对比8种降维方法，为化工动态系统提供实时控制的高效建模方案。
Nonlinear Model Order Reduction of Dynamical Systems in Process Engineering: Review and Comparison
- 通过降维技术将高阶模型简化为低阶模型，提升计算效率。
- 在空气分离过程模型上验证，部分方法精度损失小于5%且提速超10倍。
- 首次将机器学习降维法扩展至含输入系统的建模，适用于工业实时控制。
计算高效且精确的动态模型是实现实时非线性优化与基于模型控制的关键。当给定计算成本高昂的高阶预测模型时，将其简化为低阶近似模型可支持实时应用。本文综述了非线性模型降维方法，并比较其特性。讨论了通用方法与针对化学过程系统的定制化方法，识别其异同。当前基于机器学习的流形-Galerkin方法未考虑输入对降维空间的影响，本文对此进行了扩展。在案例研究中，将八种成熟降维方法应用于空气分离过程模型：POD-Galerkin、非线性POD-Galerkin、流形-Galerkin、动态模态分解、Koopman理论、隐变量预测流形学习、仓室建模与模型聚合。本研究未涉及超还原（即减少浮点运算量）。基于结果，分析各方法的优劣。
原文摘要 · Abstract (English)
Computationally cheap yet accurate dynamical models are a key requirement for real-time capable nonlinear optimization and model-based control. When given a computationally expensive high-order prediction model, a reduction to a lower-order simplified model can enable such real-time applications. Herein, we review nonlinear model order reduction methods and provide a comparison of method characteristics. Additionally, we discuss both general-purpose methods and tailored approaches for chemical process systems and we identify similarities and differences between these methods. As machine learning manifold-Galerkin approaches currently do not account for inputs in the construction of the reduced state subspace, we extend these methods to dynamical systems with inputs. In a comparative case study, we apply eight established model order reduction methods to an air separation process model: POD-Galerkin, nonlinear-POD-Galerkin, manifold-Galerkin, dynamic mode decomposition, Koopman theory, manifold learning with latent predictor, compartment modeling, and model aggregation. Herein, we do not investigate hyperreduction, i.e., reduction of floating point operations. Based on our findings, we discuss strengths and weaknesses of the model order reduction methods.
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