Publications

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Economic factors and experimental limitations often lead to sparse and/or imprecise data used for the calibration and validation of computational models. This paper addresses resource allocation for calibration and validation experiments, in order to maximize their effectiveness within given resource constraints. When observation data are used for model calibration, the quality of the inferred parameter descriptions is directly affected by the quality and quantity of the data. This paper characterizes parameter uncertainty within a probabilistic framework, which enables the uncertainty to be systematically reduced with additional data. The validation assessment is also uncertain in the presence of sparse and imprecise data; therefore, this paper proposes an approach for quantifying the resulting validation uncertainty. Since calibration and validation uncertainty affect the prediction of interest, the proposed framework explores the decision of cost versus importance of data in terms of the impact on the prediction uncertainty. Often, calibration and validation tests may be performed for different input scenarios, and this paper shows how the calibration and validation results from different conditions may be integrated into the prediction. Then, a constrained discrete optimization formulation that selects the number of tests of each type (calibration or validation at given input conditions) is proposed. Furthermore, the proposed test selection methodology is demonstrated on a microelectromechanical system (MEMS) example.

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One of the more severe environments for a store on an aircraft is during the ejection of the store. During this environment it is not possible to instrument all component responses, and it is also likely that some instruments may fail during the environment testing. This work provides a method for developing these responses from failed gages and uninstrumented locations. First, the forces observed by the store during the environment are reconstructed. A simple sampling method is used to reconstruct these forces given various parameters. Then, these forces are applied to a model to generate the component responses. Validation is performed on this methodology.

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As more and more high-consequence applications such as aerospace systems leverage computational models to support decisions, the importance of assessing the credibility of these models becomes a high priority. Two elements in the credibility assessment are verification and validation. The former focuses on convergence of the solution (i.e. solution verification) and the “pedigree” of the codes used to evaluate the model. The latter assess the agreement of the model prediction to real data. The outcome of these elements should map to a statement of credibility on the predictions. As such this credibility should be integrated into the decision making process. In this paper, we present a perspective as to how to integrate these element into a decision making process. The key challenge is to span the gap between physics-based codes, quantitative capability assessments (V&V/UQ), and qualitative risk-mitigation concepts.

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In this report we derive frequency-domain methods for inverse characterization of the constitutive parameters of viscoelastic materials. The inverse problem is cast in a PDE-constrained optimization framework with efficient computation of gradients and Hessian vector products through matrix free operations. The abstract optimization operators for first and second derivatives are derived from first principles. Various methods from the Rapid Optimization Library (ROL) are tested on the viscoelastic inversion problem. The methods described herein are applied to compute the viscoelastic bulk and shear moduli of a foam block model, which was recently used in experimental testing for viscoelastic property characterization.

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This report discusses the treatment of uncertainties stemming from relatively few samples of random quantities. The importance of this topic extends beyond experimental data uncertainty to situations involving uncertainty in model calibration, validation, and prediction. With very sparse data samples it is not practical to have a goal of accurately estimating the underlying probability density function (PDF). Rather, a pragmatic goal is that the uncertainty representation should be conservative so as to bound a specified percentile range of the actual PDF, say the range between 0.025 and .975 percentiles, with reasonable reliability. A second, opposing objective is that the representation not be overly conservative; that it minimally over-estimate the desired percentile range of the actual PDF. The presence of the two opposing objectives makes the sparse-data uncertainty representation problem interesting and difficult. In this report, five uncertainty representation techniques are characterized for their performance on twenty-one test problems (over thousands of trials for each problem) according to these two opposing objectives and other performance measures. Two of the methods, statistical Tolerance Intervals and a kernel density approach specifically developed for handling sparse data, exhibit significantly better overall performance than the others.

The Predictive Capability Maturity Model (PCMM) is an expert elicitation tool designed to characterize and communicate completeness of the approaches used for computational model definition, verification, validation, and uncertainty quantification associated for an intended application. The primary application of this tool at Sandia National Laboratories (SNL) has been for physics-based computational simulations in support of nuclear weapons applications. The two main goals of a PCMM evaluation are 1) the communication of computational simulation capability, accurately and transparently, and 2) the development of input for effective planning. As a result of the increasing importance of computational simulation to SNLs mission, the PCMM has evolved through multiple generations with the goal to provide more clarity, rigor, and completeness in its application. This report describes the approach used to develop the fourth generation of the PCMM.

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