Time-Varying Spectral Kurtosis: Generalization of Spectral Kurtosis for Local Damage Detection in Rotating Machines under Time-Varying Operating Conditions

Abstract

Vibration-based local damage detection in rotating machines (i.e., rolling element bearings) is typically a problem of detecting low-energy cyclic impulsive modulations in the measured signal. This can be challenging as both the amplitude of a single damage-related impulse and the distance between impulses might be changing in time. From the signal processing point of view, this means time varying regarding the the signal-to-noise ratio, location of information in the frequency domain, and loss of periodicity (this remains cyclic but not periodic). One of the many attempted approaches to this problem is filtration using custom filters derived in a data-driven fashion. One of the methods to obtain such filters is a selector approach, where the value of a certain statistic is calculated for individual frequency bands of a signal that results in the magnitude response of a filter. In this approach, each chosen statistic will yield different results, and the obtained filter will be focused on different frequency bands focusing on different behaviors. One of the most popular and powerful selectors is spectral kurtosis as popularized by Antoni, which uses kurtosis as an operational statistic. Unfortunately, after closer inspection, it is easy to notice that, although selectors can significantly enhance the signal, they accumulate a great deal of noise and other background content of signals, which occupies the space (or rather time) in between the impulses. Another disadvantage is that such filters are time-invariant, because, in the principle of their construction, they are not adaptive, and even slight changes in the signal yield suboptimal results either by missing relevant data when the conditions in the signal change (i.e., informative impulses widen in bandwidth), or by accumulating unnecessary noise when the relevant information is not present (in between impulses or in frequency bands that impulses no longer occupy). To address this issue, I propose generalization of the selector approach using the example of spectral kurtosis. This assumes creating a time-varying selector that can be seen as a spatial filter in the time-frequency domain. The time-varying SK (TVSK) is estimated for segments of the signal, and, instead of a vector of SK-based filter coefficients, one obtains a TVSK-based matrix of coefficients that takes into account the time-varying properties of the signal. The obtained structure is then binarized and used as a filter. The presented method is tested using a simulated signal as well as two real-life signals measured on heavy-duty bearings in two different types of machine.

On the Intersection of Signal Processing and Machine Learning: A Use Case-Driven Analysis Approach

“…Accordingly, high SK values can indicate the presence of impulses or bursts, as they cause a deviation from the Gaussian distribution typically observed in stable operating conditions. This is particularly useful in condition monitoring and fault diagnosis of rotating machinery and mechanical systems [244]- [246], where transient vibrations often indicate faults. Additionally, SK is an effective tool for distinguishing between harmonic components-which often manifest as consistent, periodic components-and noise in the signal.…”

Diagnostics of Bolted Joints in Vibrating Screens Based on a Multi-Body Dynamical Model

“…The upper deck and lower levels of sieves are subjected to blinding, which induces screen overloading and technological process interruption. Also, large falling fragments of material generate force impacts with significant amplitude; thus, those disturbances which are stochastic by nature should be considered to prevent false alarms in fault diagnostic procedures [4][5][6][7][8]. The impulsive noise cancellation method for copper ore crusher vibration signal enhancement is proposed in [9].…”

Modeling Impulsive Ball Mill Forces Effects on the Dynamic Behavior of a Single-Stage Gearbox

“…Jacek w et al [16] proposed to use nonnegative matrix factorization of spectrogram for separation cyclic and noncyclic impulsive components from a hammer crusher. Jacek w. [17] proposed the time-varying spectral kurtosis (TVSK) as a means of spectral kurtosis adaptation for frequency-band selection of bearing damage signals under variable operating conditions. In a corresponding trend, Hebda-Sobkowicz et al [18] presented a new approach to local bearing damage detection in the presence of non-Gaussian impulsive noise based on conditional variance statistics to identify cyclic and noncyclic impulses.…”