Process safety plays a vital role in the modern process industry. To prevent undesired accidents caused by malfunctions or other disturbances in complex industrial processes, considerable attention has been paid to data-driven fault detection techniques. To explore the underlying manifold structure, manifold learning methods including Laplacian eigenmaps, locally linear embedding, and Hessian eigenmaps have been utilized in data-driven fault detection. However, only the partial local structure information is extracted from the aforementioned methods. In this paper, these typical manifold learning methods are synthesized to find the underlying manifold structure from different angles. A more comprehensive local structure is discovered under a unified framework by constructing an objection optimization function for dimension reduction of the process data. The proposed method takes advantage of different manifold learning methods. Based on the proposed dimension reduction method, a new data-driven fault detection method is developed. Hotelling’s T2 and Q statistics are established for the purpose of fault detection. Experiments on an industrial benchmark Tennessee Eastman process and a real blast furnace ironmaking process are carried out to demonstrate the superiority and effectiveness of the proposed method.

This paper addresses the modeling of the iron ore direct reduction process, a process likely to reduce CO₂ emissions from the steel industry. The shaft furnace is divided into three sections (reduction, transition, and cooling), and the model is two-dimensional (cylindrical geometry for the upper sections and conical geometry for the lower one), to correctly describe the lateral gas feed and cooling gas outlet. This model relies on a detailed description of the main physical–chemical and thermal phenomena, using a multi-scale approach. The moving bed is assumed to be comprised of pellets of grains and crystallites. We also take into account eight heterogeneous and two homogeneous chemical reactions. The local mass, energy, and momentum balances are numerically solved, using the finite volume method. This model was successfully validated by simulating the shaft furnaces of two direct reduction plants of different capacities. The calculated results reveal the detailed interior behavior of the shaft furnace operation. Eight different zones can be distinguished, according to their predominant thermal and reaction characteristics. An important finding is the presence of a central zone of lesser temperature and conversion.