The present article is devoted to the development of a method and its software implementation for forecasting the critical states of a turbogenerator and its design elements that arise during starting-up & adjustment works and stopping a turbine. The method is based on a short-term prediction of the image of the spectrogram of vibrations during thermal expansion of the rotor and stator. The dependence of the increase in the vibration level in the spectrum with the failure of the turbogenerator design element is substantiated. The model takes into account the influence of thermal expansion on critical states. The technique of training a deep neural network is given in the classification of thermal influences on the level of vibration while a spectrogram receiving. For machine learning of a neural network in software, a recurrent autoencoder is used. The technique of operation is with a time sequence of spectrograms. To test the model is introduced the concept of semantic quality of clustering. Semantic quality, determined as the degree of correspondence between the information that can be extracted from the obtained cluster structure and the formalized presentation of the user. The interpretation of the results of the discovery of turbine generator defects is presented.