Synchronous median instantaneous power spectrum-gram (SM-IPSgram) : A filter banks decomposition for identifying informative frequency band and a weighting function

Abstract

Over the years, informative frequency band (IFB) identification techniques emerged with the aim of guaranteeing optimal demodulation-band for the diagnostics of rotating machinery. A measured vibration signal from complex rotating machinery, such as a gearbox system, invariantly exhibits heavy and impulsive background noises. As a result, robust IFB identification methods are needed to adapt to these background noises. In this context, a notion of spectral log-mean-exp sparsity measure using exponential function-based quasi-arithmetic mean is coined and the synchronous median instantaneous power spectrum-gram (SM-IPSgram) is proposed as an IFB identification method for gear diagnostics. The spectral log-mean-exp satisfies at least five of six criteria that are necessary for the measurement of sparsity, and its performance is comparable to that of the classical (but powerful) sparsity measures. On the other hand, the SM-IPSgram has some very attractive properties, viz: (i) it is computationally efficient, (ii) extremely robust, (iii) can cope with all kinds of background noises, e.g. strong cyclostationary interferences, Gaussian and non-Gaussian noise, and (iv) it produces a filter banks decomposition to accentuate only the carrier/spectral frequency of the defect, and thus gives much earlier warning of abnormal conditions. Eventually, the experimental and numerical results are reported to corroborate the effectiveness of the SM-IPSgram estimation of the spectral log-mean-exp, and its intrinsic properties are pointed out and compared to other advanced methods in the literature.