Improved Monthly Runoff Prediction of OSELM Based on Secondary Decomposition Technique and Optimization of Ten "Bird" Swarm Algorithms

To improve the accuracy of monthly runoff time series prediction and enhance the performance of online sequential extreme learning machine (OSELM) prediction, ten "bird" swarm algorithms were compared and validated for optimization, including satin bowerbird optimizer (SBO)/Harris hawks optimization (HHO)/seagull optimization algorithm (SOA)/African vultures optimization algorithm (AVOA)/coot optimization algorithm (COOT)/pelican optimization algorithm (POA)/eagle perching optimization (EPO)/osprey optimization algorithm (OOA). The time varying filtering based empirical mode decomposition (TVFEMD^II)–ten "bird" swarm algorithms–monthly runoff time series prediction models of OSELM were proposed. Firstly, TVFEMD^Ⅰ was used to decompose the monthly runoff time series, obtaining three decomposition components: TVFEMD₁~TVFEMD₃. By using approximate entropy (ApEn) to calculate the approximate entropy values of each component in the initial decomposition, the TVFEMD₃ component with a larger approximate entropy value was subjected to secondary decomposition using TVFEMD^II, resulting in TVFEMD^II_3–1~TVFEMD^II_3–3 components. Secondly, based on the training sets of each component, six OSELM hyperparameter optimization instance objective functions were constructed, and ten "bird" swarm algorithms were used to optimize the hyperparameters of the six instance objective functions. Finally, the TVFEMD^II–ten "bird" swarm algorithms–OSELM model was established, and various models were validated through a monthly runoff prediction example at Dishui Station in Yunnan Province. The results show that: ① The overall ranking of the ten "bird" swarm algorithms for optimizing the instance objective function is completely consistent with the overall ranking of the TVFEMD^II–RBMO/PKO/SBOA/HHO/SOA/AVOA/COOT/POA/EPO/OOA–OSELM model prediction accuracy, indicating that a better optimization effect of the ten "bird" swarm algorithms means a higher accuracy of monthly runoff prediction. ② Comparatively speaking, the TVFEMD^II–RBMO/POA/OOA/AVOA–OSELM model performs better, with predicted <italic>E</italic>_MAP, <italic>E</italic>_MA, and <italic>E</italic>_RMSranging from 0.233% to 0.397%, 0.005 m³/s to 0.008 m³/s, and 0.006 m³/s to 0.013 m³/s, respectively. The prediction error is lower than in other comparative models. ③ The decomposition effect of TVFEMD^II is better than that of TVFEMD^I. While considering the computational scale, it has a good decomposition effect and is the key to improving the accuracy of monthly runoff prediction.