ESN with Delayed Inputs to Model Industrial Processes

Modeling industrial processes is essential for optimizing performance and detecting anomalies, particularly in complex systems with delayed responses. Echo State Networks (ESNs) have demonstrated efficiency in modeling dynamic systems due to their simple and fast training process. However, standard ESNs do not account for the delayed effects of input variables, which are common in industrial environments. This work introduces a Delayed Input Echo State Network to better capture the time-dependent relationships in process modeling. The proposed method is applied to real data from the AQUASOL-II solar plant at the Plataforma Solar de Almería (PSA), focusing on modeling output temperatures in solar collector loops. Three architectures are compared: a standard ESN, an ESN with a uniform input delay, and an ESN with independent delays for each variable. Results show that this delayed approach can improve the accuracy of the models compared to both traditional ESNs and physics-based models. These findings highlight the potential of an ESN with delayed inputs for real-time industrial applications, offering a balance between computational efficiency and performance.