Mechanical Fault Diagnosis Based on Band-phase-randomized Surrogate Data and Multifractal

The vibration signals of machinery with various faults often show clear nonlinear characteristics.Currently,fractal dimension analysis as the common useful method for nonlinear signal analysis,is a kind of single fractal form,which only reflects the overall irregularity of signals,but cannot describe its local scaling properties.For comprehensive revealing of internal properties,a combinatorial method based on band-phase-randomized（BPR） surrogate data and multifractal is introduced.BPR surrogate data method is effective to eliminate nonlinearity in specified frequency band for a fault signal,which can be utilized to detect nonlinear degree in whole fault signal by nonlinear titration method,and the overall nonlinear distribution of fault signal is displayed in nonlinear characteristic curve that can be used to analyze the fault signal qualitatively.Then multifractal theory as a quantitative analysis method is used to describe geometrical characteristics and local scaling properties,and asymmetry coefficient of multifractal spectrum and multifractal entropy for fault signals are extracted as new criterions to diagnose machinery faults.Several typical faults include rotor misalignment,transversal crack,and static-dynamic rubbing fault are analyzed,and the results indicate that those faults can be distinguished by the proposed method effectively,which provides a qualitative and quantitative analysis way in the field of machinery fault diagnosis.

Test for random in electrical signals time series of CO_2 short circuit transition welding process by the method of surrogate data

This paper introduced the basic theory and algorithm of the surrogate data method, which proposed a rigorous way to detect the random and seemingly stochastic characteristics in a system. The Gaussian data and the Rossler data were used to show the availability and effectivity of this method. According to the analysis by this method based on the short-circuiting current signals under the conditions of the same voltage and different wire feed speeds, it is demonstrated that the electrical signals time series exhibit apparently randomness when the welding parameters do not match. However, the electrical signals time series are deterministic when a match is found. The stability of short-circuiting transfer process could be judged exactly by the method of surrogate data.

THE INFLUENCE OF THE DIFFERENT DISTRIBUTEDPHASE-RANDOMIZED ON THE EXPERIMENTAL DATA OBTAINEd IN DYNAMIC ANALYSIS

In this paper the influence of the differently distributed phase-randontized to the data obtained in dynamic analysis for critical value is studied.The calculation results validate that the sufficient phase-randomized of the different distributed random numbers are less influential on the critical value . This offers the theoretical foundation of the feasibility and practicality of the phase-randomized method.

New method of improving the security of the hyperchaotic cryptosystem

In chaotic cryptosysterns, using （very） high dimensional chaotic attractors for encrypting a given message maybe can improve the privacy of chaotic encoding. A kind of hyperchaotic systems are studied by using some classical methods. The results show that for improving the security of the chaotic cryptosystems, besides the high dimension, the sub-Nyquist sampling interval （SI） is also necessary. Then, we verify this result using the methods of time series analysis.

The meaning of “coherent” and its quantication in coherent hemodynamics spectroscopy

We have recently introduced a new technique,coherent hemodynamics spectroscopy(CHS),which aims at characterizing a specic kind of tissue hemodynamics that feature a high level of covariation with a given physiological quantity.In this study,we carry out a detailed analysis of the signicance of coherence and phase synchronization between oscillations of arterial blood pressure(ABP)and total hemoglobin concentration([Hbt]),measured with near-infrared spectroscopy(NIRS)during a typical protocol for CHS,based on a cyclic thigh cuffocclusion and release.Even though CHS is based on a linear time invariant model between ABP(input)and NIRS measurands(outputs),for practical reasons in a typical CHS protocol,we inducenite“groups”of ABP oscillations,in which each group is characterized by a different frequency.For this reason,ABP(input)and NIRS measurands(output)are not stationary processes,and we have used wavelet coherence and phase synchronization index(PSI),as a metric of coherence and phase synchronization,respectively.PSI was calculated by using both the wavelet cross spectrum and the Hilbert transform.We have also used linear coherence(which requires stationary process)for comparison with wavelet coherence.Themethod of surrogate data is used tond critical values for the signicance of covariation between ABP and[Hbt].Because we have found similar critical values for wavelet coherence and PSI by usingve of the most used methods of surrogate data,we propose to use the data-independent Gaussian random numbers(GRNs),for CHS.By using wavelet coherence and wavelet cross spectrum,and GRNs as surrogate data,we have found the same results for the signicance of coherence and phase synchronization between ABP and[Hbt]:on a total set of 20 periods of cuffoscillations,we have found 17 coherent oscillations and 17 phase synchronous oscillations.Phase synchronization assessed with Hilbert transform yielded similar results with 14 phase synchronous oscillations.Linear coherence and wavelet coherence overall yielded similar number of signicant values.We discuss possible reasons for this result.Despite the similarity of linear and wavelet coherence,we argue that wavelet coherence is preferable,especially if one wants to use baseline spontaneous oscillations,in which phase locking and coherence between signals might be only temporary.

