本研究應用極限學習機（extreme learning machine）建立蘭陽大橋即時水位預報模式，並與倒傳遞神經網路（back propagation neural network）、支撐向量機（support vector machine）之預報成果進行比較。本研究收集蘭陽溪流域1990年至2021年共41場洪水事件，其中26場做為模式率定使用；15場做為驗證場次。即時水位預報模式之輸入變量包含上游牛鬥橋觀測水位、牛鬥橋下游觀測雨量及蘭陽大橋觀測水位，輸出變量為蘭陽大橋未來1至6小時之預報水位。本研究探討極限學習機之激勵函數與神經元個數，據以率定極限學習機水位預報模式之最佳架構。預報結果顯示，應用極限學習機所建立之即時水位預報模式，在15場驗證的洪水事件中，水位預報值與觀測值的相關係數達0.9以上，效率係數達0.8以上。整體來說，極限學習機之預報成效，優於支撐向量機與倒傳遞神經網路。本研究並探討加入預報雨量對於即時水位預報效能的提升狀況，設定未來雨量預報值沒有誤差之情境，加入未來1至3小時雨量預報值做為輸入變量，使用極限學習機進行即時水位預報，結果顯示加入預報雨量能有效提升未來4至6小時水位預報之成效，6小時水位預報之相關係數由0.90提升至0.92，效率係數由0.79提升至0.84，均方根誤差由0.34公尺降低至0.30公尺。由本研究結果可知，應用極限學習機進行蘭陽大橋之即時水位預報，具有良好成效，並且證實加入預報雨量可以有效的提升未來水位預報結果。

This study applied the extreme learning machine (ELM) to establish the real-time flood stage forecasting model of Lan-Yang Bridge, Taiwan, and compared the forecasting results with those of the back propagation neural network (BPNN) and support vector machine (SVM). A total of 41 flood events in the Lan-Yang River Basin from 1990 to 2021 were collected; 26 of which were used for model calibrations, and 15 events were used for validation. The study explored the activation functions and the numbers of neurons in the hidden layer of the ELM, so that the optimal structure of the ELM model was determined to perform the flood stage forecasting with lead times of 1 to 6 hours. The forecasting results show that the ELM outperformed the BPNN and SVM. The forecasting results of ELM exhibits that the coefficients of correlation with lead times of 1 to 6 hours are above 0.9, and the coefficients of efficiency are above 0.8. Moreover, this study established an additional forecasting model by considering the forecasted rainfalls, and proved that adding forecasted rainfalls can effectively improve the performance of the flood stage forecasting.

Atiquzzaman, M., & Kandasamy, J. (2016). Prediction of hydrological time-series using extreme learning machine. Journal of Hydroinformatics, 18(2), 345–353.
Chang, C. C., & Lin, C. J. (2011). LIBSVM: a library for support vector machines. ACM transactions on intelligent systems and technology (TIST), 2(3), 1–27.
Chen, S. T. (2006). Real-time Probabilistic Flood Stage Forecasting Using Support Vector Machines and Fuzzy Inference Model. Ph.D., National Cheng Kung University. Taiwan.
Cortes, C., & Vapnik, V. (1995). Support-vector networks. Machine learning, 20, 273–297.
Cybenko, G. (1989). Approximation by superpositions of a sigmoidal function. Mathematics of control, signals and systems, 2(4), 303–314.
Dai, B., Gu, C., Zhao, E., Zhu, K., Cao, W., & Qin, X. (2019). Improved online sequential extreme learning machine for identifying crack behavior in concrete dam. Advances in Structural Engineering, 22(2), 402–412.
Dazzi, S., Vacondio, R., & Mignosa, P. (2021). Flood stage forecasting using machine-learning methods: a case study on the Parma River (Italy). Water, 13(12), 1612.
Ebtehaj, I., Bonakdari, H., & Shamshirband, S. (2016). Extreme learning machine assessment for estimating sediment transport in open channels. Engineering with Computers, 32, 691–704.
Fletcher, R. (1987) Practical Methods of Optimization. 2nd edition, Wiley, New York
Hornik, K. Approximation capabilities of multilayer perceptrons. Neural Networks, 4.
Hsu, C. W., Chang, C. C., & Lin, C. J. (2003). A practical guide to support vector classification.
