock mechanics symposium (pp. 843–850). Rotterdam: Balkema. Medley, E. W. (1994). The engineering characterization of melanges and similar blockin-matrix rocks (bimrocks). Ph.D. Dissertation. University of California at Berkeley, California/Ann Arbor, MI: UMI, Inc. Medley, E. W. (1997). Uncertainty in estimates of block volumetric proportions in melange bimrock. In P. G. Marinos, G. C. Koukis, G. C. Tsiambaos, & G. C. Stournaras (Eds.), Proceedings of the international symposium on engineering geology and the environment (pp. 267–272). Rotterdam: Balkema. Medley, E. W. (2001). Orderly characterization of chaotic Franciscan Melanges. Felsbau-Rock and Soil Engineering, 19, 20–33. Medley, E. W. (2002). Estimating block size distribution of melanges and similar block-in-matrix rocks (bimrocks). In R. Hammah, W. Bawden, J. Curran, & M. Telesnicki (Eds.), Proceedings of the 5th North American rock mechanics symposium (pp. 509–516). Toronto, Canada: University of Toronto Press. Medley, E. W., & Goodman, R. E. (1994). Estimating the block volumetric proportions of melanges and similar block-in-matrix rocks (bimrocks). In P. P. Nelson & S. E. Laubach (Eds.), Proceedings of the 1st North American rock mechanics symposium (pp. 851–858). Rotterdam: Balkema. Rafiq, M. Y., Bugmann, G., & Easterbrook, D. J. (2001). Neural network design for engineering applications. Computers and Structures, 79, 1541–1552. Singh, V. K., Singh, D., & Singh, T. N. (2001). Prediction of strength properties of some schistose rocks from petrographic properties using artificial neural networks. International Journal of Rock Mechanics and Mining Sciences, 38, 269–284. Sonmez, H., Gokceoglu, C., Medley, E. W., Tuncay, E., & Nefeslioglu, H. A. (2006). Estimating the uniaxial compressive strength of a volcanic bimrock. International Journal of Rock Mechanics and Mining Sciences, 43, 554–561. Sonmez, H., Gokceoglu, C., Nefeslioglu, H. A., & Kayabasi, A. (2006). Estimation of rock modulus: For intact rocks with an artificial neural network and for rock masses with a new empirical equation. International Journal of Rock Mechanics and Mining Sciences, 43(2), 224–235. Sonmez, H., Gokceoglu, C., Tuncay, E., Medley, E. W., & Nefeslioglu, H. A. (2004). Relationship between volumetric block proportion and overall UCS of a volcanic bimrock. Felsbau-Rock and Soil Engineering, 22, 27–34. Yang, Y., & Zhang, Q. (1998). The applications of neural networks to rock engineering systems (RES). International Journal of Rock Mechanics and Mining Sciences, 35(6), 727–745. Yuanyou, X., Yanming, X., & Ruigeng, Z. (1997). An engineering geology evaluation method based on an artificial neural network and its application. Engineering Geology, 47, 149–156. Zorlu, K., Gokceoglu, C., Ocakoglu, F., Nefeslioglu, H. A., & Acikalin, S. (2008). Prediction of uniaxial compressive strength of sandstones using petrographybased models. Engineering Geology, 96, 141–158.
