Data-driven fault diagnosis methods have become a research hotspot recently. However, the following two problems are still barring them from the application: (1) Most of the existing models rely deeply on sufficient labeled samples and neglect the high cost of labeled data collection in reality; (2) The existing models usually focus on the single-level attribute of the sample and ignore the latent hierarchical fault attributes. To address these issues, a novel semi-supervised multi-layer non-negative matrix factorization (SMNMF) method is proposed in this study. The fault pattern and severity identification problems are converted into a hierarchical fault attribute representation task, which can reduce the complexity of the classification task and improve the fault diagnosis accuracy. The hierarchical attribute representations of different fault locations and sizes are learned from the time-frequency distribution (TFD) of signals by a newly constructed two-layer non-negative matrix factorization model. The graph-based semi-supervised learning method is adopted to lead the attributes of the hierarchy structure and carry out label propagation from labeled samples to unlabeled samples for more accurate fault diagnosis. The fault diagnosis experiments executed in the aeroengine bearings and a diesel engine demonstrated the feasibility and superiority of the proposed method.

数据驱动的故障诊断方法成为近年来的研究热点。但是，以下两个问题仍然阻碍了它们的应用：（1）现有模型大多过于依赖足够的标记样本，而忽视了现实中标记数据收集的高成本；(2) 现有模型通常关注样本的单级属性，而忽略了潜在的分层故障属性。为了解决这些问题，本研究提出了一种新的半监督多层非负矩阵分解（SMNMF）方法。将故障模式和严重性识别问题转化为分层故障属性表示任务，可以降低分类任务的复杂度，提高故障诊断的准确性。通过新构建的两层非负矩阵分解模型，从信号的时频分布（TFD）中学习不同故障位置和大小的层次属性表示。采用基于图的半监督学习方法，引导层次结构的属性，进行从标记样本到未标记样本的标签传播，实现更准确的故障诊断。在航空发动机轴承和柴油发动机上进行的故障诊断实验证明了该方法的可行性和优越性。采用基于图的半监督学习方法，引导层次结构的属性，进行从标记样本到未标记样本的标签传播，实现更准确的故障诊断。在航空发动机轴承和柴油发动机上进行的故障诊断实验证明了该方法的可行性和优越性。采用基于图的半监督学习方法，引导层次结构的属性，进行从标记样本到未标记样本的标签传播，实现更准确的故障诊断。在航空发动机轴承和柴油发动机上进行的故障诊断实验证明了该方法的可行性和优越性。