# FOCUSED–Short-Term Wind Speed Forecast Correction Algorithm Based on Successive NWP Forecasts for Use in Traffic Control Decision Support Systems

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Materials and Methods

#### 3.1. Forecasting Setup

#### 3.2. The FOCUSED Algorithm

_{1}and lasts for n 12 h time slots. The oldest forecast FD

_{1}(Forecasted Data 1) starts at t

_{1}and contributes to the model with its fifth (training/test data set) and sixth (evaluation data set) time slots. The next forecast FD

_{2}starts at t

_{2}and contributes to the model with its fourth and fifth time slots, and so on until the last forecast FD

_{6}starts at t

_{n−1}and contributes to the model with its first two time slots.

_{1}–FD

_{n}) for the respective periods ${F}_{p}$, denoted in yellow. The white boxes denote the forecasts used as the data-mining model’s input variables and the blue box denotes actual measured wind speed used as a target variable. Gray colors denote successive forecasts predicted by the NWP model for the observed future 12 h period.

_{1}, the NWP model has created a forecast for the next 72 h, denoted as FD

_{1}. At the time t

_{2}, the NWP model makes a new forecast for the next 72 h denoted as FD

_{2}, and so on. During one ${F}_{p}$ period, the NWP model makes six forecasts whose lengths are equal to the ${T}_{s}$ period. In application where the proposed algorithm is used as a part of real-time decision support system, the modelling process should repeat each hour, immediately after receiving new measured hourly wind-speed data. When the critical wind situation lasts longer than ${F}_{p}$, the training set becomes larger than ${F}_{p}$ (Figure 6). Every new NWP forecast becomes FD

_{n.}Previous FD

_{n}becomes FD

_{n−1}, and at the end FD

_{2}becomes FD

_{1}, hence the training set could grow indefinitely.

_{0+}

_{12h}(12 h after start of critical wind condition) and t

_{obs}(observation point) as input vectors to train the model. The model’s performance was tested on time-slot data between t

_{obs}and t

_{obs+}

_{12h}.

#### 3.3. Training the Model (ANN Example)

- sigmoid

- 2.
- tanh

- 3.
- ReLU

## 4. Results

#### 4.1. Statistical Evaluation of Using Successive Forecasts Instead of the Last Forecast

_{6}prediction was compared with each of the four data-mining models predictions, respectively. Input samples were created as lists of percentages of forecast/correction errors compared to actual measured wind speed, calculated as:

_{6}is the last NWP model’s forecast, MLM is the machine-learning model’s corrected forecast value, and sp

_{mean}is actual measured wind speed.

- H
_{0}(null hypothesis): There is no tendency for ranks of corrected forecasts based on tested models to be significantly different than ranks of the original NWP (FD_{6}). - H
_{1}(research hypothesis): The ranks of corrected forecasts are significantly different than those of the FD_{6}.

_{6}predictions. We calculated ${U}_{1}$ for FD

_{6}predictions and ${U}_{2}$ for respective data-mining corrections.

_{1}+ n

_{2}, ${t}_{i}$ is the number of subjects sharing rank i, and k is the number of distinct ranks.

#### 4.2. Statistical Comparison with Autoregressive Moving Average (ARMA) Model

_{1}and U

_{2}values indicate that errors of FOCUSED corrections are systematically ranked lower than FD

_{6}forecasts and ARMA correction method applied to the last received forecast.

#### 4.3. Empirical Evaluation

_{s}= 12 h, F

_{p}= 72 h, T

_{p}= 6 h

_{1}and presented with the light grey line. It refers to the forecast created 72 h ago. The next one, created 60 h ago, is marked FD

_{2}and is a bit darker than FD

_{1}. The last (most shaded grey) forecast, marked as FD

_{6}, represents the newest result of the ALADIN model. FC represents the direct output of the ANN model. A challenge has arisen as the prediction of the model revealed the most probable shape of the final forecast, but the overall wind speed was often shifted across ordinate of the graph, causing increased RMSE. To correct that, we aligned the curve’s wind speed starting point with the last measured data point. The FCA represents the aligned (final) corrected forecast.

