Different from the latent variables which characterize the implicit relation, the proposed method focuses on discovery and description of the explicit relation between measured variables, based on which a novel statistical process monitoring approach is then derived for both static and dynamic processes. First, the canonical correlation analysis (CCA) algorithm is employed to find a set of interacted variables for every single variable individually, a regression model is then used to describe the explicit relation between the interacted variables. Second, on the basis of an ensemble representation of the mathematically defined explicit relation, fault detection and reconstruction-based contribution for fault diagnosis through the residual can be implemented. Finally, the effectiveness and superiority of the proposed approach are validated through comparisons with other state-of-the-art methods that based on latent variable models.
