Chaotic Time Series Analysis And The Research Of Its Application In Melt Index Prediction Of Propylene Polymerization

With the rapid development of nonlinear science,the research of chaos theory has become an important field of nonlinear scientific research.Especially the analysis and prediction of chaotic time series has become a very important research direction.Melt index is one of the most important indicators of propylene polymerization.It is very important to establish a reliable prediction model of melt index.Aiming at the complex process of propylene polymerization,chaos theory is introduced to mine the information of time series of melt index to explore the information contained in the time series and to establish a relatively accurate soft-sensor model.In this paper,chaotic time series analysis and its application in polypropylene melt index prediction are studied.The main work is the recognition of chaotic characteristics,soft-sensor modeling and multi-scale modeling.The main work and innovation of this paper are as follows:(1)Identify the chaotic characteristics of the melt index time series.First use the unit root test methods of ADF and KPSS to analyze the stability,and calculate the Hurst index by R/S analysis.Then discuss the phase space reconstruction based on the Takens theorem.Moreover,three important parameters which describe the singular attractor are calculated,that is the correlation dimension,the Lyapunov exponent and the Kolmogorov entropy.Combining different chaotic characteristics,the chaotic characteristics of the melt index time series are finally determined.(2)Based on the chaotic characteristics of the melt index time series,a chaos prediction model of melt index is established based on phase space reconstruction and relevance vector machine(RVM).Considering that the validity of the RVM model depends largely on the choice of the kernel parameter,the HACDE algorithm is proposed to optimize the the kernel parameter of RVM.It is improved and combined according to the respective characteristics of differential evolution algorithm(DE)and continuous ant colony optimization algorithm(ACO).The HACDE-RVM chaotic prediction model is used to predict the actual melt index of polypropylene.The results show that the HACDE-RVM chaotic prediction model has good forecasting performance and HACDE algorithm can effectively solve the RVM parameter optimization problem.(3)Based on the chaotic characteristics of the melt index time series,a fuzzy wavelet neural network(FWNN)based melt index chaotic prediction model is established.Gradient descent algorithm is used to derive the FWNN structure learning algorithm and the learning rate to be optimized are determined.After analyzing the advantages and disadvantages of the gravitational search algorithm(GSA),an improved gravitational search algorithm(MGSA)is proposed to adjust the learning rates of FWNN on-line so as to improve the prediction accuracy.The MGSA-FWNN chaotic prediction model is used to predict the melt index of polypropylene.The prediciton results fully demonstrate the forecasting accuracy and good generalization ability of the MGSA-FWNN model.(4)Wavelet transform and empirical mode decomposition are used for multi-scale analysis of the melt index time series,respectively.The decomposition and reconstruction results show that,compared with wavelet decomposition,empirical mode decomposition can better distinguish the different frequency data in the original signal,and have a smaller reconstruction error.By analyzing the characteristics of the five intrinsic mode functions(IMF)obtained by empirical mode decomposition,we finally determine that IMF2,IMF3 and IMF5 are chaotic sequences,while IMF1 and IMF4 do not possess chaotic characteristics.The above analysis finally determines that the melt index time series has multi-scale characteristics.(5)Based on the multi-scale characteristics of the melt index,the concept of combined forecast is introduced to establish a combined forecasting model of melt index.According to the different characteristics of each decomposition sequence,different prediction methods are used.Finally,the combined forecasting model is used to predict the melt index of polypropylene,and the prediction results are compared with the single prediction models in Chapter Three and Chapter Four.The prediction results fully demonstrate the forecasting accuracy and good generalization ability of the combined forecasting model based on multi-scale analysis.The combined forecasting model can overcome some problems of the single forecasting model and the modeling method is more reasonable and effective.