径流过程是地球上水文循环中的关键一环，科学准确地预测月径流的来水量对于流域的水量调度、水资源规划及管理具有十分重要的意义。然而由于径流过程的复杂性以及人类活动的影响，在变化环境中精准捕捉月径流时间序列的变化规律变得十分困难。针对月径流时间序列预测中存在的对于样本数据中先验信息识别不够彻底以及对时间步长嵌入维度难以有效地自适应选取这两点问题，设计了基于VMD-PSR-BNN的月径流时间序列预测模型。基于变分模态分解（VMD）算法对噪声良好的鲁棒性和对时序信号精确分解的特性，将月径流时间序列视为一种时序信号，利用VMD方法将月径流时间序列分解为多个相对平稳的固有模态函数（IMF），再基于相空间重构（PSR）理论对各个IMF分别进行重构，对各个重构后的IMF分别采用基于变分推理的贝叶斯神经网络（BNN）进行预测，最后将各个BNN的预测结果进行聚合重构得到月径流时间序列的最终预测结果。选取渭河流域咸阳和华县两个水文站1953-2018年的月径流时间序列进行实例分析。结果表明：VMD对月径流时间序列具有很好的分解效果，两个水文站基于VMD-PSR-BNN模型的月径流预测结果均可达到水文预报的甲级标准，并且对于样本中的极端值具有较好的拟合效果，为月径流时间序列的预测提供了新的方法参考。

The runoff process is a vital part of the earth’s hydrological cycle. Scientific and accurate prediction of monthly runoff inflow is of great significance for water flow scheduling， water resources planning and management in the basin. However， due to the complexity of the runoff process and the influence of human activities， it is very difficult to accurately capture the variation law of the monthly runoff time series in a changing environment. Because of the two problems in the prediction of monthly runoff time series， the prior information identification in the sample data is not thorough enough， and the time step embedding dimension is difficult to be effectively and adaptively selected. This paper designs a model for monthly runoff time series based on VMD-PSR-BNN. Based on the good robustness of variational mode decomposition （VMD） algorithm to noise and the characteristics of accurate decomposition of time series signals， the monthly runoff time series is regarded as a time series signal， and the VMD method is used to decompose the monthly runoff time series into multiple relatively stationary intrinsic mode function （IMF）. Then， each IMF is reconstructed based on the phase space reconstruction （PSR） theory， and the Bayesian neural network （BNN） based on variational inference is used to predict each reconstructed IMF. Finally， the prediction results of each BNN are aggregated and reconstructed to obtain the final prediction result. The monthly runoff time series from 1953 to 2018 of two hydrological stations in Xianyang and Huaxian in the Weihe River Basin are selected for case analysis. The results show that the prediction results of the two hydrological stations based on the VMD-PSR-BNN model can reach the first-class standard of hydrological forecasting， and have a good fitting effect for the extreme values ??in the sample， which provides a new method reference for the prediction of monthly runoff time series.

为提高日径流多步预测精度，减少模型计算规模，同时提升浣熊优化（COA）算法和混合核极限学习机（HKELM）性能，提出多极小波包变换（MWPT）－改进COA算法（ICOA）－HKELM日径流时间序列预测模型。首先，利用MWPT将日径流时序数据分解为1个低频分量和2个高频分量，并构建局部高斯径向基核函数和全局多项式核函数相混合的HKELM；其次，简要介绍COA算法原理，基于Circle映射等策略对COA进行改进，提出ICOA算法，通过8个典型函数对ICOA算法进行仿真验证，并与基本COA算法、鲸鱼优化算法（WOA）、灰狼优化算法（GWO）作对比，旨在验证ICOA算法的优化性能；最后，利用ICOA优化HKELM超参数（正则化参数、核参数、权重系数），建立MWPT-ICOA-HKELM模型，并构建MWPT-COA-HKELM、MWPT-WOA-HKELM、MWPT-GWO-HKELM、小波包变换（WPT）-ICOA-HKELM、小波变换（WT）-ICOA-HKELM、MWPT-ICOA-BP模型作对比分析，通过云南省景东、把边水文站2016-2020年日径流时间序列多步预测实例对各模型进行验证。结果表明：①ICOA具有较好的改进效果，仿真精度优于COA、WOA、GWO算法。②MWPT-ICOA-HKELM模型预测效果优于其他对比模型，其对实例单步预测效果“最好”，超前3步和超前5步“较好”，超前7步“较差”，预测精度随预测步长的增加而降低。③利用ICOA优化HKELM超参数，可显著提高HKELM预测性能，超参数优化效果优于COA、WOA、GWO算法。

