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also devise a filter-based trust-region framework. This hybrid framework utilizes both ZOC and FOC to save on the computational effort of computing exact gradients. When applied to the PSA case study, filter TR algorithm converges to a local optimum within 51 trust-region iterations consuming 1.36 hrs of CPU time, which is significantly smaller than the penalty algorithm. Our major contributions for this part of the thesis are given below: • First use of POD-based ROMs for large-scale application Although POD-based reduced order modeling technique has been used for a variety of disciplines, its utilization has remained limited to small-scale optimal control or dynamic optimization problems. This is the first instance when the use of POD-based ROM is successfully demonstrated for a large-scale challenging application, which contains multiple sets of PDAEs, state variables, and boundary conditions. Moreover, this is the first instance when POD-based ROMs are used for adsorption systems. • Unique model reduction technique for PSA Although studies in the literature have attempted model simplification for PSA processes, this is the first successful study which reports the use of a POD-based technique to de- velop low-order approximations for PSA models. Also, we present a unique construction technique for ROMs for PSA which is different from other dynamic processes in the sense that we develop separate ROMs for each state variable and each operating step. • Trust-region algorithms for ROM-based constrained optimization Trust-region algorithms have been developed to handle approximate models for uncon- strained optimization. In this work, we extend the use of approximate models to con- strained optimization problems. In particular, our accomplishments are novel trust- region frameworks based on the exact penalty and filter approaches, and their successful demonstration on a challenging PSA process. More importantly, these frameworks are quite generic, do not make any assumption on the optimization problem, and can be extended for a wide variety of applications. 8.1 Thesis Summary and Contributions Chapter 8. Conclusions 188PDF Image | Design and Operation of Pressure Swing Adsorption Processes
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