Abstract:

This paper focuses on the fault detection of a class of discrete-time systems with random faults and proposes a fault-dependent approach. Firstly, a mathematical model is constructed to describe the above problems, and the characteristics of fault signals are transformed into matrices containing uncertainties. By constructing a fault detection filter as a residual generator, the fault detection and isolation (FDI) problem is transformed into a H_∞filtering problem. Based on the established model, the  H_∞ performance is analyzed by adopting a fault-dependent method. The parameter-dependent Lyapunov function is selected for processing. On this basis, the existence condition of the fault detection filter is given in the form of linear matrix inequalities. Finally, an example is used to verify the effectiveness and practicability of the theoretical results.

Key words: Fault detection and isolation, Fault dependence method, Random fault, H_&infin,  filtering, Linear matrix inequality

摘要： 主要研究一类具有随机故障发生的离散时间系统的故障检测问题, 提出了一种故障依赖方法。首先构建一种数学模型来描述上述问题, 将故障信号的特征转化为含有不确定性的矩阵。通过构造一个故障检测滤波器作为残差发生器, 将故障检测与隔离问题转化为H_∞滤波问题。基于所建立的模型, 通过采用故障依赖的方法对 H_∞性能进行分析, 选用参数依赖的李雅普诺夫函数进行处理。在此基础上, 以线性矩阵不等式的形式给出故障检测滤波器的存在条件。最后通过实例验证理论结果的有效性和实用性。

关键词: 故障检测与隔离, 故障依赖方法, 随机故障, H_∞滤波, 线性矩阵不等式