The reliable operation of automatic systems is heavily dependent on the ability to detect faults in the underlying dynamical system. While traditional model-based methods have been widely used for fault detection, data-driven approaches have garnered increasing attention due to their ease of deployment and minimal need for expert knowledge. In this paper, we present a novel principal component analysis (PCA) method that uses occupation kernels. Occupation kernels result in feature maps that are tailored to the measured data, have inherent noise-robustness due to the use of integration, and can utilize irregularly sampled system trajectories of variable lengths for PCA. The occupation kernel PCA method is used to develop a reconstruction error approach to fault detection and its efficacy is validated using numerical simulations.

翻译：自动系统的可靠运行高度依赖于对底层动态系统中故障的检测能力。虽然传统的基于模型的方法已广泛用于故障检测，但数据驱动方法因其易于部署且对专家知识需求极少而日益受到关注。本文提出了一种利用占用核的新型主成分分析方法。占用核产生的特征映射针对测量数据定制，由于采用了积分而具有固有的噪声鲁棒性，并且能够利用长度可变的非均匀采样系统轨迹进行主成分分析。通过占用核主成分分析方法，开发了一种基于重构误差的故障检测方法，并通过数值仿真验证了其有效性。