_{1}–FD

_{6}forecasts.

_{6}(and, in this case, all previous forecasts).

_{6}) and the corrected forecast (FCA) during a longer period, we can spot better prevailing accuracy of FCA for one year. Figure 14 shows an example for year 2016—the comparison of FD

_{6}(the newest and considered the most relevant before correction) and FCA for all training samples longer than or equal to 12 h. Comparison is made for all observation points (hours) in the whole data set, using only data from the 12th hour after the bora start (minimal training sample size is 12). The figure also shows relatively rare “Worse” situations, represented as high peaks on the graph. Those periods are typically short and followed by fast stabilization, resulting in further improvement of the model’s accuracy.

_{1}–FD

_{6}and FCA forecasts shows that the FCA outperforms all original forecasts (FD

_{1}-FD

_{6}), as presented in Figure 15.

## 5. Conclusions and Future Work

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 10.**Distribution of the results of the correction algorithm applied to a real five-year data set from Croatian bridge Krk.

**Figure 12.**An example of improved accuracy: the final correction (RMSE_FCA) has better accuracy than any of the previous forecasts.

**Figure 13.**An example of the “Worse” category of the corrected forecast at the moment of a sudden large speed jump.

**Figure 14.**Comparison of hourly RMSE between corrected and uncorrected forecasts for one year. A reliable algorithm should fit the FCA curve inside FD

_{6}(grey) area most of the time.

Algorithm Run Number | Training Set Samples | Test Samples |
---|---|---|

1 | 1–12 | 13–24 |

2 | 1–13 | 14–25 |

3 | 1–14 | 15–26 |

4 | 1–15 | 16–27 |

Tested Model | p-Value | U_{1}-FOCUSED | U_{2}-FD_{6} |
---|---|---|---|

FCA_ANN | 0.0015 | 109,164 | 135,861 |

FCA_RFR | 0.0017 | 109,366 | 135,659 |

FCA_SVM | 0.0322 | 114,195 | 130,830 |

FCA_LRM | 0.0348 | 114,348 | 130,677 |

Tested Algorithm | p-Value | U_{1}-FOCUSED | U_{2}-ARMA |
---|---|---|---|

FOCUSED | 0.0015 | 109,164 | 135,861 |

ARMA | 0.0139 | 113,076 | 132,940 |

Category | Description |
---|---|

Better | RMSE FCA lower than any RMSE of original NWP forecasts |

Comparable | RMSE FCA between lowest and highest RMSE of original NWP forecasts |

Worse | RMSE FCA higher than any RMSE of original NWP forecasts |

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**MDPI and ACS Style**

Kunić, Z.; Ženko, B.; Boshkoska, B.M.
FOCUSED–Short-Term Wind Speed Forecast Correction Algorithm Based on Successive NWP Forecasts for Use in Traffic Control Decision Support Systems. *Sensors* **2021**, *21*, 3405.
https://doi.org/10.3390/s21103405

**AMA Style**

Kunić Z, Ženko B, Boshkoska BM.
FOCUSED–Short-Term Wind Speed Forecast Correction Algorithm Based on Successive NWP Forecasts for Use in Traffic Control Decision Support Systems. *Sensors*. 2021; 21(10):3405.
https://doi.org/10.3390/s21103405

**Chicago/Turabian Style**

Kunić, Zdravko, Bernard Ženko, and Biljana Mileva Boshkoska.
2021. "FOCUSED–Short-Term Wind Speed Forecast Correction Algorithm Based on Successive NWP Forecasts for Use in Traffic Control Decision Support Systems" *Sensors* 21, no. 10: 3405.
https://doi.org/10.3390/s21103405