Optimal Data based ANFIS Modeling
Case 2:- Modeling results for the thermal power plant data (i) Data set-I
5.4. EXPERIMENTAL RESULTS AND DISCUSSION 68 Table 5.2: Modeling results for the Box and Jenkins gas furnace data and the thermal power plant data using V-fold based ANFIS model
No of
Number RMSE (testing)
Sl. No. Data training Input variables
of rules (Grid partition (Subtractive
data based) clustering based)
1
Box and
Jenkins 18 x(t−3),y(t−1) 4 0.5943 0.5556
gas furnace Thermal
2 power plant 81 x(t−6),y(t−1) 4 0.0110 0.0115
(Data set-I) Thermal
3 power plant 72 x(t−3),y(t−1) 4 0.0092 0.0104
(Data set-II) Thermal
4 power plant 72 x(t−1),y(t−1) 4 0.0078 0.0082
(Data set-III) Thermal
5 power plant 72 x(t−1),y(t−1) 4 0.0034 0.0036
(Data set-IV) Thermal
6 power plant 36 x(t−1),y(t−1) 4 0.6508 0.6097
(Data set-V)
5.4.3 Modeling results with FFD-V-fold technique based ANFIS model
The V-fold technique is now combined with the FFD based ANFIS. The following experiments are carried out with this combined model.
5.4. EXPERIMENTAL RESULTS AND DISCUSSION 69 set the best result was obtained for the 2-level FFD-V-fold based ANFIS model.
(ii) Data set-II
The two optimal inputs used here arex(t−3)andy(t−1). The 3(1)-level FFD-V-fold based ANFIS model produced the best result.
(iii) Data set-III
The optimal inputs used here for modeling arex(t−1)andy(t−1). The FFD-V-fold based ANFIS model with the 3(2) level showed the least MSE.
(iv) Data set-IV
Herex(t−1)andy(t−1)are the optimal inputs used for modeling and the least MSE was obtained for the 2-level FFD-V-fold based ANFIS model.
(vi) Data set-V
Here the modeling is carried out by using the optimal inputs x(t−1) and y(t−1). The 3(1)-level FFD-V-fold based ANFIS model shows the least MSE.
The results obtained by using the combined FFD-V-fold technique based ANFIS model are tabulated in Table 5.3. In Table 5.4, the results obtained by using the different models viz conventional ANFIS, FFD based ANFIS, V-fold based ANFIS and FFD-V-fold based ANFIS are compared with respect to their RMSE. From Table 5.4, it is observed that the best modeling results are obtained with the FFD-V-fold based ANFIS model as the RMSE (testing) is the least in this case for all the different types of data.
The modeling results for the different data sets as obtained by using different modeling methodologies are shown in Figs. 5.3 - 5.8. In Fig. 5.3 the actual output is plotted vs the predicted output for the FFD-V-fold based ANFIS model using the Box and Jenkins gas furnace data. Fig. 5.4 shows the actual and the predicted output for the FFD-V-fold based ANFIS model using the data set-I for the thermal power plant. Fig. 5.5 shows the actual and the predicted output for the FFD-V-fold based ANFIS model using the data set-II for the thermal power plant. Fig. 5.6 shows the actual and the predicted output for the FFD-V-fold based ANFIS model using the data set-III for the thermal power plant. Fig. 5.7 shows the actual and the predicted output for the FFD-V-fold based ANFIS model using the data set-IV for the thermal power plant. Fig. 5.8 shows the actual and the predicted output for the FFD-V-fold based ANFIS model using the data set-V of the thermal power plant.
