Non-equidistance Fractional Order Accumulation Grey Model NFGM (1, 1) and Its Application

In scientific research and engineering applications, there are a large number of research objects with non-equidistant fractional-order characteristics. The existing fractional-order grey theory model was no longer suitable for solving such problems. Based on the integer-order grey theory model, the non-equidistant fractional-order accumulation generation and subtraction generation operators are proposed. The background value of the non-equidistant grey theory analysis model is reconstructed. By taking fractional-order as a design variable and minimum mean relative error and minimum mean square as an objective function, two kinds of optimization models are established. In the application of strength, it is found that the accuracy of the background values reconstructed by the two models is much higher than that of the reference analysis results. The proposed model in the present paper improves the accuracy of the grey theory analysis model, expands the scope of application of the model, and provides references for scientific research and practical application of engineering.