This article is devoted to the development of a classification method based on an artificial neural network architecture to solve the problem of recognizing the sources of acoustic influences recorded by a phase-sensitive OTDR. At the initial stage of signal processing, we propose the use of a band-pass filter to collect data sets with an increased signal-to-noise ratio. When solving the classification problem, we study three widely used convolutional neural network architectures: AlexNet, ResNet50, and DenseNet169. As a result of computational experiments, it is shown that the AlexNet and DenseNet169 architectures can obtain accuracies above 90%. In addition, we propose a novel CNN architecture based on AlexNet, which obtains the best results; in particular, its accuracy is above 98%. The advantages of the proposed model include low power consumption (400 mW) and high speed (0.032 s per net evaluation). In further studies, in order to increase the accuracy, reliability, and data invariance, the use of new algorithms for the filtering and extraction of acoustic signals recorded by a phase-sensitive reflectometer will be considered.