Ensemble Framework for Multistep Carbon Emission Prediction: An Improved Bi-LSTM Model Based on the Bayesian Optimization Algorithm and Two-Stage Decomposition

Abstract

Effective prediction of carbon dioxide emissions is crucial for the real-time monitoring of carbon emission dynamics and the formulation of emission reduction policies. For the accurate and stable prediction of carbon emission data, multiple challenges must be addressed, mainly including nonlinearity, nonstationarity, and dynamic uncertainty. To further improve the accuracy of carbon emission prediction, an ensemble framework for daily CO₂ emission forecasting based on data decomposition-reconstruction is proposed. First, the original data are decomposed into trend, seasonal, and residual components using seasonal trend decomposition via the Loess method. For the trend and seasonal components, the Bayesian optimization algorithm (BOA) is applied to optimize a bidirectional long short-term memory (Bi-LSTM) neural network for further prediction. The Bi-LSTM adopts a novel LeakyReLU activation function to effectively extract data features, thereby enhancing the model's expressive power. Meanwhile, the Nadam optimizer is employed, which combines the adaptive learning rate mechanism of the Adam algorithm with the Nesterov momentum to update weights and biases, enabling efficient model training, accelerating convergence, and improving model performance. Then, the residual component is decomposed again using gray wolf optimizer (GWO)-optimized variational mode decomposition (VMD), VMD incorporates a quadratic penalty function and Lagrange multipliers to derive the input series. and the decomposed subsequences are predicted using gated recurrent unit (GRU) networks. Finally, the predictions of each subsequence are stacked and reconstructed to obtain the final forecast value, creating an ensemble framework referred to as STL-BOA-Bi-LSTM-GWO-VMD-GRU. The proposed ensemble framework is tested on real data from seven different regions. In both single-step and multistep prediction processes, the proposed ensemble framework has higher prediction accuracy and stability than other models, demonstrating significant advantages.