Online three-point frequency tracking method for structural health monitoring

This paper presents and evaluates in detail a harmonics tracking method (HTM) for tracking the instantaneous frequency and amplitude of a vibration signal by processing only three most recent data points. Teager-Kaiser algorithm (TKA) is a popular 4-point method for online frequency tracking, but its accuracy is easily destroyed by measurement noise due to the use of finite difference. Moreover, because a signal is assumed to be a pure harmonic in TKA, any moving average in the signal can destroy the accuracy of TKA. On the other hand, HTM uses a constant and a pair of harmonics to fit three recent data points and estimate the instantaneous frequency and amplitude, and it dramatically reduces the influence of any moving average. Moreover, noise filtering is an implicit capability of HTM if more than three points are processed, and this capability increases with the number of processed data points. However, HTM depends on TKA to provide the first frequency estimation in order to start online tracking. To compare HTM and TKA and evaluate the accuracy of HTM, Hilbert-Huang transform (HHT) is used to extract accurate time-varying frequency and amplitude by processing the whole data set without assuming the signal to be harmonic. Frequency and amplitude tracking of different amplitude- and/or frequency-modulated signals, nonlinear dynamic signals, and transient signals due to damage propagation is studied. Results show that HTM is more accurate, robust, and versatile than TKA for online frequency tracking. Moreover, the frequencies and amplitudes tracked by HTM have about the same accuracy as those extracted by HHT but without the edge effect that HHT suffers from. Hence, HTM is valuable for structural health monitoring by online frequency tracking.