基于隐变量空间载荷余弦相似度的间歇过程递推优化

针对间歇过程基于主元相似度优化方法中存在的变量相关性信息损失问题，提出一种单位化隐变量空间下利用载荷余弦相似度进行递推优化的新策略。首先将各时段变量与指标变量构成的扩展矩阵进行主元分解，通过信息的重新分配使得由主元构成的隐变量空间是单位正交的，从而得到包含更多变量相关信息的非单位化载荷矩阵，进一步计算隐变量空间下各时段变量与指标变量之间载荷余弦相似度和批次间指标增量，并对操作曲线进行递推修正。这种非单位化载荷矩阵的主元分解形式，不仅降低了隐变量空间下变量相关性信息损失，也使得更新操作曲线的递推算法更为简化。最后，通过间歇过程某一化工产品结晶纯度的优化研究，验证了所提方法的有效性。

Recursive optimization of batch processes based on load cosine similarity in latent variable space

A recursive optimization strategy using load cosine similarity in unitized latent variable space was proposed to address information loss problem of variable correlation in batch process when optimized by principal component similarity. An extension matrix of time-segment and index variables was broken down by principal component analysis. The information redistribution generated orthogonal unitized latent variable space of principal components and a non-unitized load matrix containing much more variable information. Load cosine similarity between time-segment and index variables in the latent variable space as well as index increment between each time segment were calculated to recursively correct operation trajectory. The non-unitized load matrix by principal component decomposition not only reduced information loss of variable correlation in the latent variable space but also simplified recursive algorithm for updating operation trajectory. Finally, the effectiveness of the proposed method was verified by batch process optimization of one chemical crystal purification.