Theoretical Studies On The Methods Of Statistical Modelling And Their Applications

In today's information age, the statistical knowledge has been used more and more widely in practice with the development of statistic methods emerging in an endless stream. The multi-scale modelling of statistics has been a hot subject whether in theoretical statistics or applied statistics which impacts both the statistical methods and the development in all fields of science. The study methods based on kernel method have resulted in a revolution in the field of data analysis. The high mobility of generalized additive models (GAMs) provides a valid method which can reveal the implicit various relationships among data.The predictive functional model is proposed based on wavelet function and Hammerstein model on the basis of the multi-scale characteristic of wavelet, and the inner model parameters can adjust automatically depended on the repeated identification. The multi-scale analysis characteristics of wavelet and the properties of compact support can not only guarantee the optimization of the integrated error, but also highlight the approaching requirement of the important fit points as well as fulfill the aggregation of the optimized variables. Both the theoretical analysis and simulation applications showed that this method had the performance of more fast and less mismatching of the model.Based on the theories of wavelet analysis and kernel method, a wavelet fusion kernels modelling method was proposed. It performed multiple-scaled decomposition on sampled data series using wavelet transform firstly, the reconstructed approximate series and detail series were then regressed depending on kernel method, and the outputs were fused finally. This modelling method owning the traits of wavelet multiple solution analysis and kernel method's insensitiveness toward the input dimension has faster modelling speed on the premise of ensuring satisfied modelling precision. On this basis, the simulations were carried out through one dimensional function and the data from the chemical process. The simulation results also showed the effectiveness of the proposed algorithm. When the Hilbert space and L~2 ( R ) are defined isomorphic, linear operators of inner product isomorphic can convert the scaling functions of wavelet subspace in L~2 ( R ) space into other scaling functions of Wavelet Subspace in Hilbert space. Morlet wavelet kernel function is proposed in Hilbert space based on the conditions of the support vector kernel function and wavelet multi-resolution theory. The simulation experiment results showed that the scaling reproducing kernel function had better accuracy and generalization capability as compared with the traditional support vector machine with radial base function (RBF) kernel function. When trying to apply the SVM modelling so as to improve the generalization ability and the precision of models, sample data were mapped to sparse feature space to prevent the loss of SVM's sparsity when the kernels were fused. Through the simulation, the results showed that this modelling method could improve the modelling accuracy under the premise of guaranteeing sparsity, which verified effectiveness of the method and of significant practical application.The GAMs provide an effective way to model the fermentation process of glutamate (Glu). By this model, the effect of the different modelling variables on the production of Glu can be easily analyzed and the relationships between modelling variables and the production of Glu can be discovered. Three significant factors, fermentation time (T), dissolved oxygen (DO) and oxygen uptake rate (OUR), were finally selected based on the analysis of the effect of the different factors using the data from 15 batches of Glu fermentation to construct the GAM model. The constructed GAM model could capture 97% variance of the production of Glu during the fermentation process. This model was applied to investigate the single and combined effects of T, DO and OUR on the production of Glu, and the conditions to optimize fermentation process were proposed based on this model. Results showed that the production of Glu can reach a high level by control the concentration levels of DO and OUR during the fermentation process following the optimization conditions proposed by GAM-2. The successful construction of this mode provides the bases to study the effect of different factors on the production of Glu, and we can study of fermentation conditions with specific aims to optimize the fermentation of Glu. This study not only provides an effective way to predict the production of Glu using online data but also provide a novel idea for online-fault diagnosis during the fermentation of Glu. During the study on the fault diagnosis of the fermentation process of Glu, the online fault diagnostic method was proposed based on methods of GAMs and Bootstrap. This method can judge if the state of the fermentation process is normal only relying on the effective observation of the variables and also obtain the observed variables associated with the sources of the faults. This method only involved a few parameters to be determined and adjusted. During the fermentation process, on one hand, this method can provide report timely on the state of the faults, and on the other hand, provide necessary information on debug of the sources of the faults, which therefore provide a reliable way to guarantee the normal running of the fermentation process.All in all, with the rapid growth and extensive development of computer technology and the challenge of the data and information explosion, statistical modelling methods have great significances in the field of industry so as to elevate the data to information, knowledge and intelligence rapidly and effectively.