Missing data are quite common in the industrial field. Since most data driven methods used in these applications rely on complete and high-quality data set, it is important to handle the missing data problem. Also, the severity of missing data varies across factories, which means that a single factory could fail to handle missing data locally. With the rapid development of cloud–edge computing, different factories could work together to handle missing data problem by federated learning without sharing their private training data. However, popular federated imputation methods assume each edge, i.e., a factory, to be an equal participant during learning a central model in the cloud, and thus are unable to handle heterogeneous data across different clients, leading to slow convergence and degraded learning performance. In this paper, a federated transfer missing data imputation method (FedTMI) is proposed to address this dilemma. Firstly, edge models are built with traditional Generative Adversarial Imputation Nets (GAIN) trained on edge data sets and edge knowledge is extracted as knowledge vectors to identify variables which could provide room for performance improvement. Secondly, for a certain target edge, with edge models and edge knowledge being accumulated in the cloud, models from non-target edges are chosen as helper models following certain rules aided by the corresponding edge knowledge. The helper models could provide effective guidance for data imputation in the target edge. Thirdly, the target edge executes federated transfer learning with the selected helper models. Model knowledge of helper models is transferred to the target edge, forming an updated target edge model with its edge data. Case studies on steam-driven water pumps in thermal power plants show the feasibility of the proposed FedTMI. It outperforms the baseline method with model averaging (FedAvg), especially when the data are not independent and identically distributed (non-i.i.d.) across different edges.

缺失数据在工业领域非常普遍。由于这些应用程序中使用的大多数数据驱动方法都依赖于完整和高质量的数据集，因此处理缺失数据问题非常重要。此外，缺失数据的严重程度因工厂而异，这意味着单个工厂可能无法在本地处理缺失数据。随着云边缘计算的快速发展，不同的工厂可以在不共享私有训练数据的情况下，通过联合学习共同处理缺失数据问题。然而，流行的联邦插补方法假设每个边缘（即工厂）在学习云中的中心模型时都是平等的参与者，因此无法处理跨不同客户端的异构数据，导致收敛速度慢和学习性能下降。在本文中，提出了一种联合转移缺失数据插补方法（FedTMI）来解决这一困境。首先，使用在边缘数据集上训练的传统生成对抗插补网络（GAIN）构建边缘模型，并将边缘知识提取为知识向量，以识别可为性能改进提供空间的变量。其次，对于某个目标边缘，边缘模型和边缘知识在云端积累，非目标边缘的模型在相应边缘知识的辅助下按照一定的规则被选择为辅助模型。辅助模型可以为目标边缘的数据插补提供有效的指导。第三，目标边使用选定的辅助模型执行联邦迁移学习。辅助模型的模型知识转移到目标边缘，用它的边缘数据形成一个更新的目标边缘模型。火电厂蒸汽驱动水泵的案例研究表明了拟议的 FedTMI 的可行性。它在模型平均 (FedAvg) 方面优于基线方法，尤其是当数据不是独立且跨不同边缘的同分布（非独立同分布）时。