Manifold-constrained trace ratio optimization for nonstationary process performance monitoring

Data-driven control performance monitoring (CPM) is becoming increasingly important in assessing and diagnosing changes in intricate industrial processes that are challenging to investigate with precise prior knowledge. The existing data-driven CPM methods mostly set covariance or other autocorrelation indexes intended to reflect the global deviation from benchmarks and subsequently diagnose the loops or variables responsible for these changes. However, as these methods assume stationary sequences, only steady-state fluctuation is assessed and diagnosed. This limits the application to industrial processes where transient processes are negligible. A comprehensive performance index integrating the transient performance and the steady-state performance is defined in this paper. The manifold constraint is investigated to mine the transient features so that it can be merged into the variance-based assessment framework. Moreover, to address the issue of information redundancy in non-orthogonal directions, which is present in most existing methods, we proposed a trace ratio-driven framework for enhancing the accuracy of assessment and diagnosis. A numerical example and a simulated industrial cascaded continuous stirred tank heater process are used to test the assessment results and demonstrate the effectiveness of the proposed diagnosis strategy.