Predicting Monthly Runoff Interval by Using CNN-BiLSTM Optimized by Crested Porcupine Optimizer and Kernel Density Estimation - WU Xiao-tao, GUO Xin, YUAN Xiao-hui, YAN Li-juan, ZENG Zhi-qiang, LU Tao (长江科学院院报, 2025)
[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.