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Model inference aims to extract accurate models from the execution logs of software systems. However, in reality, logs may contain some "noise" that could deteriorate the performance of model inference. One form of noise can commonly be found in system logs that contain not only transactional messages---logging the functional behavior of the system---but also operational messages---recording the operational state of the system (e.g., a periodic heartbeat to keep track of the memory usage). In low-quality logs, transactional and operational messages are randomly interleaved, leading to the erroneous inclusion of operational behaviors into a system model, that ideally should only reflect the functional behavior of the system. It is therefore important to remove operational messages in the logs before inferring models. In this paper, we propose LogCleaner, a novel technique for removing operational logs messages. LogCleaner first performs a periodicity analysis to filter out periodic messages, and then it performs a dependency analysis to calculate the degree of dependency for all log messages and to remove operational messages based on their dependencies. The experimental results on two proprietary and 11 publicly available log datasets show that LogCleaner, on average, can accurately remove 98% of the operational messages and preserve 81% of the transactional messages. Furthermore, using logs pre-processed with LogCleaner decreases the execution time of model inference (with a speed-up ranging from 1.5 to 946.7 depending on the characteristics of the system) and significantly improves the accuracy of the inferred models, by increasing their ability to accept correct system behaviors (+43.8 pp on average, with pp=percentage points) and to reject incorrect system behaviors (+15.0 pp on average).