Application of Particle Swarm Optimization and Extreme Learning Machine Forecasting Models for Regional Groundwater Depth Using Nonlinear Prediction Models as Preprocessor

To solve the low-precision problem of traditional methods for groundwater depth prediction, a nonlinear prediction model based on empirical mode decomposition (EMD), phase space reconstruction (PSR), particle swarm optimization (PSO), and extreme learning machine (ELM) was proposed to predict the groundwater depth at Friendship Farm in Heilongjiang Province, China. In this study, the original time series of groundwater depth was preprocessed (decomposed and reconstructed) using EMD and PSR, and then different PSO-ELM models were constructed for the prediction of groundwater depth. The results indicated that the models had a good prediction effect and estimated the following indicators well: the posterior error ratio ($C$), small error frequency ($p$), relative mean square error ($E_1$), fitting accuracy ratio ($E_2$), and test forecast effect index ($E_3$). Comparison of PSR-ELM, PSR-PSO-ELM, and EMD-PSR-PSO-ELM showed a good agreement of root mean square error (RMSE). The results exhibited that the RMSE of PSR-ELM and EMD-PSR-PSO-ELM reduced from 0.4965 to 0.1694 m, and that of PSR-PSO-ELM and EMD-PSR-PSO-ELM reduced from 0.3418 to 0.1694 m, respectively. The results also showed that EMD and PSO effectively improved the prediction performance of the ELM model. This paper also analyzes the effects of climatic factors and human activities on the dynamic changes of local groundwater depth. The results suggest that the effect of precipitation and agricultural production mainly reflected the dynamic groundwater depth.