Real-time nonlinear multimode process monitoring of actual industrial systems has attracted increasing attention recently. In this article, the time-weighed kernel sparse representation (TWKSR) method is proposed to partition the mode of the training dataset by introducing the time-series-dependent characteristics into the kernel sparse representation algorithm. The alternating direction method of multipliers is utilized to solve the optimization problem of the proposed TWKSR method. Then, the representative samples from each identified mode are selected to update the dictionary matrix. Based on the updated dictionary matrix, the sparse coefficient is used for online mode identification, and the reconstruction error is utilized for fault detection. Finally, a numerical simulation case and the wastewater treatment process example verify the effectiveness of the proposed method.

Frequent operation changes are inevitable to achieve different production aims, which leads to mixed periods of stationarity and nonstationarity in industrial processes and increases the monitoring difficulty. In this article, a generalized monitoring scheme is proposed for industrial processes with stationary and nonstationary operational stages. First, the local average similarity (LAS) and distance average similarity (DAS) are developed on offline training data to divide operational stages and identify repeating stages. The equilibrium relationship between variables in each stage can be guaranteed rather than in the whole process, which is the premise of refined modeling. Then, multiple cointegration analysis (CA) and detrended fluctuation regression (DFR) models are proposed to handle nonstationary variables with different integrated orders, so as to map all stages into stationary space. For online monitoring, the real-time stage identification is performed based on the comprehensive similar index (CSI) that combines LAS and DAS, and the process monitoring is realized by a local static principal component analysis (PCA). Finally, the effectiveness of our proposed method is verified by an extended Tennessee Eastman simulation and batch-fed penicillin fermentation process.

Soft sensing techniques are crucial for predicting key quality indicators in industrial processes. Despite the widespread application of deep learning in the soft sensing domain, challenges such as limited sampling and the complex nonlinear relationships among process variables limit the accuracy and adaptability of soft sensing models. Consequently, this study develops a bidirectional optimization learning of data augmentation and prediction modeling framework (BOL-DAPM). Considering that the generated samples must adhere to specific distribution characteristics and maintain the relationship between feature and target variables, a regression-constrained autoencoder (R-CAE) is developed that is capable of generating higher-quality new samples. To address the lack of consideration for maintaining intervariable correlation during the feature extraction process of soft sensing models, a nonlinear correlation index-constrained stacked target-related autoencoder (NC-STAE) is established, enhancing the accuracy of the predictive model. Considering the strong dependency between data generation and predictive models, a bidirectional optimization strategy is implemented through the loss function flow between the two models. This approach further improves the predictive accuracy of soft sensing with limited data. Experimental validation on datasets from the debutanizer column and concrete compressive strength confirmed that the proposed methods surpass recent comparative approaches in reducing prediction error, improving the coefficient of determination ( $R^{2}$ ) and lowering the mean absolute error (MAE), with an average precision performance increase of 35%.

Many industrial processes are operated in multiple modes due to different manufacturing strategies. Multimodality of process data is often accompanied with nonlinear and non‐Gaussian characteristics, which makes data‐driven monitoring more complicated. In this paper, statistics pattern analysis (SPA) is introduced to extract low‐ and high‐order statistics from raw process data. Support vector data description (SVDD), which can deal with nonlinear and non‐Gaussian problems, is applied to monitor multimode process in this paper. To improve detection performance of SVDD for training multimode data with outliers, modified local reachability density ratio (mLRDR) is proposed as a weight factor to be embedded in the weighted‐SVDD (wSVDD) model, in which the local neighbors in terms of both space and time are considered. Finally, the effectiveness and superiority of our proposed method are demonstrated by the Tennessee‐Eastman (TE) process and wastewater treatment process (WWTP).

This article discusses the event-triggered consensus problem for a switched multi-agent system (MASs) with switching topologies. An observer-based dynamic event-triggered (DET) controller with a discontinuous nonlinear term is designed to reduce arduous communication. With the designed approach, the error system can reach a tracking consensus. Then, a continuous observer-based DET protocol is created using the boundary layer method to prevent chattering effects. Moreover, by employing the Riccati equation and the switched Lyapunov function method, some sufficient criteria are put forward to guarantee the tracking consensus of the systems. The suggested observer-based DET protocol can also exclude the Zeno behavior. Finally, two examples verify the validity of the analysis.