Study on rail fastener failure testing based on fractal theory

Huijian Zhang1, Qiang Liu2

Beijing Municipal Institute of Labour Protection, Beijing, China

1Corresponding author


Received 19 September 2017; accepted 26 September 2017



Abstract. The residual vibration of steel rail is rich in the mechanical properties, which include the constraint, that was, the degree of tightness of the fastener. The aim of this research is to characterize the tightness of rail fastener. A fractal analysis procedure based on 1-D curve length calculation is proposed, which applies a length unit to cover fastening the behavior of fasteners. Using the rail vibration data under periodic pulse excitation measured by a track fastener inspection vehicle, this method can derive the fractal dimension of fastener tightness directly
[1, 2)). Furthermore, 1-D curve length method is also introduced into multi-fractal spectrum analysis for investigating fine scale information. The statistical analysis demonstrates that, fractal dimension , , and multi-fractal parameters , can reflect the change process of the tightness of rail fasteners effectively. Therefore, it shows potential to use the fractal parameters of the rail vibration signal to characterize the tightness of the fastener.

Keywords: fractal, rail fastener, unfastening.


[1]        Huijuan Z., Qiang L., Wencheng H. Study on rail fastener failure testing with pulse stimulation and synchronized detection method. Noise and Vibration Control. Vol. 35, Issue 1, 2015, p. 349‑353.

[2]        Qiang L., Huijuan Z., Wencheng H., Ruixiang S. Identification of loose rail fasteners by sound signals. Inter-Noise, 2017.

[3]        Jianqiang Q., Xiangyu K., Shaolin H., et al. Performance comparison of methods for estimating fractal dimension of time series. Computer Engineering and Applications, Vol. 52, Issue 22, 2016, p. 33‑38.

[4]        Esteller R., Vachtsevanos G., Echauz J., et al. A comparison of waveform fractal dimension algorithms. IEEE Transactions of Circuits and Systems I: Fundamental Theory and Applications, Vol. 48, Issue 2, 2001, p. 177‑183.

[5]        Grassberger P., Procaccia I. Characterization of stranger attractors. Physical Review Letters, Vol. 50, Issue 5, 1983, p. 346‑349.

[6]        Grassberger P., Procaccia I. Measuring the strangeness of strange attractors. Physica D: Nonlinear henomena, Vol. 9, Issue 2, 1983, p. 189‑208.

[7]        Kai Y., Rencheng Z., Jianhong Y., et al. Series Arc fault diagnostic method based on fractal dimension and support vector machine. Transactions of China Electrotechnical Society, 2016.

[8]        Xia S., Ziqin W., Yun H. Fractal Principle and Application. China University of Science and Technology Press, 2006, p. 53‑88.

[9]        Suang L., Jing Y. Research on DEM Data Uncertainty Based on Fractal. Science Press, 2007.

[10]     Xie Heping, Wang Jinan Multi-fractal behaviors of fracture surfaces in rocks. Acta Mechanica Sinica, Vol. 30, Issue 3, 1998, p. 314‑320.

[11]     Raghavendra B. S., Narayana Dutt D. A note on fractal dimensions of biomedical waveforms. Computers in Biology and Medicine, Vol. 3, 2009, p. 1006‑1012.

[12]     Castiglioni P. What is wrong in Katz's method? Comments on: A note on fractal dimensions of biomedical waveforms. Computers in Biology and Medicine, Vol. 40, 2010, p. 950‑952.

[13]     Zhu W., Liang S., Wei Y., et al. Saliency optimization from robust background detection. Proceedings of IEEE Conference on Computer Vision and Pattern Recognition, 2014, p. 2814‑2821.

[14]     Borji A., Cheng M. M., Jiang H., et al. Salient object detection: a benchmark. IEEE Transactions on Image Processing, Vol. 24, Issue 12, 2015, p. 706‑5722.

Cite this article

Zhang Huijian, Liu Qiang Study on rail fastener failure testing based on fractal theory. Vibroengineering PROCEDIA, Vol. 14, 2017, p. 208‑213.


JVE International Ltd. Vibroengineering PROCEDIA. Oct 2017, Vol. 14. ISSN 2345-0533