The present work proposes a fast-convergent fault detection and isolation (FDI) scheme for linear systems affected by model uncertainties, such as unknown inputs or unbounded nonlinearities. The finite-time convergence is attained by transforming the I/O signals through Volterra operators with suitably designed kernel functions. A novel feature of the proposed approach is the exploitation of a system decomposition that allows removing the effect of intractable uncertainties while recasting the system dynamics in a form applicable for Volterra operators to achieve non-asymptotic estimation. Remarkably, the proposed approach can reconstruct the state variables of the system in an arbitrarily short time and the fault can be diagnosed efficiently by imposing detection and isolation thresholds on transformed signals. The detectability and isolability of the fault are also characterized. The proposed FDI scheme is applied in simulation to a web process system to diagnose the presence of actuator faults. Simulation results confirm the effectiveness of the proposed scheme in two scenarios with nonlinear uncertainties. Furthermore, comparisons are made between the proposed method and a Sliding Mode Control (SMC) method in terms of estimation performance and computational complexity.

本工作为受模型不确定性（例如未知输入或无界非线性）影响的线性系统提出了一种快速收敛的故障检测和隔离（FDI）方案。通过具有适当设计的内核功能的Volterra运算符对I / O信号进行转换，可以实现有限时收敛。所提出方法的新颖特征是利用系统分解功能，该功能可以消除难以解决的不确定性的影响，同时以适用于Volterra算子的形式重铸系统动力学，以实现非渐近估计。值得注意的是，所提出的方法可以在任意短的时间内重建系统的状态变量，并且可以通过对转换后的信号施加检测和隔离阈值来有效地诊断故障。还对故障的可检测性和可隔离性进行了表征。所提出的FDI方案在仿真中应用于Web处理系统，以诊断执行器故障的存在。仿真结果证实了该方案在具有非线性不确定性的两种情况下的有效性。此外，在估计性能和计算复杂度方面，对提出的方法和滑模控制（SMC）方法进行了比较。