Research And Implementation Of Fractional Order Grey Prediction Model

The grey system theory is an important method to solve the problem of uncertainty in the objective world of poor information.The main research object is small sample data lacking statistical laws.In fact,compared with the integer order,fractional calculus can better mine the essence of the object and solve complex problems flexibly.The fractional gray system just combines the advantages of both,which can reveal the development law of the gray system more deeply.Therefore,the thesis conducts in-depth research on fractional-order gray systems from the aspects of pre-processing of data,establishment of models,and improvement of models.The main research work is as follows:(1)A preprocessing method for improving the original sequence of the gray model.For the system noise problem,the Kalman filter is introduced into the preprocessing process of the sequence,which reduces the random error generated during data acquisition,smoothes the fitting curve,facilitates modeling,and combines with the fractional-order accumulator operator to reflect the new information priority.Principles to further improve the accuracy of the model's fit prediction.Finally,an example is given to show the effectiveness and practicability of the method.(2)Direct modeling and analysis of the gray model using the Simulink block diagram method.Based on the FOTF toolbox,the Simulink block diagram method is applied to the gray system,the model parameters are optimized,the solution process is simplified,and the practicability of the block diagram method is verified by an example.The method is applied to the fractional gray model GM(r,1).The comparison between the example and the high order gray model shows the universality of the fractional gray model.To solve the lag problem of the delay system data,the fractional-order gray time delay model GM(r,1,?)is established by the block diagram method.Good fitting prediction results were obtained in the example application.(3)Based on the fractional gray model,a new fractional gray combination model HMGM(?,1)is proposed to reveal the development law of the research object more comprehensively,to solve the prediction problem that cannot be satisfied by the single gray model,and to compare the single gray model with the example of power consumption.Verify the validity and practicability of the combined model HMGM(?,1).The analysis and research of the above problems provide a reference for improving the prediction accuracy of the gray model,expanding the scope of application of the model,and enriching the grey system theory.