基于高阶偏最小二乘的间歇过程建模

doi:10.3969/j.issn.0438-1157.2014.09.030

化工学报 ›› 2014, Vol. 65 ›› Issue (9): 3527-3534.DOI: 10.3969/j.issn.0438-1157.2014.09.030

基于高阶偏最小二乘的间歇过程建模

王建平, 胡益, 侍洪波

华东理工大学化工过程先进控制和优化技术教育部重点实验室, 上海 200237

收稿日期:2013-12-13 修回日期:2014-03-17 出版日期:2014-09-05 发布日期:2014-09-05
通讯作者: 侍洪波
基金资助:
国家自然科学基金项目（61374140）；上海浦江计划项目（12PJ1402200）。

Modeling of batch process based on higher order partial least squares

WANG Jianping, HU Yi, SHI Hongbo

Key Laboratory of Advanced Control and Optimization for Chemical Process of Ministry of Education, East China University of Science and Technology, Shanghai 200237, China

Received:2013-12-13 Revised:2014-03-17 Online:2014-09-05 Published:2014-09-05
Supported by:
supported by the National Natural Science Foundation of China (61374140) and Shanghai Pujiang Program (12PJ1402200).

摘要/Abstract

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

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

中图分类号:

TP277

王建平, 胡益, 侍洪波. 基于高阶偏最小二乘的间歇过程建模[J]. 化工学报, 2014, 65(9): 3527-3534.

WANG Jianping, HU Yi, SHI Hongbo. Modeling of batch process based on higher order partial least squares[J]. CIESC Journal, 2014, 65(9): 3527-3534.

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基于高阶偏最小二乘的间歇过程建模

Modeling of batch process based on higher order partial least squares

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