非线性椭球集员滤波及其在故障诊断中的应用

Nonlinear Set Membership Filtering Using Ellipsoids and Its Application in Fault Diagnosis

针对带有未知但有界噪声的非线性系统,提出一种椭球集员滤波算法,并将其应用于保证故障检测与隔离。对非线性状态方程和量测方程进行泰勒展开之后,通过区间分析的方法给出线性化余项存在区域的盒子外界描述。假设过程和量测噪声由盒子限界,在算法的时间更新和量测更新过程中,分别计算包含椭球与线段的向量和及椭球与带的交的次最小容积椭球。在椭球集员滤波算法的基础之上,给出传感器故障检测与隔离的方法。由于集员滤波是保证状态估计,因而基于集员滤波算法的故障检测与隔离方法也具有保证性,即如果发出故障警报,则一定有故障发生。一个二维非线性系统的例子说明了该方法的有效性。

A set membership filtering algorithm using ellipsoidal sets for nonlinear systems with unknown but bounded noises is proposed and applied to guaranteed fault detection and isolation （FDI）. After the nonlinear state and observation equations are expended in a Taylor series, a tight box outerbounding the region in which the linearization remainder potentially lies is found using interval analysis. Assuming that boxes are employed to hound the process and observation noises, the time and observation updates in the algorithm require computing a subminimal-volume ellipsoid containing the vector sum of an ellipsoid and segments and the intersection of an ellipsoid and strips respectively. Based on the filtering algorithm, sensor FDI approaches are developed. Since the set membership filtering is a guaranteed state estimation, the FDI approaches are guaranteed FDI approaches, which means that if a fault is detected, there is truly a fault in the system. The proposed approaches are applied to a two-state nonlinear system to gain insight into their inner-workings.