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 Gaussi-an 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 Learn-ing 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 sta-tions in the Heihe River Basin.Our findings indicate that:(1)The WPT-ZOA-HKELM model achieves average ab-solute 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 hyperpa-rameters 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 e-quivalent decomposition and optimization conditions,the predictive performance of HKELM is superior to ELM and LSSVM.
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