Sensor faults in wireless structural health monitoring (SHM) systems may reduce the monitoring quality and, if remaining undetected, might cause substantial economic loss due to inaccurate or missing sensor data required for structural assessment and life-cycle management of the monitored structure. Usually, fault detection in sensor networks is achieved through a redundant deployment of sensors and further hardware components ("physical redundancy"), which involves considerable penalties in cost and maintainability. Overcoming these drawbacks, in this study the information inherent in the SHM system and the known relationships between the sensors are used for fault detection without the need for additional sensors ("analytical redundancy"). Furthermore, the analytical redundancy approach is implemented in a fully decentralized manner: Partial models of the SHM system, being embedded directly into the wireless sensor nodes, enable each sensor node to autonomously detect sensor faults in real time while efficiently using the limited computing resources.