A theoretical approach for incipient fault severity assessment using the Kullback-Leibler Divergence

The limitations of statistical approaches used for Fault Detection and Diagnosis (FDD) of processes, are related to the local character of used statistics. For the sake of enhancing the detectability of incipient faults and assessing efficiently the fault level, that is the quality of operation, one should investigate the benefits a 'global' fault detection approach may provide. The Kullback-Leibler Divergence is proposed under the discipline of Statistical Process Control (SPC). A theoretical analysis is conducted to establish an analytical model relating the divergence to the fault severity amplitude. The model, when applied to a numerical example, provides an upper bound of the fault amplitude. While the usual statistics are not able to estimate the fault level, an upper bound is always necessary to guarantee a safety margin for the process.