Abstract: In order to enhance the precision of monthly runoff forecasts and optimize the prediction performance of the Hybrid Kernel Extreme Learning Machine (HKELM), we propose a synergistic approach integrating Wavelet Packet Decomposition (WPT), the Zebra Optimization Algorithm (ZOA), and HKELM. The approach involves applying WPT to preprocess monthly runoff time series data and constructing a HKELM that combines local Gaussian radial basis function with global polynomial kernel function. By refining HKELM hyperparameters (including regularization parameters, kernel parameters, and weight coefficients) through ZOA, we establish the WPT-ZOA-HKELM model, alongside comparative models such as WPT-Genetic Algorithm (GA)-HKELM, WPT-Grey Wolf Optimization (GWO) algorithm-HKELM, WPT-Whale Optimization (WOA)-HKELM, WPT-ZOA Extreme Learning Machine (ELM), WPT-ZOA Least Squares Support Vector Machine (LSSVM), and ZOA-HKELM. These models are evaluated using monthly runoff time series data from the Yingluoxia and Tuolai River hydrological stations in the Heihe River Basin. Our findings indicate that: (1) The WPT-ZOA-HKELM model achieves average absolute percentage errors of 1.054% and 0.761% respectively, with determination coefficients of 0.999 9, surpassing other comparative models in terms of prediction accuracy and performance. (2) Optimization of HKELM hyperparameters with ZOA enhances predictive performance compared to GWO, WOA, and GA. (3) Through leveraging WPT, ZOA, and HKELM, the prediction model significantly improves monthly runoff forecast accuracy. Under equivalent decomposition and optimization conditions, the predictive performance of HKELM is superior to ELM and LSSVM.

Key words: monthly runoff forecast, time series, zebra optimization algorithm, hybrid kernel extreme learning machine, wavelet packet transform, hyperparameter optimization