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：可靠的自动控制系统操作在很大程度上依赖于检测底层动态系统的故障能力。传统的基于模型的方法在故障检测方面已被广泛使用，但数据驱动方法由于不需要专业知识而变得越来越受关注。本文提出一种利用占位核的主成分分析 (PCA) 方法。占位核可以生成适合测量数据的特征映射，由于使用积分具有内在的噪声鲁棒性，并且可以利用变长的不规则采样系统轨迹进行 PCA。利用占位核 PCA 方法，本文提出了一种基于重建误差的故障检测方法，并利用数值模拟验证了其有效性。
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