Deep Echo State Networks for Modelling of Industrial Systems

In the industrial field, the modelling of complex systems is a relevant task to understand their evolution, to infer their most representative characteristics, or to detect anomalous situations. Nevertheless, this modelling is notably challenging within the industrial environment, with large amounts of data to be processed but several difficulties in extracting knowledge from these data. In this paper, we work with an industrial plant with four water tanks, focusing on estimating the levels of two sequentially connected tanks. For this purpose, Deep Echo State Networks (Deep ESNs), within the framework of Reservoir Computing (RC), are used, representing an increasingly popular methodology for efficient learning to modelling systems with diverse time-scale dynamics. Specifically, we have designed a learning system that makes use of a dedicated Deep ESN module for the prediction of the level of each tank. We conducted numerical experiments to examine how the performance of the predictions is affected by the number of layers. Our findings indicate that increasing the number of recurrent layers leads to better predictions, and also highlight noteworthy differences in the dynamics of the upper and lower tanks.