Multi-Step Natural Gas Load Forecasting Incorporating Data Complexity Analysis with Finite Features

Data complexity directly affects the dynamics of complex systems, which in turn influences the accuracy and robustness of forecasting models. However, the load data exhibit complex features such as self-similarity, long-term memory, randomness, and chaos. This study aims to quantify and evaluate the complexity features of natural gas loads and to develop a multi-step-ahead forecasting model that integrates data decomposition and ensemble deep learning while considering these complexity features. Firstly, the complexity features of the series are quantified by rolling the fractal dimension, Hurst exponent, sample entropy, and maximum Lyapunov exponent. The analysis contributes to understanding data characteristics and provides information on complex features. Secondly, the ensemble learning eXtreme Gradient Boosting (XGBoost) can effectively screen complexity features and meteorological factors. Concurrently, variational mode decomposition (VMD) provides frequency-domain decomposition capability, while the gated recurrent unit (GRU) captures long-term dependencies. This synergy enables effective learning of local features and long-term temporal patterns, resulting in precise predictions. The results indicate that compared to other models, the proposed method (XGBoost-VMD-GRU considering complex features) demonstrates superior performance in forecasting, with R² of 0.9922, 0.9860, and 0.9679 for one-step, three-step, and six-step prediction, respectively. This study aims to bring innovative ideas to load forecasting by integrating complex features into the decomposition forecasting framework.