The Fourier spectral Poincare map method for damage detection via single type of measurement

This paper deals with the problem of vibration health monitoring based on Poincare map method, which has been numerically and experimentally verified as an effective tool in damage assessment. We aim to introduce the Fourier-spectral derivative method into the Poincare maps method. Thereafter, a damage detection method via single type of measurement is developed. The proposed improvement focuses on the reconstruction of state space via single type observation, namely only deflection responses are obtained and the velocity and acceleration responses are estimated by numerical derives. In order to address the unstable problem of numerical derivatives, the Fourier-spectral derivative method is introduced into calculations and hence the robust estimations of velocity and acceleration responses are obtained to reconstruct the corresponding Poincare maps in state space. The proposed method is validated by numerical and experimental investigations.