Research On Grey Self-memory Combination Prediction Models And Their Applications

As an important theoretical component of grey system theory, the grey prediction models can weaken the randomness of original statistical data by means of accumulated generating operation. They have unique advantages for the short-term prediction of small sample sequences. And they have already been broadly and effectively utilized in numerous ?elds, such as social economy, geographical environment, energy, engineering, transportation, and so on. Moreover, the self-memory principle is a statistical-dynamic method to solve the problems of nonlinear dynamic systems. The method is a breakthrough to numerical solution of traditional initial-value problems and statistical approaches, and it has been increasingly applied to time-series forecasting in numerous fields such as meteorology, hydrology, and engineering science.Based on the composable modeling methodology, this paper applies the self-memory prediction technique in some special grey models, namely, univariate grey models, multivariable grey model, and interval grey number model. The series of grey self-memory combined prediction models have remarkably improved the fitting and forecasting accuracy of the traditional grey prediction models. Its excellent predictive performance lies in that the weakness of traditional grey models, i.e., sensitivity to initial values, can be overcome by replacing multi-time-point initial ?eld with single-time-point initial ?eld. The research results can enrich and optimize the grey prediction model system, as well as extend its applicable range.The main research results are summarized as follows:(1) The self-memory optimized GM(1,1) power model is studied to predict the nonlinear dynamic system accompanied by irregular fluctuations. It is appropriate for the fluctuating sequences with the characteristics of approximate exponential increase or decrease, saturation growth, or single-peak. The superiority and effectiveness of this combined model have been proved by two cases of port cargo throughput forecasting and enrolment rate forecasting.(2) Two specific univariate grey self-memory prediction models are studied by combining the self-memory component with GM(1,1,tφ) model and NGM(1,1,k) model, which are appropriate for the engineering systems characterized by partial exponential law with time power, and the approximate non-homogeneous exponential data sequence, respectively. And the stochastic fluctuating law can be revealed effectively. The illustrative examples of foundation settlement and energy consumption indicate that the self-memory prediction technique can improve the accuracy and robustness of the traditional univariate grey prediction model remarkably.(3) The multivariable grey self-memory combined prediction model(SMGM(1,m)) is studied for use in multi-variable systems with interactional relationship under the condition of small sample size. It can uniformly describe the relationships among system variables and tightly catch the random fluctuation tendency of engineering system. And the reliability and stability of the SMGM(1,m) model have been verified by two case studies of engineering settlement deformation prediction.(4) The interval grey number self-memory combined prediction model is studied based on the grey degree of compound grey number. The simulation example takes an interval grey number sequence with the characteristic of saturated development as an object and obtain the effective prediction effect. Meanwhile, the discrete prediction model of development belt is studied. It is appropriate for forecasting the evolutionary interval of interval grey numbers in terms of sharply-swinging and overall-growing trend.(5) The grey self-memory combined prediction method is utilized into the field of prophylactic medicine and drug research. First, the GM(1,1) self-memory model is used to forecast the incidence rates of two notifiable infectious diseases(dysentery and gonorrhea). Second, the GM(1,1) self-memory power model is used to forecast the serum concentration in human body.