Time Series Nonlinearity Measuring Method Research And Application Based On L-DVV Method

In recent years, nonlinearity is a more and more significant indicator that widelyused in signal processing, geosciences, medical science and economics etc. Therefore,accurately measuring nonlinearity of time series is of great theoretical and practicalsignificance. At present, there are two kinds of methods for time series nonlinearityanalysis: mathematical statistics based methods (such as setting AR or ARMA linearmodel etc) and surrogate data based method (such as delay vector variance method,DVV method). The former methods need a mass of data, so its instantaneity is low;the latter methods may produce bias when generating the surrogate data. DVVmethod based on surrogate data usually generates surrogate data with iterativeAmplitude Adjusted Fourier Transformation (iAAFT) method and breaks the regularnonlinearity of original series to construct the surrogate data and the nonlinearity canbe estimated through the difference of DVV data between original series andsurrogate data. This kind method has very strict demand for surrogate data: surrogatedata must have some similarities with original series in statistical property. And fortime series with certain nonlinearity, we can upset its nonlinearity rule with theexisting surrogate data construction method; but for time series with uncertainnonlinearity, the existing surrogate data construction method can not upset itsnonlinearity rule. Thus through the hypothesis testing method based on surrogate data,we could not distinguish the nonlinearity of original series, especially the nonlinearityof time series with uncertain nonlinearity.Based on deep research into the nonlinearity measuring of time series and manytests, this paper provides DVV method base on linear standard series (L-DVV method)for time series nonlinearity measuring. In L-DVV method, linear standard seriesserves as the surrogate data in DVV method. By comparing the difference of DVVdata between linear standard series and original time series, L-DVV method caneffectively measure the nonlinearity degree with the L-DVV scatter diagram. In orderto test the performance of L-DVV method, experiments on nonlinearity measuring ofdifferent time series have been done and the results show that L-DVV method is moreeffective, more stable and faster than DVV method. And then, field seismic recordseries and real ECG series were used to test the performance of L-DVV method andthe results also shows the advantage of L-DVV method.After proving the performance of L-DVV method, in allusion to the nonlinearsensitivity of time frequency peaking filter (TFPF), which is widely used in noiseattenuation of seismic record, this paper would test the nonlinearity of time seriesbefore TFPF, according to the nonlinearity degree of time series, the parameter ofTFPF could be setting more reasonably than before, and the results would be better. Due to the inequality distribution of signal and noise in seismic record, thenonlinearity of a seismic record series can not be tested in one time. So in this paper,Pulse Coupled Neural Network (PCNN) which is widely used in image processingwould be introduced into the segmentation of time series before nonlinearitymeasuring. After preliminary segmentation, L-DVV method would be used tomeasure nonlinearity of time series, and by the difference of nonlinearity time serieswould be divided into two parts: high nonlinearity parts and low nonlinearity parts.The high nonlinearity parts include a mass of noises; so long time window would beused in TFPF, so that the noise can be attenuated more thoroughly. The lownonlinearity parts include more signals, so short time window would be used in TFPF,so that the signal can be reserved better. The general thought of this paper is: usePCNN to divide time series preliminary, then use L-DVV method to measurenonlinearity of divided time series and divide time series into two parts: highnonlinearity parts and low nonlinearity parts, last use time windows of differentlength to TFPF for different parts.In order to test the validity of the algorithm presented in this paper, firstly rickerwavelet series with random noise is used to introduce the detail process of thealgorithm, and the result certifies the validity of the algorithm. Then synthesizedseismic records with weak noise and powerful noise are respectively used to test thealgorithm, and the results certify the validity of the algorithm in signal reserving andnoise attenuation is better than conventional TFPF method. At last the algorithmwould be used to process filed seismic records, the results of the test with a recordwith160time series show that the algorithm can reserve signal and attenuate noisemore effectively than conventional TFPF. Through the results of the tests withsynthetic and filed records show that the algorithm presented in this paper is moresuperior than conventional TFPF method, and with real applied worth in seismicrecords processing.