Adaptive feature selection for rolling bearing condition monitoring Stefan Goreczka and Jens Strackeljan Otto-von-Guericke-Universität Magdeburg, Fakultät für Maschinenbau Institut für Mechanik, Universitätsplatz, 31 Magdeburg e-mail: stefan.goreczka@ovgu.de e-mail: jens.strackeljan@ovgu.de Abstract From today s point of view rolling element bearing diagnostic techniques based on vibration analysis seem to be consolidated. Several signal processing methods for noise reduction and aggregation of fault information such as frequency and wavelet filtering were reviewed in detail for the use in condition monitoring. There are many other techniques with more or less credible effect on the observed vibration signal. The adaption of a diagnostic system in the data processing part is time consuming and static regarding the dynamic of changing conditions in and outside the bearing. Choosing a feature selection strategy regarding these aspects is supposed to have a high potential solving problems of this domain. Some current examination results were discussed in this paper. Keywords: rolling element bearing, vibration analysis, condition monitoring, signal processing, feature selection 1 Introduction There are a few access difficulties starting with condition monitoring (CM) in a real world application due to the complex nature of such techniques. Referring to this, the main questions are how to solve a new monitoring and classification task without beginning at the basics of CM theory concerning the measured variable, signal processing, feature selection and classification techniques. Where to start getting good results having only few resources of man power and research time or little access to research knowledge in a company. In such cases there is a need of any formalized technique and
in this way simplified use in multiple CM scenarios. But also ambitions of automation in asset management applications could benefit from such formalization. Problem The adaptive feature concept is here studied in an application on a pump. The rotor could be operated in a vertical and horizontal position. Depending from this shaft position the rotor weight leads to different loads in the bearing. In addition a rotor unbalance could occur. For the present investigations two different levels of unbalance were adjusted. They indicate a lower and upper limitation of unbalance regarding the instruction manual. The bearing damage is characterized by increased roughness along the whole circumference of the raceway placed at different axial positions depending on the operating points (Figure 1). Figure 1. Outer ring defect (left) and inner ring defect (right) The vibration of the rotor and bearing unit was measured by an acceleration sensor which was mounted on the bearing housing. Recording samples with a acquisition rate of 1 khz at the rotational frequency of Hz lead to an acceleration signal without a clear impact structure.
-.....1 1 3 frequency [Hz] x 1 -.....1 1 3 frequency [Hz] x 1 Figure. Acceleration signals and frequency spectra for a new bearing (left) and a defect bearing (right) obtained from the horizontal shaft in maximum unbalance -.....1 1 3 frequency [Hz] x 1 -.....1 1 3 frequency [Hz] x 1 Figure 3. Acceleration signals and frequency spectra for a new bearing (left) and a defect bearing (right) obtained from the horizontal shaft in minimum unbalance -.....1 1 3 frequency [Hz] x 1 -.....1 1 3 frequency [Hz] x 1 Figure. Acceleration signals and frequency spectra for a new bearing (left) and a defect bearing (right) obtained from the vertical shaft in minimum unbalance 3
-.....1 1 3 frequency [Hz] x 1 -.....1 1 3 frequency [Hz] x 1 Figure. Acceleration signals and frequency spectra for a new bearing (left) and a defect bearing (right) obtained from the vertical shaft in minimum unbalance Regarding the s (Figures -) and the scatter plot (Figure ) the dependence of the shaft position and the unbalance on the vibration level is clearly visible even in a high frequency range. The effect of the unbalance and the related load variation could not be seperated by a high pass filter. In consequence the operation mode (shaft position) and the severity of unbalance is needed as an input to classify all samples in a correct way. The main objective of the present concept is to develop a strategy to classify these samples with least possible information and calculations for efficient use. RMS of acceleration [m/s ] 1 NL maxu hor NL maxu vert NL minu hor NL minu vert SL maxu hor SL maxu vert SL minu hor SL minu vert Amplitude of velocity [mm/s] Figure. Scatter plot of the features: RMS of acceleration and the amplitude of velocity at Hz as unbalance criteria (NL - new bearing, SL - damaged bearing, maxu high unbalance, minu low unbalance, hor horizontal, ver - vertical)
3 Adaptive feature concept The adaptive quality of the features refers to processes of the operating machine and the monitoring system. Good experiences were made by choosing an evaluation method comparing understandable features calculated also after applying some credible signal processing techniques to the vibration signal. Using hardly understandable features make it difficult to perform any plausibility check during the work. For evaluation best to use are e.g. cross validation of classification results or other statistical performance indicators concerning the diversity of samples. Statistical moments such as mean, variance and kurtosis are easy to calculate and interpret. The same applies to the classical values RMS and Crest Factor. Several signal processing techniques are approved in CM. In most cases some frequency or wavelet filtering (1,) or even higher derivations will improve the diagnostic (3,). For extreme cases there are more detailed analyses of the investigating the peaks (,,7) and their surroundings. For the problem introduced at the beginning, the adaptive approach starts with a process of feature selection. The imperfect bearing race generates a stochastic excitation of different eigenfrequencies. The concept should be able to find optimal frequency ranges for separating the two bearing condition states. A practical frequency bandwidth has to be tolerant against little shift in these frequencies or in slight changes in the signal transmission path (frequency and damping). In this application or 1 khz seems to be a suited bandwidth and is used performing signal analysis while comparing the behaviour of features. For evaluation purposes, the distances of the mean of different feature samples were referred to their variation. Actually, this value is dimensionless, x defect - x defect int act int act, (1) and has to be increasing at increasing separability of monitoring indicators using any classification technique.
