Data-driven assessment of VI diagrams for inference on pantograph quantities waveform distortion in AC railways

This work proposes an application of unsupervised deep learning (DL) on 2-D images containing VI diagrams of measured railway pantograph quantities to find patterns in operating conditions (OCs) and waveform distortion. Measurement data consist of pantograph voltage and current measurements from a Swiss 15 kV 16.7 Hz commercial locomotive and a French 2x25 kV 50 Hz test-dedicated locomotive, containing more than 4000 records of 5-cycle snippets for each system. The variational autoencoder (VAE), followed by feature clustering, finds patterns in the input data. Each cluster captures patterns from the VI diagrams, which contain information from current and voltage waveshapes and sub-second variations. The time-domain admittance allows inference about the rolling stock (RS) operation and the waveform distortion spectra, including harmonics and supraharmonics characteristics from both RS and traction supply. The VAE successfully performs data embedding using only 16 channels in the latent space. The effectiveness of the method is quantified by means of the mean square reconstruction error (never larger than 1.5% and equal to 0.31% and 0.33% on average for the Swiss and French case, respectively). The t-SNE visualization confirms that overlapping of clusters is negligible, with a percentage of “misplaced” cluster points of 2.18% and 2.50%, again for the Swiss and French case, respectively. The computation time for the VAE prediction could be brought to some tens of ms representing a performance reference for future implementations. The proposed VI diagram assessment covers emissions for different OCs, rapid changes in power supply conditions, and background distortion caused by other trains on the same line, including line and impedance changes due to the moving load. In this perspective physical justification is found by domain knowledge integration for the identified clusters. A concluding discussion regarding advantages, limitations, and potential improvements or diversification is also included.