Contents lists available at ScienceDirect
Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa
The usability of Cerchar abrasivity index for the prediction of UCS and E of Misis Fault Breccia: Regression and artificial neural networks analysis S. Kahraman a,*, M. Alber b, M. Fener c, O. Gunaydin c a
Nigde University, Mining Engineering Department, Nigde, Turkey Ruhr University-Bochum, Applied Geology Department, Bochum, Germany c Nigde University, Geological Engineering Department, Nigde, Turkey b
a r t i c l e
i n f o
Keywords: Fault breccia Uniaxial compressive strength Elastic modulus Physical and textural properties Cerchar abrasivity index Artificial neural networks
a b s t r a c t The derivation of some predictive models for the geomechanical properties of fault breccias will be useful due to the fact that the preparation of smooth specimens from the fault breccias is usually difficult and expensive. To develop some predictive models for the uniaxial compressive strength (UCS) and elastic modulus (E) from the indirect methods including the Cerchar abrasivity index (CAI), regression and artificial neural networks (ANNs) analysis were applied on the data pertaining to Misis Fault Breccia. The CAI was included to the best regression model for the prediction of UCS. However, the CAI was not included to the best regression model for the prediction of E. The developed ANNs model was also compared with the regression model. It was concluded that the CAI is a useful property for the prediction of UCS of Misis Fault Breccia. Another conclusion is that ANNs model is more reliable than the regression models. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction Artificial neural networks (ANNs) are being used commonly in science and engineering applications in recent years, since they have some important features such as self-learning, adaptive recognition, and non-linear dynamic processing comparing to the traditional expert systems. In recent years, numerous geoscientists (Kahraman, Altun, Tezekici, & Fener, 2005; Singh, Singh, & Singh, 2001; Sonmez, Gokceoglu, Nefeslioglu, & Kayabasi, 2006; Yang & Zhang, 1998; Yuanyou, Yanming, & Ruigeng, 1997; Zorlu, Gokceoglu, Ocakoglu, Nefeslioglu, & Acikalin, 2008) have applied the ANNs to many studies in geosciences since ANNs models show a good performance in the solving of non-linear multivariable problems. Knowing the geomechanical properties of fault breccias is very important in rock engineering because the fault breccias usually cause problems in geo-engineering applications. However, the fault breccias are usually not suitable for preparing smooth specimens or the preparation of such specimens is tedious, time consuming and expensive for the standard tests. So, the derivation of some predictive models for the geomechanical properties of fault breccias will be useful. The characteristics of geologically complex rocks such as melanges, sheared serpentinites, coarse pyroclastic rocks and fault rocks have been investigated by some researchers (Buergi, Parriaux, Franciosi, & Rey, 1999; Chester & Logan, 1986; Ehrbar & * Corresponding author. Tel.: +90 388 2252264; fax: +90 388 2250112. E-mail address: [email protected] (S. Kahraman). 0957-4174/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2010.06.039
Pfenniger, 1999; Goodman & Ahlgren, 2000; Habimana, Labiouse, & Descoeudres, 2002; Laws, Eberhardt, Loew, & Descoeudres, 2003; Lindquist & Goodman, 1994; Medley, 1994, 2001, 2002; Medley & Goodman, 1994; Sonmez, Gokceoglu, Medley, Tuncay, & Nefeslioglu, 2006; Sonmez, Gokceoglu, Tuncay, Medley, & Nefeslioglu, 2004). The reviews of these studies were presented by Kahraman and Alber (2006) and will not be repeated here. There are no apparent predictive models except the authors’ models in the literature for the geomechanical properties of fault breccias. Kahraman and Alber (2006) and Alber and Kahraman (2009) correlated the uniaxial compressive strength (UCS) and elastic modulus (E) values of Ahauser fault breccia (Germany) having blocks weaker than the matrix with volumetric block proportion (VBP) and texture coefficient (TC) and found strong correlations between UCS and both VBP and TC. In addition, Kahraman, Alber, Fener, and Gunaydin (2008) investigated the geomechanical properties of the Misis Fault Breccia from Turkey. As a result of multiple regression analysis, they found some significant alternative models including density, P- and S-wave velocity and textural properties for the prediction of UCS and deviator stress. Recently, Kahraman, Gunaydin, Alber, and Fener (2009) investigated the predictability of UCS and E values of Misis Fault Breccia from some indirect methods using ANNs and the results were compared with the regression models. They derived very good models for both UCS and E estimation from ANNs analysis comparing to the regression models. VBP, density, S-wave velocity, the roundness of blocks, and the average block diameter factor were included to the models.
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In this study, the usability of Cerchar abrasivity test for the determination of UCS and E of Misis Fault Breccia using ANNs analysis was investigated. The Cerchar abrasivity test which is a nondestructive method is one of the most common testing methods used for the assessment of hard rock abrasivity. Although it is developed for abrasivity, some researchers (Al-Ameen & Waller, 1994; Evenden & Edwards, 1985) showed that there are some correlations between rock strength and Cerchar abrasivity index (CAI). Since the device has a small testing pin and the scratching distance is 10 mm, it can be used for scratching on matrix area of a breccia core sample. Average CAI values obtained from the scratching procedures on the different matrix surface of a core sample may be an indirect measure of the matrix strength. 2. The rock tested and sampling Fig. 2. Prepared core samples.
