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Extreme learning machine based on particle swarm optimization for estimation of reference evapotranspiration

Reference evapotranspiration (ET0) plays an important role in water resources scheduling of irrigation systems. This paper proposes a novel extreme learning machine (ELM) method optimized by particle swarm optimization (PSO) algorithm (PSO-SWELM) to realize more accurate evapotranspiration estimation with limited environmental and meteorological data. The weights and thresholds between input and hidden layers of ELM is optimized by PSO algorithm and a function based on the two-wave superposition is selected as the activation function of ELM, which both enhances the accuracy of estimation. The Penman-Monteith model (FAO-56 PM) is used as the standard model to estimate ET0. The root of mean squared error (RMSE) and coefficient of determination (R2) are set as the two evaluation criteria to compare the performances of BP, PSO-BP, SVM, ELM, PSO-ELM and PSO-SWELM in estimating ET0. The simulation results show that the PSO-SWELM method has better performance in predicting the ET0 than the currently prevailing methods.