Study And Application Of Chaotic Time Series Prediction Based On Machine Learning

Chaotic time series exists in natural and man-made environment widely.The prediction of chaotic time series is often an actual task.Chaotic time series which is generated by chaotic system behaves differently compared with general time series.Chaotic time series behaves like random signal exteriorly and is sensitive to initial state,which makes it unpredictable in the long term.However,the intrinsic essence of chaotic time series is that it is generated by the deterministic nolinear dynamical system,which makes it predictable in the short term.To make better prediction of chaotic time series,it is suitable to recover the chaotic system information and make full use of the chaotic characteristic.This thesis focuses on chaotic time series prediction,making a study on related steps of the prediction process.The steps include phase space reconstruction,modeling of chaotic time series prediction,machine learning model construction,model evaluation and selection,weak signal detection and so on.Eventually,with the help of machine learning models,the prediction is conducted in reconstructed phase space,achieving good performance.The main work and study is as follow:(1)The meaning and theory of phase space reconstruction as well as the delay coordinate reconstruction method are studied.Then,the methods of determining the two important parameters delay time and embedding dimension in phase space reconstruction are introduced in detail.(2)The single step prediction model of chaotic time series is studied.The predictable property is analyzed from theory,and the prediction problem is modeled as a nolinear mapping.Firstly,the k-nearest neighbors,support vector regression,neural networks and polynomial regression are introduced,which all make good prediction.Then,the Bagging,weighted average,Stacking ensemble models are introduced,making use of the above models so as to make better predictions.(3)The multiple steps prediction model of chaotic time series is studied.Two different methods are introduced.The first method is to conduct single step prediction recursively using the trained single step prediction model.The second method is to train a multiple step prediction model directly.(4)The applications of chaotic time series prediction are introduced.Firstly,it is applied to weak signal detection.The weak target signal can be detected indirectly by making use of the predictable property of strong chaotic background noise.Then,it is applied to sunspot number prediction.The sunspot number sequence can be treated as chaotic time series for its chaotic characteristic.The future sunspot number can be predicted by appropriate model after phase space reconstruction of the sunspot number sequence.(5)The above algorithms,models and applications are implemented in Python programs.Enough experiments are carried out to validate the theoretical analyses.