Suboptimal Recursive Methodology for Takagi-Sugeno Fuzzy Models Identification - Fuzzy Modeling and Control: Theory and Applications - page 42

Table 2.3 Comparison of the
prediction RMSE for
validation data

EKF(c) EKF ( c + a )

v ( t + 6 ) 0 . 0094 0 . 0091

v ( t + 12 ) 0 . 0058 0 . 0045

v ( t + 85 ) 0 . 0810 0 . 0767

1.5

v ( t +6)
EKF(c)
EKF(c+a)

1

0.5

0

0 50 100 150 200 250 300

1.5

v ( t +12)
EKF(c)
EKF(c+a)

1

0.5

0

0 50 100 150 200 250 300

1.5

v ( t +85)
EKF(c)
EKF(c+a)

1

0.5

0

0 50 100 150 200 250 300

Fig. 2.16 Model training in prediction 6, 12 and 85 steps ahead of Mackey Glass chaotic time
series

1.5

v ( t +6)
EKF(c)
EKF(c+a)

1

0.5

0

0 50 100 150 200 250 300 350 400 450 500

1.5

v ( t +12)
EKF(c)
EKF(c+a)

1

0.5

0

0 50 100 150 200 250 300 350 400 450 500

1.5

v ( t +85)
EKF(c)
EKF(c+a)

1

0.5

0

0 50 100 150 200 250 300 350 400 450 500

Fig. 2.17 Model validation in prediction 6, 12 and 85 steps ahead

10 12

covariance matrix is initialized as α = 1,000 for EKF(c) algorithm, and α = 9 ×

10 − 6 for EKF and algorithm.

The results of the execution of the two algorithm are shown in Table 2.3 .
Figures 2.16 and 2.17 show the Mackey Glass chaotic series and the predictions
for training and validation data respectively.

β = ( c + a )