具有非线性等式约束的故障诊断集员滤波器设计
Fault diagnosis based on the set membership filter with nonlinear equality constraint

为了解决具有非线性等式约束的故障诊断问题，提出集员滤波器的设计方法，该方法不仅可以对故障程度进行估计，有效检测出故障，还能解决运行系统中要求的100%包含真实最小域的需要，判定出故障类型. 首先对非线性等式约束线性化，通过S-过程方法和线性矩阵不等式方法设计集员滤波器；而后用Finsler引理把非约束状态下的集员滤波投射到约束表面，得到状态约束下的集员滤波器；最后运用递归优化算法对集员滤波器进行优化. 数值仿真说明了该方法的可行性和有效性.
The design method of set membership filter is proposed to solve the problem fault diagnosis with nonlinear equality constraint，this method not only can estimate the size of the fault and delete the fault effectively，but also can guarantee the system requiring 100％confidence to be estimated. Furthermore it can detect the type of fault signal. In this note the nonlinear equality constraint is first linearized，then S-procedure and linear matrix inequalities(LMI) method is applied to design set membership filter. The set membership filter with nonlinear equality constraint is finally derived from projecting the unconstrained set-membership filter onto the constrained surface by using Finsler’s Lemma. Finally，a recursive algorithm is developed for computing the set membership filter. The simulation result shows that the method presented is available and effective