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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 Radoslaw Zimroz1, a*, Walter Bartelmus2,b 1,2
Wroclaw University of Technology, Diagnostics and Vibro-Acoustic Laboratory, Wroclaw, Poland a
[email protected],
[email protected],*corresponding author
Keywords: rolling element bearings, local damage, detection, vibration, adaptive filter, NLMS algorithm, weak signal extraction
Abstract. The paper shows application of an adaptive filter as a pre-processor for impulsive cyclic weak signal recovery from raw vibration signals captured from complex mechanical systems used in the industry (namely bearings used in pulleys – parts of driving units for belt conveyors). Periodic/cyclic impulses are related to local faults which cause impulse/concentric forces/stresses in kinematic pairs. Typical examples of such local faults which cause mechanical system condition change are spall/pitting on bearings elements: outer/inner races and/or rolling elements. For analyzed objects, impulses associated with local faults are masked by other signal sources. In the first part of the paper objects are presented for the better understanding of mechanical phenomena that exist in the system, then preliminary signal analysis will be performed (in time, frequency and time-frequency domain) for the identification of signal nature. Next the idea of an adaptive system and the brief description of Normalized Least Mean Square (NLMS) algorithm will be presented. Application of NLMS is better than classical LMS due to stability of the adaptation. In the last section the results of adaptive filtering for signals from bearings is discussed. Authors show application of NLMS (for the first time in literature) for the case when signals are received from machines working in industrial condition. There were made only trails when the machines were investigated in laboratory conditions. Introduction The appearance of a cyclic event with some period and impulsive character of the vibration signals is very often associated with a mechanical fault. This kind of the fault is related to the local increase of forces/stresses in kinematic pairs and is commonly called as “local fault “. Typical examples of such a change of condition are a spall/pitting in rolling element bearings - outer/inner race, ball local damage, Fig 1.
Fig. 1 – examples of local damages in bearings If one considers cases that happen in practice, i.e. complex mechanical systems during normal operation (for example a driving unit for a conveyor system) with medium (expected due to lifetime) wear of some elements and many potential sources of vibrations, it is clear that a task defined as detection of an impulsive component in the raw signal becomes almost impossible. It is well known that especially at an early stage local damage produces weak low energy signals [16]. A 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 TTP, www.ttp.net. (ID: 156.17.73.88-05/08/11,10:48:43)
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suggested approach is to use some signal processing technique to enhance an interesting signal – to “extract” the signal for further analysis. Signal enhancement issue – a short review There are many techniques [18] that exploit time signal averaging (TSA), different forms of signal filtering [10], signal decomposition using wavelets or very advanced so-called “blind” extraction/separation techniques for extraction of the signal of interest [23,26]. Classic, basic filters (high pass, band pass) are not sufficient due to spectral overlapping (a frequency range occupied by a signal of interest (SOI) and a frequency range containing deterministic components may have some overlap) [4]. There is a need to use an other criterion for signal separation. Blind techniques are very powerful, especially blind extraction of the SOI based on cyclo-stationary properties of the signal is a very promising direction of research [9], however, it is very time and computation consuming (first cyclo-stationary phenomena need to be found – sometimes more than just one [3], then blind separation may be performed). The variation of speed [24], requires re-sampling of the signal. Another interesting approach is to apply an adaptive filter for signal separation. The adaptive filtering – known as Adaptive Line Enhancement (ALE) [21] or Self Adaptive Noise Cancellation was introduced to the condition monitoring community by Lee and White [15] (for gearboxes and reciprocating machinery) and Randall (with colleagues [1,2,17,26]) for bearings. Just a few papers related to the application of ALE to bearing vibration written by other authors may be found in the literature [11, 13, 14, 20, 25]. The purpose of this paper is to apply the adaptive filtering to signals from bearings used in pulleys in belt conveyor systems. It should be stressed that cited before papers present results, which were done in laboratory condition. The obtained results may only give a promise that when using in industry condition would be successful. Object and experiment description In this section a brief description of the diagnosed objects is provided. A deep understanding [8] of machine design and the condition of operation is a fundamental issue in condition monitoring (selection of parameters for data acquisition system, choice of signal processing methods, reasoning rules etc). Mining machines seem to be a special class of machines – high-power, complex design, time-varying load, unique scenario of degradation (due to environmental impact), etc [5,6,7,24]. a) b) BEARING DRIVE PULLEY GEARBOX
LOAD BEARING
COUPLING DRIVE
Fig 2. Diagnosed object: a) scheme, b) view of motor, coupling and gearboxes On Fig 2a the scheme of the driving unit for a belt conveyor is shown – it consists of two sets: motor, coupling and two stage gearbox (Fig 2b), that are connected with a pulley (Fig 3a). The connection between gearbox output shaft and a pulley is given by coupling (Fig 3b). The diagnostic task is to detect a local damage/fault in the pulley’s rolling element bearings.
