Neuro-fuzzy Approach - Computational Intelligence in Time Series Forecasting - page 245

TrnfLV2MIMO:SSE-Vs-Epoch

800

700

600

500

400

300

200

100

20 40 60 80 100 120 140 160 180 200

No of Epochs

TrnfLV2MIMO: Neuro-fuzzy output-Vs-Actual

150

100

50

0

-50

-100

-150

0 500 1000 1500

Time

Figure 6.7(c). Training performance of the Takagi-Sugeno-type multi-input multi-output
neuro-fuzzy network with n = 4 inputs, m = 3 outputs, M = 15 fuzzy rules and 15 GMFs for
short-term forecasting of electrical load time series with the proposed Levenberg-Marquardt
algorithm. Training parameters of Levenberg-Marquardt algorithm:

P , J = 0.1, mo
= 0.1, maximum epoch = 200, training (pre-scaled) data = 1 to 500 rows of XIO matrix,
initial SSE = 868.9336 (with random starting parameter of neuro-fuzzy network), final SSE
= 22.5777, data scaling factor = 0.01.

0.001

simfmimo.m: Neuro-fuzzy output vs. Actual

200

150

100

50

0

-50

0 500 1000 1500 2000 2500 3000 3500

time

simfmimo.m: Neuro-fuzzy prediction error

150

100

50

0

-50

-100

-150

0 500 1000 1500 2000 2500 3000 3500

time

Figure 6.7(d). Forecasting performance of the Takagi-Sugeno-type multi-input multi-output
neuro-fuzzy network with n = 4 inputs, m = 3 outputs, M = 15 fuzzy rules and 15 GMFs for
short-term forecasting of electrical load after the training with the proposed Levenberg-
Marquardt algorithm. Note that in both Figures 6.7(b) and 6.7(d) data from 1 to 1500
correspond to training data and data from 1501 to 3489 represent the forecasting
performance with validation data set. It is important to note that data within the time points
2200 to 2510 are different from the training data. Still the Takagi-Sugeno-type multi-input