Performances theoretical model-based optimization for incipient fault detection with KL Divergence

Sensible and reliable incipient fault detection methods are major concerns in industrial processes. The Kullback Leibler Divergence (KLD) has proven to be particularly efficient. However, the performance of the technique is highly dependent on the detection threshold and the Signal to Noise Ratio (SNR). In this paper, we develop an analytical model of the fault detection performances (False Alarm Probability and Miss Detection Probability) based on the KLD including the noisy environment characteristics. Thanks to this model, an optimization procedure is applied to set the optimal fault detection threshold depending on the SNR and the fault severity.