# Combined Forecasting Model of Precipitation Based on the CEEMD-ELM-FFOA Coupling Model

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## Abstract

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## 1. Introduction

## 2. Research Method

#### 2.1. Complementary Ensemble Empirical Mode Decomposition

#### 2.2. Extreme Learning Machine

#### 2.3. Fruit Fly Optimization Algorithm

#### 2.4. Evaluation Method

## 3. Case Study

#### 3.1. Research Area Survey

#### 3.2. Multi-Scale Decomposition of Precipitation Time Series Data Based on CEEMD

#### 3.3. Model Prediction

_{q}of each decomposition item and the embedded dimension m

_{q}wolf method to calculate the maximum Lyapunov index of each decomposition amount. The calculation results are shown in Table 1. The table of the Lyapunov index value greater than 0 illustrates that the decomposition sequence has chaotic characteristics.

#### 3.4. Determining the Correlation Coefficient of Combination of Decomposed Sequences

#### 3.5. Model Validation

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**The technical route of the CEEMD-ELM-FFOA Coupling Prediction Model (* Marks training data and # marks test data).

IMF1 | IMF2 | IMF3 | IMF4 | IMF5 | IMF6 | IMF7 | IMF8 | |
---|---|---|---|---|---|---|---|---|

τ_{q} | 2 | 1 | 3 | 6 | 11 | 12 | 15 | 20 |

m_{q} | 13 | 12 | 7 | 4 | 2 | 4 | 5 | 2 |

Lyapunov | 0.105 | 0.0583 | 0.048 | 0.0524 | 0.0936 | 0.0208 | 0.0232 | 0.0335 |

IMF1 | IMF2 | IMF3 | IMF4 | IMF5 | IMF6 | IMF7 | IMF8 | R | |
---|---|---|---|---|---|---|---|---|---|

Optimization coefficient | 1.005 | 0.987 | 0.971 | 1.131 | 1.126 | 0.897 | 0.999 | 1.073 | 1.001 |

Month | Precipitation | Absolute Error /mm | RE /% | |
---|---|---|---|---|

True Value | Forecasting Value | |||

2020.01 | 44.40 | 42.45 | 1.95 | 4.40 |

2020.02 | 34.60 | 34.27 | 0.33 | 0.96 |

2020.03 | 8.40 | 8.42 | 0.02 | 0.19 |

2020.04 | 17.00 | 17.32 | 0.32 | 1.87 |

2020.05 | 37.50 | 37.38 | 0.12 | 0.32 |

2020.06 | 116.90 | 115.99 | 0.91 | 0.78 |

2020.07 | 83.70 | 82.12 | 1.58 | 1.89 |

2020.08 | 146.03 | 145.83 | 0.47 | 0.32 |

2020.09 | 15.60 | 15.47 | 0.13 | 0.81 |

2020.10 | 33.90 | 33.73 | 0.17 | 0.49 |

2020.11 | 33.50 | 33.95 | 0.45 | 1.35 |

2020.12 | 5.80 | 5.60 | 0.20 | 3.38 |

Mean relative error = 1.39% |

Predictive Model | MAE (mm) | RMSE (mm) | MAPE (%) |
---|---|---|---|

CEEMD-ELM-FFOA | 0.55 | 0.81 | 1.39 |

CEEMD-ELM | 0.63 | 0.92 | 3.23 |

EMD-HHT | 5.64 | 8.22 | 10.92 |

ELM | 6.83 | 10.70 | 13.33 |

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**MDPI and ACS Style**

Zhang, X.; Wu, X.
Combined Forecasting Model of Precipitation Based on the CEEMD-ELM-FFOA Coupling Model. *Water* **2023**, *15*, 1485.
https://doi.org/10.3390/w15081485

**AMA Style**

Zhang X, Wu X.
Combined Forecasting Model of Precipitation Based on the CEEMD-ELM-FFOA Coupling Model. *Water*. 2023; 15(8):1485.
https://doi.org/10.3390/w15081485

**Chicago/Turabian Style**

Zhang, Xianqi, and Xiaoyan Wu.
2023. "Combined Forecasting Model of Precipitation Based on the CEEMD-ELM-FFOA Coupling Model" *Water* 15, no. 8: 1485.
https://doi.org/10.3390/w15081485