A Novel Fractional-Order Grey Prediction Model and Its Modeling Error Analysis

Wei Meng,Shuliang Li,Bo Zeng

doi:10.3390/info10050167

Abstract

Based on the grey prediction model GM(1,1), a novel fractional-order grey prediction model is proposed and its modeling error is systematically studied. In this paper, exponential data sequences are generated for numerical simulation. Via the numerical simulation method, the mean absolute percentage error (MAPE) of the fractional-order GM(1,1) with different values of order and development coefficient is compared to the GM(1,1) and the discrete GM(1,1). The error distribution of the sequences of exponential data is given. The GM(1,1) and the direct modeling GM(1,1) are both special cases of the fractional-order GM(1,1). The conclusion is helpful to further optimize the grey model using fractional-order operators and to expand the applicable bound of GM(1,1).

Highlights

Grey system theory was developed to study uncertainty systems with small samples and poor information by Chinese scholar, Professor Deng Julong [1]
This paper mainly studies a novel fractional-order grey prediction model based on the fractional-order operators and applies numerical simulation to study the error distribution of grey model (GM)(1,1) with different values of order and development coefficient
This paper presented the modeling method for the fractional-order GM(1,1)

Summary

Introduction

Grey system theory was developed to study uncertainty systems with small samples and poor information by Chinese scholar, Professor Deng Julong [1]. The grey system theory uses the generation and development method to extract valuable information of some known information in the unknown system, recognizes the correct description of the system’s operational behavior and evolution law, and realizes the quantitative prediction of future changes [2,3] Extant studies focused on the optimization and applicable bounds of traditional grey prediction models and the modeling method of fractional-order operators. The error distribution and applicable bound of grey prediction models with fractional-order operators has not been studied. This paper mainly studies a novel fractional-order grey prediction model based on the fractional-order operators and applies numerical simulation to study the error distribution of GM(1,1) with different values of order and development coefficient.

Fractional-Order Grey Prediction Model

Data Preparation

Results and Discussion

Conclusions