Research On Sequence Operators-Based Grey Forcasting Models And Their Applications

The grey system theory deals with the uncertain problems with little data and scare information. It extracts the valuable information by creating and developing the partial known information to describe and control the rules of systems well. Grey forecasting model is the core of grey system theory, and the characteristics of grey forecasting model are grey generating and grey differential equation. Grey generating is a method of transferring the grey process into white process. It can provide middle information for grey forecasting model and weaken the randomness of the raw data. This paper has analysed the roles of sequence operators in grey generating, grey modeling and its pretreatment. The initial parameter estimate of least square has been established and some properties of grey system forecasting models are discussed. The main innovations of this paper are as follows.(1)Some compared weak buffer operators and strengthening buffer operators are established and analysed which have the universality and practicability. The buffer operators program has compiled by C + + builder. The buffer operator sequences are researched and their compared relations are required. These buffer operators are applied for vibration data sequences, some contradictions between qualitative analysis and quantitative forecast can be resolved effectively.(2)The definition of linear sequence operator matrix is given, their characters and inherent relations are studied. The generating of data's accumulating - mean is suggested. The matrix of the generating and some linear buffer operators are described. The initialed and unified formula of multi-step buffer operator was proved by the buffer operator matrix.(3)The least square regression of GM(1,1) model parameter based on the generating of data's accumulating - mean is proposed. The estimate improves the initial level of solving GM(1,1) model parameter. The modeling steps of vibration data sequences have summed up. Based on the method, the modeling steps of other special data sequences ( such as unusual value sequence and stage sequence, or random vibration sequence) can also reduce the modeling steps and raise the modeling speed.(4)The whole algorithm of GM(1,1) models is established. The benefits of the algorithm have avoided the lose of modeling information and the work of remodeling. It has strengthened the connection between GM(1,1) models and has improved the whole ability of GM(1,1) models'explanation. The Characteristic properties of grey system forecasting models are researched. The study has been made on the data processing of grey system forecasting models. The parameter properties of a series of GM(n, h) model, grey power model and discrete grey model are proved simply based on the data's inherent multiply nature.