An Initial Condition Optimization Approach for Improving the Prediction Precision of a GM(1,1) Model

Abstract

Grey model GM(1,1) has attained excellent prediction accuracy with restricted data and has been broadly utilized in a range of areas. However, the GM(1,1) forecasting model sometimes yields large forecasting errors which directlyaffect the simulation and prediction precision directly. Therefore, the improvement of the GM(1,1) model is an essential issue, and the current study aims to enhance the prediction precision of the GM(1,1) model. Specifically, in order to improve the prediction precision of GM(1,1) model, it is necessary to consider improving the initial condition in the response function of the model. Consequently, the purpose of this paper is to put forward a new method to enhance the performance of the GM(1,1) model by optimizing its initial condition. The minimum sum of squared error was used to optimize the new initial condition of the model. The numerical outcomes show that the improved GM(1,1) model provides considerably better performance than traditional grey model GM(1,1) . The result demonstrates that the improved grey model GM(1,1) achieves the objective of minimizing the forecast errors.

Improved GM (1,1) Model by Optimizing Initial Condition to Predict Satellite Clock Bias

“…GM (1,1) model is used extensively in time series prediction, where the symbol GM (1,1) indicates "first-order grey model in one variable" [27]. GM (1,1) model is a system of the exponential function, which can utilize N known sequences before a certain moment as input and output wanton number of sequences behind that certain moment after a series of processing such as 1-AGO, modelling, 1-IAGO, and prediction.…”

“…And Xie [26] added a constant disturbance component to the latest component of the 1-AGO sequence to generate the initial condition. Furthermore, Madhi and Mohamed [27] gained the estimated value of the initial condition by minimizing the sum of the square errors of the reduced value and the real value.…”

Improved application of GM(1,1) model in turnaround fault prediction

“…Therefore, in this paper, the GM(1,1) model is selected to take advantage of the obvious advantages of the GM(1,1) model in processing irregular small sample data to predict the failure of the turnout [5]. At the same time, aiming at the common drawbacks of the GM(1,1) model [6], the sliding average method and indirect multi-step prediction are introduced to improve the prediction accuracy of turnout faults, thereby improving the disposal efficiency of turnout faults.…”

A new GM (1,1) model suitable for short‐term prediction of satellite clock bias

“…The grey model plays an important role for prediction, decision‐making, evaluation, planning, control, system analysis and modelling in many fields such as society, economy, science and technology because of its advantages of simple expression, less modelling data and excellent prediction effect [12, 13]. The GM (1,1) model is an important part of grey model, in which the first ‘1’ in brackets represents the first‐order differential equation, and the second ‘1’ indicates one variable of the differential equation [14]. The prediction accuracy of GM (1,1) model is very high for the data sequence that conforms to the structural characteristics of the model; otherwise, it is relatively low.…”