Statistical Inference of Heterogeneous Surface Catalycity Models Using Simulated Laser Absorption Spectroscopy in Reacting Flow
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With the current widespread availability of large scale computing resources, modeling of complex physical systems governed by partial differential equations (PDEs) is becoming commonplace in many engineering and scientific disciplines. Methods and tools to gain an understanding of the effects of uncertainty in the predicted states of these complex systems are of great current interest. A critical step towards this goal is the solution of statistical inverse problems to allow us to incorporate uncertainty in underlying physical models, and subsequently into model predictions. The development of such methodologies and tools are at the forefront of research in computational science and high-performance computing and is a major open problem in general.This dissertation focuses on the development of a computational framework for solving statistical inverse problems in complex multiphysics systems, with application to heterogeneous surface catalycity in the context of chemically reacting flows. Furthermore, this work provides infrastructure for experimental design in the presence of uncertainty wherein the selection of experimental scenarios to gather data is informed by a quantitative comparison of simulated potential experiments. These developments provide a robust framework to facilitate minimizing the number of costly physical experiments that must be performed in order to best inform the unknown model parameters.To demonstrate these capabilities, an important example application relevant to the modeling of hypersonic flows was developed with the goal of demonstrating the efficacy of this framework. Specifically, we focus on heterogeneous surface catalycity models that govern the reaction of atomic oxygen and solid carbon that produces carbon monoxide in a reacting flow. As physical laboratory experiments are outside the scope of this work, we simulate laser absorption spectroscopy measurements of CO with added Gaussian noise as the synthetic data for the inverse problem to demonstrate the developments made in this work. Previous work using this example scenario in the context of determining the effects in realistic uncertainty values in flow parameters, laser optical path configuration, and catalycity values demonstrated that uncertainty in catalycity models had the largest impact on the simulated absorption measurement. This indicated a sufficient sensitivity to catalycity model parameters for study using statistical inverse problems, which is the goal of this work.We investigated the performance of our inverse problem framework for three different catalycity models: one that is constant, and two that are temperature-dependent. These represent increasingly complex models for the same physical phenomenon, thus both providing a demonstration of the inverse problem framework as well as exposing any limitations or shortcomings therein. Reference values for the unknown model parameters were determined from experimental data in literature.The constant model, being the simplest, was easily inferred, with the known reference value within one standard deviation of the mean. “Reduced” versions of the temperature-dependent models were considered, wherein the unknown temperature parameter was treated as known and the other pa-rameters were inferred. These cases demonstrated an interesting limitation wherein we were unable to improve the mean or variance of the inferred belief distribution through the incorporation of additional temperature data. Although these models depend solely on temperature, the simulated absorption measurements apparently do not provide enough additional information to continually improve the inferred values through the addition of more data. From this, we conclude that improvement for these inferences necessitates varying additional system parameters.With successful inferences of the simple and reduced catalycity models, we then attempted inference on the “full” temperature-dependent models. However, we show the absorption measurement does not provide enough sensitivity to parameters strongly coupled to temperature. This shows a limitation of arbitrarily choosing experimental scenarios that may not provide enough information to successfully infer the desired model parameters. Our experimental design infrastructure seeks to address this issue.The culminating development in this work is the deployment and application of algorithms and software to facilitate Bayesian experimental design. We studied the constant and one reduced model within an experimental design loop. Here, three relevant, controllable experimental scenario parameters were varied to allow us to identify those most informative to the model parameter beliefs. This was measured using two different metrics: minimum variance and expected information gain. Several studies were performed, first by varying a single scenario parameter, and later, multiple scenario parameters simultaneously to show that significant improvements over initial beliefs can be obtained with judicious choices of experimental scenarios.The penultimate demonstration is a full experimental design using simulated noisy data. Given a budget of five experiments that could be performed, we used our experimental design infrastructure to select experimental scenarios using two methods: batch design, where all experiments are chosen a priori, and sequential design, where the next experiment is selected after completing the current experiment. For both design methodologies, significant benefit, in the form of reduced uncertainty, was obtained in the final informed catalytic parameters. In particular, the sequential design results were measurably superior to the batch design for both catalycity models, confirming our initial hypothesis and demonstrating the superiority of the methodology and infrastructure presented herein.