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

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.

[1]  Stephen J. Sangwine,et al.  Hypercomplex Fourier Transforms of Color Images , 2001, IEEE Transactions on Image Processing.

[2]  H. Yamamoto,et al.  3D vibration-scope with quaternion processing , 2003, SICE 2003 Annual Conference (IEEE Cat. No.03TH8734).

[3]  A. S. Naser,et al.  Structural Health Monitoring Using Transmittance Functions , 1999 .

[4]  Pizhong Qiao,et al.  Vibration-based Damage Identification Methods: A Review and Comparative Study , 2011 .

[5]  Charles R. Farrar,et al.  A summary review of vibration-based damage identification methods , 1998 .

[6]  Shuncong Zhong,et al.  Response-only method for damage detection of beam-like structures using high accuracy frequencies with auxiliary mass spatial probing , 2008 .

[7]  Charles R. Farrar,et al.  Transmissibility of non-linear output frequency response functions with application in detection and location of damage in MDOF structural systems , 2011 .

[8]  T. Ell,et al.  Quaternion-Fourier transforms for analysis of two-dimensional linear time-invariant partial differential systems , 1993, Proceedings of 32nd IEEE Conference on Decision and Control.

[9]  Guirong Yan,et al.  Damage localization in ambient vibration by constructing proportional flexibility matrix , 2003 .

[10]  E. Parloo,et al.  AUTONOMOUS STRUCTURAL HEALTH MONITORING—PART II: VIBRATION-BASED IN-OPERATION DAMAGE ASSESSMENT , 2002 .

[11]  T. Ell.  Hypercomplex spectral transformations , 1992 .

[12]  Keith Worden,et al.  Structural fault diagnosis and isolation using neural networks based on response-only data , 2003 .

[13]  Feng Gao,et al.  A novel time-domain auto-regressive model for structural damage diagnosis , 2005 .

[14]  Zhu Mao,et al.  A structural transmissibility measurements-based approach for system damage detection , 2010, Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[15]  Danilo P. Mandic,et al.  Empirical Mode Decomposition for Trivariate Signals , 2010, IEEE Transactions on Signal Processing.

[16]  Y. Yana,et al.  Development in vibration-based structural damage detection technique , 2007 .

[17]  Tong Jia.  Feature Extraction for Vibration Signal of Asynchronous Motor Based on Quaternion K-L Transform , 2010, 2010 International Conference on Electrical and Control Engineering.