The rock tested in this study pertains to the Misis Fault Breccia (Ceyhan–Adana–Turkey). A view of crust crop in the fault zone is shown in Fig. 1. Block samples were collected from the site and transported to the laboratory. Misis Fault Breccia is composed of dolomitic limestone blocks embedded in fine-grained matrix of red-coloured claystone containing Fe-rich clay. For the laboratory tests, a total of 125 core samples having different volumetric block proportion were prepared (Fig. 2). 3. Determination of textural properties The circumferential surface of the each core was scanned by the DMT (Deutsche Montan Technologie GmbH) CoreScan II-Digital Core Imaging System. The estimation of VBP, and the calculation of the average block diameter factor (ABDF), aspect ratio and roundness of blocks were performed on the scanned images of cores using a computer package (Image Pro-Plus 5.0). Fig. 3 shows the original and processed images of a sample. 3.1. Estimation of volumetric block proportion Volumetric block proportion (VBP) is defined as the total volume of blocks divided by the total volume of the rock mass. Some researchers (Goodman & Ahlgren, 2000; Haneberg, 2004; Medley, 1997, 2002; Medley & Goodman, 1994) have explained the estimation or determination methods of VBP and discussed the uncertainties in estimating three-dimensional block size distributions from one- or two-dimensional measurements. Although the sieve analysis is the best method, the separation of blocks from the matrix is very difficult in most situations. For this reason, the estimation
Fig. 3. Original (a) and processed (b) images of a sample.
of VBP from one- or two-dimensional methods such as using the drill core/block intersection lengths or scanlines, geological mapping, and image analysis is commonly applied. In this study, the scanned images of the circumferential surfaces of the cores were processed and used for the estimation of VBP.
3.2. Average block diameter factor (ABDF) The two-dimensional diameter (assumed to be the same as three-dimensional diameter) was estimated by measuring the length of the line passing through the 2° centroid of each block. Then these lines were averaged. Since the core samples prepared for the UCS and E test had different diameters, these values were converted to ABDF using the following formula:
ABDF ¼
Fig. 1. A view of crust crop in the Misis fault zone.
Dblock 100 Dsample
ð1Þ
where ABDF is the average block diameter factor (%), Dblock is the average block diameter (mm), Dsample is the core sample diameter (mm).
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several calliper readings. The weights of the specimens were determined by a balance, capable of weighing to an accuracy of 0.1 of the sample weight. The density values were obtained from the ratio of the specimen weight to the specimen volume. 4.2. Ultrasonic test The ultrasonic generator USG 40, manufactured by Geotron GmbH in Pirna, Germany, was used to evaluate the elastic properties of the samples (Fig. 4). Ultrasonic transducers of 20–250 kHz were used depending on the geometry of specimen. 4.3. Cerchar abrasivity test
Aspect ratio describes the elongation of blocks, and is the ratio of the length of the major axis and minor axis of the ellipse with an area equivalent to that of the block.
The Cerchar abrasivity index (CAI) tests were performed using the original Cerchar apparatus by scratching pins of HRC 54-56 loaded with 70 N in 1 s over a distance of 10 mm. The tests were carried out on the blocks and the matrix areas of each core sample before the UCS and deformability tests. After performing the tests on 10 limestone blocks, it was seen that the CAI values of limestone blocks were approximately same, i.e. 1.22 ± 0.12. However, the CAI values of matrix ranges from 0.00 to 0.83.
3.4. Roundness of blocks
4.4. Uniaxial compressive strength test
Roundness can also be described as a form factor. Roundness is 1 for a perfect circle. When the shape deviates from circularity, the roundness decreases.
Uniaxial compression tests were performed on trimmed core samples, which had height to diameter ratios of 2 to 2.5. The tests were performed using an electro-hydraulic servo-controlled stiff testing machine (MTS). The samples were loaded in axial strain control at a rate of 105 mm/mm/s beyond peak strength according to ISRM suggested method (Fairhurst & Hudson, 1999).
