Periodically correlated random processes: Application in early diagnostics of mechanical systems

Abstract The covariance and spectral characteristics of periodically correlated random processes (PCRP) are used to describe the state of rotary mechanical systems and in their fault detection. The methods for estimation of mean function, covariance function, instantaneous spectral density and their Fourier coefficients for a given class of non-stationary random processes on the basis of experimental data, namely: the synchronous averaging, component, least squares method and linear filtration methods are considered. The first and second order periodicity detection methods are used for vibration signals analysis. A method for mechanical system fault identification and classification based on a harmonic series representation is developed. Examples of fault detection in rolling/sliding bearings and gearboxes are given.

[1]  Kenneth P. Maynard,et al.  RESIDUAL AND DIFFERENCE FEATURE ANALYSIS WITH TRANSITIONAL GEARBOX DATA , 2001 .

[2]  Asoke K. Nandi,et al.  CYCLOSTATIONARITY IN ROTATING MACHINE VIBRATIONS , 1998 .

[3]  Hisanao Ogura,et al.  Spectral representation of a periodic nonstationary random process , 1971, IEEE Trans. Inf. Theory.

[4]  L. Qu,et al.  Cyclic statistics in rolling bearing diagnosis , 2003 .

[5]  Antonio Napolitano,et al.  Cyclostationarity: Half a century of research , 2006, Signal Process..

[6]  B. B. Seth,et al.  Analysis of repetitive mechanism signatures , 1980 .

[7]  M. P. Norton,et al.  Fundamentals of Noise and Vibration Analysis for Engineers , 1990 .

[8]  Andrew D. Dimarogonas,et al.  Vibration of cracked structures: A state of the art review , 1996 .

[9]  I. Javorskyj,et al.  Component statistical analysis of second order hidden periodicities , 2014, Digit. Signal Process..

[10]  I. Javors'kyj,et al.  Least squares method for statistical analysis of polyrhythmics , 2003, Appl. Math. Lett..

[11]  O. S. Salawu.  Detection of structural damage through changes in frequency: a review , 1997 .

[12]  N. Tandon,et al.  A review of vibration and acoustic measurement methods for the detection of defects in rolling element bearings , 1999 .

[13]  Antonio Napolitano,et al.  Generalizations of Cyclostationary Signal Processing: Spectral Analysis and Applications , 2012 .

[14]  Harry L. Hurd,et al.  Periodically correlated random sequences : spectral theory and practice , 2007 .

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

[16]  William A. Gardner,et al.  Degrees of cyclostationarity and their application to signal detection and estimation , 1991, Signal Process..

[17]  Jacek Majewski,et al.  Component covariance analysis for periodically correlated random processes , 2010, Signal Process..

[18]  J. Antoni.  Cyclic spectral analysis of rolling-element bearing signals : Facts and fictions , 2007 .

[19]  Jacek Leskow,et al.  Linear filtration methods for statistical analysis of periodically correlated random processes , 2011, Proceedings of International Conference on Modern Problem of Radio Engineering, Telecommunications and Computer Science.

[20]  I. Iavors'kyj,et al.  Probabilistic models and investigation of hidden periodicities , 1996 .

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

[22]  J. I. Taylor,et al.  Identification of Bearing Defects by Spectral Analysis , 1980 .

[23]  Jacek Leskow,et al.  Linear filtration methods for statistical analysis of periodically correlated random processes - Part I: Coherent and component methods and their generalization , 2012, Signal Process..

[24]  Harry L. Hurd,et al.  Representation of strongly harmonizable periodically correlated processes and their covariances , 1989 .

[25]  T. A. Harris,et al.  Rolling Bearing Analysis , 1967 .

[26]  Menad Sidahmed,et al.  CYCLOSTATIONARY APPROACH AND BILINEAR APPROACH: COMPARISON, APPLICATIONS TO EARLY DIAGNOSIS FOR HELICOPTER GEARBOX AND CLASSIFICATION METHOD BASED ON HOCS , 2001 .

[27]  Ioannis Antoniadis,et al.  CYCLOSTATIONARY ANALYSIS OF ROLLING-ELEMENT BEARING VIBRATION SIGNALS , 2001 .

[28]  Marek Krawczuk,et al.  Damage indicators for diagnostic of fatigue cracks in structures by vibration measurements – a survey , 1996 .

[29]  Cécile Capdessus,et al.  CYCLOSTATIONARY PROCESSES: APPLICATION IN GEAR FAULTS EARLY DIAGNOSIS , 2000 .

[30]  E. Parzen.  Time Series Analysis Papers , 1967 .

[31]  J. W. Tukey,et al.  The Measurement of Power Spectra from the Point of View of Communications Engineering , 1958 .

[32]  Zbigniew Zakrzewski,et al.  Least squares method in the statistic analysis of periodically correlated random processes , 2011 .

[33]  A. Braun,et al.  The Extraction of Periodic Waveforms by Time Domain Averaging , 1975 .

[34]  I. Javorskyj,et al.  Methods of Periodically Correlated Random Processes and Their Generalizations , 2014 .