张量鲁棒主成分分析及其在故障诊断中的应用

Tensor Robust Principal Component Analysis and its Application in Fault Diagnosis

通常采集到的机械设备振动信号具有典型的非线性、非平稳特性,并且含有强背景噪声。一种新的张量鲁棒主成分分析方法被提出,该方法假设张量数据能被分解为代表信号特征的低秩成分和代表噪声的稀疏成分的叠加。首先将采集的一维信号重构到三维张量空间,然后通过求解一个凸优化问题来提取张量数据的低秩特征成分,从而实现信号的特征提取。该问题实质是由Tucker分解模型相关的Tucker秩凸包络的核范数和稀疏成分范数的联合最小化问题。分别通过仿真实验和实测的轴承外圈故障信号进行分析,结果表明提出的方法能成功的提取故障特征信息。

The acquired mechanical equipment fault vibration signals generally possess the characteristic of non-linear and non-stationary,in addition,it always contains strong background noise.A new method of tensor robust principal component analysis is presented.The method assumes that the tensor data can be decomposed into the sum of low-rank components representing signal features and sparse components representing noise.Firstly,the collected one-dimensional data is converted into a three-dimensional tensor space.Then the low rank component can be accurately extracted by solving a convex optimization problem which aims to obtain the combination minimum of the nuclear norm of Tucker rank in Tucker Decomposition and the-norm of sparse component.The numerical simulation experiments and the measured bearing outer ring fault signal are analyzed,respectively.The results shows the proposed method can successfully extracted the fault feature information.