Research On Grey Prediction Models And Its Applications In Traffic Management

Grey systems theory has worked out many problems with poor information and uncertainty. Along the development of application, new problems rise and it is necessary to improve theoretical research. This dissertation bases the principle of “propose question, analyze question, theoretical derivation and solution” to advance studies of grey prediction, proposed new theory and modeling method. The theoretical studies were used in traffic modeling, for supporting traffic management and decision. Main contains are summarized as following:(1) We studied the prediction problem of disturbance systems, and a novel kind of buffer operators with variable parameter were proposed. For disturbance systems, we constructed a new kind of buffer operator with smoothing effect, of which the structure was based on iteration generation. Then we analyzed its properties, and three other new buffer operators were expanded from the this new buffer operator. Besides, a new kind of buffer operator was constructed based on trigonometric function. We analyzed the properties of the new trigonometric buffer operator and analyzed its application scope. The new buffer operator was employed in the prediction problem of traffic infrastructure construction, and the causal information played a better role in the application.(2) We studied the optimization methods of GM(1,1) model and put forwards a new optimized GM(1,1) model which was used to forecast driver’s amount. First, we analyzed grey modeling mechanism and algorithm process, and concluded how to improve modeling precision for quasi-exponential sequence. New optimized GM(1,1) model was constructed based on relationship research between background values and development parameters. The numerical case demonstrated that the new optimized GM(1,1) model breaks the limitation for sequence with high development rate and is effective and practicable. The new model was used to predict quantity growth of Chinese drivers and the results were analyzed further compared with total population.(3) Modeling method for improving geometric fitting was studied, and we proposed a new kind grey prediction model, namely GRGM(1,1) model, which was used to predict development of automobile. This study proposed a new grey prediction model based on GM(1,1), which progressed the model group of GM(1,1). For sequence with randomness, the absolute grey incidence method was employed to improve grey model. GRGM(1,1) model improved the reflection equation, from which the restored response function was derived. Undetermined variables were used to adjust fitting precision and the particle swarm optimization algorithm was used to calculate best values. The new model changed characteristics of fixed exponential form in traditional GM(1,1) model, and the improvement of geometric fitting was prominent. The new model was applied to analyze the automobile development and predict the tendency in future five years.(4) The modeling method for high-order grey generation was studied and we constructed new model based on high-order generation. Grey generation for raw data bases the prediction model in grey system theory, randomness is weakened further after multi-generation of data accumulation and quasi-exponential law is present clearly. We proposed GHM(p,1) model on raw data high-order generation and analyzed the properties. For second-order model which is commonly in applications, we proposed modeling method, constructed its reflection equation, derived time response function and studied the method of initial values. According to modeling program, this study analyzed prediction application for automobile in a region of China. The new model was used to compare with GM(1,1) and GM(2,1) models and computational results demonstrated that the new high-order grey model has a higher precision than other twos.(5) We studied grey relationships between systems and proposed the grey projection pursuit incidence model, which combined grey incidence method with projection pursuit method. First, we proposed mechanism of grey projection pursuit incidence method, and derived its algorithm, in which particle swarm optimization method was used to calculate the best values of projection vector. Then program of this new method was put forwards. The new grey incidence method was used to analyze the relations between systems with multi-factors and analyze relative importance of the factors in each system. The grey projection pursuit incidence method was applied to analyze relations of economic system, traffic system and population system, for investigating development law of automobile.The new models and methods solved problems existing in grey theory, and improved the effectiveness. These methods and models were applied mainly in traffic management for supporting its management and decisions.