Enabling multi-step forecasting with structured state space learning module

Abstract

Data-driven soft sensor incorporated with the model predictive control (MPC) algorithms facilitating product quality and cost control is of imperative importance in industrial processes. However, the widely used one-step forecasting method can not incorporate with MPC and therefore restricts the practical usage of soft sensor. Multi-step forecasting introduces long-term dependencies problems yet has not been effectively resolved within traditional model structure. To address this problem, this paper proposes the deep learning network architecture named Extended State Space Learning Module (ESSLM). ESSLM extends the nonlinear mapping architecture of deep learning based on state space and retains state transfer matrices to characterize the dynamics of the system. ESSLM distinguishes itself from explicit network architectures such as gated RNNs by addressing the long-term dependencies problems through an implicit initialization method, and the MLP and RNN algorithms can be regarded as the manifestation of ESSLM in special cases. ESSLM characterizes the latent space as the coefficients of the orthogonal basis functions so that the input data can be encoded into a high-dimensional feature space with minimal information loss which efficiently achieves multi-step forecasting and give greater utility and practical significance.