To monitor industrial processes properly, softsensors are widely used to predict significant but difficultto-measure quality variables. However, the prediction performances of traditional data-driven soft-sensors are usually unacceptable once suffering from high-nonlinear, high-dimension and imblance data issues. Therefore, a semi-supervised soft-sensor, which is learned by a just-intime method with structure entropy clustering (SS-JITL-SEC), is proposed aiming to improve prediction performance with a simpler way. Inspired by a divide and conquer strategy, a novel SEC method is proposed to achieve several clusters and then to translate the highly complex and nonlinear modeling problems into simple and linear ones. Moreover, the training dataset is extended through a mixed semi-supervised (SS) labeling approach. Finally, dissimilarity-based just-in-time learning (JITL) works together with the resulting clustering sub-datasets to formulate a local adaptive prediction model. Two datasets from different types of wastewater treatment plants are used to verify the effectiveness of the proposed soft-sensor. The results show that the SS-JITL-SEC soft-sensor can achieve better prediction performance than other standard counterparts, and even for effective process monitoring with the resulted residuals.Impact Statement -Proper processes monitoring of difficult-tomeasure quality-related variables is imperative for safe and stable operation of industrial processes, particularly under the case of suffering from significantly dynamic, highly dimensional behaviors during supervised learning. Data-driven soft-sensors together with adaptive learning and semi-supervised learning are currently the alternatives to achieve this goal. The novelty of

Data-driven soft sensors are usually used to predict quality-related but hard-to-measure variables in industrial systems. However, the acceptable prediction performance mainly relies on the premise that training data are sufficient for model training. To acquire more training data, this paper proposes an adversarial transfer learning (ATL) methodology to enhance soft sensor learning. Firstly, a hierarchical transfer learning algorithm, which integrates a feature extraction method with model-based transfer learning, is proposed to refine the useful hidden information from both historical variables and samples. Then, a novel adversarial learning network is designed to prevent the deterioration of transferred results at each transfer learning stage. Thirdly, a Granger causality analysis (GCA)-based rationale analyzer is added to unfold the internal causality among input variables and between input and output variables simultaneously. Finally, the effectiveness of the proposed soft sensor and the rationale analyzer is validated in a simulated wastewater plant, Benchmark Simulation Model No.2 (BSM2), and a full-scale oxidation ditch (OD) wastewater plant. The experimental results demonstrate that the ATL-based soft sensor can achieve more accurate prediction in terms of RMSE and R, and the GCA-based rationale analyzer can provide a visual explanation for the corresponding model and prediction results.