One of the most critical issues when deploying wireless sensor networks for long-term structural health monitoring (SHM) is the correct and reliable operation of sensors. Sensor faults may reduce the quality of monitoring and, if remaining undetected, might cause significant economic loss due to inaccurate or missing sensor data required for structural assessment and life-cycle management of the monitored structure. This paper presents a fully decentralized approach towards autonomous sensor fault detection and isolation in wireless SHM systems. Instead of physically installing multiple redundant sensors in the monitored structure ("physical redundancy"), which would involve substantial penalties in cost and maintainability, the information inherent in the SHM system is used for fault detection and isolation ("analytical redundancy"). Unlike traditional centralized approaches, the analytical redundancy approach is implemented distributively: Partial models of the wireless SHM system, implemented in terms of artificial neural networks in an object-oriented fashion, are embedded into the wireless sensor nodes deployed for monitoring. In this paper, the design and the prototype implementation of a wireless SHM system capable of autonomously detecting and isolating various types of sensor faults are shown. In laboratory experiments, the prototype SHM system is validated by injecting faults into the wireless sensor nodes while being deployed on a test structure. The paper concludes with a discussion of the results and an outlook on possible future research directions.