径流预测对水资源合理配置、制定水力发电计划等非常重要,针对月径流点预测精度不高以及点预测结果难以描述月径流不确定性等问题,提出基于冠豪猪优化算法、卷积神经网络、双向长短时记忆网络和非参数核密度估计的月径流点预测模型和区间预测模型。首先,构建组合卷积神经网络和双向长短时记忆网络的月径流点预测模型,并采用冠豪猪优化算法优化模型的隐藏层单元数等参数,将月径流及影响因素数据输入模型得到月径流的点预测结果。然后采用极差分割法将点预测结果排序后划分为低流量段、中流量段和高流量段,再利用冠豪猪优化算法优化窗宽的非参数核密度估计方法估计3个流量段预测值误差的概率分布,并采用三次样条插值法进行曲线拟合,得到3个流量段的分位点。最后叠加点预测结果和点预测结果所属流量段的分位点得到月径流区间预测结果。通过实例分析,与其他模型相比,提出的CPO-CNN-BiLSTM点预测模型预测精度更高,能较好地追踪月径流的变化趋势,提出的CPO-CNN-BiLSTM-NKDE区间预测模型可有效减少月径流预测的不确定性,能够为决策者提供更多信息。

[Objective] To address the low accuracy of monthly runoff point prediction and the difficulty in describing the uncertainty of point prediction results, this study proposes a monthly runoff point prediction model and an interval prediction model based on the Crested Porcupine Optimizer (CPO), Convolutional Neural Network (CNN), Bidirectional Long Short-Term Memory (BiLSTM) network, and Nonparametric Kernel Density Estimation (NKDE). [Methods] First, a hybrid point prediction model (CPO-CNN-BiLSTM) was developed. CPO was used to optimize key model parameters such as the number of hidden layer nodes, initial learning rate, and regularization coefficient. Monthly runoff data and its influencing factors were input to the model to obtain point prediction results. Next, the point forecasts were sorted using a range segmentation method and divided into low, medium, and high flow segments. The relative error for each predicted value within these segments was calculated. The NKDE method, with window width optimized by CPO, was employed to estimate the error probability distribution function for each segment. Cubic spline interpolation was then applied to fit the probability distribution functions of the three segments and derive segment-specific quantiles, forming a monthly runoff interval prediction model (CPO-CNN-BiLSTM-NKDE) based on NKDE method and the CPO-CNN-BiLSTM model. Finally, the runoff point forecasts were combined with the corresponding quantiles of their flow segments to generate monthly runoff interval predictions. Case studies compared the proposed CPO-CNN-BiLSTM point prediction model with traditional models including Least Squares Support Vector Machine (LSSVM), Kernel Extreme Learning Machine (KELM), LSTM, and BiLSTM, using RMSE, MRE, and MAPE as evaluation metrics. [Results] The CPO-CNN-BiLSTM model’s prediction accuracy was significantly better than the other models, especially during flood and dry seasons. Compared with the best-performing among the other four models in terms of RMSE, MRE, and MAPE, the values decreased by 43.71%, 38.56%, and 24.38%, respectively. This indicated a superior ability to accurately predict peak and valley runoff values. Additionally, deep learning models (LSTM, BiLSTM, CNN-BiLSTM) outperformed machine learning models (LSSVM, KELM), with the BiLSTM model surpassing LSTM, and the CNN-BiLSTM hybrid outperforming both. The proposed CPO-CNN-BiLSTM-NKDE interval prediction model was compared with other interval prediction models at confidence levels of 95%, 90%, and 85%, and it exhibited the highest Prediction Interval Coverage Probability (PICP)and the lowest Prediction Interval Normalized Average Width (PINAW), indicating strong reliability and superior capability in capturing uncertainty. This demonstrated that the interval prediction results of the proposed model could help decision-makers better understand and respond to the uncertainty and variability in the data. [Conclusion] The proposed CPO-CNN-BiLSTM point prediction model and the CPO-CNN-BiLSTM-NKDE interval prediction model effectively address the challenges posed by the spatial-temporal complexity of monthly runoff sequences and the uncertainty of monthly runoff point predictions. This provides new ideas for monthly runoff prediction and offers useful reference for fields such as wind speed and solar irradiance forecasting.