Abstract

The central idea behind this paper is to propose a means to filter out vibration signals of interest from a fault detection perspective without actually having knowledge about the kinematics of the machine. In other words, this paper investigates blind deconvolution filters that do not require a-priori knowledge about the fault frequencies, e.g. of a bearing or gear. This kind of approach opens the door for the condition monitoring of complex machines where insufficient information is available about the inner components or where replacements have been carried out that changed characteristic frequencies and that were not logged. In recent years there has been a fair amount of renewed interest in fault detection using blind separation or deconvolution techniques [1, 2, 3].
Many look at the time-domain vibration signal itself to maximize a certain indicator on. Examples include maximization of the Jarque–Bera statistic [1] of the time waveform to detect deviation from a normal distribution and the lp/lq-norm [2] to maximize the sparsity of the signal. Recently the degree of second-order cyclostationarity (CS2), a familiar quantity in the mechanical signal processing community, has been used as an objective to be maximized [3]. While maximizing the cyclostationarity of a signal directly influences the envelope spectrum of a signal (since it will try to maximize the peak at the desired cyclic frequency), it still requires a-priori knowledge of the characteristic frequency of interest. This paper however proposes to employ the envelope spectrum directly as a metric for the blind filter. The main assumption of the proposed method is that when a fault occurs, it introduces a CS2 component in the vibration and thus this component shows up in the (squared) envelope spectrum (SES) as a discrete peak at its corresponding fault frequency. This discrete peak correspondingly also increases the sparsity of the SES. To avoid interfering influences of CS1 components, the signal has to be pre-whitened, e.g. through linear prediction filtering, cepstrum editing, etc. This is essential because these interfering components produce high-amplitude discrete peaks in the envelope spectrum skewing the sparsity of the SES. The paper investigates the maximization of the L2/L1-norm, a common measure of sparsity, of the SES for use in the iterative updating procedure of the blind filter.

Keywords
Blind deconvolution, vibrations, sparsity, envelope spectrum, L2=L1-norm, fault detection

References
[1] Obuchowski J, Wylomanska A and Zimroz R 2016 New criteria for adaptive blind deconvolution of vibration
signals from planetary gearbox Advances in Condition Monitoring of Machinery in Non-Stationary
Operations (Springer) pp 111–125
[2] Jia X, Zhao M, Buzza M, Di Y and Lee J 2017 Signal Processing 134 63–69
[3] Buzzoni M, Antoni J and D'Elia G 2018 Journal of Sound and Vibration 432 569–601