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a)
b)
c)
Fig 3. a) Pulley with bearing housing mounted on shaft, b)View on joint of output shaft in gearbox with pulley, c)View on sensor location on pulley Preliminary Signal Analysis In this section basic signal analysis is performed in order to understand signal properties in the time and frequency domains. There are identified the main sources of signals and next the concepts of separation is considered. A raw vibration signal captured from a bearing housing supported a pulley (Fig4a) and its spectrum on a logarithmic scale (Fig4b) and linear scale (Fig 4c) are presented. From the time signal, amplitude modulation can be noticed (period is related to the rotation of a pulley). From Fig 4b one may say that most of energy is located in the 0-1000Hz frequency range. Also a resonance between 2kHz-4kHz is clearly seen. The detailed analysis of the frequency content in the frequency band 0-1kHz (Fig. 4c) may give the conclusion that components in this range are related to the gearbox. It means that the signal from the gearbox is transmitted through the shaft and coupling to the bearing housing. Because the energy of the gear signal in this range is dominating, one may say that the signal generated by the mesh (especially second stage) [4,23] is masking the signal of interest generated by the damaged bearing. Although the bearings are located in the pulley supports – outside the gearbox, signals captured from a bearing housing are significantly corrupted by the signal generated by the last stage of a gearbox. So the local fault/damage detection in bearings used in pulleys is a very similar task to that defined by Randall for helicopter gearboxes, which were investigated in laboratory condition. a) b) c)
Fig. 4. Vibration signal from pulley and its spectrum (Identification of components in spectrum b) On log scale, c) On linear scale) Adaptive filters - Normalised Least Square Mean (NMLS) Algorithm – brief description The Adaptive Filtering (AF) of signals is a well-known technique used in many fields of science [12]. One of most known applications of AF is Adaptive Noise Cancellation introduced by Widrow [19]. From the condition monitoring point of view the concept proposed by Widrow is difficult to use, due to a problem with finding a reference signal. However, if one considers the vibration signal as the mixture of deterministic (with discrete components in the spectrum – in our case mainly related to geared wheels) and stochastic, random (related to wideband excitation caused by fault) signals it is possible to use the block diagram presented in Fig. 5. This method is based on linear prediction theory (deterministic signal may be predicted, random not). Application of AF (called
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Self Adaptive Noise Cancellation (SANC)) to faulty bearing signal extraction (from planetary gearboxes used in helicopters) was proposed by Randall (with colleagues [1,2,13,17]). Lee and White [15] used the same technique for signal pre-processing on diagnostics of gearboxes, but experiments were done in laboratory condition. In this paper the application of SANC for bearings is presented. For the rolling elements bearings of the pulley, the SOI related to the bearing fault/damage is corrupted by an interference, which comes from a two-stage gearbox located nearby, with shafts and a pulley connected by couplings. So, the raw signal may really be considered as the “mixture” of deterministic and random signals. The basic idea of adaptive filtering using the adaptive line enhancement (ALE) scheme is thus to modify filter coefficients (transfer function) according to the current value of an error signal [19] that is the difference between the desired and the estimated signal: e(n) = d (n) − dˆ (n)
(1)
filter updates the filter coefficients at every time instant “n”:
w n+1 = w n + ∆w n
(2)
where ∆w n is a correction factor for the filter coefficients: w n = [w n (0), w n (1),..., w n ( L − 1)]T
(3)
Prediction error Stochastic signal(SOI) ε = d − dˆ
+ Raw vibration: Stochastic and deterministic mixture d
Delay
+ -
Adaptive Filter
Estimated deterministic signal dˆ
Adaptive algorithm Reference signal for filter updating
Fig 5. The idea of ALE/SANC The adaptive algorithm generates this correction factor basing on the input and error signals. For processing the most commonly is used the Least Mean Squares "LMS” algorithm whose update equation is (details one may found for example in [22]): w n+1 = w n + µε n xn
.
