Large-Scale Decentralized Fault Diagnosis for Multi-Group Data with Auxiliary Information via Distributed Multiple Testing

In the era of big data, efficiently diagnosing faults in high-dimensional data streams (HDS) is critical for numerous industrial applications. This paper addresses a novel decentralized fault diagnosis problem involving multi-group HDS with multi-sequence auxiliary information (MAI). Traditional diagnostic methods, which are designed for a single group of single-sequence HDS, struggle with the complexity and volume of such data, often leading to suboptimal diagnostic performance. To overcome this challenge, we propose a distributed fault diagnosis framework that leverages advanced multiple testing techniques and data fusion strategies to analyze multi-group HDS with MAI. Under this framework, we introduce a generalized multi-sequence local index of significance for the data streams in each group, based on a Cartesian hidden Markov model, to effectively fuse information from auxiliary sequences. This is then integrated into a distributed multiple testing procedure for group-wise diagnosis of the target data sequence. The proposed procedure minimizes the group-wise expected number of false positives in the target sequence while controlling the overall group-wise missed discovery rate at a specified level. Numerical studies demonstrate that the proposed method outperforms state-of-the-art diagnostic techniques, providing more reliable and effective fault diagnostics.