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In recent years, the industrial use of the internet of things (IoT) has been constantly growing and is now widespread. Wireless sensor networks (WSNs) are a fundamental technology that has enabled such prevalent adoption of IoT in industry. WSNs can connect IoT sensors and monitor the working conditions of such sensors and of the overall environment, as well as detect unexpected system events in a timely and accurate manner. Monitoring large amounts of unstructured data generated by IoT devices and collected by the big-data analytics systems is a challenging task. Furthermore, detecting anomalies within the vast amount of data collected in real time by a centralized monitoring system is an even bigger challenge. In the context of the industrial use of the IoT, solutions for monitoring anomalies in distributed data flow need to be explored. In this paper, a low-power distributed data flow anomaly-monitoring model (LP-DDAM) is proposed to mitigate the communication overhead problem. As the data flow monitoring system is only interested in anomalies, which are rare, and the relationship among objects in terms of the size of their attribute values remains stable within any specific period of time, LP-DDAM integrates multiple objects as a complete set for processing, makes full use of the relationship among the objects, selects only one "representative" object for continuous monitoring, establishes certain constraints to ensure correctness, and reduces communication overheads by maintaining the overheads of constraints in exchange for a reduction in the number of monitored objects. Experiments on real data sets show that LP-DDAM can reduce communication overheads by approximately 70% when compared to an equivalent method that continuously monitors all objects under the same conditions. [ABSTRACT FROM AUTHOR]