Structure-Adaptive Graph Embedding With Fractal Analysis for Industrial Process Monitoring

This paper focuses on the monitoring problem of the Magnesium Smelting Process (MSP). First, the paper systematically analyzes the key adjustable external variables that affect the temperature in the furnace from the perspective of heat transfer theory, and elaborates on the necessity of monitoring for the MSP. Second, existing process monitoring methods have some primary limitations: (1) Methods that only consider single structural information can only preserve partial data features, making it difficult to fully characterize the inherent data structure. (2) Methods that simultaneously consider both local and global structural information typically construct similarity matrices with fixed neighbor relationships, which is difficult to adapt to the complex changes in actual data. (3) The selection of dimensions for the low-dimensional feature space lacks an objective, quantifiable criterion. To address these challenges, this paper proposes a Structure-Adaptive Graph Embedding with Fractal Analysis (SAGE-FA) algorithm. This algorithm offers three key advantages: (1) It integrates the projection matrix and similarity matrix into a unified objective function for joint optimization, enabling the preservation of the global geometric structure while more effectively capturing local adjacency relationships. (2) By incorporating an adaptive neighborhood strategy, SAGE-FA dynamically mines local adjacency relationships, enabling more flexible adaptation to the characteristics of complex industrial data. (3) A fractal dimension evaluation method is introduced to establish an objective criterion for determining the dimensionality of the low-dimensional feature space. On this basis, a two-stage monitoring method incorporating fault detection and fault localization is designed. Finally, experiments on the Tennessee Eastman process (TEP) and actual MSP datasets, achieving average fault detection rates of 80.28% and 94.5%, respectively. These results demonstrate the effectiveness of the proposed method.