Fast just-in-time-learning recursive multi-output LSSVR for quality prediction and control of multivariable dynamic systems

Abstract

Aiming at quality prediction and control of blast furnace (BF) ironmaking process characterized by complicated nonlinear time-varying dynamics, this paper proposes a just-in-time-learning (JITL) recursive multi-output least squares support vector regression (JITL-R-M-LSSVR) algorithm with fast nonlinear local learning capability for multivariable dynamic systems. The proposed fast JITL-R-M-LSSVR effectively combines the online local learning of JITL with the multi-output LSSVR (M-LSSVR) based on multi-task transfer learning, and focuses on how to ensure the rapid verification of the local model during online learning of M-LSSVR, and how to perform model pruning while recursively updating the model parameters to improve the calculation efficiency. To this end, the proposed algorithm uses a derived multi-output incremental learning algorithm to recursively update model parameters online in a gentle way, which has better modeling stability and smoothness than the traditional way that discards old models. At the same time, when the model is pruned, a novel multi-output reverse decremental learning algorithm is proposed to adaptively delete the modeling data, so as to effectively control the sample size and reduces the calculation cost. In particular, the model verification of the proposed algorithm only needs to construct the M-LSSVR modeling matrix and the matrix inverse operation once, and the matrix after deleting each modeling sample can be easily obtained by reverse decremental learning of the original modeling matrix, which can achieve fast and efficient model verification. Finally, the effectiveness and practicability of the proposed method are verified by applying it to prediction modeling and predictive control of the molten iron quality in BF ironmaking process.