一类非线性系统的故障可诊断性量化评价方法

为将提高卫星控制系统故障诊断能力的工作重点前移到地面设计阶段,针对其中的关键问题--可诊断性评价,提出一种适用于非线性模型的可诊断性量化评价方法,对传统定性评价研究进行了有效的扩展和延伸。鉴于线性化处理导致非线性因素引起的故障被忽略,将卫星控制系统描述成一类仿射非线性模型;并基于微分几何理论,给出可诊断性（包括可检测性和可隔离性）的定义和定性评价指标--不变最小对偶分布。通过子空间相似度判别准则,根据故障方向矢量和所得不变分布以及不同故障方向矢量之间的夹角关系,分别设计可检测性和可隔离性的量化指标,并给出具体评价流程;该指标能够明确故障被检测和隔离的难易程度,并可用于指导诊断算法的设计和传感器的优化配置。最后,以动量轮为仿真实例校验本文所提方法的正确性;仿真结果表明：该方法在不依赖任何诊断算法和具体故障模式的前提下,可以实现可检测性和可隔离性的准确量化评价。

An Approach to Fault Diagnosability Quantitative Evaluation for a Class of Nonlinear Systems

To improve the fault diagnosis ability of satellite control systems in the design phase, a novel approach to quantitatively evaluate fault diagnosability of nonlinear models is proposed. This approach is the extension of the previous researches on qualitative fault diagnosability analysis. Considering the faults caused by nonlinear factors are ignored because of linearization, satellite control systems are described a class of affine nonlinear models. The definition of fault diagnosability based on the minimal invariant dual-distribution is presented through the differential-geometric approach. According to the discriminant function of subspace similarity, the relationships of the angle included between the fault directional vector and the minimal invariant dual-distribution and the angle included between directional vectors of different faults are used to design quantitative criteria of detectability and isolability respectively. The criteria can actually exploited for answering an question like "How difficult is it to detect/isolate a fault?" and for guiding the design of fault diagnosis algorithms and the optimal placement of sensors. And then a specific evaluation process is provided. Finally, the momentum wheel is taken as an illustrative example applied to verify the correctness of the proposed approach. The simulation results show that this approach can exactly quantify the difficult levels to detect and isolate a fault before designing a fault diagnosis algorithm.