Fusion Maximal Information Coefficient-Based Quality-Related Kernel Component Analysis: Mathematical Formulation and an Application for Nonlinear Fault Detection

Amid intensifying global competition, industrial product quality has become a critical determinant of competitive advantage. However, persistent quality-related faults in production environments threaten product integrity. To address this challenge, a Fusion Maximal Information Coefficient-based Quality-Related Kernel Component Analysis (FMIC-QRKCA) methodology is proposed in this paper by capitalizing on information fusion principles and statistical metric theory. Based on information fusion principles, a Fusion Maximal Information Coefficient (FMIC) strategy is first studied to quantify correlations between process variables and multivariate quality indicators. Subsequently, by integrating the proposed FMIC method with Kernel Principal Component Analysis (KPCA), a Quality-Related Kernel Component Analysis (QRKCA) method is proposed. In the proposed QRKCA strategy, the complete latent variable space is first obtained; on this basis, FMIC is further applied to quantify the correlation between each latent variable and quality variables, thereby completing the screening of quality-related latent variables. Additionally, the $T^2$ and squared prediction error monitoring statistics are used as the key indices to determine the occurrence of faults. This integration overcomes the limitation of conventional KPCA, which does not explicitly consider quality indicators during the principal component extraction, thereby enabling precise isolation of quality-related fault features. Validation through the numerical case and the industrial process case demonstrates that FMIC-QRKCA significantly outperforms established methods in detection accuracy for quality-related faults.