SANC (self adaptive noise cancellation) has been found to be a useful technique for separating gear and bearing signals, to vastly improve the diagnostics of the latter, often masked by the strong gear signals. Gear signals are composed primarily of sinusoidal components phase-locked to shaft speeds (with a long correlation length), whereas bearing signals can be called "pseudo-periodic", with a small random variation of the apparent period because of slip (and thus with a short correlation length). An adaptive filter separates the two components on the basis of the correlation length. In earlier work, rules were given for the optimum selection of the three main SANC parameters, filter order, delay time, and a "forgetting factor" used in the adaptation. These were determined and checked empirically. The current paper uses a different approach based on linear prediction, where the gear signal is assumed to be the predictable part, and the bearing signal the difference between the actual and predicted signal. Using this approach, it is possible to obtain analytical expressions for factors defining the optimisation of the process, and thus put the previous recommendations on a more solid theoretical basis, even though the agreement between them is good. Methods are also suggested to achieve further optimisation of the process, by determining an optimal set of initial filter coefficients from the signal itself, and by using a varying forgetting factor to improve the accuracy of the final separation without greatly extending the analysis time.
