Nonstationarity in industrial processes, guided by factors, such as equipment aging and changing upstream load demands, inherently exhibits heterogeneous characteristics. This complex overlay of homogeneous stationarity poses great difficulty in process monitoring and analysis. Therefore, this study presents a new model (Hs- ${\mathrm {H}}_{\mathrm {n}}$ ) that peels the homogeneous and heterogeneous nonstationarity, which has four components: a differentiated learning network (DL-Net), a peeling network (Pe-Net), an adaptive reweighting network (AR-Net), and a global decoder network. DL-Net obtains the differentiated representation by leveraging a new differentiated learning approach to unique inputs, which is based on the cognitive understanding and derivation of functional specialization and content learning during network training. The aim is to maximize functional diversity and minimize content overlap. Furthermore, Pe-Net extracts the stationarity and nonstationarity (S-N) components from each differentiated scale, formulated as an encoder–decoder–encoder architecture with an integrated identity subtraction skip connection. A min–max S-N constraint regulates the peeling process and controls the extracted content. AR-Net additionally refines homogeneous stationarity across each scale and reweights the individual components to adaptively adjust their contributions. Last, reweighted components are fused and input into the global decoder to facilitate unsupervised learning. Experimental results on three processes demonstrate the effectiveness of Hs-Hn.

Fault detection is crucial for ensuring the reliability and safety of industrial processes, as it helps prevent equipment failures and minimizes downtime. It has wide applications in industrial processes and machine intelligence but remains unsolved problems. Major challenges include the variations in data distribution and temporal dynamics due to the nonstationary nature, which is driven by factors such as frequent switching between operational modes, aging of distributed control sensors, and environmental variability. Traditional fault detectors are suboptimal, while nonstationary-aided methods easily make biased detections towards the multiple complex nonstationary components. In this paper, we present a new fault detection model for nonstationary processes through multiscale content learning to disentangle feature representations (MCD). MCD consists of three sub-modules: Diverse Content Module (DCM), Stationary and Nonstationary Disentanglement Module (SNDM), and Component Reweighting and Reconstruction Module (CR²M). DCM enriches multiple representations via multiscale modeling of network informational content. SNDM disentangles the homogeneous stationary and heterogeneous nonstationary (S-N) features from multiple local representations, which is formulated as an encoding-decoding-encoding process with a skip disentanglement and min-max constraint. CR²M further fuses local S-N features with an adaptive learnable reweighting strategy, achieving a fine-grained reallocation of the importance of global S-N attributes. Experimental results on a numerical process and a real-world process demonstrate the superiority of MCD in fault detection for nonstationary processes.

Due to the scarcity of fault samples in real-world industrial scenarios, few-shot fault diagnosis (FSFD) has attracted increasing attention, as it is vital for ensuring industrial safety and engineering reliability. However, existing metrics-based meta-learning approaches generally calculate fault similarity relying on global pairwise, which insufficiently exploit fault information and thus limit discrimination among fault types. To address the insensitivity to buried fault information in complete processes, we propose a novel framework called the local–global consistency relation network (LGCRN). The framework captures more comprehensive fault feature information through two components: the global branch, which focuses on macroinformation involving all join process units, and the local branch, which emphasizes finer granularity from specific units. In addition, a local–global alignment loss is utilized to optimize LGCRN, where self-cross relation improves the discriminability and stability of fault features by maintaining consistency between local and global branches. The self-cross relation comprises self-sample relation, ensuring consistency within the same sample at different granularities, and cross-sample relation, maintaining consistency across samples within the same class. Experiments on two benchmarks and a real semiconductor process demonstrate the feasibility and superiority of the proposed method, confirming its effectiveness in addressing limited-sample industrial fault diagnosis tasks and enabling timely maintenance crucial for operational safety in real-world scenarios.