多约束鲁棒非负矩阵分解的冲击特征频带自适应分解方法  

Adaptive Decomposition Method for Impact Characteristic Frequency Bands of Multi-Constrained Robust Non-Negative Matrix Factorization

作　　者：梁霖[1] 崔旭军 胡文昊 代普淼 LIANG Lin;CUI Xujun;HU Wenhao;DAI Pumiao(School of Instrument Science and Technology,Xi’an Jiaotong University,Xi’an 710049,China;School of Mechanical Engineering,Xi’an Jiaotong University,Xi’an 710049,China)

机构地区：[1]西安交通大学仪器科学与技术学院,710049西安 [2]西安交通大学机械工程学院,710049西安

出　　处：《西安交通大学学报》2025年第4期171-179,192,共10页Journal of Xi'an Jiaotong University

基　　金：国家自然科学基金资助项目(52075431)。

摘　　要：针对非负矩阵分解(NMF)在轴承故障的冲击振动频带分解中存在能量导向引起的频带混叠问题,提出了一种面向冲击故障频带自适应分解的多约束鲁棒非负矩阵分解方法。首先,采用β散度自适应加权的误差函数来避免信号未知分布引起的风险,以信号频带数量作为分解秩的选择参考,通过对基矩阵施加正交约束实现自适应频带划分;其次,结合周期冲击响应时频谱的光滑频域和稀疏时域的特性,引入具有良好物理意义的光滑、稀疏约束,构建了面向振动时频谱的多约束鲁棒非负矩阵分解模型;最后,借助正则化技术和Stiefel流形优化方法设计了求解算法。仿真和实验结果表明,与多种NMF方法和典型频带选择方法相比,在面对缺陷引起的微弱冲击时,低频区间中往往存在着多种干扰源影响,所提分解模型能准确提取出高频区间的冲击响应频带,避免了能量导向的传统频带分解方式不足,约束项的引入则有效地提升了NMF的求解结果,增强了NMF方法在冲击特征频带微弱时的辨识能力。In response to the issue of frequency band mixing caused by energy orientation in the decomposition of impact vibration frequency bands related to bearing faults using non-negative matrix factorization(NMF),a multi-constrained robust non-negative matrix factorization method for adaptive decomposition of impact fault bands is proposed.Firstly,an error function with adaptive weightedβ-divergence is utilized to mitigate risks arising from unknown signal distributions,with the number of signal frequency bands serving as a reference for selecting the decomposition rank.Adaptive band division is achieved by imposing orthogonal constraints on the basis matrix.Secondly,considering the smooth frequency domain of the periodic impact response spectrogram and the sparse time domain characteristics,physically meaningful smooth and sparse constraints are introduced to establish a multi-constrained robust non-negative matrix factorization model tailored to vibration time-frequency spectra.Finally,a solution algorithm is designed leveraging regularization techniques and Stiefel manifold optimization methods.Simulation and experimental results demonstrate that,compared to various NMF methods and typical band selection methods,when facing weak impacts caused by defects,the low-frequency range often harbors multiple sources of interference.The proposed decomposition model accurately extracts the impact response bands in the high-frequency range,circumventing the shortcomings of traditional energy-oriented band decomposition methods.The introduction of constraints effectively enhances the solution results of NMF,reinforcing its discriminative capability when dealing with weak impact characteristic frequency bands.

关 键 词：冲击特征频带 非负矩阵分解 多约束 频带分解 

分 类 号：TH133.33[机械工程—机械制造及自动化]