(4)
where w n is a vector containing the L coefficients of the Finite impulse response (FIR) filter, x n is a vector containing the L most recent samples of the reference time series and µ is a constant that determines the convergence. One may define the cost function as:
CFn = E{ e n } 2
.
(5)
where e n is defined above adaptive filter prediction error and E{.} denotes the expected value. The idea behind LMS filters is to use the method of steepest descent to find a coefficient vector w n which minimizes a cost function (i.e. prediction error).
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The main drawback of the "pure" LMS algorithm is that it is sensitive to the scaling of its input x(n). This makes it very hard (if not impossible) to choose a learning rate µ that guarantees stability of the algorithm. The normalized least mean squares filter (NLMS) is a modification of the LMS algorithm that solves this problem by normalizing with the power of the input. The NLMS algorithm can be summarized as:
µn =
µ γ + ∑k =0 x 2 ( n − k ) L
.
w n+1 = w n + µ nε n xn
(6) (7)
Parameter selection for Adaptive Filtering of industrial signals For adaptive filters there are a few crucial parameters that need to be set up: filter length N, decorrelation delay ∆ , convergence and forgetting factor λ . Parameters were selected based on advice provided in the paper by Antoni [2] and our own experience. Filter length According to Antoni [2 ], the choice of N should be a compromise between sufficient selectivity of the frequency response and convergence. Selection of N should assure frequency resolution for separating two closely spaced sinusoids in noise i.e filter frequency response should resolve the spacing between the two components and act independently on each of them. Then for two 1 sinusoids separated by B in the normalized frequency domain, the minimum filter length is L = B Antoni [2] has considered a case where a gear signal is likely to show families of closely spaced sinusoids due to slow modulations of the gear-mesh by shaft rotations. In that case the necessary filter length for resolving the modulation effect should therefore be at least as long as the slowest modulation period. Especially for low speed machines filters may have a few thousand coefficients, and that is quite difficult, even for very fast PC. Delay The value of time (decorrelation) delay λ , should be chosen large enough so as to exceed the memory of the noise in the input signal, but not that of the periodic components. Since in theory the correlation time of a periodic signal is infinite, delay λ , could be set as large as possible. However it is impossible due to limited signal duration. Antoni [2] suggested also that practical vibration (deterministic) signals may not be exactly periodic but rather pseudo-periodic—that is with a small distribution in their periodicity. It is the case here that the signal autocorrelation tends to zero, so the delay cannot be too large.
Forgetting factor, Convergence 1 . Value of convergence µ =0,05 L was setting up experimentally. If convergence is fast, quality of results are worse.
Value of forgetting factor is related to filter length as λ = 1 −
Application of Adaptive Filtering to industrial signals from rolling element bearings In this section results for rolling element bearing signals with two types of fault are presented.
