Bearing Signal Enhancement Using Taylor-<inline-formula> <tex-math notation="LaTeX">$H_{\infty}$ </tex-math> </inline-formula> Estimator Under Variable Speed Condition

Abstract

This paper presents a new approach to enhance a random bearing vibration signal (repetitive character with a random part) corrupted by an oscillatory gear vibration signal. This approach, called the Taylor- $H_{\infty }$ (TH) estimator, is proposed in a variable speed condition. The latter is designed using the mathematical modeling of the raw signal in the state space. It is used to remove the oscillatory signal from the raw signal. The obtained residual signal is the enhanced signal of the bearing contribution. Different from the Vold–Kalman (VK) estimator, which results from the minimization of the mean squared error, the proposed method is based on the minimax optimization. The minimax approach for the TH estimator leads to the minimization of the estimation error for the worst possible amplification of the random signals. No prior knowledge about the statistical properties of the random signals is required. The proposed approach is assessed using both synthetic and experimental nonstationary vibration data. In addition, the squared envelope spectrum of the residual signal is analyzed to diagnose the bearings state. This paper shows the