Detector design for active fault diagnosis in closed‐loop systems

Abstract

Fault diagnosis of closed-loop systems is extremely relevant for high-precision equipment and safety critical systems. Fault diagnosis is usually divided into 2 schemes: active and passive fault diagnosis. Recent studies have highlighted some advantages of active fault diagnosis based on dual Youla-Jabr-Bongiorno-Kucera parameters. In this paper, a method for closed-loop active fault diagnosis based on statistical detectors is given using dual Youla-Jabr-Bongiorno-Kucera parameters. The goal of this paper is 2-fold.First, the authors introduce a method for measuring a residual signal subject to white noise. Second, an optimal detector design is presented for single and multiple faults using the amplitude and phase shift of the residual signal to conduct diagnosis. Here, both the optimal case of a perfect model and the suboptimal case of a model with uncertainties are discussed. The method is successfully tested on a simulated system with parametric faults.

Parametric Fault Diagnosis of an Active Gas Bearing

“…It is therefore convenient to use an excitation signal that makes it possible to detect the faults while trying not to disturb the process. A method for determining the frequency of the sinusoidal excitation signal was introduced in [24]. The goal of the method is to maximise the impact of faults on the fault signature system while minimising the impact of the excitation signal on the outputs.…”

“…It is decided in this paper to use a matched filter detector design. Such a matched filter detector design was introduced in [26] and it was shown in [24] how to apply it to the case of active fault detection based on the fault signature system. Based on Figure 8, diagnosis is based on equation (22) where the disturbance is introduced.…”

“…Here the disturbance d is assumed to be white gaussian noise (WGN). Based on the results in [26] it is possible to formulate a H 0 hypothesis as in equation (24) and a H 1 hypothesis as in equation (25).…”

“…The residual signal used in [21] and here denoted as β is filtering a systems noise signals through a linear filter. The detector design is based on the noise in equation (24) being white. This will in general not be satisfied when using the β signal as the residual for fault detection on the active gas bearing.…”

“…Using the signal β as the residual signal results in that the measurement noise is subject to a linear filter. It was proposed in [24] to design a whitening filter for the fault free case. Since the active gas bearing is open loop stable it is possible to find a whitening filter that also keep the variance of the noise the same on the residual signal as on the measurements.…”