Order Tracking by Square-Root Cubature Kalman Filter with Constraints

Condition monitoring of mechanical systems is an important topic for the industry because it helps to improve the machine maintenance and reduce the total operational cost associated. In that sense, the vibration analysis is an useful tool for failure prevention in rotating machines, and its main challenge is estimating on-line the dynamic behavior due to non-stationary operating conditions. Nevertheless, approaches for estimating time-varying parameters require the shaft speed reference signal, which is not always provided, or are oriented to off-line processing, being not useful on industrial applications. In this paper, a novel Order Tracking (OT) is employed to estimating both the instantaneous frequency (IF) and the spectral component amplitudes, which does not require the shaft speed reference signal and may be computed on-line. In particular, a nonlinear filter (Square-Root Cubature Kalman Filter) is used to estimate the spectral components from the vibration signal that provide the necessary information to detect damage on a machine under time-varying regimes. An optimization problem is proposed, which is based on the frequency constraints to improve the algorithm convergency. To validate the proposed constrained OT scheme, both synthetic and real-world application are considered. The results show that the proposed approach is robust and it successfully estimates the order components and the instantaneous frequency under different operating conditions, capturing the dynamic behavior of the machine.