Why EMD and similar decompositions are of little benefit for bearing diagnostics. (1st June 2023) - Randall, Robert B.; Antoni, Jérôme
Abstract: Empirical mode decomposition (EMD) is a way of decomposing complex signals into a sum of "mono-components", i.e. intrinsic mode functions (IMFs), each of which can be considered as a single carrier frequency, modulated in both amplitude and phase/frequency (an analytic signal), so that both amplitude and phase remain continuous and differentiable, the latter to instantaneous frequency. In many cases, the instantaneous frequency and amplitude could be valuable diagnostic features, for example with gear vibrations. Many authors have suggested applying this technique to the diagnostics of rolling element bearings (REBs), but this paper shows that REB signals intrinsically do not have such properties, except perhaps in short bursts, so that the excessive computation time trying to ensure continuous phase is wasted. Much more appropriate methods exist to extract the optimum envelope signal, which contains the desired diagnostic information, based on more relevant criteria. As its name suggests, the EMD process is empirical, with no analytical solution, so that different results can be obtained from different segments of the same signal, partly because of different noise content. Another way of obtaining IMFs is by using variational mode decomposition (VMD), which does have an analytical solution, making it less sensitive to noise, but still assumes that the signal can be validly decomposed into mono-components, which is not the case for bearing signals. The EMD process has two additional problems which make difficult its use for REB signals; (1) end effects, which usually mean that many, perhaps a majority, of IMFs are required purely to compensate for them, and which cannot be truncated for signals consisting of short bursts with sections of noise between them; and (2) mode mixing, meaning that repeatable results cannot be guaranteed, even for valid mono-components, let alone REB signals which are of a stochastic nature. The paper explains in detail why REB signals cannot be validly decomposed by EMD and similar methods, to give sub-components with properties directly related to bearing faults, even though many existing papers describe how the IMFs found by the EMD process might be selected or re-combined to have properties of interest in bearing diagnostics. In particular, the paper shows that the equivalent bandpass filters given by EMD have much poorer selectivity than most alternative filters. The paper uses many simulated and measured examples and demonstrations, to discuss these claims, including a number based on results from already published papers.