In this paper, we investigate different scenarios of anomaly detection on decentralised Internet of Things (IoT) applications. Specifically, an anomaly detector is devised to detect different types of anomalies for an IoT data management system, based on the decentralised alternating direction method of multipliers (ADMM), which was proposed in our previous work. The anomaly detector only requires limited information from the IoT system, and can be operated using both a mathematical-rule-based approach and the deep learning approach proposed in the paper. Our experimental results show that detection based on mathematical approach is simple to implement, but it also comes with lower detection accuracy (78.88%). In contrast, the deep-learning-enabled approach can easily achieve a higher detection accuracy (96.28%) in the real world working environment.