A Satellite Incipient Fault Detection Method Based on Local Optimum Projection Vector and Kullback-Leibler Divergence

Abstract

Timely and effective detection of potential incipient faults in satellites plays an important role in improving their availability and extending their service life. In this paper, the problem of detecting incipient faults using projection vector (PV) and Kullback-Leibler (KL) divergence is studied in the context of detecting incipient faults in satellites. Under the assumption that the variables obey a multidimensional Gaussian distribution and using KL divergence to detect incipient faults, this paper models the optimum PV for detecting incipient faults as an optimization problem. It proves that the PVs obtained by principal component analysis (PCA) are not necessarily the optimum PV for detecting incipient faults. It then compares the on-line probability density function (PDF) with the reference PDF for detecting incipient faults on the local optimum PV. A numerical example and a real satellite fault case were used to assess the validity and superiority of the method proposed in this paper over conventional methods. Since the method takes into account the characteristics of the actual incipient faults, it is more adaptable to various possible incipient faults. Fault detection rates of three simulated faults and the real satellite fault are 98%, 84%, 93% and 92%, respectively.

A Satellite Incipient Fault Detection Method Based on Decomposed Kullback–Leibler Divergence

“…In this case, what is the point of decomposing ? According to reference [ 30 ], the ultimate goal of maximizing is to determine the PV that is most sensitive to the incipient fault; that is, our ultimate goal is to detect the incipient fault. From the aspect of fault detection, although the PV obtained by maximizing the subfunction may not be optimal for the original function, the PV has its own value if it can detect the fault and be obtained in a fast manner.…”

“…Under the assumption that the data obey a multidimensional Gaussian distribution, and using the KL divergence to detect incipient faults, the problem of finding the optimum projection vector (PV) is modeled as follows [ 30 ]: …”

“…In Equations (3) and (4), is a PV, is the KL divergence of the projections of normal historical data and online data . Both the normal historical data and the online data obey dimensional joint Gaussian distributions, , [ 30 ]. Let , ; the KL divergence can be expressed as the sum of two GRQs, as shown in Equation (5): where , , , .…”

“…Similarly, the optimization problem in Equation (3) is NP-hard. In Reference [ 30 ], a ready-made optimization solution tool (the fmincon function in MATLAB) is used to solve the optimization problem. However, this method can only obtain the local optimum PV, rather than the global optimum PV.…”

“…Deng et al [ 29 ] combined two-step localized kernel PCA with the KL divergence for nonlinear system incipient fault monitoring. Zhang et al [ 30 ] proposed that the principal components obtained by PCA are not necessarily the optimum projection vector (PV) for detecting incipient faults. Furthermore, the problem of finding the optimum PV was modeled as an optimization model.…”