Secondary-diagonal mean transformation Partial Grey Model based on matrix series

Grey Model (GM) deals with the systems where certain information about the systems is unknown or incomplete. GM has been successfully used in many engineering areas, including agriculture, energy, economy, and environmental engineering where prediction needs to be made with uncertain factors. Particularly, GM is widely applied in image processing and data filtering. In a GM defined by matrix series, the prediction is made by solving these matrixes through a sequence of matrix operations. To improve the simulation and prediction accuracy of GM matrix solving, a novel secondary-diagonal mean transformation Partial GM (mtP-GM) is developed in this paper. We first defined a mean transformation in the secondary-diagonal direction of the matrix series. We then defined the mtP Accumulating Generation Operation (mtP-AGO) according to the principles of AGO, matrix-AGO (m-AGO), and Partial-AGO (P-AGO). The principles of GM are followed in the modeling process, and grey impact factors of the model are encapsulated in a matrix with m2 unknown elements. Finally, four real data sets with long-running data and multi-stream series are imported for comparing the performance of the developed mtP-GM with several other grey models, such as RGM, dtP-GM, and GM(1,1). The comparison results show that dtP-GM can obtain a better accuracy for periodic data sequences. However, our mtP-GM outperforms the other three models for non-periodic data sequences.