A Novel Fractional Order Multivariate Partial Grey Model and Its Application in Natural Gas Production

Accurate prediction of natural gas production is of great significance for optimizing development strategies, simplifying production management, and promoting decision-making. This paper utilizes partial differentiation to effectively capture the spatiotemporal characteristics of natural gas data and the advantages of grey prediction models. By introducing the fractional damping accumulation operator, a new fractional order partial grey prediction model is established. The new model utilizes partial capture of details and features in the data, improves model accuracy through fractional order accumulation, and extends the metadata of the classic grey prediction model from time series to matrix series, effectively compensating for the phenomenon of inaccurate results caused by data fluctuations in the model. Meanwhile, the principle of data accumulation is effectively expressed in matrix form, and the least squares method is used to estimate the parameters of the model. The time response equation of the model is obtained through multiplication transformation, and the modelling steps are elaborated in detail. Finally, the new model is applied to the prediction of natural gas production in Qinghai Province, China, selecting energy production related to natural gas production, including raw coal production, oil production, and electricity generation, as relevant variables. To verify the effectiveness of the new model, we started by selecting the number of relevant variables, divided them into three categories for analysis based on the number of relevant variables, and compared them with five other grey prediction models. The results showed that in the seven simulation experiments of the three types of experiments, the average relative error of the new model was less than 2%, indicating that the new model has strong stability. When selecting the other three types of energy production as related variables, the best effect was achieved with an average relative error of 0.3821%, and the natural gas production for the next nine months was successfully predicted.