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

. | 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

Figure 11

Figure 12

Figure 13

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