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TrnfLMT1:SSE-Vs-Epoch
500
400
300
200
100
0
10
20
30
40
50
60
70
80
90
100
No of Epochs
T rn fL M T 1 : N e uro -fuzzy o utp ut-V s -A c tu a l
1.5
1
0.5
0
-0 .5
0
20
40
60
80
100
120
140
160
180
200
Tim e
Figure 6.8(a). Training performance of Levenberg-Marquardt algorithm for Takagi-Sugeno-
type of multi-input single-output neuro-fuzzy network (using seven fuzzy rules and seven
GMFs) with Mackey-Glass chaotic time series data. Parameters of Levenberg-Marquardt
algorithm: P = 10, J = 0.001, mo = 0.098, WF = 1.01.
Table 6.2(a). Training and forecasting performance of Takagi-Sugeno-type of multi-input
single-output neuro-fuzzy network (with M = 7 fuzzy rules) with proposed Levenberg-
Marquardt algorithm for Mackey-Glass chaotic time series (SSE = sum square error, MSE =
mean square error, MAE = mean absolute error, RMSE = root mean square error)
Sl. No.
Input data
SSE, MSE
achieved
RMSE, MAE
achieved
1.
1-200
(Training in 95 epochs)
SSE = 0.0026
MSE = 2.5571e-005
RMSE = 0.0051
MAE = 0.0039
2.
201-500
(Forecasting)
SSE = 0.0047
MSE = 3.1120e-005
RMSE = 0.0056
MAE = 0.0043
3.
501-1000
SSE = 0.0071
RMSE = 0.0053
(Forecasting)
4.
201-1000
SSE = 0.0118
RMSE = 0.0054
(Forecasting)
MSE = 2.9427e-005
MAE = 0.0042
N
N
N
2
, MSE = 2
1
2
SSE =
, RMSE =
0.5
¦
e
e
N
e
N
, and MAE =
¦
¦
r
r
r
r
1
r
r
1
N
abs e
N
,
where e r is the error due to r th data sample and N is the number of data
¦
r
r
1
samples.
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