DBN based SD-ARX model for nonlinear time series prediction and analysis

One of the main purposes of nonlinear system modeling is to design model-based controllers such as model predictive control (MPC). A group of deep belief networks (DBNs) are used to approximate the function type coefficients of a state dependent autoregressive model with exogenous variables (SD-ARX), which can represent nonlinear dynamics, and thus a DBN-based state-dependent ARX (DBN-ARX) model is obtained in this paper. The DBN-ARX model has the function approximation ability of single DBN model and the nonlinear description advantage of SD-ARX model. All parameters of the DBN-ARX model are estimated by the pre-training and fine-tuning strategies and the stability condition of the model are also discussed. The proposed DBN-ARX model is a pseudo-linear ARX model identified offline, and its function type coefficients are composed of the operating-point dependent DBNs. The usefulness of the DBN-ARX model is illustrated by modeling a continuously stirred tank reactor (CSTR) time series, Box and Jenkins data, a nonlinear process and a water tank system. The four experimental results show that the one-step-ahead and multi-step-ahead prediction accuracy of the proposed DBN-ARX model is improved comparing with the modeling results of several existing models.