The early and automatic detection of faulty behavior is essential for maintaining the reliability of a cyber-physical system. In this paper we describe a fault localization approach for such a highly complex distributed system, the optical synchronization system of the European X-ray free-electron laser. Using a dependency graph, we model the relationships between the components and the influences of environmental effects. After we first resolve linear long-term dependencies between dependent components with a correlation analysis, we then use an unsupervised fault detection pipeline consisting of statistical feature extraction and unsupervised anomaly detection to accurately identify anomalies and localize their origins in the system.