(572h) Model Reduction in Multi-Scale Simulation and Optimization

Simulation and optimization of advanced chemical and energy processes are often challenged by conventional homogeneous or mono-scale models. Instead, these processes are usually modeled through a heterogeneous collection of device-scale and process scale models, which contain distributed and lumped parameter models of varying complexities with different simulators. In our previous work, we presented the methodology of model reduction which produced reduced order model (ROM) (Lang et al (2009)). Later we integrated ROMs for gasifiers and gas-turbine-combustors within an IGCC process flowsheet optimization (Lang et al (2011)). In this study we present recent work to support our previous work by applying convergence and approximation theory for multi-scale energy system optimization.  This theory allows us to determine a sampling set (size and locations) which can guarantee that the approximation errors of functions and first order derivatives of the ROM for process simulation are bounded.  We show that the ROM can possess these necessary mathematical properties through the use of radial basis functions (RBF, e.g. Kriging). Furthermore, we propose an algorithm for process optimization and prove that the optimal solution with an integrated ROM is close to or equivalent to the true optimum of the process optimization. This study is heavily based on the theories of derivative free optimization (DFO), although in this case, the actual optimization algorithms are gradient based.