Nonlinear MIMO System Identification with Echo-State Networks

This paper presents a formalization of steps for identification of echo-state network (ESN)-based models for multiple-input and multiple-output (MIMO) nonlinear dynamic systems models, employing the best practices found in the literature. The ESN is a recurrent neural network capable to model nonlinear dynamics and it can be trained using computationally efficient algorithms. A simplified ESN architecture from the literature for process identification tasks is used and a procedure to create the model and tune the main hyperparameters is proposed. The proposed method is evaluated using both a simulated pH neutralization process and a real refrigeration compressor test rig. For each case study, the procedure to obtain the data series, the model creation, and the influence of each hyperparameter in the model performance are discussed. In both cases, the proposed model architecture presented better results than the linear model and the two nonlinear models used as baseline, namely an extreme learning machine-based Hammerstein model and a long short-term memory network model. The results show that the proposed ESN-based system identification method can be used to obtain MIMO models for nonlinear processes using a computationally efficient training algorithm. For the ESN architecture considered in the case studies, the training time is about 80 s, while a prediction can be obtained in about 15 ms.