With the advent of big data and the information age, the data magnitude of various complex networks is growing rapidly. Many real-life situations cannot be portrayed by ordinary networks, while hypergraphs have the ability to describe and characterize higher order relationships, which have attracted extensive attention from academia and industry in recent years. Firstly, this paper described the development process, the application areas, and the existing review research of hypergraphs; secondly, introduced the theory of hypergraphs briefly; then, compared the learning methods of ordinary graphs and hypergraphs from three aspects: matrix decomposition, random walk, and deep learning; next, introduced the structural optimization of hypergraphs from three perspectives: dynamic hypergraphs, hyperedge weight optimization, and multimodal hypergraph generation; after that, the applicability of three uncertain hypergraph models were analyzed based on three uncertainty theories: probability theory, fuzzy set, and rough set; finally, the future research directions of hypergraphs and uncertain hypergraphs were prospected.

Since supervised learning intrusion detection models rely on manually labeled data, the process often requires a lot of time and effort. To make full use of unlabeled network traffic data and improve intrusion detection, this paper proposes an intrusion detection method for industrial control systems based on improved comparative learning SimCLR. Firstly, a feature extraction network is trained on SimCLR using unlabeled data; a linear classification layer is added to the trained feature extraction network model; and a small amount of labeled data is used for supervised training and fine-tuning of the model parameters. The trained model is simulated on the Secure Water Treatment (SWaT) dataset and the publicly available industrial control dataset from Mississippi State University, and the results show that the method has better results in all evaluation metrics compared with the deep learning algorithm using supervised learning directly, and the comparative learning has research value in industrial control system intrusion detection.

With the rapid development of cyber-physical systems (CPS), constructing information systems with high-quality services has become an urgent requirement in both academia and industry. Hypergraphs are widely used in graph data analysis tasks due to their wide node-aware range and reasonable interpretability. This article proposes a model known as the relation-aggregated hypergraph neural network, which aims to better describe and apply complex structures and relationships in the physical world, thereby improving the management efficiency and service quality of service recommendation in CPS. First, explicit and implicit hyperedges are constructed based on the explicit and implicit relationships between nodes, respectively. Second, a global attention mechanism is adopted to calculate the importance between neighbor nodes that share implicit hyperedges with the current node, generating a relation-aggregated hypergraph. Finally, by weighting the generated hypergraph association matrix and passing the aggregated features through the hypergraph neural network, we obtain the embedding representation of nodes. Node classification experiments were conducted on three public network datasets, and the accuracy rates were 83.7%, 88.8%, and 84.9%, respectively, which were higher than those of the baseline model.

Pellet quality including chemical composition, physical properties and metallurgical performance of three parts, its quality and mineral composition, properties and structure of the pellets has the close relation, studies show that the mineralogical micro structure and distribution of pellets had significant effects on the metallurgical properties, so the analysis and determination of pellets of mineral composition and micro structure is very important to improve the quality of pellets. Paper to pellets micro mineral as the research object, mainly studies the CNN and PCA two kinds of image processing algorithm, in the heart of the traditional model of CNN structure characteristics obtained by convolution PCA dimension reduction at a time, will be the main features of PCA to extract into the depth of the CNN learning, realize the mineral phase of shallow and deep information of the image to do effective fusion, in a larger extent, reflects the mineralogical characteristics, thus more intuitive response metallurgical properties. The location and alkalinity of the ore phase were identified by the extracted deep fusion feature, and the results were compared with those of the traditional CNN algorithm. It was found that the accuracy of location and alkalinity recognition of PCA and CNN coupling algorithm was 93.82% and 91.26%, respectively, which were higher than the accuracy of traditional CNN algorithm 92.73% and 88.93%, which verified the accuracy of PCA and CNN coupling model and its applicability in mineral phase recognition.

Accurate prediction of carbon monoxide (CO) concentration at the main exhaust outlet of the sintering process is important for combustion state assessment and CO emission control. Existing data-driven methods treat process variables as homogeneous inputs, neglecting their process affiliations and cross-system interactions. This study proposes a process-guided Kolmogorov–Arnold network (PG-KAN) for CO concentration soft measurement. According to process relationships, 230 process variables are organized into material, flue gas, and auxiliary systems, and independent radial basis function-based Kolmogorov–Arnold network (RBF-KAN) encoding branches extract system-specific nonlinear representations. Cross-system interaction modules capture interactions among these systems. A tail coverage-aware loss reduces large errors and underestimation bias in high-CO concentration intervals. Experiments on 18,749 industrial samples show that PG-KAN achieves a mean absolute error (MAE) of 107.700 mg/m³, a coefficient of determination (R²) of 0.9105, and a Pearson correlation coefficient of 0.9542, outperforming six baseline models. Ablation studies verify the effectiveness of process-guided variable organization, cross-system interactions, and the proposed loss. Edge-function and SHapley Additive exPlanations (SHAP) analyses provide insights into nonlinear mappings and feature contributions learned by the model. The proposed method provides an interpretable, process-guided framework for CO concentration soft measurement in industrial sintering processes.