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This paper focuses on using machine learning methods to detect and monitor fatigue crack propagation using ultrasonic signals. The basic principle is the detection of a prolonged transit time of the signal as an indicator of changes in the material caused by growth of the failure. A multilayer perceptron (MLP) network supplemented with simple convolutional layers is employed to analyse the signal parameters. First, synthetic data are generated using basic physical principles to verify the underlying phenomenology and the network's ability to detect material changes based on prolonged elastic wave transit times. The focus is particularly on methods to suppress the over-training phenomenon. Subsequently, the approach is applied to real pipeline fatigue test data. The results demonstrate the potential of even small neural architectures for the early detection of failures in engineering components.