1564. Structural state detection using quaternion‑based three‑channel joint transmissibility

Tongqun Ren1, Liang He2, Dazhi Wang3, Junsheng Liang4, Meiling Hui5

1, 4Key Laboratory for Precision & Non-traditional Machining of the Ministry of Education,
Dalian University of Technology, Dalian, 116024, China

1, 2, 3, 4, 5Key Laboratory for Micro/Nano Technology and System of Liao Ning Province,
Dalian University of Technology, Dalian, 116024, China

3Corresponding author

E-mail: 1ren_tq@dlut.edu.cn, 2hll8905@163.com, 3d.wang@dlut.edu.cn, 4jsliang@dlut.edu.cn, 5hml8585660@sina.com

(Received 28 July 2014; received in revised form 19 November 2014; accepted 20 January 2015)

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.

Keywords: quaternion-based three-channel joint transmissibility, state detection, quaternion sequences, Karhunen-Loeve transform.


[1]        Doebling Scott W., Farrar Chareles R., Prime Michael B. A summary review of vibration-based damage identification methods. The Shock and Vibration Digest, Vol. 30, Issue 2, 1998, p. 91‑105.

[2]        Yan Y. J., Cheng L., Wu Z. Y., Yam L. H. Development in vibration-based structural damage detection technique. Mechanical Systems and Signal Processing, Vol. 21, Issue 5, 2007, p. 2198‑2211.

[3]        Fan W., Qiao P. Z. Vibration-based damage identification methods: a review and comparative study. Structural Health Monitoring, Vol. 10, Issue 1, 2011, p. 83‑111.

[4]        Duan Z. D., Yan G. R., Ou J. P., Spencer B. F. Damage localization in ambient vibration by constructing proportional flexibility matrix. Journal of Sound and Vibration, Vol. 284, 2005, p. 455‑466.

[5]        Parloo E., Verboven P., Guillaume P., van Overmeire M. Autonomous structural health monitoring part II: vibration-based in-operation damage assessment. Mechanical Systems and Signal Processing, Vol. 16, Issue 4, 2002, p. 659‑675.

[6]        Lu Y., Gao F. A novel time-domain auto-regressive model for structural damage diagnosis. Journal of Sound and Vibration, Vol. 283, 2005, p. 1031‑1049.

[7]        Zhong S. C., Oyadiji S. O., Ding K. Response-only method for damage detection of beam-like structures using high accuracy frequencies with auxiliary mass spatial probing. Journal of Sound and Vibration, Vol. 311, 2008, p. 1075‑1099.

[8]        Zhang H., Schulz M. J., Ferguson F. Structure health monitoring using transmittance functions. Mechanical Systems and Signal Processing, Vol. 13, Issue 5, 1999, p. 765‑787.

[9]        Chen Q., Chan Y. W., Worden K. Structural fault diagnosis and isolation using neural networks based on response-only data. Computers and Structures, Vol. 81, 2003, p. 2165‑2172.

[10]     Mao Z., Todd M. A structural transmissibility measurements-based approach for system damage detection. Proceedings of SPIE The International Society for Optical Engineering, Vol. 7650, 2010, p. 76500G.

[11]     Lang Z. Q., Park G., Farrar C. R., Todd M. D., Mao Z., Zhao L., Worden K. Transmissibility of non‑linear output frequency response functions with application in detection and location of damage in MDOF structural systems. International Journal of Non-Linear Mechanics, Vol. 46, 2011, p. 841‑853.

[12]     Rehman N., Mandic D. P. Empirical mode decomposition for trivariate signals. IEEE Transactions on Signal Processing, Vol. 58, Issue 3, 2010, p. 1059‑1068.

[13]     Yamamoto H., Aoshima N. 3D vibration-scope with quaternion processing. SICE Annual Conference in Fukui, 2003, p. 2373-2376.

[14]     Tong J. Feature extraction for vibration signal of asynchronous motor based on quaternion K-L transform. International Conference on Electrical and Control Engineering, 2010, p. 1006‑1009.

[15]     Ell T. A. Hypercomplex Spectral Transforms. Ph.D. dissertation, University of Minnesota, Minneapolis, 1992.

[16]     Ell T. A. Quaternion-Fourier transforms for analysis of two-dimensional linear time-invariant partial-differential systems. Proceedings of 32nd IEEE Conference on Decision and Control, San Antonio, TX, Vols. 1‑4, 1993, p. 1830‑1841.

[17]     Ell T. A., Sangwine S. J. Hypercomplex fourier transforms of color images. IEEE Transactions on Image Processing, Vol. 16, Issue l, 2007, p. 22‑35.

[18]     Moxey C. E., Sangwine S. J., Ell T. A. Hypercomplex correlation techniques for vector images. IEEE Transactions on Signal Processing, Vol. 51, Issue 7, 2003, p. 1941‑1953.

Cite this article

Ren Tongqun, He Liang, Wang Dazhi, Liang Junsheng, Hui Meiling Structural state detection using quaternion‑based three‑channel joint transmissibility. Journal of Vibroengineering, Vol. 17, Issue 2, 2015, p. 928‑938.


JVE International Ltd. Journal of Vibroengineering. Mar 2015, Volume 17, Issue 2. ISSN 1392-8716