Ensemble Forecasting Method Of Molten Magnesium Load Based On Parameter Hierarchical Optimization

Fused magnesium oxide has excellent fire resistance,insulation,and corrosion resistance,widely used in metallurgy,building materials,aerospace,and other fields.However,the electrically fused magnesium consumes huge electricity and the load fluctuation is the dramatic,accurate prediction of load change is conducive to peak shaving and valley filling,saving power supply capacity,which not only can reduce the cost of electricity for enterprises but also can realize energy saving and emission reduction,with important research significance and application value.In the dynamic change of electric fused magnesium working condition,the electricity load is affected by intermittent,periodic,and random factors together,and its fluctuation has the characteristics of non-stationary,strong non-linearity,multi-mode,and involving different time scales,which increases the difficulty for prediction.To address this problem,this paper researches the integrated prediction method of electric molten magnesium load based on parametric recursive optimization,which achieves integrated prediction by decomposing the sequence with recursive optimization and heterogeneous reconstruction,and also designs a weighted integrated prediction model of sub-series based on multi-objective evolutionary optimization,which improves the accuracy and robustness of load prediction.The main research works are as follows:First,for the fluctuation of electric molten magnesium load has the characteristics of nonstationary,multi-modal and involving different time scales,the integrated forecasting method of electric molten magnesium load based on sequence decomposition and heterogeneous reconstruction is designed.Three methods of discrete wavelet transform(DWT),adaptive noise-complete ensemble empirical modal decomposition(CEEMDAN)and variable modal decomposition(VMD)are used to decompose the time series,and homogeneous and heterogeneous models are used to reconstruct the sub-series for prediction,respectively.The experimental results show that all three decomposition strategies can effectively extract the information features in the load series,and the integrated model significantly improves the prediction accuracy compared with the single model.In addition,the heterogeneous reconstruction model shows a better prediction performance compared to the homogeneous reconstruction model when dealing with subsequences with different frequency characteristics.Second,the traditional integrated prediction method rectifies the decomposition and model parameters separately without considering their coupling.An integrated prediction method based on parameter recursive optimization is proposed to address this problem.The decomposition and model parameters selection is considered an upper and lower recursive optimization problem.The lower layer aims at minimizing the sum of the prediction errors of the lowest frequency sequence and the highest ranked entropy sequence and fixes the model parameters to optimize the decomposition parameters.The upper layer aims at the highest integrated prediction accuracy and optimizes the model parameters by substituting the decomposition parameter optimization results.To reduce the number of iterations,the initial values of the decomposition parameters are determined based on the energy entropy and central frequency method,and the initial values of the model parameters are determined by substituting them into the optimization solution of the upper layer problem.For the characteristics of the parameter optimization problem with multiple peaks and difficult-to-obtain gradient information,the natural heuristic algorithm is used to find the optimal parameters.The variational operator is introduced into the particle swarm optimization algorithm to avoid premature convergence,and the trade-off between global exploration and the local convergence ability of the algorithm is achieved by adjusting the adaptive factor.Experimental results show that the proposed HO-DWT-RF-LSTM and HO-VMD-RF-LSTM improve the RMSE index and MAPE index by 8.75%,8.29%,and 12.5%,5.73%,respectively,indicating that the recursive optimization strategy can effectively improve the prediction accuracy of the model.In particular,the integrated prediction method based on parametric recursive optimization shows higher robustness when the load fluctuates drastically due to changes in operating conditions,and therefore better meets the needs of actual industrial load prediction.Third,the integrated prediction method trains the model based on deviation metrics,which can improve the fitting accuracy but cannot guarantee the generalization performance.A weighted integrated prediction method based on multi-objective parameter evolutionary optimization is designed by simultaneously optimizing the variance and deviation indicators to train the model.The heterogeneous models are used to fit the implied information of a single subsequence from different perspectives,and the subseries heterogeneous models are weighted and combined before being used in the integrated prediction model.With the minimization of mean relative error(MAE)and maximization of interpretable variance score(EVS)as the optimization objectives,a fast non-dominated ranking genetic algorithm(NSGA-II)is used to search for the Pareto optimal solution set of the weighted parameters.The combined performance of the optimal solutions on MAE and EVS is shown by the Pareto frontier on the two-dimensional objective space,and the decision maker can choose among the results according to their preference.Meanwhile,a Pareto optimal solution policy method based on adaptive variance risk threshold is designed,i.e.,the EVS interval of the Pareto optimal solution set is determined according to the Pareto frontier obtained by optimization,the threshold value of EVS is determined according to the constraint ratio,the EVS optimization objective is upgraded to a constraint not smaller than the threshold value,and the optimal MAE result is selected basis on satisfying the constraint.The experimental results show that the weighted combined model of subseries can not only track the trend change effectively on the lowfrequency subseries but also has a better ability to fit the detailed fluctuation information efficiently on the high-frequency subseries;the proposed weighted integrated forecasting method based on multi-objective parameter evolutionary optimization,under the two decomposition methods,compared with the single-objective optimized integrated forecasting method,the MAE values obtained are improved by 4.90%and The proposed method not only improves the prediction accuracy but also ensures the generalization performance of the model.