振动信号过完备字典完整训练样本重构性能研究

Reconstruction Performance Study on the Over-Complete Dictionaryof Complete Training Samples for the Vibration Signals

针对用于训练过完备字典的样本集合中信号类型不足会影响到后续分析、分类和识别精度的问题,提出了一种基于过完备字典完整训练样本的滚动轴承振动信号压缩重构方法。该方法首先构造了用于字典学习的样本集合,使其尽可能多地包含各种信号成分;然后从所构造的多信号样本集合中随机选取K个原子作为初始字典,采用K-SVD算法对初始字典进行训练更新得到过完备字典,获得信号在K-SVD过完备字典上的最稀疏表示;最后利用高斯随机测量矩阵对振动信号进行压缩测量,并基于压缩测量数据采用正交匹配追踪(OMP)算法对原始信号进行重构。仿真实验结果表明,不同的训练样本集合对信号的重构精度有着很大的影响,且基于K-SVD过完备字典对信号进行稀疏表示时在较低的采样率下依然有着精确的重构性能。该方法在不丢失原始振动信号主要信息的情况下重构精度更高、重构时间更短。

Aiming at that samples sets used for training over-completedictionary will face problems with insufficient signal type,which causes diffitculties of the precision of subsequent analysis,classification and recognition.Therefore,a method of rolling bearing vibrationsignal compression reconstructionmethod based on complete training samples of over-completedictionary is proposed in this research.Firstly,the sample sets used for dictionary learning is constructed,which makes it contain various signal components.Then,it is time to select K-atoms randomly from the constructed signal sample sets as the initial dictionary,at the same time,K-SVD algorithm is adopt for training and updating initial dictionary and the sparse representation of signal based on K-SVD over-completedictionary will be obtained.Finally,Gaussian random matrix is used as sensing matrix to measure the vibration signal and orthogonal matching pursuit algorithm is adopt to reconstruct the original vibration signal according to the measurement data.The test results of simulated data demonstrated that different training sample sets has a great influence on the signal reconstruction precision and the sparse representation of signal based on K-SVD over-completedictionary earns high accuracy of signal reconstruction with low sampling rate by constructing different training samples.In the case of without losing most of the original vibration information,the proposed methodwons higher reconstruction accuracy and shorter reconstruction time.