Nonlinear system identification using modified variational autoencoders

This research proposes a methodology for identifying nonlinear systems using input/output data and deep learning generative models. Our framework integrates Variational Autoencoders (VAE) with Nonlinear Autoregressive with exogenous input (NARX) in a unified identification structure to address overfitting in nonlinear system identification using NARX structures. Specifically, we modify a variational autoencoder by replacing the decoder module with a NARX model using the latent space information captured from the VAE encoder module as one of the exogenous inputs. Following the training phase, the decoder module can be used as a nonlinear model of the system. We evaluate the efficacy of our approach by performing open-loop prediction tests on data from four nonlinear benchmark systems: Cascaded tanks, Gas furnace, Silverbox, and Wiener- Hammerstein. The proposed VAE-NARX method reported Root Mean Squared Error (RMSE) of 8.23 x 10-3, -3 , 16.69 x 10-3, -3 , 0.002 x 10-3 -3 and 0.037 x 10-3 -3 respectively. Our results demonstrate that our proposed method achieves similar and outperforms prediction performances to standard identification techniques and can enhance the performance of traditional nonlinear system identification methods based on multi-layer perceptron models.