Fig. 4. Ultrasonic testing device.
3.3. Aspect ratio of blocks
4. Laboratory studies Density test, ultrasonic test and Cerchar abrasivity index test were first carried out on the each core sample, and then uniaxial compressive strength and deformability tests were performed. 4.1. Density test Trimmed core samples were used in the determination of density. The specimen volume was calculated from an average of Table 1 The textural properties. Statistical parameter
Number of samples Minimum Maximum Average Standard deviation Skewness
4.5. Deformability test During the uniaxial compressive strength tests, deformation measurements were also carried out using two high resolution LVDTs (linear variable differential transformer). Elastic modulus (E) values were obtained from stress–strain curves at a stress level equal to 50% of the ultimate uniaxial compressive strength.
5. Evaluation of the test results Volumetric block proportion (%)
Average block diameter factor (%)
Aspect ratio of blocks
Roundness of blocks
125 4.0 75.9 36.9 ±15.3 0.20
125 3.1 22.7 8.8 ±3.5 0.96
125 1.7 2.2 1.9 ±0.1 0.53
125 0.62 0.84 0.75 ±0.05 0.02
Textural properties together with statistical evaluation are given in Table 1. The VBP and ABDF values are highly scattered. The VBP values range from 4.0% to 75.9%. The ABDF values range from 3.1% to 22.7%. The aspect ratio and roundness of blocks are not scattered. Statistical evaluation of the physico-mechanical tests results are given in Table 2. The results are generally scattered. For example, the UCS values range from 9.1 to 108.1 MPa and E values range from 4.3 to 39.4 GPa.
Table 2 The physico-mechanical properties of the fault breccia. Statistical parameter
Uniaxial compressive strength (MPa)
Static elastic modulus (GPa)
Dynamic elastic modulus (GPa)
Static Poisson’s ratio
Dynamic Poisson’s ratio
Dynamic rigidity modulus (GPa)
P-wave velocity (km/s)
S-wave velocity (km/s)
Density (g/cm3)
Cerchar abrasivity index for matrix
Number of samples Minimum Maximum Average Standard deviation Skewness
125 9.1 108.1 44.7 ±17.7 1.04
125 4.3 39.4 20.0 ±7.3 0.21
125 14.5 74.6 39.2 ±10.1 0.05
125 0.04 0.65 0.23 ±0.11 1.02
125 0.20 0.44 0.33 ±0.04 0.12
125 5.2 27.7 14.9 ±4.1 0.03
125 3.49 6.66 4.82 ±0.49 0.22
125 1.44 3.24 2.41 ±0.34 0.54
125 2.36 2.64 2.50 ±0.05 0.07
125 0.00 0.83 0.26 ±0.20 0.63
Table 3 Correlation matrix for the data.
Uniaxial compressive strength Static elastic modulus Static Poisson’s ratio Density P-wave velocity S-wave velocity Dynamic elastic modulus Dynamic Poisson’s ratio Dynamic rigidity modulus Cerchar abrasivity index for matrix Volumetric block proportion Average block diameter factor Aspect ratio of blocks Roundness of blocks
Static elastic modulus
Static Poisson’s ratio
Density
P-wave velocity
S-wave velocity
Dynamic elastic modulus
Dynamic Poisson’s ratio
Dynamic rigidity modulus
Cerchar abrasivity index for matrix
Volumetric block proportion
Average block diameter factor
Aspect ratio of blocks
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Uniaxial compressive strength 1.00
0.76
1.00
0.01
0.13
1.00
0.01 0.32 0.44 0.43
0.27 0.45 0.50 0.53
0.04 0.15 0.12 0.12
1.00 0.60 0.31 0.44
1.00 0.73 0.81
1.00 0.98
1.00
0.31
0.27
0.04
0.15
0.04
0.70
0.59
1.00
0.43
0.53
0.12
0.39
0.74
0.98
0.99
0.66
1.00
0.49
0.37
0.17
0.09
0.26
0.38
0.35
0.27
0.35
1.00
0.46
0.15
0.08
0.71
0.35
0.06
0.18
0.26
0.14
0.32
1.00
0.03
0.05
0.31
0.00
0.03
0.03
0.01
0.07
0.02
0.05
0.12
1.00
0.25
0.17
0.21
0.02
0.21
0.20
0.17
0.10
0.18
0.30
0.23
0.05
1.00
0.25
0.22
0.15
0.04
0.02
0.19
0.16
0.25
0.17
0.21
0.18
0.52
0.40
1.00
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5.1. Regression analysis
UCS ¼ 366:0 0:9VBP þ 155:8d þ 10:7V p þ 16:7CAI; r ¼ 0:75
ð2Þ
where UCS is the uniaxial compressive strength (MPa), VBP is the volumetric block proportion (%), d is the density (g/cm3), Vp is Pwave velocity (km/s), and CAI is the Cerchar abrasivity index. The best model produced for E has a comparatively low correlation coefficient. In addition, CAI was not included to this model. The equation of this model is:
E ¼ 180:2 0:3VBP þ 74:1d þ 5:4V p ;
r ¼ 0:62
ð3Þ
