Abstract: The products of batch processes are closely related to the daily life of modern people, and it is crucial for batch process monitoring to establish a model based on the normal process data sets. In this paper, according to the characteristics of batch process, a new generalized multilinear regression model, termed the higher order partial least squares (HOPLS), is introduced with the aim to better model the three-way batch data. It differs substantially from the traditional modeling approach, and instead of unfolding the three-way array to a two-way array, it explains the data by a sum of orthogonal Tucker tensors. Higher order orthogonal iteration (HOSVD), tensor transformation and higher order orthogonal iteration (HOOI) are used to find the latent vectors, which contain the maximum information of independent variables and dependent variables simultaneously. And the loading vectors are calculated at the same time. For the new observation values, the dependent variables will be predicted through the output of the model. Finally, the feasibility and efficiency of the method are verified through the PenSim2.0 simulation platform.

Key words: batchwise, higher order partial least squares, modeling, algorithm, prediction

摘要： 间歇过程的产品与现代人的生活息息相关，而建立可靠的模型是保障间歇过程安全运行的基础。针对间歇过程的数据特点，引入一种新的广义线性回归模型--高阶偏最小二乘（higher order partial least squares，HOPLS）。它与传统的间歇过程建模方法具有本质的不同，三维数据（批次×变量×时间）不需要展开成二维矩阵，而是直接被分解成一组正交的Tucker矩阵之和。通过高阶奇异值分解（high order singular value decomposition，HOSVD），张量变换和高阶正交迭代（higher order orthogonal iteration，HOOI）找到能同时包含自变量和因变量最大信息的潜向量，与此同时得到对应的负载向量。对于新观测值，通过模型就可以实现对因变量的预测。最后利用PenSim2.0，对青霉素发酵过程进行仿真研究，验证了该间歇过程建模方法的有效性。

关键词: 间歇式, 高阶偏最小二乘, 建模, 算法, 预测