Huang, G. B., & Chen, L. (2008). Enhanced random search based incremental extreme learning machine. neurocomputing, 71(16-18), 3460–3468.
Huang, G. B., Zhu, Q. Y., & Siew, C. K. (2004, July). Extreme learning machine: a new learning scheme of feedforward neural networks. In 2004 IEEE international joint conference on neural networks (IEEE Cat. No. 04CH37541) (Vol. 2, pp. 985–990). IEEE.
Huang, G. B., Zhu, Q. Y., & Siew, C. K. (2006). Extreme learning machine: theory and applications. Neurocomputing, 70(1-3), 489–501.
Huang, G., Huang, G. B., Song, S., & You, K. (2015). Trends in extreme learning machines: A review. Neural Networks, 61, 32–48.
Jahangir, M. H., Reineh, S. M. M., & Abolghasemi, M. (2019). Spatial predication of flood zonation mapping in Kan River Basin, Iran, using artificial neural network algorithm. Weather and Climate Extremes, 25, 100215.
Li, B., & Cheng, C. (2014). Monthly discharge forecasting using wavelet neural networks with extreme learning machine. Science China Technological Sciences, 57, 2441–2452.
Lima, A. R., Cannon, A. J., & Hsieh, W. W. (2016). Forecasting daily streamflow using online sequential extreme learning machines. Journal of hydrology, 537, 431–443.
Liong, S. Y., & Sivapragasam, C. (2002). Flood stage forecasting with support vector machines 1. JAWRA Journal of the American Water Resources Association, 38(1), 173–186.
Liu, Z., Shao, J., Xu, W., Chen, H., & Zhang, Y. (2014). An extreme learning machine approach for slope stability evaluation and prediction. Natural hazards, 73, 787–804.
Malekzadeh, M., Kardar, S., & Shabanlou, S. (2019). Simulation of groundwater level using MODFLOW, extreme learning machine and Wavelet-Extreme Learning Machine models. Groundwater for Sustainable Development, 9, 100279.
Sahoo, A., Singh, U. K., Kumar, M. H., & Samantaray, S. (2021). Estimation of flood in a river basin through neural networks: a case study. In Communication Software and Networks: Proceedings of INDIA 2019 (pp. 755–763). Springer Singapore.
Sivapragasam, C., Liong, S. Y., & Pasha, M. F. K. (2001). Rainfall and runoff forecasting with SSA–SVM approach. Journal of Hydroinformatics, 3(3), 141–152.
Vapnik, V. N. (1995). The Nature of Statistical Learning Theory. Springer-Verlag, New York.
Wang, L., Wang, P., Liang, S., Qi, X., Li, L., & Xu, L. (2019). Monitoring maize growth conditions by training a BP neural network with remotely sensed vegetation temperature condition index and leaf area index. Computers and Electronics in Agriculture, 160, 82–90.
Xia, M., Lu, W., Yang, J., Ma, Y., Yao, W., & Zheng, Z. (2015). A hybrid method based on extreme learning machine and k-nearest neighbor for cloud classification of ground-based visible cloud image. Neurocomputing, 160, 238–249.
Xiong, B., Li, R., Ren, D., Liu, H., Xu, T., & Huang, Y. (2021). Prediction of flooding in the downstream of the Three Gorges Reservoir based on a back propagation neural network optimized using the AdaBoost algorithm. Natural Hazards, 107, 1559–1575.
Yadav, B., Ch, S., Mathur, S., & Adamowski, J. (2017). Assessing the suitability of extreme learning machines (ELM) for groundwater level prediction. Journal of Water and Land Development, 32(1), 103.
Yu, P. S., Chen, S. T., & Chang, I. F. (2006). Support vector regression for real-time flood stage forecasting. Journal of hydrology, 328(3–4), 704–716.
王如意、易任 (1979)「應用水文學」，上、下冊，國立編譯館出版，茂昌圖書有限公司。
陳清田、陳儒賢、陳奕任 (2012) 以支撐向量分類與倒傳遞神經網路為基礎的颱風降雨預報模式」，水保技術，7(3)，138-151。
陳憲宗、游保杉 (2007)「洪水位之即時機率預報-結合支撐向量機與模糊推理」，農業工程學報，53(4)，1–20。
鮑繼勇 (2006)「運用倒傳遞類神經網路於河川定點水位預報」，國立台灣大學土木工程研究所碩士論文。