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The paper investigates the possibility of decomposing vibration signals into deterministic and nondeterministic parts, based on the Wold theorem. A short description of the theory of adaptive filters is presented. When an adaptive filter uses the delayed version of the input signal as the reference signal, it is possible to divide the signal into a deterministic (gear and shaft related) part and a nondeterministic (noise and rolling bearings) part. The idea of the self-adaptive filter (in the literature referred to as SANC or ALE) is presented and its most important features are discussed. The flowchart of the Matlab-based SANC algorithm is also presented. In practice, bearing fault signals are in fact nondeterministic components, due to a little jitter in their fundamental period. This phenomenon is illustrated using a simple example. The paper proposes a simulation of a signal containing deterministic and nondeterministic components. The self-adaptive filter is then applied-first to the simulated data. Next, the filter is applied to a real vibration signal from a wind turbine with an outer race fault. The necessity of resampling the real signal is discussed. The signal from an actual source has a more complex structure and contains a significant noise component, which requires additional demodulation of the decomposed signal. For both types of signals the proposed SANC filter shows a very good ability to decompose the signal.

Decomposition of Vibration Signals into Deterministic and Nondeterministic Components and its Capabilities of Fault Detection and Identification