基于BMA多模型组合的疏勒河径流预测研究

准确可靠的径流预测对于水资源的科学管理与规划具有重要意义，特别是在水资源紧缺的干旱半干旱地区，径流预测对流域内水资源高效利用与水利工程经济运行具有重要现实意义。针对径流预测通常采用单一方法进行建模与预测，难以利用各预测模型优势的问题，本文利用极限学习机（ELM）模型、支持向量机（SVM）模型、多元自适应回归样条（MARS）等机器学习方法建立了疏勒河上游未来1~7日的径流预测模型。在此基础上，运用贝叶斯模型平均（BMA）方法对ELM、SVM、MARS模型的预测结果进行组合，构建了径流组合预测模型，以获取更可靠的预测结果，并采用蒙特卡洛抽样方法获取BMA的95%置信区间，对预测结果进行了不确定性分析。结果表明：ELM、SVM、MARS模型以及BMA组合模型均适用于干旱半干旱地区的中长期日径流预测；BMA的预测精度较单一模型更高，能够提供更准确的预测值；BMA的95%置信区间对实测值覆盖率高，同时能够提供较好的确定性预测和概率预测结果。表明BMA在资料有限的条件下，表现出较单一模型更高的预测性能，可以成为干旱半干旱地区中长期日径流预测的有效方法。

Study on runoff prediction of Shule River based on BMA multi-model combination

Accurate and reliable runoff prediction is of great significance for the scientific management and planning of water resources， especially in the arid and semi-arid areas where water resources are scarce. Runoff prediction has important practical significance for the efficient utilization of water resources and the economic operation of water conservation projects.In view of the problem that it is difficult to make use of the advantages of each prediction model because a single method is usually used for modeling and prediction of runoff prediction. In this paper， the Extreme Learning Machine （ELM） model， Support Vector Machine （SVM） model and Multivariate Adaptive Regression Spline （MARS） model were used to develop the runoff prediction model in the upper reaches of Shule River in 1 to 7 day. On this basis， the Bayesian Model Average （BMA） method was also used to combine the prediction results of ELM， SVM and MARS models， and a combined runoff prediction model was constructed to obtain more reliable predictions. The 95% confidence interval of BMA was obtained by Monte Carlo sampling method， and the uncertainty of the predictions was analyzed. The results show that ELM， SVM， MARS model and BMA combination model are suitable for medium and long term daily runoff prediction in arid and semi-arid areas； BMA has higher prediction accuracy than the single models and can provide more reliable and accurate predictions； The 95% confidence interval of BMA has high coverage of measured values， and can provide better deterministic and probabilistic predictions. The results suggest that BMA has better prediction performance than the single models under the condition of limited data， and can be an effective method for medium and long-term daily runoff prediction in arid and semi-arid areas.