An MSB based robust detector for bearing condition monitoring

Envelope analysis is a widely used method for bearing fault detection. To obtain high detection accuracy, it is critical to select an optimal narrowband for envelope demodulation. Fast Kurtogram is an effective method for optimal narrowband selection. However, fast Kurtogram is not sufficiently robust because it is very sensitive to random noise and large aperiodic impulses which normally exist in practical application. To achieve the purpose of denoising and frequency band optimization, this paper proposes a new fault detector based on modulation signal bispectrum analysis (MSB) for bearing fault detection. As MSB results highlight the modulation effects by suppressing stationary random noise and discrete aperiodic impulses, the detector developed using high magnitudes of MSB can provide optimal frequency bands for fault detection straightforward. Performance evaluation results using both simulated data and experimental data show that the proposed method produces more effective and robust detection results for different types of bearing faults, compared with optimal envelope analysis using fast Kurtogram. COMADEM 2015 + X CORENDE where ) (t x f is the impulse produced by the fault, ) (t xq is the modulation effect due to the non-uniform load distribution and ) (t xbs is the bearing-induced vibrations determined by the bearing structure dynamics, ) (t xs is the machinery-induced vibrations determined by the machine structure or other components, and ) (t n is the noise which is encountered inevitable in any measurement system. It shows that the fault signatures are from modulation effects between fault signatures, load distribution and structure resonances. Moreover, the signals are also contaminated by noises and different interferences. Therefore, to extract the fault signature effective, the signal must be denoised and demodulated. MSB has the capability to enhance nonlinear modulation components and suppress random noise by detecting phase coupling in the modulation signal. The definition of MSB can be described by Eq. (2). (13, 14) ) ( ) ( ) ( ) ( ) , ( * * c c x c x c x c MS f X f X f f X f f X E f f B − + = .............................................................. (2) where, x f is modulated frequency; c f is the carrier frequency and x c f f + and x c f f − are modulation frequencies. And the magnitude and phase of MSB can be expressed as Eqs. (3) and (4). ) ( ) ( ) ( ) ( ) , ( * * c c x c x c x c MS f X f X f f X f f X E f f A − + = .......................................................... (3) ) ( ) ( ) ( ) ( ) , ( c c x c x c x c MS f f f f f f f f f − f − − f + + f = f ................................................................ (4) It takes into account both x c f f + and x c f f − simultaneously in Eq. (3) for measuring the nonlinear effects of modulation signals. If they are due to the nonlinear effect between c f and x f , there will be a bispectral peak at bifrequency ) , ( x c MS f f B . On the other hand, if these components are not coupled but have random distribution the magnitude of MSB will be close to nil. In this way, it allows the wideband noise in bearing vibration signals to be suppressed effectively so that the discrete components can be obtained more accurately. To enhance the effect of the small amplitude sidebands, MSB sideband estimator (MSB-SE) (14) was proposed as express in Eq. (5) ( ) ( ) ( ) ( ) ( ) ( )     − + = 2 * * , c c c x c x c x c SE MS f X f X f X f f X f f X E f f B ............................................................... (5) Based on the MSB property of highlighting modulation effect, a MSB detector can be developed. Firstly, MSB amplitude array is averaged along the x f direction according to Eq. (6) to obtained an average spectrum at different c f . ∑ = i ij j A N A 1 ............................................................................................................................... (6) where i and j is the index of x f and c f respectively. Then, the carrier frequencies which have high amplitudes are selected as the candidates for feature extraction. Finally, the selected c f slices are further averaged to get the MSB detector as expressed by Eq. (7). ∑ = = m k k j ij dt A m MSB 1 1 ....................................................................................................................... (7) where m k k j ,... 1 = , m is the slice number that selected for calculating MSB detector. COMADEM 2015 + X CORENDE To illustrate the calculation procedure of the MSB detector, a very high SNR signal is used to show the detection using the detector. Figure 1(a) shows the result of MSB of the signal. Several distinctive peaks appear in MSB, indicating that nonlinear modulation phenomena exist significantly between frequency c f and x f in the simulated signal. Then, MSB amplitude is averaged along the x f direction, resulting in the graph in Figure 1(b). And the carrier frequencies which have high amplitudes are selected for feature extraction as marked in the graph. At last, the selected c f slices are averaged to get the MSB detector as shown in the graph of Figure 1(c). From the MSB result, it can be found that the outer race fault frequency of 88.5Hz and its harmonics can be detected by the detector. Figure 1. MSB of simulated signal and MSB detector result 3. Simulation study The simulated bearing signal with outer race fault and corresponding spectrum are given out in Figure 2(a). The spectrum of simulated signal includes three resonance frequencies at 3471Hz, 7120Hz, and 11750Hz corresponding to inner race, outer race and sensor modes respectively. Figure 2(b) and 2(c) illustrate the time domain signals and spectra for the high and low SNR cases in which the simulated signal are added with two levels of white noise and aperiodic impulsive interferences. It can be seen that in the high SNR signal the lowest resonance frequency is masked by the noise whereas in the low SNR signal the first two resonance frequencies are buried in noise. Due to the high level noise, it is quite difficult to locate the resonance frequency and hence implement accurate fault detection. Both kurtogram envelope analysis and MSB detector are applied to the two signals for fault detection for performance comparison. The optimised filter bands by Kurtogram are illustrated by dashed rectangular and the parameters are given out in the text box in Figure 2(b) and 2(c). For the high SNR case, the filter locate at the third frequency resonance with a narrow band, while for the low SNR case, the optimised filter locate at lower frequency with a very wide frequency range where too much noise is included. Figure 3(a) and 3(b) give out the MSB slice optimization results for the two cases. For the high SNR case, the two high resonance frequencies of the simulated signal can be observed. The two high amplitude carrier frequencies are selected to calculate the MSB detector. However, only one resonance frequency can be seen in Figure 3(b). Similarly, the two high amplitude carrier frequencies are selected. Figure 3(c) and 3(d) present the fault detection results comparison of Kurtogram based envelope spectrum and MSB detector. Both Kurtogram based envelope spectrum and MSB detector are effective for high SNR signal. However, for low SNR signal, Kurtogram result could not give out fault indication while MSB detector still can extract the fault frequency. Therefore, it can be concluded that MSB detector outperforms Kurtogram based envelope spectrum in detecting the small modulating components that are contaminated by white noise and aperiodic impulses. 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 x 10 4 0 2 4 6 x 10 22 X: 1.175e+04 Y: 5.525e+22 MSB mag vs fc fc(Hz) A m pl itu de X: 1.184e+04 Y: 4.127e+22 88.5 177 265.5 354 442.5 0 0.5 1 MSB result fx(Hz) A m pl itu de (a) (b)