Structural state detection using quaternion-based three-channel joint transmissibility

Abstract

This paper presented the use of quaternion-based three-channel joint transmissibility (QTJT) in structural state detection. During the detection process, the time-domain pure quaternion sequences were obtained based on the three dimensional spatial vibration signals from two different testing points. Then QTJTs of the object structure under different states were calculated by discrete quaternion Fourier transform (DQFT). Subsequently, modular vectors of the QTJTs were utilized to construct the state matrix of the object structure and the Karhunen-Loeve Transform (K-LT) was employed to calculate the state feature index vectors. Finally, Euclidean distance between state feature index vectors was obtained, which was considered as the state indicator. An actual experiment was performed on the test platform of ballastless track and the result with 100 percent correct identification was achieved. Combined with the experimental results, the advantages of QTJT comparing to transmissibility based on scalar signals were discussed. The QTJT can be used when the vibration composes from multiple dimensional synchronous vibrations. And more importantly, the QTJT is consistent with its theoretical value in spite of the installation orientation of the sensors