An optimal fault detection threshold for early detection using Kullback–Leibler Divergence for unknown distribution data

The incipient fault detection in industrial processes with unknown distribution of measurements signals and unknown changed parameters is an important problem which has received much attention these last decades. However most of the detection methods (online and offline) need a priori knowledge on the signal distribution, changed parameters, and the change amplitude (Likelihood ratio test, Cusum, etc.). In this paper, an incipient fault detection method that does not need any a priori knowledge on the signals distribution or the changed parameters is proposed. This method is based on the analysis of the Kullback–Leibler Divergence (KLD) of probability distribution functions. However, the performance of the technique is highly dependent on the setting of a detection threshold and the environment noise level described through Signal to Noise Ratio (SNR) and Fault to Noise Ratio (FNR). In this paper, we develop an analytical model of the fault detection performances (False Alarm Probability and Missed Detection Probability). Thanks to this model, an optimisation procedure is applied to optimally set the fault detection threshold depending on the SNR and the fault severity. Compared to the usual settings, through simulation results and experimental data, the optimised threshold leads to higher efficiency for incipient fault detection in noisy environment.