Due to the SD method deficiency to optimize fuzzy antecedent and consequent parameters in wave predictor models, in this stage the GA is used for optimization of fuzzy IF-THEN rules antecedent and consequent parameters.
Figures 10 and
11 show the optimization process by the GA in the models. In these figures, results of minimum, average, and maximum of the
RMSE for ten executions are reported while
Figures 12 and
13 show initial and optimized membership functions for both wave height and peak spectral period predictor models' input variables. As apparently shown in these figures, membership functions have been changed significantly by the GA. In addition, the
RMSE errors of validation and training data are presented in Table 2. As reported in the table, the GA model employed here has decreased the
RMSE error successfully for both the significant wave height and the peak spectral predictor models. The GA not only has decreased the
RMSE error from 0.1705 m to 0.1604 m for the wave height predictor model, but it has also improved the
RMSE error for the peak spectral period predictor model from 0.2114 s to 0.2018 s. Although the GA has improved the results, it can be concluded the second process of optimization to extract fuzzy antecedent and consequent parameters is less effective in comparison with the optimization of subtractive clustering parameters. In other words, tuning clustering parameters is more important than fuzzy antecedent and consequent parameters in the developed predictor models. The validation error has also reached 0.2920 m and 0.3421 s for significant wave height and peak spectral period, respectively.
Table 2RMSE errors for the wave predictor models in the FIS model in which fuzzy antecedent and consequent parameters are optimized
. | Method
. | Validation error (m)
. | Training error (m)
. |
---|
Significant wave height predictor model | ANFIS | 0.3101 | 0.1705 |
FIS and GA | 0.2920 | 0.1604 |
Peak spectral period predictor model | ANFIS | 0.3815 | 0.2114 |
FIS and GA | 0.3421 | 0.2018 |
. | Method
. | Validation error (m)
. | Training error (m)
. |
---|
Significant wave height predictor model | ANFIS | 0.3101 | 0.1705 |
FIS and GA | 0.2920 | 0.1604 |
Peak spectral period predictor model | ANFIS | 0.3815 | 0.2114 |
FIS and GA | 0.3421 | 0.2018 |
Figure 10
Variation of RMSE error in the combined FIS and GA model versus number of generations for wave height prediction.
Figure 10
Variation of RMSE error in the combined FIS and GA model versus number of generations for wave height prediction.
Close modalFigure 11
Variation of RMSE error in combined FIS and GA model versus number of generations for peak spectral period prediction.
Figure 11
Variation of RMSE error in combined FIS and GA model versus number of generations for peak spectral period prediction.
Close modalFigure 12
Initial and optimized fuzzy membership functions by the GA appropriate by each input variable for the wave height predictor model.
Figure 12
Initial and optimized fuzzy membership functions by the GA appropriate by each input variable for the wave height predictor model.
Close modalFigure 13
Initial and optimized fuzzy membership functions by the GA appropriate by each input variable for the wave peak spectral predictor model.
Figure 13
Initial and optimized fuzzy membership functions by the GA appropriate by each input variable for the wave peak spectral predictor model.
Close modal