Sanc obtains the reference signal by delaying the original signal, extracts the periodic signal component by autocorrelation analysis, and finally subtracts the extracted periodic signal from the original signal to obtain the random signal in the original signal, which realizes the separation of periodic signal and random signal. Forvibration, the gear vibration signal can be regarded as periodic signal. In theory, the original signal is still the same periodic signal after autocorrelation calculation. However, due to the random slip of gearbox bearing, its vibration is random, and it will be attenuated quickly after autocorrelation analysis. According to the above properties, the separation can be realized.
The key of Sanc algorithm is to design a suitable adaptive filter, among which the least mean square (LMS) algorithm is more efficient, so Sanc algorithm based on LMS convergence criterion is most widely used. The basic idea is to minimize the error to make the periodic signal after autocorrelation analysis approach the original signal
Where: X (n) is the original signal; X ^ (n) is the periodic signal; E (n) is the random signal; J is the mean square error; w (n) is the L + 1 weight coefficient of the filter. The model is modified by automatically adjusting the weight coefficient of the filter to minimize the error.