This paper proposes a novel geometry optimization strategy for the online robust active fault diagnosis (AFD) of discrete-time linear parameter varying (LPV) systems under set-theoretic framework. By establishing a bank of zonotopic set-value observers to match healthy/faulty system modes, the key of the optimization strategy comes down to the design of the optimal system inputs and gain matrices simultaneously. The criterion on the design of optimal inputs is characterized by fully utilizing the geometry property of zonotopes, which formulates a non-convex fractional programming problem able to be solved under 0–1 mixed integer quadratic programming framework based on a series of transformations. While the optimal gain matrices can be obtained analytically based on a so-called zonotopic kalman filtering process. The proposed method can improve the sensitivity of AFD as much as possible while ensuring the stability of the designed observer. At the end, two physical models are used to verify the effectiveness of our proposed method.

本文提出了一种新颖的几何优化策略，用于在集合论框架下对离散时间线性参数变化 (LPV) 系统进行在线鲁棒主动故障诊断 (AFD)。通过建立一组 zonotopic 设置值观察器来匹配健康/故障系统模式，优化策略的关键归结为同时设计最优系统输入和增益矩阵。最优输入设计准则的特点是充分利用了环带形体的几何特性，在一系列变换的基础上，在 0-1 混合整数二次规划框架下制定了一个可求解的非凸分数阶规划问题。虽然可以基于所谓的分区卡尔曼滤波过程分析地获得最佳增益矩阵。所提方法在保证设计观测器稳定性的同时，尽可能提高AFD的灵敏度。最后，使用两个物理模型来验证我们提出的方法的有效性。