To improve the accuracy of multi-step prediction of daily runoff， reduce the computational scale of the model， and enhance the performance of the Coati Optimization Algorithm （COA） and Hybrid Kernel Extreme Learning Machine （HKELM）， a Multi Pole Wavelet Packet Transform （MWPT） - Improved COA（ICOA） algorithm - HKELM daily runoff time series prediction model is proposed. Firstly， using MWPT， the daily runoff time series data is decomposed into 1 low-frequency component and 2 high-frequency components， and a HKELM is constructed by combining local Gaussian radial basis function kernel and global polynomial kernel function； Secondly， the principle of COA algorithm is briefly introduced， and by improving COA based on strategies such as Circle mapping， we propose the ICOA algorithm. The ICOA algorithm is simulated and verified through 8 typical functions， and is compared with the basic COA algorithm， Whale Optimization Algorithm （WOA）， and Grey Wolf Optimization Algorithm （GWO） to verify the optimization performance of the ICOA algorithm； Finally， using ICOA to optimize HKELM hyperparameters （regularization parameters， kernel parameters， weight coefficients）， a MWPT-ICOA-HKELM model is established， and MWPT-COA-HKELM， MWPT-WOA-HKELM， MWPT-GWO-HKELM， Wavelet Packet Transform （WPT） - ICOA-HKELM， Wavelet Transform （WT） - ICOA-HKELM， and MWPT-ICOA-BP models are compared and analyzed. The models are validated through multi-step prediction examples of daily runoff time series from Jingdong and Baobian hydrological stations in Yunnan Province from 2016 to 2020. The results show that： ① ICOA has a good improvement effect， and the simulation accuracy is better than COA， WOA， and GWO algorithms. ② The MWPT-ICOA-HKELM model has better prediction performance than other comparative models， with the best single step prediction performance for instances， better results with 3 and 5 steps ahead， and worse results with 7 steps ahead. The prediction accuracy decreases with the increase of prediction step size. ③ Optimizing HKELM hyperparameters using ICOA can significantly improve HKELM prediction performance， and the hyperparameter optimization effect is better than COA， WOA， and GWO algorithms.

准确的径流预测是水资源优化配置和高效利用的前提，是制定防洪减灾决策的基础，然而受到人类活动、环境、气候等因素的影响，径流序列呈现出非线性、非稳态、多尺度变化的特点，这为径流的精准预测增加了难度。为提高径流预测的精准度和可信度，结合自适应噪声完备集合经验模态分解（Complete Ensemble Empirical Mode Decomposition with Adaptive Noise，CEEMDAN）方法，量子粒子群优化算法（Quantum Particle Swarm Optimization，QPSO）、宽度学习系统（Broad Learning System， BLS）模型， 提出了一种基于CEEMDAN-QPSO-BLS组合式的径流预测模型。该组合模型首先使用CEEMDAN方法对原始径流信号进行分解，得到若干相对平稳的本征模态分量。其次利用QPSO算法对BLS模型的特征层节点组数、增强层节点组数和组内节点数进行寻优，得到最优的宽度学习网络拓扑结构，进而使用最优的QPSO-BLS对多个稳态分量进行预测，并对预测分量进行重构，从而获得更高的预测精度。以黄河流域小浪底水库的日径流值为实验数据，将EMD-QPSO-BLS、QPSO-BLS作为CEEMDAN-QPSO-BLS的对比模型，并采用纳什效率系数（NSE）、均方根误差（RMSE）、平均绝对误差（MAE）和平均绝对百分比误差（MAPE）作为模型预测可信度和精准度的评价指标。实验表明，在预见期4天内，与QPSO-BLS、EMD-QPSO-BLS模型相比，CEEMDAN-QPSO-BLS的预测精准度分别提高了79.87%、19.80%，可信度分别提高了131.2%、10.98%，径流预测精度的提高，可为防洪抗旱保护人民生命财产和可持续发展提供决策支持。

