Roughness Scaling Extraction Accelerated by Dichotomy-Binary Strategy and Its Application to Milling Vibration Signal

Abstract

Fractal algorithms for signal analysis are developed from geometric fractals and can be used to describe various complex signals in nature. A roughness scaling extraction algorithm with first-order flattening (RSE-f1) was shown in our previous studies to have a high accuracy, strong noise resistance, and a unique capacity to recognize the complexity of non-fractals that are common in signals. In this study, its disadvantage of a long calculation duration was addressed by using a dichotomy-binary strategy. The accelerated RSE-f1 algorithm (A-RSE-f1) retains the three above-mentioned advantages of the original algorithm according to theoretical analysis and artificial signal testing, while its calculation speed is significantly accelerated by 13 fold, which also makes it faster than the typical Higuchi algorithm. Afterwards, the vibration signals of the milling process are analyzed using the A-RSE-f1 algorithm, demonstrating the ability to distinguish different machining statuses (idle, stable, and chatter) effectively. The results of this study demonstrate that the RSE algorithm has been improved to meet the requirements of practical engineering with both a fast speed and a high performance.

Chatter detection in milling processes—a review on signal processing and condition classification

“…Fractal dimension (FD) is also an employed feature to measure the complexity of a pattern and the intrinsic properties of a signal, although fractal properties can also be detected by the CWT [38]. Zhuo et al [354] employed the FD in the time and frequency domains, while Chen et al [180] and Liu et al [355] evaluated multifractal-based features and Feng et al [356] utilized a dichotomy-binary strategy to reduce the time consumption required by fractal methods. Jing et al [357] designed two indicators based on the p-leader multifractal spectrum to identify the stable, weak-chatter and chatter occurrence for a micro-milling scenario, where the high spindle speed over 20,000 rpm, the reduced-sized of the cutter and the miniature dimension of the workpiece affect the process dynamics.…”

Preface to the Special Issue on “Modelling and Simulation in Engineering”

“…The paper by F. Feng et al [3] proposes an improved version of a RSE algorithm, previously developed by the same authors, used to recognize the complexity of non-fractals common in signals (roughness scaling extraction algorithm with first-order flattening (RSE-f1)). The speed of the newly proposed algorithm increases significantly (by 13 times), making it also faster than other typical algorithms.…”