This paper is devoted to the data-driven fault detection of nonlinear systems. For our purpose, the definition of Takagi–Sugeno fuzzy data-driven forms of kernel representations for nonlinear systems is introduced first, which builds the basis of our work. The major contributions consist of two parts. In the first part, a data-driven method for fuzzy process modeling is proposed, and associated with it, some modeling issues are addressed with the aid of the so-called randomized algorithm technique in the probabilistic framework. It is followed by a data-driven realization of fuzzy kernel representation and its implementation in the fault detection system design. To link the data-driven methods to the well-established observer-based fault detection approaches, the recursive form of the fuzzy kernel representation is proposed. In the second part, the fuzzy-observer-based fault detection design scheme is investigated based on the recursive fuzzy kernel representation. The main results of our study are illustrated by an experimental study on the laboratory setup of a three-tank system.

中文翻译：

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基于模糊核表示的数据驱动实现的非线性系统故障检测方法

本文致力于非线性系统的数据驱动故障检测。出于我们的目的，首先介绍了非线性系统内核表示的 Takagi-Sugeno 模糊数据驱动形式的定义，这为我们的工作奠定了基础。主要贡献包括两部分。在第一部分中，提出了一种用于模糊过程建模的数据驱动方法，并在此基础上借助概率框架中所谓的随机算法技术解决了一些建模问题。其次是模糊核表示的数据驱动实现及其在故障检测系统设计中的实现。为了将数据驱动方法与完善的基于观察器的故障检测方法联系起来，提出了模糊核表示的递归形式。在第二部分，研究了基于递归模糊核表示的基于模糊观察器的故障检测设计方案。我们研究的主要结果通过对三罐系统实验室设置的实验研究来说明。