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.

针对具有复杂的非线性时变动力学特征的高炉炼铁过程的质量预测和控制，提出一种实时学习（JITL）递归多输出最小二乘支持向量回归（JITL-RM）。 -LSSVR）算法具有用于多变量动态系统的快速非线性本地学习功能。提出的快速JITL-RM-LSSVR有效地结合了JITL的在线本地学习与基于多任务传输学习的多输出LSSVR（M-LSSVR），并着重于如何确保在线期间对本地模型的快速验证学习M-LSSVR，以及如何在递归更新模型参数的同时执行模型修剪以提高计算效率。为此，提出的算法使用派生的多输出增量学习算法以柔和的方式递归地在线更新模型参数，与丢弃旧模型的传统方法相比，具有更好的建模稳定性和平滑性。同时，在修剪模型时，提出了一种新颖的多输出逆递减学习算法，可以自适应地删除建模数据，从而有效地控制了样本量，降低了计算成本。特别是，该算法的模型验证只需构造一次M-LSSVR建模矩阵和一次矩阵逆运算，就可以通过对原始建模矩阵进行逆减量学习，轻松地删除每个建模样本后的矩阵。可以实现快速有效的模型验证。最后，