Multivariate Grey Prediction Model Application in Civil Aviation Carbon Emission Based on Fractional Order Accumulation and Background Value Optimization

The GM(1,N) model, as a classical multivariate grey prediction model, can make a holistic and dynamic analysis of multiple factors and reflect the dynamic change relationship between the variable series and the related factor series. However, numerous works in the literature show that the GM(1,N) model has mechanistic defects, parametric defects, and structural defects. Therefore, the thesis establishes the OGM(1,N) model based on the GM(1,N) model by adding the linear correction term and the amount of grey action. According to the principle of dynamic optimization, the PSO algorithm is used to determine the background value. On this basis, the fractional order idea is introduced to push the model order from the integer field to the real field, and the FOBGM(1,N) model is established to systematically reduce the model error. Second, the literature in the ScienceDirect database for the last ten years is reviewed, and the carbon emission impact factors of civil aviation are selected. The calculated carbon emission values are taken as sample data based on Method 2 of Civil Aviation in Volume 2 of the 2006 IPCC Guide to National Greenhouse Gas Inventories. The results show that the prediction accuracy of the model has an increasing trend after multi-layer and multi-angle optimization. Among them, the MAPE of the OGM model and FOBGM model decreased by 24.40% and 31.86% compared with the GM(1,N) model. The 5-year average prediction accuracy of the FOBGM model reaches 99.996%, which verifies the effectiveness and practicality of the model improvement and has certain practical significance and application prospects.