混合高斯噪声条件下稀疏表示方法及其在冲击类故障特征提取中的应用

Sparse Representation Method Under Mixed Gaussian Noise and Its Application in Impulsive Fault Feature Extraction

传统稀疏表示方法因其在冲击类信号特征提取中的独特优势而在故障诊断领域被广泛研究。然而,传统稀疏表示理论基于对干扰噪声的高斯分布假设,导致其难以适用于多种噪声分布混合的实际现场。针对上述问题,提出一种混合高斯噪声条件下的冲击类故障特征稀疏表示方法。基于传统稀疏表示理论的贝叶斯框架,借助混合高斯分布的万有逼近性质,建立了基于db4小波字典的混合高斯噪声稀疏分解模型,并推导了基于EM(Expectation-maximum,EM)和ADMM(Alternating direction method of multipliers,ADMM)的优化求解算法用于模型求解。仿真和实验结果表明,所提出的方法能够有效提取混合噪声干扰下的冲击类微弱故障特征信号。

Traditional sparse representation(SR)methods have been widely studied in fault diagnosis field due to their unique advantages in impact feature extraction.However,the traditional SR theory is based on an assumption of Gaussian distribution of interference noise,which makes it difficult to apply to the actual scenario where multiple noise distributions are involved.Regarding the issue above,a new sparse representation method of impact features under mixed Gaussian noise conditionis proposed in this study.Depending on the Bayesian framework of the traditional sparse representation theory and the universal approximation property of the mixed Gaussian distribution,a sparse decomposition model of the mixed Gaussian noiseis established based on the db4 wavelet dictionary,and an optimization algorithm based on Expectation-Maximum(EM)and Alternating Direction Method of Multipliers(ADMM)is derived for model solution.The simulation and experimental results show that the proposed method can effectively extract the weak impact feature under mixed noise interference.