In this paper, we first briefly survey the main surrogate model building approaches discussed in the literature considering also design of experiments strategies and dimensionality reduction procedures: we mainly focus on sub-set approaches and sampling strategies for constrained regression problems. We delineate a systematic methodology for surrogate modelling in presence of model constraints, such as non-negativity of the model responses. The main contribution of this paper is twofold: from one side we extend the principal component analysis framework to the case of constrained regression problem, from the other we propose a novel methodology which integrates the subset selection and the previous principal component regression procedure. Finally, we apply the two novel algorithms to two fundamental chemical processes in petroleum refinery, namely catalytic reforming and light naphtha isomerization. The numerical results show the comparisons between the two algorithms in terms of computational and accuracy trade-offs.

在本文中，我们首先简要考察了文献中讨论的主要替代模型构建方法，同时还考虑了实验策略和降维程序的设计：我们主要关注约束回归问题的子集方法和抽样策略。我们描述了一种在存在模型约束（例如模型响应的非负性）的情况下替代模型的系统方法。本文的主要贡献是双重的：一方面，我们将主成分分析框架扩展到约束回归问题的情况下；另一方面，我们提出了一种新颖的方法，该方法将子集选择和先前的主成分回归程序结合在一起。最后，我们将这两种新颖的算法应用于炼油厂的两个基本化学过程，即催化重整和轻石脑油异构化。数值结果显示了两种算法在计算和精度折衷方面的比较。