where E is the static elastic modulus (MPa), VBP is the volumetric block proportion (%), d is the density (g/cm3), and Vp is the P-wave velocity (km/s). 5.2. Artificial neural networks (ANNs) analysis ANNs take a different problem solving approach than that of numerical methods. In ANNs models, the activity of the human brain is simulated in a highly simplified way. These models consist of interconnected assembly of simple processing elements, neurons, which organized in a layered fashion. Each neuron in a layer is connected to the neurons in the subsequent layer and so on, as seen in Fig. 5. The interconnection between ith and jth layers is labelled as wij and is called ‘‘weights”. It is these interconnections between layers that provide a powerful tool for prediction and classification. During learning phase, these interconnections are optimized in order to minimize a predefined cost function. The weighted sum of inputs to a neuron is calculated and the output of a neuron, the activation of the neuron, is determined by an activation function, which is illustrated in Fig. 5 as f( ). The type of neural network used in this study is Multi Layered Perception (MLP). A MLP neural network is shown in Fig. 6. The MLP networks consist of an input layer, one or more hidden layers and an output layer. Each layer has a number of processing units (neurons) and each unit is fully interconnected with weighted connections to units in the subsequent layer. The MLP transforms i inputs into k outputs through non-linear mapping functions.
x1 x1 x2 xk xi
Input Layer
Weights wij
Hidden Layer
Output Layer
Weights wjk
Fig. 6. A Multilayered Perception Neural Network.
Some investigators (Altun, Bilgil, & Fidan, 2007; Kumar, 2005) indicated that ANNs models are not consistently good in estimation for highly skewed data. When the data is skewed, some transformation like power transformation can be used for reducing the skewness before performing neural network analysis. The skewness is a measure for the degree of symmetry in the normal distribution. If the skewness coefficient is 0, the distribution is symmetric (not skewed). Positive skewness indicates the distribution is skewed to the right, and negative skewness indicates the distribution is skewed to the left. As indicated in Tables 1 and 2, the skewness values of parameters are generally small. Furthermore, histograms of variables exhibited that the data of variables are generally show normal distribution. Figs. 7 and 8 are given as examples. Therefore, it can be said that the transformation or the treatment of data is not necessary. The data set is usually normalized to obtain better convergence in the ANNs analysis. The data set used in this study was scaled between 0 and 1 using the following equation (Rafiq, Bugmann, & Easterbrook, 2001):
U norm ¼
U actual U min U max U min
ð4Þ
where Unorm is the normalized value, Uactual is the actual value, Umax is the maximum value of the data set and Umin is the minimum value of the data set. The data pertaining to 125 rock sample were used in the ANNs analysis. The first group consisting of 100 data points was used to train the network and to develop ANNs models. The second group consisting of 25 data points was used to test the accuracy of the
30 25
Frequency
Firstly the correlation matrix was constructed for the all data. As shown in Table 3, CAI exhibits the highest correlation coefficient (r = 0.49) with UCS. However, CAI does not exhibit the highest correlation coefficient with E. When the correlation coefficient (r) values among the dynamic elastic parameters are checked, it was found that a high redundancy exists between these independent variables. Since the determination of P-wave velocity is easy and practical compared to the other elastic parameters, this parameter was selected for the multiple regression analysis. Multiple regression analysis was performed for the estimation of UCS and E. The independent variables used in the multiple regression analysis are density, P-wave velocity, CAI, VBP, ABDF, aspect ratio and roundness of blocks. The stepwise regression method was used to obtain the best model. The best model developed for the UCS estimation is given below:
20 15 10
x1 The output of previous layer
wij 5
x2 x3
f(Σxiwij)
xi Fig. 5. A simple block diagram of a neuron.
