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Compressive sensing is an efficient machinery monitoring framework, which just needs to sample and store a small amount of observed signal. However, traditional reconstruction and fault detection methods cost great time and the accuracy is not satisfied. For this problem, a 1D convolutional neural network (CNN) is adopted here for fault diagnosis using the compressed signal. CNN replaces the reconstruction and fault detection processes and greatly improves the performance. Since the main information has been reserved in the compressed signal, the CNN is able to extract features from it automatically. The experiments on compressed gearbox signal demonstrated that CNN not only achieves better accuracy but also costs less time. The influencing factors of CNN have been discussed, and we compared the CNN with other classifiers. Moreover, the CNN model was also tested on bearing dataset from Case Western Reserve University. The proposed model achieves more than 90 % accuracy even for 50 % compressed signal. [ABSTRACT FROM AUTHOR]