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Technical Committee 204 /
Comité technique 204
present in the database are UCS, Brazilian Tensile Strength
(BTS), PSI, DPW and α and the dependent variable is ROP.
However, according to Yagiz (2008), BTS is the property that
presents the lowest correlation with the ROP. Therefore, it was
excluded from the dataset.
Table 1 presents some statistical attributes from the database.
Table 1. Statistics of the input and output parameters.
Parameter
Min Mean
Max Std. Dev.
Inputs
UCS (MPa)
118.30 149.89
199.70
22.09
PSI (kN/mm)
25
34.64
58
8.42
DPW (m)
0.050
1.023
2.00
0.642
α (º)
2
44.57
89
23.21
Output
ROP
(
m/h)
1.27
2.05
3.07
0.36
Yagiz (2008) performed several statistical analyses with the
database to develop a predictive equation of TBM performance.
The commercial software package for standard statistical
analysis (SPSS) allowed the author to generate several models
and to obtain empirically the best predictive equation of ROP:
DPW
Log
UCS
PSI
hm ROP
.
219 .0
.
437 .0
.
003 .0
.
029 .0 093 .1 ) /
(4)
Yagiz and Karahan (2011) using partial swarm optimization
obtained the following equation:
827 .2
.
6756 .1
.
4016 .0
.
0292 .0
.
0041 .0
/
217 .0
584 .0
DPW
PSI
UCS
hm ROP
(5)
Table 2 shows the values of the errors and Pearson’s
product-moment correlation coefficient (R) using a linear
regression between the measured and the predicted values
obtained with both equations and using all the dataset. A slight
improvement was obtained from equation 4 to equation 5.
Table 2. Performances of Equations 4 and 5.
Parameter
Eq. 4
Eq. 5
MAD
0.184
0.178
RMSE
0.216
0.207
R
0.815
0.817
5 PREDICTION OF ROP USING ANN AND SVM
The ANN and SVM were applied using the R program
environment (R Development Core Team 2010) which is an
open source freeware statistical package. This software can be
used with other packages that allow performing DM analyses.
Therefore, a specific program R-Miner developed by Cortez
(2010) was used to apply the SVM and the ANN and evaluate
their behaviour under a different set of metrics. It must be
emphasized that R-Miner allows the application of other DM
algorithms and was already applied before by Martins and
Miranda (2012).
The ANN and SVM were tested in predicting the ROP being
adopted an assessment scheme using 10 runs in a 10-fold cross-
validation (Efron and Tibshirani, 1993), where the records were
divided into 10 parts of equal size. Sequentially, each subset
was tested with the adjusted model with the leftover records.
The overall performance is given by the mean values of the
errors (MAD and RMSE) and the Pearson’s product-moment
correlation coefficient (R) in 10 runs.
The errors (MAD and RMSE) and the Pearson’s product-
moment correlation coefficient (R) obtained during the training
phase of the models that allow evaluating the performance of
ANN and SVM are presented in Table 3. It can be seen that
both algorithms have good behavior. However there is a slightly
better performance of SVM.
To evaluate the importance given by the models to the input
parameters it is necessary to perform a sensibility analysis. In
this analysis each parameter is changed over its range of
variation, while maintaining the others constant, and calculated
the variance of the output parameter. The input parameter that
induces a higher variance in the output parameter is the most
important one. The relative importance is given in Table 4.
Based on these results, we can state that both techniques give
almost the same importance to all the parameters. The most
influential parameters is PSI, followed by α and DPW. The less
important parameter is UCS. The database used in this paper
corresponds to a rock mass with a lot of joints and faults. This
can explain the low influence of the UCS in the machine
performance. PSI translates the influence of rock toughness and
brittleness in machine performance. Therefore it is
understandable its great influence on ROP.
Table 3. Performances of ANN and SVM obtained in the training phase.
Parameter
ANN
SVM
MAD
0.196
0.192
RMSE
0.234
0.231
R
0.760
0.765
Table 4. Relative importance (%) of the input parameters.
Parameter
ANN
SVM
UCS
5.49
5.33
PSI
65.94
65.90
DPW
12.39
11.69
α
16.18
17.08
Table 5. Metrics obtained adjusting the models with all the dataset.
Parameter
ANN
SVM
MAD
0.163
0.185
RMSE
0.195
0.227
R
0.838
0.796
Figures 3 and 4 show the comparisons between the measured
and predicted ROP for ANN and SVM. It can be seen for both
models that for ROP values between 1.5 and 2.5 the set of
points is near the 45º slope line. Outside this range it seems that
the ANN model provides better results. The errors and R
associated to these figures are presented in Table 5.
It can be seen that the ANN models have lower errors and
higher R than the SVM.
Comparing the results of Tables 2 and 5 it is possible to
conclude that the ANN model has better performance than the
Equations 4 and 5.
