Parameterized Domain Mapping for Order Tracking of Rotating Machinery

Because of the periodicity of vibration signals from the cyclic motion of rotating machinery, many spectrum-based methods are widely applied. However, frequency distortion often occurs under nonstationary conditions, which weakens the effectiveness of spectrum-based methods. Order tracking can overcome the frequency distortion problem, but the instantaneous angular speed is hard to detect, especially under strong noise or with close-spaced frequencies. In this article, we map the signal into a new domain called the pseudo-time domain to eliminate the nonstationarity based on the mechanism of rotating machinery. A parameterized domain mapping function (PDMF) is used to represent the relationship between the time and pseudo-time domains. Instead of conducting order tracking after detecting the instantaneous angular speed, we directly optimize the parameter set of the PDMF to construct an appropriate pseudo-time domain. A new spectrum concentration indicator considering the continuity of the spectrum is built as the optimization objective. The Legendre polynomial, which shows good approximation property, is applied as the general kernel function of PDMF. Numerical and experimental verification shows a good antinoise performance and the ability to deal with complex and close-spaced frequencies under speed variation or speed fluctuation conditions.