In chemical processes, products of different grades are often produced. Data measured in each grade have different latent features. Multiple data sets can be measured corresponding to different grades. To handle the modeling of multiple nonlinear data sets, multiple two-dimensional matrices of various grades are stacked into a three-dimensional tensor. Then a high-order tensor-based method, named high-order partial least squares (HOPLS), determines the common features among the multiple data sets. PLS is sequentially used to calculate the implied special features of each grade so that the grades can be distinguished from one another. A dual-layer feature extraction method is also proposed. To keep the prediction accuracy of HOPLS-PLS in nonlinear multi-grade processes, a just-in-time learning strategy, named JHOPLS-PLS, is used to establish local HOPLS-PLS models for each query sample. JHOPLS-PLS can extract both common and special features of multi-grade process data. The proposed JHOPLS-PLS has obvious advantages over existing methods.

在化学过程中，经常生产不同等级的产品。每个年级测量的数据具有不同的潜在特征。可以测量多个数据集对应不同的等级。为了处理多个非线性数据集的建模，多个不同等级的二维矩阵堆叠成一个三维张量。然后，基于高阶张量的方法，称为高阶偏最小二乘法 (HOPLS)，确定多个数据集之间的共同特征。PLS 依次用于计算每个等级的隐含特征，以便可以将等级彼此区分开。还提出了一种双层特征提取方法。为了在非线性多级过程中保持 HOPLS-PLS 的预测准确性，一种名为 JHOPLS-PLS 的即时学习策略，用于为每个查询样本建立本地 HOPLS-PLS 模型。JHOPLS-PLS 可以提取多级过程数据的共同特征和特殊特征。所提出的 JHOPLS-PLS 与现有方法相比具有明显的优势。