In this paper we propose a novel machine-learning method for anomaly detection applicable to data with periodic characteristics where randomly varying period lengths are explicitly allowed. A multi-dimensional time series analysis is conducted by training a data-adapted classifier consisting of deep convolutional neural networks performing phase classification. The entire algorithm including data pre-processing, period detection, segmentation, and even dynamic adjustment of the neural networks is implemented for fully automatic execution. The proposed method is evaluated on three example datasets from the areas of cardiology, intrusion detection, and signal processing, presenting reasonable performance.