Periodic Autoregressive Modeling of Vibration Time Series From Planetary Gearbox Used in Bucket Wheel Excavator

  • Agnieszka WyłomańskaEmail author
  • Jakub Obuchowski
  • Radosław Zimroz
  • Harry Hurd
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


Vibration signals acquired from machines operating under non-stationary operations are difficult to process due to their time varying spectral content, statistical properties, signal to noise ratio etc. In case of damaged machine vibration analysis, the classical damage detection approach might be defined as informative and non-informative contents separation. It can be done in many ways, including model based approaches. One of the most known solutions for constant load/speed operations exploits autoregressive (AR) modeling of the deterministic high energy components that often mask the weak impulsive and stochastic part of the signal. After establishing the model, the residual signal is extracted and further analyzed. In the case presented here, AR modeling is considered inappropriate because of the variation of speed/load conditions. To illustrate importance of the problem and novelty of our approach, a planetary gearbox vibration will be analyzed. The gearbox operates in a bucket wheel excavator (heavy duty mining machine) subjected to cyclic load/speed variation due to the digging/excavating process. Due to periodicity of the excavation process, it seems appropriate to assume a periodic autoregressive (PAR) model for the deterministic high energy components. In the chapter several topics will be discussed: real data inspired motivation for PAR modeling, estimation details, simulations and PAR based inverse filtering for extraction of the informative stochastic part of the signal. Finally, we present some comparison of PAR and AR for modeling the deterministic high energy part.


Non-stationary signals Autoregressive modeling Cyclic frequency modulation PAR Local damage detection Bearings Gearbox 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Agnieszka Wyłomańska
    • 1
    Email author
  • Jakub Obuchowski
    • 2
  • Radosław Zimroz
    • 2
  • Harry Hurd
    • 3
  1. 1.Hugo Steinhaus CenterInstitute of Mathematics and Computer Science, Wroclaw University of TechnologyWroclawPoland
  2. 2.Diagnostics and Vibro-Acoustics Science LaboratoryWroclaw University of TechnologyWroclawPoland
  3. 3.Department of StatisticsThe University of North Carolina at Chapel HillChapel HillUSA

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