This report describes the credibility activities undertaken in support of Gemma code development in FY20, which include Verification & Validation (V&V), Uncertainty Quantification (UQ), and Credibility process application. The main goal of these activities is to establish capabilities and process frameworks that can be more broadly applied to new and more advanced problems as the Gemma code development effort matures. This will provide Gemma developers and analysts with the tools needed to generate credibility evidence in support of Gemma predictions for future use cases. The FY20 Gemma V&V/UQ/Credibility activities described in this report include experimental uncertainty analysis, the development and use of methods for optimal design of computer experiments, and the development of a framework for validation. These initial activities supported the development of broader credibility planning for Gemma that continued into FY21.
In Bayesian model calibration, evaluation of the likelihood function usually involves finding the inverse and determinant of a covariance matrix. When Markov Chain Monte Carlo (MCMC) methods are used to sample from the posterior, hundreds of thousands of likelihood evaluations may be required. In this paper, we demonstrate that the structure of the covariance matrix can be exploited, leading to substantial time savings in practice. We also derive two simple equations for approximating the inverse of the covariance matrix in this setting, which can be computed in near-quadratic time. The practical implications of these strategies are demonstrated using a simple numerical case study and the "quack"R package. For a covariance matrix with 1000 rows, application of these strategies for a million likelihood evaluations leads to a speedup of roughly 4000 compared to the naive implementation.
In this article, we examine the coupling into an electrically short azimuthal slot on a cylindrical cavity operating at fundamental cavity modal frequencies. We first develop a matched bound formulation through which we can gather information for maximum achievable levels of interior cavity fields. Actual field levels are below this matched bound; therefore, we also develop an unmatched formulation for frequencies below the slot resonance to achieve a better insight on the physics of this coupling. Good agreement is observed between the unmatched formulation, full-wave simulations, and experimental data, providing a validation of our analytical models. We then extend the unmatched formulation to treat an array of slots, found again in good agreement with full-wave simulations. These analytical models can be used to investigate ways to mitigate electromagnetic interference and electromagnetic compatibility effects within cavities.
Understanding the effect of a high-altitude electromagnetic pulse (HEMP) on the equipment in the United States electrical power grid is important to national security. A present challenge to this understanding is evaluating the vulnerability of transformers to a HEMP. Evaluating vulnerability by direct testing is cost-prohibitive, due to the wide variation in transformers, their high cost, and the large number of tests required to establish vulnerability with confidence. Alternatively, material and component testing can be performed to quantify a model for transformer failure, and the model can be used to assess vulnerability of a wide variety of transformers. This project develops a model of the probability of equipment failure due to effects of a HEMP. Potential failure modes are cataloged, and a model structure is presented which can be quantified by the results of small-scale coupon tests.
In the presence of model discrepancy, the calibration of physics-based models for physical parameter inference is a challenging problem. Lack of identifiability between calibration parameters and model discrepancy requires additional identifiability constraints to be placed on the model discrepancy to obtain unique physical parameter estimates. If these assumptions are violated, the inference for the calibration parameters can be systematically biased. In many applications, such as in dynamic material property experiments, many of the calibration inputs refer to measurement uncertainties. In this setting, we develop a metric for identifying overfitting of these measurement uncertainties, propose a prior capable of reducing this overfitting, and show how this leads to a diagnostic tool for validation of physical parameter inference. The approach is demonstrated for a benchmark example and applied for a material property application to perform inference on the equation of state parameters of tantalum.
