Deep learning-based fault diagnosis (FD) approaches require a large amount of training data, which are difficult to obtain since they are located across different entities. Federated learning (FL) enables multiple clients to collaboratively train a shared model with data privacy guaranteed. However, the domain discrepancy and data scarcity problems among clients deteriorate the performance of the global FL model. To tackle these issues, we propose a novel framework called representation encoding-based federated meta-learning (REFML) for few-shot FD. First, a novel training strategy based on representation encoding and meta-learning is developed. It harnesses the inherent heterogeneity among training clients, effectively transforming it into an advantage for out-of-distribution generalization on unseen working conditions or equipment types. Additionally, an adaptive interpolation method that calculates the optimal combination of local and global models as the initialization of local training is proposed. This helps to further utilize local information to mitigate the negative effects of domain discrepancy. As a result, high diagnostic accuracy can be achieved on unseen working conditions or equipment types with limited training data. Compared with the state-of-the-art methods, such as FedProx, the proposed REFML framework achieves an increase in accuracy by 2.17%-6.50% when tested on unseen working conditions of the same equipment type and 13.44%-18.33% when tested on totally unseen equipment types, respectively.

翻译：基于深度学习的故障诊断方法需要大量训练数据，然而这些数据分散在不同实体中难以获取。联邦学习能够在保障数据隐私的前提下，使多个客户端协同训练共享模型。然而，客户端间的域差异和数据稀缺问题会降低全局联邦模型的性能。为解决这些问题，我们提出了一种名为基于表示编码的联邦元学习（REFML）的小样本故障诊断新框架。首先，我们提出基于表示编码和元学习的新型训练策略，该策略利用训练客户端固有的异质性，将其有效转化为在未知工况或设备类型上实现分布外泛化的优势。其次，我们提出自适应插值方法，通过计算本地模型和全局模型的最优组合作为本地训练的初始参数，从而进一步利用本地信息减轻域差异的负面影响。实验结果表明，即使在训练数据有限的情况下，该方法仍能在未知工况或设备类型上实现高诊断精度。与FedProx等先进方法相比，所提出的REFML框架在同类型设备未知工况测试中准确率提升2.17%-6.50%，在完全未见设备类型测试中准确率提升13.44%-18.33%。