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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 2

RMSE errors for the wave predictor models in the FIS model in which fuzzy antecedent and consequent parameters are optimized

 MethodValidation 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 
 MethodValidation 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.

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Figure 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.

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Figure 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.

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Figure 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.

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