高速切削欠采样动态信号的压缩感知恢复方法

doi:10.19665/j.issn1001-2400.2022.04.010

西安电子科技大学学报 ›› 2022, Vol. 49 ›› Issue (4): 82-89.doi: 10.19665/j.issn1001-2400.2022.04.010

高速切削欠采样动态信号的压缩感知恢复方法

贺王鹏¹(),陈彬强²(),李阳²(),陈晶¹(),郭宝龙¹()

1.西安电子科技大学空间科学与技术学院,陕西西安 710071
2.厦门大学航空航天学院,福建厦门 361005

收稿日期:2021-05-12 出版日期:2022-08-20 发布日期:2022-08-15
通讯作者: 陈彬强
作者简介:贺王鹏(1989—),男,副教授,博士,E-mail: hewp@xidian.edu.cn|李阳(1994—),女,厦门大学硕士研究生,E-mail: liyangxdjx@163.com|陈晶(1997—),女,西安电子科技大学硕士研究生,E-mail: jchen1235@163.com|郭宝龙(1962—),男,教授,博士,E-mail: blguo@xidian.edu.cn
基金资助:
国家重点研发计划(2020YFB1713500);国家自然科学基金(51805398);陕西省高校科协青年人才托举计划(20200408);陕西省自然科学基础研究计划(2020JM-196)

Compressed sensing of subsampled dynamic signals during high-speed machining

HE Wangpeng¹(),CHEN Binqiang²(),LI Yang²(),CHEN Jing¹(),GUO Baolong¹()

1. School of Aerospace Science & Technology,Xidian University,Xi’an 710071,China
2. School of Aerospace Engineering,Xiamen University,Xiamen 361005,China

Received:2021-05-12 Online:2022-08-20 Published:2022-08-15
Contact: Binqiang CHEN

摘要/Abstract

摘要：

针对高速切削状态监测系统中采样参数设置不合理以及抗混叠滤波器存在滤波陡度导致输出的切削力信号频谱混叠问题,提出了一种基于频域近似稀疏的频谱校正方法。切削系统及采样过程中的非线性往往导致状态监测系统输出波形中含有主轴频率的高次谐波,在傅里叶矩阵上表现出明显的近似稀疏性(傅里叶系数中大多数元素的幅值近似为零,能量主要集中在若干个频率区间上)。通过仅保留频谱上若干个频率区间对其实现稀疏逼近,得到若干个频带子集,并利用欠采样混频原则计算出每个频带子集的真实频率范围,构造切削力信号的真实频谱进而恢复出真实的时间序列。根据频带子集时域波形特点,构造具有一般物理意义的线性调幅正弦波模型,通过对线性调幅正弦波仿真分析及高速铣削铝合金实验验证了该方法的有效性。结果表明,这种方法能够有效地恢复出测试信号的谐波信息,恢复信号与测试信号时域波形的相对包络误差小于4%。该研究成果为稀疏表示理论应用于欠采样信号分析提供了一定的工程技术支撑。

关键词: 高速切削, 状态监测, 欠采样, 稀疏表示, 快速傅里叶变换

Abstract:

Aiming at the problem of spectrum aliasing of the cutting force caused by unreasonable setting of sampling parameters and filtering steepness of anti-aliasing filtering in the high-speed machining condition monitoring system,a spectrum sensing method based on the principle of frequency domain approximate sparseness is proposed.The non-linearity of the machining system and sampling process makes the output waveform of the monitoring system contain high order harmonics,which shows obvious approximate sparsity under the Fourier matrix (with the amplitude of most elements in the Fourier coefficients approximately zero,and the energy mainly concentrated in several frequency points).Several spectrum subsets are the result of spectrum approximation by retaining few spectral lines with a large amplitude only.Using the principle of subsampling mixing,the true frequency range of each spectrum subset is calculated,and the true frequency spectrum of the cutting force is corrected.According to the time-domain waveform characteristics of the subset of frequency bands,a general Linear Amplitude Modulation Sinusoidal Wave (LAMSW) model is constructed.The effectiveness of the proposed method is verified by LAMSW simulation analysis and high-speed milling aluminum alloy experiments.The results show that the proposed method is effective enough to recover the true waveform of the milling force signal,and that the relative envelope error between the recovery time-domain wave and the test signal is less than 4%.The research results provide a certain engineering and technical support for applying the sparse theory to the analysis of subsampling signals.

Key words: high-speed milling, condition monitoring, subsampling signal, spare representation, fast fourier transform

中图分类号:

TH17

贺王鹏,陈彬强,李阳,陈晶,郭宝龙. 高速切削欠采样动态信号的压缩感知恢复方法[J]. 西安电子科技大学学报, 2022, 49(4): 82-89.

HE Wangpeng,CHEN Binqiang,LI Yang,CHEN Jing,GUO Baolong. Compressed sensing of subsampled dynamic signals during high-speed machining[J]. Journal of Xidian University, 2022, 49(4): 82-89.

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参考文献 17

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参数	数值
径向切深/mm	3.0
轴向切深/mm	6.0
每齿进给/mm	0.08
切削速度/(m·min^-1)	800
主轴转速/(r·min^-1)	17 520

序号	混叠频带	混叠峰值频点	真实峰值频点	真实频带
1	[0,64]	44	2 044	[2 000,2 064]
2	[65,142]	132	6 132	[6 065,6 142]
3	[143,270]	250	1 750	[1 730,1 857]
4	[271,313]	292	292	[271,313]
5	[314,350]	334	2 334	[2 314,2 350]
6	[351,520]	499	3 501	[3 480,3 649]
7	[521,560]	541	1 459	[1 440,1 479]
8	[561,625]	583	583	[561,625]
9	[626,870]	833	1 167	[1 130,1 374]
10	[871,1 000]	875	875	[871,1 000]

高速切削欠采样动态信号的压缩感知恢复方法

Compressed sensing of subsampled dynamic signals during high-speed machining

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