Semi-Infinite Optimization with Hybrid Models

: The robust design of performance/safety-critical process systems, from a model-based perspective, remains an existing challenge. Hybrid firstprinciples data-driven models offer the potential to dramatically improve model prediction accuracy, stepping closer to the digital twin concept. Within this context, worst-case engineering design feasibility and reliability problems give rise to a class of semi-infinite program (SIP) formulations with hybrid models as coupling equality constraints. Reduced-space deterministic global optimization methods are exploited to solve this class of SIPs to ??-global optimality in finitely many iterations. This approach is demonstrated on two challenging case studies: a nitrification reactor for a wastewater treatment system to address worst-case feasibility verification of dynamical systems and a three-phase separation system plagued by numerical domain violations to demonstrate how they can be overcome using a nonsmooth SIP formulation with hybrid models and a validity constraint incorporated.

Automated summary

The robust design of performance/safety-critical process systems from a model-based perspective remains a challenge. Hybrid first-principles data-driven models can improve model prediction accuracy, moving closer to the concept of a digital twin. This study addresses worst-case engineering design feasibility and reliability problems using a class of semi-infinite program formulations with hybrid models as equality constraints. The reduced-space deterministic global optimization methods used in this approach demonstrate their effectiveness in solving the problems with a finite number of iterations. Two case studies are presented to showcase the application of this approach in addressing worst-case feasibility verification of dynamical systems and overcoming numerical domain violations in a three-phase separation system.