Bayesian Estimation of Instantaneous Speed for Rotating Machinery Fault Diagnosis

The instantaneous speed (IS), i.e., instantaneous frequency, is an important feature to exploit the time-frequency characteristic of nonstationary signals. The IS estimation is widely used in various fields of signal processing. The IS estimation can also be regarded as a useful tool for rotating machinery fault diagnosis under nonstationary conditions. However, most of the current IS estimation methods improve the IS estimation accuracy at the cost of increasing the computational time. In this article, a method based on Bayesian estimation is proposed for estimating the fast time-varying IS in a computationally efficient manner. A linear chirp signal is modeled within the Bayesian framework, where the likelihood function and the prior probability function of the IS are derived. The past information is used as the prior to guarantee the continuity of the IS ridge, which improves the robustness against the noise or other interferences. The maximum a posteriori rule is used to estimate the IS. The proposed method not only obtains a high IS estimation accuracy for the signal whose IS is fast time-varying and broadband but also improves the computational efficiency. A simulated signal and two experimental signals are considered for investigating the performance of the proposed method.