The Compound Indexing of Human Self-Similar Behavioural Patterns

Applications of a constitutive framework providing compound complexity analysis and indexing of coarse-grained self-similar time series representing behavioural data are presented. A notion of behavioural entropy and hysteresis is introduced as two different forms of compound measures. These measures provide clinically applicable complexity analysis of behavioural patterns yielding scalar characterisation of time-varying behaviours registered over an extended period of time. The behavioural data are obtained using body attached sensors providing non-invasive readings of heart rate, skin blood perfusion, blood oxygenation, skin temperature, movement and steps frequency. The results using compound measures of behavioural patterns of fifteen healthy individuals are presented. The application of the compound measures is shown to correlate with complexity analysis. The correlation is demonstrated using two healthy subjects compared against a control group. This indicates a possibility to use these measures in place of fractional dimensions to provide a finer characterisation of behavioural patterns observed using sensory data acquired over a long period of time.

Analysis of Non-stationary Signals Based on Nonlinear Chaotic Theories

In the paper, two nonlinear parameter estimation methods based on chaotic theory, surrogate data method and Lyapunov exponents, are used to distinguish the difference of non-stationary signals. After brief introducting of the corresponding algorithms, two typical different non-stationary signals with different nonlinear constraining boundaries are taken to be compared by using the above two methods respectively. The obtained results demonstrate that the apparently similar signals are distinguished effectively in a quantitative way by applying above nonlinear chaotic analyses.

LEARNING GRANGER CAUSALITY GRAPHS FOR MULTIVARIATE NONLINEAR TIME SERIES

An information theory method is proposed to test the. Granger causality and contemporaneous conditional independence in Granger causality graph models. In the graphs, the vertex set denotes the component series of the multivariate time series, and the directed edges denote causal dependence, while the undirected edges reflect the instantaneous dependence. The presence of the edges is measured by a statistics based on conditional mutual information and tested by a permutation procedure. Furthermore, for the existed relations, a statistics based on the difference between general conditional mutual information and linear conditional mutual information is proposed to test the nonlinearity. The significance of the nonlinear test statistics is determined by a bootstrap method based on surrogate data. We investigate the finite sample behavior of the procedure through simulation time series with different dependence structures, including linear and nonlinear relations.

Detecting Stationarity and Nonlinearity in Propeller Singing Signal

<Abstract>The propeller singing is such a complex fluid-structure coupling phenomenon that needs to study intensively.In this paper,the stationarity of propeller singing signal is tested by the recurrence plot technique. According to surrogate data,the singing time series has nonlinearity character.And the nonlinearity of time series is not caused by the static nonlinear measurement function but the intrinsic character itself based on further research.The results provide an objective basis for analyzing the propeller singing signal with the nonlinear time series technique.

Nonlinear Analyses of Exchange Rates of Six Emerging Markets

This paper presents some empirical evidences on the presence of nonlinearity of exchange rates of six emerging markets by using Brock-Dechert-Scheinkman(BDS)test and Volterra-Wiener-Korenberg(VWK)model,respectively.The nonlinear dependences are found in the exchange rates of six emerging markets.Furthermore,this paper applies the VWK model with surrogate data method to detect if their nonlinear dependences are deterministic or not.The results show that the above exchange rates are deterministic and nonlinear time series.These imply that the exchange rate markets do not conform to the requirements of the random walk hypothesis.Therefore,the nonlinear dynamic model should be used to analyze the exchange rates.