Fractal dimension in the diagnosis of rotating machinery – based on numerical analysis

  • Łukasz Breńkacz
  • Jędrzej Blaut
A fractal dimension is a ratio providing a statistical index of complexity comparing how detail in a pattern changes with the scale at which it is measured. Several types of fractal dimensions can be measured theoretically and empirically. Self-similarity is understood as symmetry concerning the scale, which means that to a given structure (usually fractal) in space there is a similar section of this structure in magnification. Fractal dimensions are used to characterize a broad spectrum of objects ranging from the abstract to practical phenomena, including turbulence, river networks, urban growth, human physiology, medicine, and market trends. The fractal dimension is increasingly appearing in technical applications. An example of such an application would be the use of the fractal dimension to identify the similarity of the surface. It was shown in previous paper that this measure is sensitive to the structure of the surface. This article attempts to implement the fractal dimension as a diagnostic factor for the first time. The assumptions are that with a stable operating rotating machinery, the vibration signal recorded by, for example, eddy current or laser sensors will be repeatable. In the case of damage to the structure, e.g., related to damage to the bearings or clutch, the vibration signal will change. After comparing these signals, we will get a different value of the fractal dimension than in the case of the base signal. The ability to perform quick calculations to compare the base signal and the one after changes is invaluable and makes it no longer necessary to "visually" compare signals. Assessment using the fractal dimension of vibration signals is fast and gives unprecedented diagnostic possibilities.
Type of Publication:
Proceedings of 7th International Congress on Technical Diagnostics
Radom, Poland
Kazimierz Pulaski University of Technology and Humanities in Radom