Stochastic Modeling of Time Series with Application to Local Damage Detection in Rotating Machinery

Raw vibration signals measured on the machine housing in industrial conditions are complex and can be modeled as an additive mixture of several processes (with different statistical properties) related to normal operation of machine, damage related to one (or more) of its part, some noise, etc. In the case of local damage in rotating machines, contribution of informative process related to damage is hidden in the raw signal so its detection is difficult. In this paper we propose to use the statistical modeling of vibration time series to identify these components. Building the model of raw signal may be ineffective. It is proposed to decompose signal into set of narrowband sub-signals using time-frequency representation. Next, it is proposed to model each sub-signal in the given frequency range and classify all signals using their statistical properties. We have used several parameters (called selectors because they will be used for selection of sub-signals from time-frequency map for further processing) for analysis of sub-signals. They have base in statistics theory and can be useful for example in testing of normality of data set (vibration time series from machine in good condition is close to Gaussian, damaged not). Results of such modeling will be used in the sub-signals classification procedure but also in defects detection. We illustrate effectiveness of novel technique using real data from heavy machinery system.

[1]  Radoslaw Zimroz,et al.  A procedure for weighted summation of the derivatives of reflection coefficients in adaptive Schur filter with application to fault detection in rolling element bearings , 2013 .

[2]  Radoslaw Zimroz,et al.  Adaptive Bearings Vibration Modelling for Diagnosis , 2011, ICAIS.

[3]  Gregory W. Corder,et al.  Nonparametric Statistics for Non-Statisticians: A Step-by-Step Approach , 2009 .

[4]  Jérôme Antoni,et al.  Cyclostationary modelling of rotating machine vibration signals , 2004 .

[5]  Jérôme Antoni,et al.  Time-frequency approach to extraction of selected second-order cyclostationary vibration components for varying operational conditions , 2013 .

[6]  Issei Fujishiro,et al.  The elements of graphing data , 2005, The Visual Computer.

[7]  Tomasz Barszcz,et al.  A novel method for the optimal band selection for vibration signal demodulation and comparison with the Kurtogram , 2011 .

[8]  Robert B. Randall,et al.  Rolling element bearing diagnostics—A tutorial , 2011 .

[9]  Wlodzimierz Bryc,et al.  The Normal Distribution , 1995 .

[10]  Wei He,et al.  Bearing fault detection based on optimal wavelet filter and sparse code shrinkage , 2009 .

[11]  Jérôme Antoni,et al.  Application of averaged instantaneous power spectrum for diagnostics of machinery operating under non-stationary operational conditions , 2012 .

[12]  Jont B. Allen,et al.  Short term spectral analysis, synthesis, and modification by discrete Fourier transform , 1977 .

[13]  Luca Viganò,et al.  Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) , 2015, IWSEC 2015.

[14]  Wensheng Su,et al.  Rolling element bearing faults diagnosis based on optimal Morlet wavelet filter and autocorrelation enhancement , 2010 .

[15]  B D.C.,et al.  A COMPARISON OF AUTOREGRESSIVE MODELING TECHNIQUES FOR FAULT DIAGNOSIS OF ROLLING ELEMENT BEARINGS , 1996 .

[16]  Radoslaw Zimroz,et al.  Gearbox Condition Estimation Using Cyclo-Stationary Properties of Vibration Signal , 2009 .

[17]  P. D. McFadden,et al.  Detecting Fatigue Cracks in Gears by Amplitude and Phase Demodulation of the Meshing Vibration , 1986 .

[18]  Robert B. Randall,et al.  Differential Diagnosis of Gear and Bearing Faults , 2002 .

[19]  W. Bryc.  The Normal Distribution: Characterizations with Applications , 1995 .

[20]  Fakher Chaari,et al.  Gearbox Vibration Signal Amplitude and Frequency Modulation , 2012 .

[21]  Darryll J. Pines,et al.  A review of vibration-based techniques for helicopter transmission diagnostics , 2005 .

[22]  M. Stephens.  Tests of fit for the logistic distribution based on the empirical distribution function , 1979 .

[23]  Ming J. Zuo,et al.  GEARBOX FAULT DIAGNOSIS USING ADAPTIVE WAVELET FILTER , 2003 .

[24]  Spilios D. Fassois,et al.  Parametric time-domain methods for non-stationary random vibration modelling and analysis — A critical survey and comparison , 2006 .

[25]  Agnieszka Wyłomańska,et al.  Recognition of stable distribution with Lévy index α close to 2. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  Tomasz Barszcz.  Decomposition of Vibration Signals into Deterministic and Nondeterministic Components and its Capabilities of Fault Detection and Identification , 2009, Int. J. Appl. Math. Comput. Sci..

[27]  T. W. Anderson,et al.  Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes , 1952 .

[28]  Jérôme Antoni,et al.  Detection of signal component modulations using modulation intensity distribution , 2012 .

[29]  J. Antoni.  Cyclostationarity by examples , 2009 .

[30]  P. McFadden.  Examination of a technique for the early detection of failure in gears by signal processing of the time domain average of the meshing vibration , 1987 .

[31]  F. Combet,et al.  Optimal filtering of gear signals for early damage detection based on the spectral kurtosis , 2009 .

[32]  Yimin Zhan,et al.  Robust detection of gearbox deterioration using compromised autoregressive modeling and Kolmogorov–Smirnov test statistic—Part I: Compromised autoregressive modeling with the aid of hypothesis tests and simulation analysis , 2007 .

[33]  Radoslaw Zimroz,et al.  Application of Adaptive Filtering for Weak Impulsive Signal Recovery for Bearings Local Damage Detection in Complex Mining Mechanical Systems Working under Condition of Varying Load , 2011 .

[34]  Viliam Makis,et al.  Adaptive state detection of gearboxes under varying load conditions based on parametric modelling , 2006 .