1 1 1 Crest RMS variance kurtosis 1 Crest RMS variance kurtosis Figure 7. Evaluation criteria of features as a function of frequency bandwidth in the horizontal shaft: maximum unbalance (left) and minimum unbalance (right) 1 1 1 Crest RMS variance kurtosis 1 1 1 Crest RMS variance kurtosis Figure. Evaluation criteria of features as a function of frequency bandwidth in the vertical shaft: maximum unbalance (left) and minimum unbalance (right) As seen in Figures 7 and the most relevant features are variance and RMS because no typical small area defect fault structure is in the acceleration signal. Calculating the kurtosis searching of any non-normality in the signal is senseless regarding the stochastic structure of the raceway surface (Figure 1). The excitation of the system, when the rolling elements pass the raceway deformation, is still normally distributed. This probabilistic nature also makes the vibration measurement normally distributed. There is no high frequency impact-like structure useable for deterministic analysis in this case (Figures 9 and 1).
3 1 1 3 frequency [Hz] Figure 9. Envelope of a defect bearing (lowpass filtering khz) For the ball passing frequencies (for this bearing SKF 3 at 31 rpm: BPFI = 31 Hz, BPFO = 1 Hz, BSF = 13 Hz) there is only the shaft rotational frequency Hz visible in the envelope (Figure 9). The spectral kurtosis factor () also reveals no indication of peaks in the vibration signal usable for condition monitoring tasks (Figure 1). The spectral kurtosis is a statistical tool which can indicate the presence of series of transients and their locations in the frequency domain. The evaluation of the variance as seen in Figure could be improved equivalent by filtering and higher derivatives (Figure 11). Doing so higher derivations as used by Lahdelma (9) in combination with kurtosis could be used together with other features and CM scenarios in the same manner. The positive effect on the separability of fault states was observed anyway, although the signal included high level noise caused by wide area raceway roughness. 7
Kurtogramm spectral kurtosis 1-1 1 x 1 Figure 1. Spectral kurtosis of acceleration obtained from a damaged bearing 1 1 1 Figure 11. Evaluation criteria of features as a function of frequency bandwidth: physical value (left), and only physical value without filtering (right) 3 frequency [Hz] nd derivative of nd acceleration deriv. acceleration velocity path displacement 1 1 path displacement velocity 1 1 window length [ n ] nd deriv. nd derivative ofacceleration acceleration The effect of the signal processing procedure on the features of the fault states and the associated fault free states is shown in Figure 1. In the optimum the distance of the feature clouds are greater and the distribution of the features itself is lower.
RMS of acceleration [m/s ] 1 1 NL maxu hor NL maxu vert NL minu hor NL minu vert SL maxu hor SL maxu vert SL minu hor SL minu vert RMS of acceleration [m/s ] 1 1 Amplitude of velocity [mm/s] Amplitude of velocity [mm/s] Figure 1. Scatter plot of feature obtained for the unbalance cases at bandpass frequencies 1-kHz (left) and 3-kHz (right), rotational frequency is Hz Classification concept On the bases of the selected features a classification without any faults using the test data set is possible if the classify has the two classes: a) fault free state and b) one faulty state regardless of the shaft position or unbalance information (concept 1). But the classification results could be improved significantly when other process information is considered in addition (Figures 13 and 1). A decision tree can provide reliable results during the work life of the classification system (1), since the physics of the bearing part contact is not known exactly (Figure 1). shaft position vertical horizontal low adaptive feature unbalance high adaptive feature Figure 13. Classification concept for a bearing fault 9
shaft position vertical horizontal unbalance unbalance low high low high adaptive feature Ad. feature adaptive feature adaptive feature Figure 1. Classification concept 3 for a bearing fault 1 1 1 concept 1 concept concept 3 1 1 path displacement velocity concept 3 concept acceleration concept 1 nd derivative deriv. of acceleration Figure 1. Evaluation criteria of features as a function of frequency bandwith and classification concept (left) and as a function of signal and classification concept (right) Conclusion It was shown that hardly any monitoring task could be described as a process of sequentially executable steps. The challenging part is the decision making and reaction on changes. An automation potential of such procedure lies in the formalization of approved CM methods using in addition data mining and furthermore knowledge discovery applications. 1
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