Two-phase extreme learning machines integrated with the complete ensemble empirical mode decomposition with adaptive noise algorithm for multi-scale runoff prediction problems

Expert systems adopted in real-time multi-scale runoff prediction are useful decision-making tools for hydrologists but the stochastic nature of any hydrological variable can pose significant challenges in attaining a reliable predictive model. This paper advocates a data-driven approach used to design two-phase hybrid model (i.e., CVEE-ELM). The model utilizes complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) coupled with the variational mode decomposition (VMD) algorithms for better frequency resolution of the input datasets and the extreme learning machine (ELM) algorithm as the objective predictive model. In the first stage of the presented model design, notable frequencies in the predictor-target data series are uncovered, utilizing the CEEMDAN algorithm where the model's inputs are decomposed into their respective Intrinsic Mode Functions (IMFs) and the Residual (Res) series. The second stage entails a VMD approach, used to decompose the yet-unresolved high frequencies (i.e., IMF1 ) into their variational modes, further discerning and establishing the data attributes to be incorporated into the ELM model to simulate the respective IMFs, Res and VM data series, aggregated as an integrative tool for multiscale runoff prediction. In the model evaluative phase, the hybrid CVEE-ELM is cross-validated with a single-phase hybrid ELM and an autoregressive integrated moving average (ARIMA) model to benchmark its accuracy for predicting 1-, 3- and 6-month ahead runoff in Yingluoxia watershed, Northwestern China. Two-phase hybrid model exhibits superior accuracy at all lead times, to accord with high degree of correlations between the observed and the forecasted runoff, a relatively large Nash-Sutcliffe and the Legate-McCabe Index. Taylor diagrams depict the two-phase hybrid CVEE-ELM model generated forecasts located close to a reference (i.e., a perfect) model, with a lower root-mean square centered difference, and a correspondingly large correlation for all forecast horizons, although the model's accuracy for shorter lead times (1-month), as expected, are better than the 3- and 6-month horizon. The study shows that the two-phase hybrid CVEE-ELM model where an integration of two frequency resolution algorithms are made, is a preferred data-driven tool that can be explored for real-life decision-system design, particularly for hydrological forecasting problems that have significantly stochastic data features, and thus, will require reliable forecasts to be generated at multi-step horizons.