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基础动态系统故障的检测能力。虽然传统的基于模型的方法已广泛应用于故障检测，但数据驱动方法因其易于部署且对专家知识需求较少而日益受到关注。本文提出一种利用占据核的新型主成分分析方法。占据核能够构建与测量数据相匹配的特征映射，通过积分操作具有固有的抗噪鲁棒性，并可利用长度不一的非均匀采样系统轨迹进行主成分分析。该方法基于占据核主成分分析构建重构误差实现故障检测，并通过数值仿真验证其有效性。