Further Promotion of Quadratic Time-Varying Parameters Discrete Grey Model

Mengdi Jin

doi:10.11648/j.ajist.20180203.12

Abstract

Based on the reason that the traditional buffer operator cannot adjust the action intensity, this paper proposes a positive real order weakening buffer operator, which solves the disadvantage that the original operator cannot be fine-tuned, and is more suitable for real life systems. By defining positive real order weakening buffer operator and according to the combination number and the nature of gamma function, the two are connected, and the positive real order weakening buffer sequence is transformed by gamma function. Next a quadratic time-varying linear parameter grey discrete prediction model (QTDGM) is established by using the constructed positive real order weakening buffer operator. The iterative optimization method of simulation base value is given, and the optimization model is established and the solution algorithm is proposed. Finally, the steps of modeling and forecasting by using QDGM model are described. In the case of science popularization fund forecast and raw coal output forecast, QTDGM model shows superior prediction effect. The relative error of the model is 0.34% ~ 7% in the three cases, which is much lower than that of the model using integer order weakening buffer operator and also lower than that of the linear time-varying parameter grey discrete model. QTDGM is more suitable for complex sample systems.

Highlights

Data prediction is to infer the law of development of things from the observed data, and predict and estimate the unknown data according to the inferred law
The positive real order weakening buffer operator is more suitable for complex real systems
The classical weakening buffer operator fully considers the priority of each data, while the variable weight weakening buffer operator only considers the priority of the latest data

Summary

Introduction

Data prediction is to infer the law of development of things from the observed data, and predict and estimate the unknown data according to the inferred law. From the point of view of prediction error, besides choosing a good prediction model, the model-based prediction method will face two problems in the process of dealing with the actual system: Firstly, due to the limitation of actual conditions, the observed data cannot accurately map with the actual data, and there are often uncertain disturbance components, that is, the observed data is noisy; The law of development of things is not constant, it is usually a slow process, that is to say, the parameters of the model are time-varying. From the point of view of the realization of model parameter estimation, the two problems are contradictory: Because the parameters of the model are time-varying, the weight of the parameters should be concentrated on the observation values closest to the predicted data as far as possible, so that the parameters of the model can be matched quickly and the errors caused by the changes of the parameters can be reduced. The positive real order weakening buffer operator is more suitable for complex real systems

The Construction of Positive Real Order Weakening Buffer Operator

Model Properties

Model Base Value Iterative Optimization

Case Study

Findings

Conclusion