Subjects: Mathematics >> Modeling and Simulation submitted time 2021-05-07
Abstract： In recent years, Grey system theory has been widely used in various fields. Among the Grey Prediction Models, the GM (1,1) model is the core and foundation. However, due to the exponential time response sequence, GM (1,1) model is difficult to simulate the oscillation sequence, and the oscillation sequence can not pass the GM (1,1) pre modeling test. These factors weaken the application of GM (1,1) model. The paper establishes GM (1,1) model for the 1-AGO sequence of oscillation sequence, by using the advantage of monotone sequence simulation of GM (1,1) model. Then, the IAGO operation with correction term is introduced to restore the simulation of oscillation sequence. Finally, an improved GM (1,1) model is established to make up for the defect of the traditional GM (1,1) model in the simulation of oscillation sequence.
Peer Review Status:
Awaiting Review
Subjects: Mathematics >> Modeling and Simulation submitted time 2021-04-23
Abstract： Grey system model is widely used in mathematical modeling and approximate calculation because of its simplicity and clear mathematical background. The principle of grey system model can be summarized as the use of time response function to simulate the evolution of data series. Among them, GM (1,1) model is the most basic and can reflect the idea of grey modeling most widely. The time response function of the traditional GM (1,1) model is constructed by the exponent of natural constant . Also, for this characteristic, the GM (1,1) model has strong limitations. In practical application, people often modify the time response function of GM (1,1) model. One of the most important correction methods is to couple the original time response function with other functions that can describe the properties of data series. For example, for data series with certain periodicity or quasi periodicity, the original time response function can be coupled with trigonometric function to form GM (1,1) - trigonometric function coupling model. In this paper, the feasibility of this model is deeply discussed, and the estimation method of the parameters in the time response function of the coupled model and the error analysis are proposed.
Peer Review Status:Awaiting Review
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