Quaternion analysis of beam multi-type vibration data for damage detection

In this paper two damage sensitive features (DSF), one baseline dependent (DSF1) and the other one baseline free (DSF2), are proposed based on the Quaternion analysis of the phase trajectory of a beam vibration due to a moving mass. To that end, new Quaternions are constructed with the displacement, velocity and acceleration of the beam mid-span as the elements of the Quaternion vectors. The new DSFs are obtained based on the concept of the angular velocity of a curve in 3D space characterised by a Quaternion. For the baseline dependent case, the proposed DSF1 needs to be calculated for both intact and damaged beam subjected to the same experiment, whereas in the baseline free case DSF2 data from only the damaged beam are sufficient for damage detection. The performance of the proposed DSFs is compared against another technique introduced in the literature through several examples and Monte Carlo simulations. Both road roughness and 10% measurement noise effects are taken into account in performance evaluation of the proposed DSFs. The results show that the proposed DSFs are more successful in locating damage on a simply supported beam.