A data‐driven optimization algorithm for differential algebraic equations with numerical infeasibilities

• Published in: AIChE journal Vol. 66; no. 10
• Main Authors: Beykal, Burcu, Onel, Melis, Onel, Onur, Pistikopoulos, Efstratios N.
• Format: Journal Article
• Language: English
• Published: Hoboken, USA John Wiley & Sons, Inc 01.10.2020; American Institute of Chemical Engineers
• Subjects: Algebra; Algorithms; Case studies; Constraint modelling; data‐driven optimization; differential algebraic equations; Differential equations; dynamic optimization; Integration; Natural gas; Numerical integration; Optimization; Optimization algorithms; steam cracking; Support vector machines
• ISSN: 0001-1541; 1547-5905; 1547-5905
• DOI: 10.1002/aic.16657

Support vector machines (SVMs) based optimization framework is presented for the data‐driven optimization of numerically infeasible differential algebraic equations (DAEs) without the full discretization of the underlying first‐principles model. By formulating the stability constraint of the numerical integration of a DAE system as a supervised classification problem, we are able to demonstrate that SVMs can accurately map the boundary of numerical infeasibility. The necessity of this data‐driven approach is demonstrated on a two‐dimensional motivating example, where highly accurate SVM models are trained, validated, and tested using the data collected from the numerical integration of DAEs. Furthermore, this methodology is extended and tested for a multidimensional case study from reaction engineering (i.e., thermal cracking of natural gas liquids). The data‐driven optimization of this complex case study is explored through integrating the SVM models with a constrained global grey‐box optimization algorithm, namely the ARGONAUT framework.