Research On Non-classical Mathematics Applied To Nonlinear Time Series Forecasting

Non-linear time series analysis can explore non-linear essence and rule suitably, it has important significant to forecasting the trend of object, in this issue, Artifical Neural Network (ANN) representing non-classical mathematics will apply to non-linear time series forecasting, fault diagnosis of aeroengine is studied detailedly, and it apply the paper methods to this field.Firstly, the phase reconstruction theory is studied in this paper; secondly, ANN is introduced into non-linear time series forecasting, and the issues are studied as follows:â‘ the forecasting model is built based on ANN,â‘¡the influence factor of ANN forecasting precision is discussed,â‘¢Genetic Algorithm (GA) is used to establish structure adaptive ANN forecasting model,â‘£the structure adaptive ANN forecasting model is validated detailedly by international standard data; thirdly, because ANN has the limitation of the bad generalation and training uncertainty, the Support Vector Machine (SVM) which is based on Statistical Learning Theory (SLT) and has good generalization is introduced, and the issues are studied as follows:â‘ the forecasting model of SVM is constructed,â‘¡Sequential Minimal Optimization (SMO) algorithm is studied realized in order to improve the computation speed of SVM,â‘¢the choice of SVM model parameters is analyzed, and then GA is utilized to optimize parameters of SMO forecasting model;â‘£the model is validated detailedly by international standard data, and the result shows the correctness of the model.Aeroengine is a typical complicated non-linear system, the time series coming from key parameters which can reflect synthetically areoengine work state is a representative non-linear time series, and the changing trend forecasting of areoengine state parameters play an important role in judging the systemic working state in future, and it has important significance to carry out the aeroengine on-condition maintaince. In the thesis the adaptive ANN and SMO forecasting model were applied to practical performance, wear, and vibration data of aeroengine, and the examples fully indicated validity and correctness of the methods put forward in this paper.