Autoregressive Model Estimation Theory And Its Application In Deformation Monitoring Data Processing

Deformation is a common phenomenon in nature and every year the harm and loss caused by deformation disaster are countless in the whole world.Therefore, scientific, accurate and timely deformation monitoring and analysis and prediction of deformation are particularly important. Time series analysis method is a method of dynamic data processing. It can use parametric model which is established according to the auto-correlation of observed data to scientifically analyze and handle dynamic data and predict the future trend of data. Considering that compared with other models the order selection and parameter estimation of AR model among the time series analysis methods are relatively simple and it has been proved in theory that even if the true model is MA or ARMA sequences, can also be described as the high order AR model, systematically researching on the AR model has important theoretical significance and practical value. This paper systematically studies estimation theory of the stable autoregressive model including one-dimensional AR (P) model, multi-dimensional AR(P) model and the fuzzy AR (P) model.A series of problems of estimation theory of AR model are deeply discussed including inspection and preprocessing of data, preliminary identification of model,order selection of model,parameter estimation of model and prediction of model etc. Based on matlab the corresponding modeling and forecasting programs are written. Finally based on examples this paper discusses the application of autoregressive model estimation theory in the field of deformation monitoring data processing.Followings are the main research contents and achievements of this paper:1. This paper systematically studies estimation theory of the one-dimensional AR (p) model and discusses a series of problems of the one-dimensional AR (p) model in detail including inspection and preprocessing of data, preliminary identification of model,order selection of model,parameter estimation of model and prediction of model etc. In the parameter estimation of the one-dimensional AR (p) model,the moment estimation and the least squares estimation are introduced and the ridge estimation is derived.Least squares estimation only considered the error of vector Y and ignored the error of coefficient matrix X.But the total least squares method can consider both the accidental error of coefficient matrix X and observation vector Y, and carry on the correction at the same time.Based on this idea, the total least squares estimation criterion is applied to the parameter estimation of AR(p) model. The specific calculation steps are given in the paper. 2. Considering that one-dimensional time series cannot represent complex interaction among multiple factors and the multidimensional time series can describe the interaction among multiple factors and better reflect the real data, researching on multidimensional time series has great significance.The paper studies the stationary condition of multidimensional autoregressive model and discusses the methods of parameter estimation of VAR(p) model in detail such as the least squares estimation, Yule-Walker method and Levinson method etc.To make it more easily to program,the improved least squares estimation is proposed. And the caiman filter algorithm is applied to parameter estimation of multidimensional AR (P) model.Then the paper introduces several methods of order selection of multidimensional model and the minimum variance prediction and accuracy analysis are given.3. Since the uncertainty of the measurement data has not only the randomness, but also the fuzziness,the paper presents fuzzy AR(p) model to predict the fuzzy data.Fuzzy AR(p) model is given and the method of constructing fuzzy numbers is proposed.Two kinds of methods of parameter estimation of fuzzy AR(p) model such as linear programming method and fuzzy least squares estimation are introduced.The F test order selection method and rapid F test order selection method are given.Finally,the prediction formula of fuzzy AR(p) model is proposed.4. Based on matlab platform, modeling and forecasting process of the three AR (P) models are programmed. At last,by application examples, the specific application of three models in data processing of deformation monitoring are discussed and the prediction precision are analyzed and compared.Some useful conclusions are given.