Key points are not available for this paper at this time.
The fractal dimension (FD) is an effective indicator to characterize various signals in engineering. However, the FD is nearly twice that of its maximum value when examining high-frequency-dominant signals, such as those in milling chatter. Previous studies in the literature have generally employed signal-pre-processing methods that require a significant amount of time to lower the FD range, thus enabling the distinguishment of different states while disabling online monitoring. A new quantitative method based on the FD within a fixed interval was constructed in this study to address this issue. First, the relationship between the fixed-interval fractal dimension (FFD) and the energy ratio (ER), named the fractal complexity curve (FC-Curve), was established, and the sensitivity region of the FFD was determined. Second, a high-frequency suppression filter (HSF) with a high calculation speed was proposed to suppress the signal’s ER so the FFD could be adjusted within its sensitivity region. Moreover, a fast energy ratio (FER) correlated with the FFD was proposed using the FC-Curve and HSF to quantitatively analyze dominant high-frequency signals. Finally, the proposed method was verified via its application in milling chatter identification. The FER method accomplished signal analysis more quickly than the traditional energy ratio difference and entropy methods, demonstrating its feasibility for online monitoring and chatter suppression in practical engineering applications.
Feng et al. (Wed,) studied this question.