An accurate runoff prediction is the prerequisite for the optimal allocation and efficient utilization of water resources， and the basis for making flood control and disaster reduction decisions. However， due to the influence of human activities， environment， climate and other factors， runoff series show nonlinear， unsteady and multi-scale changes， which increases the difficulty of accurate runoff prediction. In order to improve the accuracy and credibility of runoff prediction， this paper combines the Complete Ensemble Empirical Mode Decomposition with Adaptive Noise （CEEMDAN） method. Quantum Particle Swarm Optimization （QPSO）， Broad Learning System （BLS） model， a combined runoff prediction model based on CEEEDAN-QPSO-BLS is proposed. Firstly， CEEMDAN method is used to decompose the original runoff signal to obtain several relatively stationary intrinsic mode components. Secondly， the QPSO algorithm is used to optimize the number of node groups in the feature layer， the number of node groups in the enhancement layer and the number of nodes in the group of BLS model， and the optimal topology structure of the width learning network is obtained. Then， the optimal QPSO-BLS is used to predict multiple steady-state components， and the prediction components are reconstructed so as to obtain higher prediction accuracy. In this model， the daily runoff value of Xiaolangdi Reservoir in the Yellow River Basin is used as the experimental data， and EMD-QPSO-BLS and QPSO-BLS are used as the comparison model of CEEMDAN-QPSO-BLS. Nash-Sutcliffe efficiency coefficient （NSE）， Root Mean Squared Error （RMSE）， Mean Absolute Error （MAE） and Mean Absolute Percentage Error （MAPE） are used to evaluate the reliability and accuracy of the model prediction. The experimental results show that， compared with QPSO-BLS with EMD-QPSO-BLS models， the prediction accuracy of CEEMDAN-QPSO-BLS is improved by 79.87% and 19.80%， and the credibility is improved by 131.2% and 10.98%， respectively. This paper provides decision-making support for flood control and drought relief to protect people’s lives and property and sustainable development.

为提高月径流预测精度,改进混合核极限学习机(HKELM)预测性能,提出小波包分解(WPT)－斑马优化算法(ZOA)－HKELM组合模型。利用WPT处理月径流时序数据,构建局部高斯径向基核函数和全局多项式核函数相混合的HKELM;通过ZOA优化HKELM超参数(正则化参数、核参数、权重系数),建立WPT-ZOA-HKELM组合模型,并构建WPT-遗传算法(GA)-HKELM、WPT-灰狼优化(GWO)算法-HKELM、WPT-鲸鱼优化算法(WOA)-HKELM、WPT-ZOA-极限学习机(ELM)、WPT-ZOA-最小二乘支持向量机(LSSVM)、ZOA-HKELM作对比模型,通过黑河流域莺落峡、讨赖河水文站月径流时间序列预测实例对各模型进行检验。结果表明:①莺落峡、讨赖河水文站月径流时间序列WPT-ZOA-HKELM模型预测的平均绝对百分比误差分别为1.054%、0.761%,决定系数均达0.999 9,优于其他对比模型,具有更高的预测精度,预测效果更好。②利用ZOA优化HKELM超参数,可提高HKELM预测性能,优化效果优于GWO、WOA、GA。③预测模型能充分发挥WPT、ZOA和HKELM优势,提高月径流预测精度;在相同分解和优化情形下,HKELM的预测性能优于ELM、LSSVM。