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Fig. 6 for a fault in outer race and Fig.7 for a fault in inner race. First it is compared the raw and extracted signals Fig 6a) and b). It is easy to see that the impulsive nature of the SOI is very clear – the signal is spiky with a high value of kurtosis (for the raw signal absolutely not). There is also presentation STFT, Fig. 6c) and envelope analysis Fig.6d). Similar analysis is given in Fig.7 for a fault in inner race. a)
b)
c)
d)
Fig 6 Bearing signal analysis- outer race fault: a) Raw signal, b) extracted SOI, c) STFT of Raw signal, d) envelope and PSD of envelope for SOI a) b)
c)
d)
Fig 7 Bearing signal analysis - inner race fault: a) Raw signal, b) extracted SOI, c) STFT of Raw signal, d) envelope and PSD of envelope for SOI
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After filtering, obtained signal is very clear to interpret. Cyclic (nearly periodic) impulses come from mechanical impacts (contact between damaged surface with other surface in good condition). Further processing and analysis is classical one [26]. Extracted signal is demodulated (amplitude demodulation) and obtained envelope is analysed via Power Spectral Density in frequency domain. Depends on bearings geometry, rotational speed and type of damage (location of damage) one may get characteristic frequencies that are related to periods (cycles) between impacts in time domain. To be sure those impulsive disturbances really exist in raw signal examples of time-frequency representation are also provided. It is well known that impulsive signal in time domain is equivalent to wideband excitation in frequency domain. One may easily see such signature in spectrograms (6c,7c). Location and shape of frequency domain excitation are different for different damages (35.5 } and {1.2-4.5}[kHz] for outer and inner race, respectively.) Summary In this paper, application of adaptive filtering to vibration signals from complex mechanical systems has been presented. The main purpose of AF was to recover the SOI related to cyclic wideband, impulsive excitations, that are usually associated with local faults. It was shown that for signals from pulley bearings, it is possible to extract the SOI, after which diagnosis of the fault becomes much easier and more reliable. As an adaptation algorithm the normalized LMS (NLMS) was used. The benefit of NLMS usage is that this algorithm is a modification of the LMS algorithm that avoids the problem with selection of learning rate µ. NLSM guarantees stability of the algorithm by normalising by the power of the input. The paper shows that in some cases using AF for diagnostic signals received from objects, which work under the condition of varying load can be successful. The purpose of this paper is not to compare algorithms but to apply a better one for industrial signals. Similarly to the other authors, we would like to emphasize that the first step in DSP technique selection is to understand the signal; one should consider the possibility of using simple tools first. The Adaptive Filter is one of the most advanced, blind extraction technique that can be used in online diagnostics. Other approaches (wavelet decomposition, blind cyclo-stationary source separation etc) may provide sometimes better results but they require some a priori knowledge and it makes industrial application difficult. We state that the most important thing is the extraction process; in the next step for spiky signals one may use statistical indicators as detectors (e.g. kurtosis) or classical envelope analysis (for fault recognition/localisation). We want to underline the practical (industry driven research) aspects of this paper. Previously, damage in bearings happened very often because the SOI was seriously masked by the “mesh signal”. Adaptive filtering may be an automatic, kind of blind technique, which has a good chance of being applicable to industrial systems. Acknowledgement This paper was financially supported by State Committee for Scientific Research as a research project 2009-12 References [1] [2] [3] [4]
J. Antoni, R.B. Randall, Differential diagnosis of gear and bearing faults, ASME Journal of Vibration and Acoustics 124/2 (2002) 165–171. J. Antoni, R.B. Randall, Unsupervised noise cancellation for vibration signals. Part I— evaluation of adaptive algorithms, Mechanical Systems and Sign. Proc. 18/1 (2003) 89–101. R. Zimroz, W. Bartelmus, Gearbox condition estimation using cyclo-stationary properties of vibration signal, Key Engineering Materials 413-414 (2009) 471-478. R. Boustany, W. Bartelmus, J. Antoni, R. Zimroz, Application of Spectral Correlation Techniques on Mining Machines Signals: Extraction of Fault Signatures, 2nd World Congress
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