SSA-ELM Hydrological Time Series Forecast Model Based on Wavelet Packet Decomposition and Phase Space Reconstruction - LI Lude; CUI Dongwen (Renmin Zhujiang)
Considering the nonlinear and multi-scale characteristics of hydrological time series,this paper proposes a squirrel search algorithm (SSA)-extreme learning machine (ELM) forecasting model based on wavelet packet decomposition (WPD) and phase space reconstruction.It is then applied to the Shangguo Hydrological Station in Yunnan Province for monthly runoff and precipitation forecasting.Specifically,WPD is performed to decompose the runoff and precipitation time series data,and the Cao method is applied to reconstruct the phase space of each subseries component.Then,the principle of SSA is outlined,and objective functions are constructed through the training samples of each component.The objective functions are optimized by SSA,and the results are compared with the optimization results of the whale optimization algorithm (WOA),the gray wolf optimization (GWO) algorithm,and the particle swarm optimization (PSO) algorithm.Finally,the weight of the ELM input layer and the hidden layer bias obtained by optimization based on SSA,WOA,GWO algorithm,and PSO algorithm,respectively,are utilized to build SSA-ELM,WOA-ELM,GWO-ELM,and PSO-ELM models,which,in addition to the unoptimized ELM models,are applied to forecast each subseries component,and the forecast results are summed and reconstructed to obtain the final forecasting results.The results show that SSA outperforms WOA,GWO algorithm,and PSO algorithm in optimizing the objective functions of each component and that it offers better optimization accuracy.The mean relative error,mean absolute error,mean square root error,and forecast pass rate of the proposed SSA-ELM model for monthly runoff and monthly precipitation forecast are 5.32% and 3.84%,0.078 m3/s and 0.169 mm,0.103 m3/s and 0.209 mm,97.5% and 95.8%,respectively,indicating that its forecasting accuracy is higher than that of other models such as the WOA-ELM model.