Small faults (some weak faults with a tiny magnitude) are difficult to detect and may cause severe problems leading to degrading the system performance. This paper proposes an approach to estimate, detect, and isolate small faults in uncertain nonlinear systems subjected to model uncertainties, disturbances, and measurement noise. A robust observer is developed to alleviate the lack of full state measurement. Using the estimated state, a dynamical radial basis function neural networks observer is designed in form of LMI problem to accurately learn the function of the inseparable mixture between modeling uncertainty and the small fault. By exploiting the knowledge obtained by the learning phase, a bank of observers is constructed for both normal and fault modes. A set of residues is achieved by filtering the differences between the outputs of the bank of observers and the monitored system output. Due to the noise dampening characteristics of the filters and according to the smallest residual principle, the small faults can be detected and isolated successfully. Finally, rigorous analysis is performed to characterize the detection and isolation capabilities of the proposed scheme. Simulation results are used to prove the efficacy and merits of the proposed approach.

中文翻译：

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基于神经观测器的不确定非线性系统小故障检测与隔离

小故障（一些微弱的故障，其幅度很小）很难检测到，并且可能导致严重的问题，从而导致系统性能下降。本文提出了一种方法，用于估计，检测和隔离受模型不确定性，干扰和测量噪声影响的不确定非线性系统中的小故障。开发了一个健壮的观察器来缓解缺乏完整状态测量的情况。利用估计状态，以LMI问题的形式设计了动态径向基函数神经网络观察器，以准确地学习建模不确定性和小故障之间不可分割的混合函数。通过利用在学习阶段获得的知识，针对正常模式和故障模式构建了一组观察者。通过过滤观察者组的输出和受监视的系统输出之间的差异，可以实现一组残差。由于滤波器的噪声衰减特性，并且根据最小残留原理，可以成功检测并隔离小故障。最后，进行严格的分析以表征所提出方案的检测和隔离能力。仿真结果证明了该方法的有效性和优越性。