Bearing Fault Detection Using Higher-Order Statistics Based ARMA Model

Impulse response provides important information about flaws in mechanical system. Deconvolution is one system identification technique for fault detection when signals captured from bearings with and without flaw are both available. However effects of measurement systems and noise are obstacles to the technique. In the present study, a model, namely autoregressive-moving average (ARMA), is used to estimate vibration pattern of rolling element bearings for fault detection. The frequently used ARMA estimator cannot characterize non-Gaussian noise completely. Aimed at circumventing the inefficiency of the second-order statistics-based ARMA estimator, higher-order statistics (HOS) was introduced to ARMA estimator, which eliminates the effect of noise greatly and, therefore, offers more accurate estimation of the system. Furthermore, bispectrums of the estimated HOS-based ARMA models were subsequently applied to get clearer information. Impulse responses of signals captured from the test bearings without and with flaws and their bispectra were compared for the purpose of fault detection. The results demonstrated the excellent capability of this method in vibration signal processing and fault detection. Introduction Rolling element bearing is one of the most important parts of rotating machinery. Any flaw in bearing may result in malfunction and even lead to catastrophic failure. Hitherto, many techniques have been used in bearing fault diagnosis in the literature. Vibration signal processing is among the most frequently applied techniques. When a defect in one surface of a bearing encounters another surface, an extra vibration may be excited and extra vibration signal component is therefore introduced to measured signals. Hence, feature extraction for the extra vibration becomes the primary task of fault detection. However, measured vibration signals are always submerged in heavy background noise, such as sampling noise, unwanted vibration from other components and surrounding noise, which makes feature extraction more difficult. Effective vibration signal processing methods are therefore required for the purpose of fault detection. Being a branch of signal processing, pattern recognition is a significant fault detection technique. Deconvolution is one of the popular pattern recognition methods and it has been used in nondestructive evaluation (NDE) [1-3]. However, noise is obstacle to this technique and both input and output signals are required in application of deconvolution for system identification, which is infeasible in rotating machinery fault detection. Using measurements of the output signal only, autoregressive-moving average (ARMA) model estimator is therefore more applicable in bearing vibration system identification. Higher-order statistics (HOS) play an important role in system identification because they are capable of identifying unknown systems from output observation even when contaminated with additive Gaussian/non-Gaussian noise. Besides, they can track down the non-linearity in the system’s amplitude and/or phase characteristics. Extracted features using different processing methods may be different. Patterns of bearings with various health statuses are concerned in the present study. Aimed at fault detection, HOS were Key Engineering Materials Vol. 347 (2007) pp 271-276 online at http://www.scientific.net © (2007) Trans Tech Publications, Switzerland Online available since 2007/Sep/15 All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of the publisher: Trans Tech Publications Ltd, Switzerland, www.ttp.net. (ID: 130.203.133.33-17/04/08,14:16:02) introduced to estimate coefficients of ARMA model of a system, termed HOS-based ARMA model. The method was used to analyze vibration signals collected from bearings without and with flaws in races and ball. ARMA models of the test bearings with different health statuses were estimated, which were depicted using impulse response curves. To get more detail comparison, bispectrum, one of the higher-order spectra, was subsequently introduced to the estimated ARMA models. Comparison of the spectrograms proved the effectiveness of the method for bearing damage detection. HOS-Based ARMA Model ARMA Model. A typical single channel input-output system model is depicted in Fig. 1. In this model, ) (k u is input; ) (k x is theoretical output; ) (k n is additive noise; and ) (k y is real output of the system. The convolutional equation describing the noise-free output of this system is