http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
Non-Intrusive Reduced Order Model for Parametric Reactor Kinetics Simulations
This work develops a non-intrusive, equation-free reduced-order model (ROM) for parametric reactor kinetics simulations. Non-intrusive, equation-free ROMs have many distinctive advantages compared to their intrusive counterparts. First, lower-dimensional auxiliary simulation data can be used in lieu of potentially very high-dimensional simulation outputs. Additionally, non-intrusive ROMs are agnostic to the underlying source of data, allowing them to be applied without modification to different computational models or experimental data. The method is comprised of two independent components: parametric prediction and dynamics characterization. Parametric prediction uses Proper Orthogonal Decomposition Mode Coefficient Interpolation (POD-MCI) to predict high-dimensional reactor kinetics simulation results for unseen parametric configurations. This is done by mapping the simulation outputs for different parametric configurations to a low-dimensional coordinate system defined by POD modes extracted from the data. Predictions are then made by performing parametric interpolations on the mode coefficients and mapping the result back into high-dimensional space. The dynamics characterization stage is utilized when specific information about the underlying dynamics is desired. In these cases, Dynamic Mode Decomposition (DMD) is applied to each of the predictions to yield spatiotemporal structures and associated time eigenvalues. Many reactor kinetics simulations fall outside of the assumptions made in the standard DMD algorithm. When necessary, variants of the standard algorithm such as Partitioned DMD (PDMD) and Multi-Resolution DMD (MRDMD) are characterized and used in the ROM. This method is applied to five reactor kinetics problems of increasing complexity, culminating with the two-dimensional LRA benchmark problem, which models a control rod ejection reactor pulse with nonlinear temperature feedback and a coupled adiabatic heat up model. For each example, the POD-MCI method produced accurate predictions of the high-dimensional, time-dependent solutions in multi-dimensional parameter spaces orders of magnitude faster than the full-order model (FOM). Additionally, it was shown that PDMD is far superior to MRDMD for problems with transient material properties or nonlinearities in terms of both reconstruction accuracy and number of modes required. Lastly, when applying DMD or one of its variants to POD-MCI predictions, it was shown that with the correct choice of hyper-parameters, the DMD approximation results in no additional incurred error relative to the original data. The electronic version of this dissertation is accessible from https://hdl.handle.net/1969.1/197269
Doctor of Philosophy Texas A&M University 2022 https://hdl.handle.net/1969.1/197269