Unsupervised Identification Methodology Using Hybrid Entropy for Milling Vibration States under Variable Operating Conditions

doi:10.3969/j.issn.1004-132X.2026.07.013

China Mechanical Engineering ›› 2026, Vol. 37 ›› Issue (7): 1641-1650.DOI: 10.3969/j.issn.1004-132X.2026.07.013

Unsupervised Identification Methodology Using Hybrid Entropy for Milling Vibration States under Variable Operating Conditions

WU Yanqing¹(), HU Teng¹(), WANG Xiaohu¹, MI Liang², YIN Guofu³

^1.College of Electromagnetically Engineering，Southwest Petroleum University，Chengdu，610500
^2.Institute of Mechanical Manufacturing Technology，China Academy of Engineering Physics，Mianyang，Sichuan，621999
^3.School of Mechanical Engineering，Sichuan University，Chengdu，610065

Received:2024-10-12 Revised:2026-04-21 Online:2026-07-25 Published:2026-08-18
Contact: HU Teng

基于混合熵的变工况铣削振动状态无监督辨识方法

吴炎青¹(), 胡腾¹(), 王小虎¹, 米良², 殷国富³

^1.西南石油大学机电工程学院, 成都, 610500
^2.中国工程物理研究院机械制造工艺研究所, 绵阳, 621999
^3.四川大学机械工程学院, 成都, 610065

通讯作者: 胡腾
作者简介:吴炎青，男，1999年生，硕士研究生。研究方向为机械系统稳定性预报。E-mail：15351249852@163.com
胡腾^*（通信作者），男，1982年生，副教授。研究方向为故障智能诊断与靶向修复技术。发表论文30余篇。E-mail：tenghu@alu.scu.edu.cn。
第一联系人：啜世达，男，1998年生，博士研究生。研究方向为超精密智能制造、特种加工技术。发表论文5篇。E-mail：chuaisd@163.com。叶林征^*（通信作者），男，1990年生，教授、博士研究生导师。研究方向为超精密与特种加工技术、超声空化理论及应用、机器人、智能制造。发表论文60余篇。E-mail：lz09020141@163.com。
基金资助:
四川省重大科技专项(2020ZDZX0003);四川省重大科技专项(2019ZDZX0055);四川省重点研发计划(2017GZ0057)

Abstract

Abstract:

To address the limitations in accuracy and efficiency of existing techniques for identifying milling vibration states under variable operating conditions， this paper proposes an unsupervised identification method based on hybrid entropy. The proposed method first denoised the milling force signals using bias-compensated sub-band adaptive filtering. A hybrid entropy metric was then derived through the weighted summation of fuzzy entropy and power spectrum entropy to characterize the vibration states. Subsequently， a collaborative clustering model was employed for unsupervised learning and classification of the hybrid entropy， ultimately outputting the identification results over the signal time history. Experimental results demonstrate that the proposed method requires only 16.55 s for model training and eliminates the need for labeled sample sets， demonstrating significant advantages in computational efficiency and practical engineering applications.

Key words: hybrid entropy, unsupervised learning, variable operating conditions, vibration state identification

摘要：

针对现有变工况铣削振动状态辨识技术在精准性与高效性的局限性，提出一种基于混合熵的无监督辨识方法。以基于偏差补偿子带自适应滤波的铣削力信号降噪为切入点，通过对信号模糊熵与功率谱熵的加权求和获取铣削振动状态混合熵；借助协同聚类模型对混合熵进行无监督学习及分类，进而依据信号采样时间历程，输出变工况铣削振动状态的辨识结果。实验表明，所提方法训练模型仅需16.55 s，且无需样本，优势显著。

关键词: 混合熵, 无监督学习, 变工况铣削, 振动状态辨识

CLC Number:

TP18

WU Yanqing, HU Teng, WANG Xiaohu, MI Liang, YIN Guofu. Unsupervised Identification Methodology Using Hybrid Entropy for Milling Vibration States under Variable Operating Conditions[J]. China Mechanical Engineering, 2026, 37(7): 1641-1650.

吴炎青, 胡腾, 王小虎, 米良, 殷国富. 基于混合熵的变工况铣削振动状态无监督辨识方法[J]. 中国机械工程, 2026, 37(7): 1641-1650.

Figures/Tables 22

Fig.1 K-means-GMM Technical Route

Fig.2 Overall technique flowchart

Fig.3 Impact modal test

Fig.4 Milling stability blade diagram

Fig.5 Varying depth milling path

Fig.6 Original and filtered signals

Fig.7 Filtered signal and its Hybrid entropy

Fig.8 Hybrid entropy before and after filtering

Fig.9 Hybrid entropy clustering

Fig.10 Vibration state hybrid entropy - kernel density distribution

Tab.1 Weight Parameter Setting

w₁	0.1	0.2	0.3	0.4	0.5	0.6
w₂	0.9	0.8	0.7	0.6	0.5	0.4

Fig.11 Vibration state hybrid entropy-kernel density distribution under different weight combinations

Fig.12 Different entropy calculations

Fig.13 Comparison of different entropy clustering results

Tab.2 Milling vibration state classifications

	铣削状态
	稳定铣削	颤振孕育	颤振爆发
时间范围（s）	10.0-29.5	29.5-30.4	30.4-32.0

Tab.3 Supervised model hyperparameters

网络模型	AlexNet	SVM	MobileNetV2
学习率	0.01	0.01	0.01
Epoch/次	20	20	20
batch size/张	32	32	32
优化器	ADAM	SMO	ADAM
损失函数	交叉熵	Soft Margin Loss	交叉熵

Tab.4 Hardware and software configuration

配置名称	配置参数
CPU	Intel Xeon E5-2678 v3
GPU	NVIDIA GeForce 2080Ti 11GB
计算环境	Win11+Python3.9+MatlabR2022b

Fig.14 IMF of milling force signal

Fig.15 Principal component analysis visualization

Tab.5 Comparison of model abilities

辨识模型	训练时间/s	测试时间/s	精确率/%	准确率/%
AlexNet	146.35	4.28	70.71	84.09
SVM	28.27	0.18	98.64	99.13
MobileNetV2	230.88	1.20	97.73	98.52
K-means-GMM	16.55	-	-	-

Fig.16 Time domain signal of milling force with variable cutting width

Fig.17 Hybrid entropy - kernel density distribution of milling vibration state with varying cutting width

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Unsupervised Identification Methodology Using Hybrid Entropy for Milling Vibration States under Variable Operating Conditions

基于混合熵的变工况铣削振动状态无监督辨识方法

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References 32

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