Fractal box dimension of discrete vibration signals: Improved algorithm and applications

Fractal Box Dimension (BD), which can represent self-similarity and complexity of nonstationary vibration signal, provides a new tool for fault diagnosis of mechanical equipment. In this paper, we first analyze the shortcoming of conventional method for calculating BD of discrete vibration signal. Then we propose an improved algorithm of BD which include two key technologies. First, square box is replaced with rectangle box due to the biscale characteristic of vibration signal. Second, an empirical formula is derived for choosing scale-invariant region of periodic or quasi-periodic signals. Experimental results show that the improved algorithm of BD is simple and effective. As a successful application, BD is used to detect looseness fault in bearing bushing of turbo-generator set.