摘要针对工业机械设备实时监测中不可控因素导致的振动信号数据缺失问题，提出一种基于自适应二次临近项交替方向乘子算法(Adaptive Quadratic Proximity-Alternating Direction Method of Multipliers, AQ-ADMM)的压缩感知缺失信号重构方法。AQ-ADMM算法在经典ADMM算法迭代过程中添加二次临近项，且能够自适应选取惩罚参数。首先在数据中心建立信号参考数据库用于构造初始字典，然后将K-奇异值分解(K-Singular Value Decomposition, K-SVD)字典学习算法和AQ-ADMM算法结合重构缺失信号。对仿真信号和两种真实轴承信号数据集添加高斯白噪声后作为样本，实验结果表明当信号压缩率在50%～70%时，所提方法性能指标明显优于其它传统方法，在重构信号的同时实现了对含缺失数据机械振动信号的快速精确修复。
Abstract：In order to address the issue of missing vibration signal data in real-time monitoring of industrial machinery due to uncontrollable factors, a Compressed sensing missing signal reconstruction method based on the Adaptive Quadratic Proximity-Alternating Direction Method of Multipliers (AQ-ADMM) was proposed. The AQ-ADMM algorithm introduced a quadratic proximity term into the classic ADMM iterative process and adaptively selected penalty parameters. First, a signal reference database was established at the data center for creating an initial dictionary. Then, the missing signals were repaired using a reconstruction method based on the K-Singular Value Decomposition (K-SVD) dictionary learning algorithm and AQ-ADMM. Gaussian white noise was added to simulated signals and two real bearing signal datasets to serve as samples, the experimental results demonstrate that the proposed method exhibits significantly better performance indicators than other traditional methods when the signal compression ratio ranges from 50% to 70%. It achieves fast and accurate recovery of missing data signals while reconstructing the signals.
郭俊锋1，胡婧怡1，王智明1. 基于压缩感知的缺失机械振动信号重构新方法[J]. 振动与冲击, 2024, 43(10): 197-204.
GUO Junfeng1,HU Jingyi1,WANG Zhiming1. Novel method for missing mechanical vibration signal reconstruction based on compressed sensing. JOURNAL OF VIBRATION AND SHOCK, 2024, 43(10): 197-204.
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