5.4. EXPERIMENTAL RESULTS AND DISCUSSION 70
Table 5.3: Modeling results for the Box and Jenkins gas furnace data and the thermal power plant data using FFD-V-fold based ANFIS
Sl. No. Data Input variables
No of Model No of RMSE (testing)
rules FFD-V-fold training (Grid (Subtractive data partition clustering
based) based) 1
Box and
x(t−3),y(t−1) 4
2-level 18 0.5378 0.5332
Jenkins 3(1)-level 18 0.5705 0.6017
gas 3(2)-level 18 0.6153 0.5373
furnace 4-level 18 0.5627 0.5684
2
Thermal
x(t−6),y(t−1) 4
2-level 81 0.0110 0.0108
power plant 3(1)-level 81 0.0116 0.0109
(Data 3(2)-level 81 0.0109 0.0112
set-I) 4-level 81 0.0112 0.0114
3
Thermal
x(t−3),y(t−1) 4
2-level 72 0.0092 0.0092
power plant 3(1)-level 72 0.0086 0.0089
(Data 3(2)-level 72 0.0091 0.0093
set-II) 4-level 72 0.0088 0.0091
4
Thermal
x(t−1),y(t−1) 4
2-level 72 0.0084 0.0079
power plant 3(1)-level 72 0.0082 0.0080
(Data 3(2)-level 72 0.0076 0.0075
set-III) 4-level 72 0.0083 0.0082
5
Thermal
x(t−1),y(t−1) 4
2-level 72 0.0033 0.0034
power plant 3(1)-level 72 0.0036 0.0035
(Data 3(2)-level 72 0.0035 0.0035
set-IV) 4-level 72 0.0035 0.0036
6
Thermal
x(t−1),y(t−1) 4
2-level 36 0.5740 0.5293
power plant 3(1)-level 36 0.5687 0.5118
(Data 3(2)-level 36 0.6651 0.5900
set-V) 4-level 36 0.5174 0.5312
5.4. EXPERIMENTAL RESULTS AND DISCUSSION 71
Table 5.4: Comparison of modeling results for the Box and Jenkins gas furnace data and the thermal power plant data using various ANFIS models
Sl. No. Data Input variables
No of RMSE (testing) No of Model training (Grid (Subtractive
rules data partition clustering
based) based) 1
Box and
x(t−3),y(t−1) 4
ANFIS 145 0.5382 0.5724
Jenkins FFD 18 0.5589 0.5972
gas V-Fold 18 0.5943 0.5556
furnace FFD-V-fold 18 0.5378 0.5332
2
Thermal
x(t−6),y(t−1) 4
ANFIS 699 0.0114 0.0111
power plant FFD 46,25 0.0151 0.0117
(Data V-Fold 81 0.0110 0.0115
set-I) FFD-V-fold 81 0.0109 0.0108
3
Thermal
x(t−3),y(t−1) 4
ANFIS 675 0.0118 0.0111
power plant FFD 36 0.0097 0.0090
(Data V-Fold 72 0.0092 0.0104
set-II) FFD-V-fold 72 0.0086 0.0089
4
Thermal
x(t−1),y(t−1) 4
ANFIS 713 0.0081 0.0076
power plant FFD 27 0.0090 0.0083
(Data V-Fold 72 0.0078 0.0082
set-III) FFD-V-fold 72 0.0076 0.0075
5
Thermal
x(t−1),y(t−1) 4
ANFIS 494 0.0037 0.0035
power plant FFD 29 0.0036 0.0035
(Data V-Fold 72 0.0034 0.0036
set-IV) FFD-V-fold 72 0.0033 0.0034
6
Thermal
x(t−1),y(t−1) 4
ANFIS 319 0.5591 0.5361
power plant FFD 16,27 0.5890 0.5347
(Data V-Fold 36 0.6508 0.6097
set-V) FFD-V-fold 36 0.5174 0.5118
5.4. EXPERIMENTAL RESULTS AND DISCUSSION 72
0 50 100 150 200 250 300
44 46 48 50 52 54 56 58 60 62
sample number
% of CO 2 in the outlet gas
actual output predicted output
Figure 5.3: Actual and FFD-V-fold based ANFIS model predicted output with the Box and Jenkins gas furnace data
0 200 400 600 800 1000 1200 1400
0 0.05 0.1 0.15 0.2 0.25
sample number
power output (GW)
actual output predicted output
Figure 5.4: Actual and FFD-V-fold based ANFIS model predicted output with data set-I of thermal power plant
5.4. EXPERIMENTAL RESULTS AND DISCUSSION 73
0 200 400 600 800 1000 1200 1400
0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22
sample number
power output (GW)
actual output predicted output
Figure 5.5: Actual and FFD-V-fold based ANFIS model predicted output with data set-II of thermal power plant
0 500 1000 1500
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
sample number
power output (GW)
actual output predicted output
Figure 5.6: Actual and FFD-V-fold based ANFIS model predicted output with data set-III of thermal power plant
5.4. EXPERIMENTAL RESULTS AND DISCUSSION 74
0 100 200 300 400 500 600 700 800 900 1000
0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24 0.26
sample number
power output (GW)
actual output predicted output
Figure 5.7: Actual and FFD-V-fold based ANFIS model predicted output with data set-IV of thermal power plant
0 100 200 300 400 500 600 700
−2
−1 0 1 2 3 4 5 6 7
sample number
energy output (MU)
actual output predicted output
Figure 5.8: Actual and FFD-V-fold based ANFIS model predicted output with data set-V of thermal power plant
5.5. CONCLUSION 75
5.5 Conclusion
From Table 5.4 it is observed that the FFD-V-fold based ANFIS model shows the best performance even though only around one-eighth of the dataset used in the conventional ANFIS model has been selected for training. The FFD-V-fold based ANFIS model was built on the basis of optimally chosen data for modeling. This shows that the ANFIS model based on the training data set selected by using the FFD-V-fold technique shows the best prediction capability. To further test the performance of the proposed FFD-V-fold based ANFIS model, the modeling results of this chapter are compared with standard statistical models as well as another soft computing based model in the next chapter. The two types of models that are chosen for the comparative analysis are the statistical model and the GA based fuzzy model.