Study And Application Of Dynamic Modeling For Non-stationary Time Series Signal

Time series signal is common in the world that can reflect the state or changes degree of things,phenomena,etc.over time.At present,the research on time series data has been continuously deepening where dynamic modeling of non-stationary time series signals is an important research direction in time series data analysis field.It plays an important role in financial sector,climate analysis field,network security,human health,machine condition monitoring and other fields.Aiming at the non-stationary time series signal,this study proposes effective dynamic modeling algorithms in time domain and time-frequency domain according to the innovative idea of "mechanical model-complex data model".And then the change point monitoring is adopted as typical scenarios to valid the effect of the method along the technical route of "dynamic modeling-stationary index extraction-decision making".For time-domain analysis,this paper proposes an effective dynamic modeling method of time series data by combining the mechanical-driven method and the data-driven method.Firstly,in order to extract the mechanism of time series,autoregressive integrated moving average model is adopted to model the periodic time series signals.The cyclic analysis is realized by dynamic cycle segmentation and cycle regularization,and then the in-phase points of the time series data are extracted according to the autoregressive integrated moving average model.Then,one-class support vector machine is adopted as a complex data model to describe the in-phase point of the time series data,so as to use the support vector machine sequence to describe the time series data.In order to valid the effect of dynamic modeling method,the support vector machine sequence is utilized to predict whether each point is an outlier compared with its corresponding in-phase point data distribution.And the intensity of outlier distribution is taken as a stationary index.Then,a general decision-making algorithm is adopted to judge whether the condition of the time series has changed.For time-frequency domain analysis,this paper proposes an effective dynamic modeling method by combining the time-frequency transform with the limited penetrate visibility graph.Firstly,short-time Fourier transform is adopted to convert the original signal into time-frequency spectrum so as to extract its mechanism information.And then power spectrum is obtained through periodogram method on the basis of the frequency spectrum.Then limited penetrable visibility graph is built based on the power spectrum to extract the correlation information between the frequency components of the power spectrum.Then a limited penetrable visibility graph sequence is obtained through construct graph at each moment,which can be used to describe the state of the time series signal.In order to valid the effect of dynamic modeling method,a novel distance metric for limited penetrable visibility graph is proposed by fusing structured distance and unstructured distance.Then the median graph is adopted to describe the historical data and the distance between the median graph and the candidate graph is calculated as a stationary index.Finally,the decision algorithm is implemented to determine the stationarity of the original signal.In order to verify the effectiveness of the proposed methods,machine is adopted as a typical application scenario to explore the application of the proposed in-phased analysis based time-domain algorithm in machine condition change monitoring.Then the electroencephalogram signal is used as another typical application scenario to verify the effectiveness of the proposed correlation based time-frequency domain method in electroencephalogram change monitoring.Finally,the main content of this research is summarized,and the shortcomings and follow-up work are discussed.