Multivariable Non-equidistance Grey Model with Fractional Order Accumulation and its Application

In order to meet the characteristic offractional order in engineering system and the need of non-equidistance, the non-equidistance fractional order accumulating operators and fractional order inverse accumulating operators were researched. The multivariable non-equidistance grey model NFMGM (1, n) with fractional order accumulation was established, and the error mechanism of NFMGM (1, n) was analyzed. The accumulation generating sequence with fractional order was fitted with non-homogeneous discrete exponential function, and the reconstructing method of background value of NFMGM (1, n) was proposed. The optimizing model was built with the fractional order number as a design variable and the minimum average relative error as objective function, and the programs were written in Matlab. Example shows NFMGM (1, n) has better precision, which has higher appropriate for not only equidistance model but also non-equidistance model, and worth to be popularized in engineering field and other related fields.