xj 0 5
15
25
35
45
55
65
75
85
95
105
Uniaxial compressive strength (MPa) Fig. 7. The histogram of uniaxial compressive strength values.
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100
35
90
Predicted UCS (MPa)
40
Frequency
30 25 20 15 10 5
80 70 60 50 40 30 20 10 0
0 2.350
2.425
2.500
2.575
0
2.650
10
20
3
30
40
50
60
70
80
90
100
Measured UCS (MPa)
Density (g/cm ) Fig. 8. The histogram of density values.
Fig. 9. Measured versus predicted UCS for the ANNs model.
developed models. The ANNs analysis was only applied for the prediction of the UCS. Since the CAI was not included to the best regression model for the prediction of E, the ANNs analysis was not applied for the prediction of this parameter.
Table 5 Correlation coefficients and standard error of estimates for the models produced from ANNs and regression analysis.
5.2.1. The development of ANN models for the prediction of UCS A four entries neural network structure is implemented in MATLAB environment for the prediction of UCS to compare with the regression model (Eq. (2)). The structure of the ANNs model, i.e. the number of input layer neurons, the number of hidden layer neurons and the number of output layer neurons, is given in Table 4. The training parameters and the algorithm which employed in the training phase are also shown Table 4. A neural network with the structure 4–6–1 as shown in Table 4 is employed. This structure is used to construct a model, which delineates the non-linear relation between the independent variables and UCS value. The model is as follows
UCS ¼ f ðVBP; d; V p ; CAIÞ
ð5Þ
where UCS is the uniaxial compressive strength (MPa), VBP is the volumetric block proportion (%), d is the density (g/cm3), Vp is Pwave velocity (km/s), and CAI is the Cerchar abrasivity index. The scatter diagrams of the observed and estimated values can be plotted to see the estimation capability of the derived model. Ideally, on a plot of observed versus estimated, the points should be scattered around the 1:1 diagonal straight line. A point lying on the line indicates an exact estimation. A systematic deviation from this line may indicate, for example, that larger errors tend to accompany larger estimations, suggesting non-linearity in one or more variables. The plot of estimated UCS versus observed UCS for the ANNs model is shown in Fig. 9. In the plot the points are scattered uniformly about the diagonal line, suggesting that the models are reasonable.
Model type
Coefficient of correlation (r)
Standard error of estimate
Regression model (Eq. (2)) ANNs model
0.75 0.86
11.89 9.91
6. The comparison of regression and ANNs models The correlation coefficients and the standard error of estimates were used for the comparison of the models produced from ANNs and regression analysis. As shown in Table 5, the correlation coefficient of regression model (Eq. (2)) for the estimation of UCS is good. However, corresponding ANNs model for the estimation of UCS have much stronger correlation coefficient that that of regression model. The values of standard error of estimates for ANNs model is lower than that of the regression model as shown in Table 5. The comparison of the model produced from ANNs and regression analysis using the correlation coefficients and the standard error of estimates shows that ANNs model for the prediction of UCS is more reliable than the regression model.
7. Conclusions The predictability of UCS and E values of Misis Fault Breccia from some indirect methods including the CAI was investigated using the regression and ANNs analysis. The CAI was included to the best regression model for the prediction of UCS. However, the CAI was not included to the best regression model for the prediction of E. The derived ANNs model was also compared with the regression model. Concluding remark is that the CAI can be used
Table 4 The structures of the ANNs model. Number of input neuron
Number of hidden neuron
Number of output neuron
Network type
Transfer function
Training parameters
Training algorithm
4
6
1
Feed-forward back propagation
logsig
Learning rate: Adaptive Momentum coeff.: 0.9 Epochs: 500
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