Fault Detection for Nonlinear Process Using Data-Based Dissipativity in a Lifted Space

In this work, a novel data-based fault monitoring scheme for nonlinear processes is formulated using data-based dissipativity theory. The basic idea is mapping the nonlinear dynamics into a higher-dimensional space, wherein the evolution approximates linearity. Dissipativity properties are learned from available input/output trajectories in a data-driven manner. However, the dissipative nature of a process may not effectively respond during fault occurrences as an input/output property. To address this, the proposed method tailors the dissipative properties of the process to be fault-sensitive (i.e., no longer efficient during fault occurrences). By employing the supply rates and storage functions in quadratic-difference form (QdF), the dissipation condition is formulated as a quadratic function of the process input/output trajectory, which captures a more detailed dynamical characterization than conventional dissipativity. The dissipative properties are determined offline through the solution of an optimization problem with linear matrix inequality (LMI) constraints, then applied online to design a monitoring algorithm that only involves verifying the inequalities of the input/output trajectories. Finally, a numerical example is presented to demon-strate the effectiveness of the proposed approach.