A new stepwise decomposition ensemble model based on two-stage particle swarm optimization algorithm for the runoff prediction

The traditional decomposition ensemble runoff prediction model firstly decomposes the entire runoff series into several subseries, and then divides the subseries into training and validation periods for modeling, which wrongly treats the predictor data of validation period as known data and is difficult to be applied to actual runoff forecasting. Moreover, the prediction results of such models are only definite values, which is difficult to describe the prediction uncertainty caused by the randomness and volatility of runoff series. To solve the above problems, this study proposes a stepwise decomposition ensemble (VMD-SVM-KDE) model combining variable mode decomposition method, support vector machine model and kernel density estimation method, which performs both point prediction and interval prediction, and proposes a two-stage particle swarm optimization (TSCPSO) algorithm. The monthly runoff series of the Yellow River Basin is used to evaluate the model performance, and the study results show that: (1) the VMD-SVM-KDE model improves the coefficient of determination (R2) and Nash efficiency coefficient (NSE) values of the single SVM-KDE model from the range of 0.145 to 0.630 to the range of 0.872 to 0.921, and reduces the interval average deviation (INAD) values from the range of 0.046 to 95.844 to the range of 0.005 to 0.034, indicating that the VMD-SVM-KDE model significantly improves the point prediction and interval prediction performance of a single SVM-KDE model; (2) compared with the traditional one-stage PSO algorithm, the TSCPSO algorithm improves the R2 and NSE values of the single model from the range of 0.145 to 0.480 to the range of 0.309 to 0.630, and reduces the INAD value from the range of 48.813 to 95.844 to the range of 0.046 to 0.195, and also improves the R2 and NSE values of the decomposition ensemble model from the range of 0.872 to 0.912 to the range of 0.876 to 0.921, and reduces the INAD values from the range of 0.007 to 0.034 to the range of 0.005 to 0.014, indicating that the TSCPSO optimization algorithm overcomes the overfitting problem of support vector machine models and effectively improves the prediction accuracy of the single and decomposition ensemble models; (3) the VMD-SVM-KDE-TSCPSO model addressed the mistakes of traditional decomposition ensemble models that forecast factor data of validation period, and has higher accuracy of point prediction and interval prediction with R2 and NSE values of about 0.9 and the INAD values ranging from 0.005 to 0.014. The VMD-SVM-KDE-TSCPSO model can provide a basis for practical forecasting of non-stationary and non-linear hydrological series. © 2022 China Water Power Press. All rights reserved.