Source-free domain adaptation (SFDA) enables knowledge transfer without source data, addressing privacy constraints of the transfer learning. However, existing methods often depend on fixed confidence thresholds for pseudolabeling, which are poorly adaptable and lead to unstable performance. Moreover, class distribution mismatch is frequently ignored, further hindering adaptation. To tackle these challenges, incremental contrastive learning with dual distilling for SFDA is proposed and applied in industrial process fault diagnosis in this article. A threshold-free pseudolabeling strategy is first introduced to dynamically assess label reliability. Then, a stage-wise incremental contrastive learning framework progressively expands from per-class Top-K samples to the full target set, effectively mitigating class imbalance. In addition, a dual distilling mechanism at both feature and label levels is employed to alleviate model drift caused by forgetting source knowledge. Finally, extensive experiments on three-phase flow and wastewater treatment datasets demonstrate the effectiveness of the proposed method.

This article focuses on fault detection for nonlinear industrial processes with multiple operating conditions, in which transfer learning is used to deal with the limited training data issue for unusual operating conditions. To this end, the Tucker decomposition is first implemented to deliver the Gaussian kernel of the nonlinear processes with multiple operation conditions. Then, transfer learning is carried out based on correlation analysis to achieve fault detection for the target process. It is noted that the traditional statistic will lead to false alarms due to the switching of the operating conditions. To deal with this issue, a stationary statistic is investigated based on co-integration analysis. Finally, by transferring the fault detection systems from multiple operating conditions to unusual operating conditions based on extended manifold regularization, fault detection for unusual operating condition can be achieved with both the traditional statistics and the stationary statistic. The experimental result demonstrates the efficiency of the proposed fault detection method for the wastewater treatment process.

Data-driven methods for predicting quality variables in wastewater treatment processes (WWTPs) have mostly ignored the slow time-varying nature of WWTP, and they are data-consuming that need a large amount of independent and homogeneously distributed data, which makes it difficult to collect. To address this issue with few-shot and inconsistent distribution, a transfer learning method called transferable deep slow feature network (TDSFN) for time-series prediction is proposed by leveraging the knowledge of relevant datasets. TDSFN extracts nonlinear slow features of WWTP with inertia from the time series through a deep slow feature network and constructs the domain invariant features based on them. Target feature attention is designed in TDSFN to enhance the predictor adaptability to the target domain by assigning weights to the source features based on their similarity to target features. Furthermore, a variational Bayesian inference framework is introduced to learn the parameters of TDSFN. The effectiveness of TDSFN is verified through prediction experiments based on WWTP.

Under closed-set scenarios (CSS), distributed modeling performs well in fault diagnosis of plant-wide industrial processes due to its flexibility and robustness. However, a more realistic scenario is often open, where unseen situations may arise unexpectedly, rendering existing methods infeasible. The advent of open-set recognition algorithms that can effectively distinguish known samples and reject unknown ones bridges this gap. Nevertheless, the poor scalability of these algorithms prevents them from being elegantly embedded in popular distributed modeling schemes, which hinders the implementation of plant-wide industrial process fault diagnosis toward open-set scenarios (OSS). In this work, we formulate a novel distributed fault diagnosis scheme toward OSS to solve this problem. First, a mutual information-based local module decomposition and expansion strategy is proposed to minimize the loss of intermodule relevant information. Second, a novel generalized basic probability assignments generation technique based on extreme value theory is developed for modeling unknown information. It enables any classifier capable of probabilistic prediction to be applied to OSS and easily embedded in distributed modeling schemes. Finally, a conflict management scheme combining supervised and unsupervised is devised to address the vulnerability of the modified generalized combination rule to counter-intuitive results from fusing conflicting evidence. Experimental results on two plant-wide industrial process datasets demonstrate the proposed approach's feasibility and superiority.

In soft sensing, relationship variation of process variables and quality indicators may cause the model trained from the training datasets unsuitable for the prediction on the testing datasets. As the model-agnostic meta-learning can utilize the supporting datasets to strengthen the prediction performance of the query samples, it can maintain reliable prediction performance in relationship variation. However, the traditional model-agnostic meta-learning contains inconsistencies between the parameters evaluated in the training stage and those adapted in the predicting stage. The phenomenon is inferred as the dilemma of getting valuable evaluated parameters related to the initial parameters and accurate parameters representing the parameters adapted in the predicting stage. In this article, we propose the stage-related adaption block to use the model-agnostic meta-learning modularly. Finally, the model-agnostic meta-learning method based on the optimal alternative scaling value is proposed and verified in a numerical example and an industrial application.