風場歷時數據包含了風速與風壓等歷時資料，準確預測風速和風壓可以幫助我們更好地了解大氣環境，評估風能資源，設計安全和節能的建築，並提供準確的天氣預報。含外部輸入之非線性自迴歸(Nonlinear AutoRegressive with eXogenous inputs, NARX)類神經網路具有可有效解決較複雜的非線性問題與能夠考慮到時間的動態性，並利用歷史資料建立有效之預測模型的特性，並且已在多個不同領域有所發展。因此本研究嘗試利用NARX類神經網路的非線性建模能力和時間序列預測能力，建立預測風壓與風速之NARX模型，測試其模型參數並嘗試提高預測風速、風壓資料之準確性。本研究發現增加合適的外部輸入與時間延遲能夠有效幫助模型預測，合適的時間延遲包含與當前待預測值相關係數較高之歷史資料；合適的外部輸入則可嘗試輸入與待預測測點相鄰的周圍測點。當歷史資料與目標預測資料的相關性較低時，加入與目標預測資料相同時間點之外部輸入能夠有效提升模型性能。此外當訓練資料較少而待預測資料較多時，NARX類神經網路依然能夠掌握待預測目標之整體趨勢，但誤差會隨訓練資料較少而相應增加，預測準確程度下降。

Wind field data, including wind speed time data and wind pressure time data, play a crucial role in predicting and analyzing wind energy utilization, wind power generation, civil engineering design, architecture design and meteorology. Accurate prediction of wind speed and wind pressure help us better understand the atmospheric environment, assess wind energy resources, design safe and energy-efficient buildings, and provide accurate weather forecasts. NARX (Nonlinear AutoRegressive with eXogenous inputs) neural networks have proven to be effective in solving complex nonlinear problems and capturing temporal dynamics. The model can apply historical data to establish predictive models effectively and have been applied in various fields. Therefore, in this study, we aim to utilize the nonlinear modeling capability and time series prediction ability of the NARX model. We develop a NARX prediction model, test its model parameters, and try to enhance the prediction accuracy of wond speed and wind pressure data. In this study, it was found that increasing appropriate exogenous inputs and time delays can effectively improve the predictive performance of the model. Suitable time delays include historical data with high correlation to the current target values. Relevant exogenous inputs can involve neighboring measuring points adjacent to the target prediction point. When there is a low correlation between historical data and the target prediction data, adding exogenous inputs at the same time as the target prediction data can significantly enhance the model's performance. Additionally, even with limited training data and a larger set of data to be predicted, the NARX neural network is still capable of capturing the overall trend of the target variable. However, the errors may increase and the accuracy of prediction may decrease due to the limited training data.

1. 林柏宇，2022年，以倒傳遞類神經網路預測氣象站不足之風速資料，國立臺灣科技大學營建工程系碩士論文。
2. 馬瑞貽，2020年，基於循環神經網路的風力風速歷時資料預測模型，淡江大學土木工程系碩士論文。
3. Cadenas, E., Rivera, W., Campos-Amezcua, R., & Heard, C. (2016). Wind speed prediction using a univariate ARIMA model and a multivariate NARX model. Energies, 9(2), 109.
4. Boussaada, Z., Curea, O., Remaci, A., Camblong, H., & Mrabet Bellaaj, N. (2018). A nonlinear autoregressive exogenous (NARX) neural network model for the prediction of the daily direct solar radiation. Energies, 11(3), 620.
5. Lin, T., Horne, B. G., Tino, P., & Giles, C. L. (1996). Learning long-term dependencies in NARX recurrent neural networks. IEEE transactions on neural networks, 7(6), 1329-1338.
6. Xie, H., Tang, H., & Liao, Y.-H. (2009). Time series prediction based on NARX neural networks: An advanced approach. Paper presented at the 2009 International conference on machine learning and cybernetics.
7. Wibowo, A., Pujianto, H., & Saputro, D. R. S. (2017). Nonlinear autoregressive exogenous model (NARX) in stock price index's prediction. Paper presented at the 2017 2nd International conferences on Information Technology, Information Systems and Electrical Engineering (ICITISEE).
8. McCulloch, W. S., & Pitts, W. (1943). A logical calculus of the ideas immanent in nervous activity. The bulletin of mathematical biophysics, 5, 115-133.
9. Minsky, M. a. S. P. (1969). Perceptrons.
10. Hopfield, J. J. (1982). Neural networks and physical systems with emergent collective computational abilities. Proceedings of the national academy of sciences, 79(8), 2554-2558.
11. Rumelhart, D. E., McClelland, J. L., & Group, P. R. (1988). Parallel distributed processing. Foundations, 1.
12. Li, Y.-C., Cheng, C.-M., Lo, Y.-L., Fang, F.-M., & Zheng, D.-q. (2015). Simulation of turbulent flows around a prism in suburban terrain inflow based on random flow generation method simulation. Journal of Wind Engineering and Industrial Aerodynamics, 146, 51-58.
13. 朱佳仁，2006年，風工程概論，科技圖書股份有限公司。
14. Goodfellow, I., Bengio, Y., & Courville, A. (2016). Deep learning: MIT press.
15. 中國文化大學大氣科學系，大氣水文研究資料庫，資料來源： https://dbar.pccu.edu.tw/，2018年。
16. 中央氣象局，氣象資料開放平台，資料來源： https://opendata.cwb.gov.tw/index，2017年。