Publications

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This paper examines the variability of predicted responses when multiple stress-strain curves (reflecting variability from replicate material tests) are propagated through a finite element model of a ductile steel can being slowly crushed. Over 140 response quantities of interest (including displacements, stresses, strains, and calculated measures of material damage) are tracked in the simulations. Each response quantity’s behavior varies according to the particular stress-strain curves used for the materials in the model. We desire to estimate response variability when only a few stress-strain curve samples are available from material testing. Propagation of just a few samples will usually result in significantly underestimated response uncertainty relative to propagation of a much larger population that adequately samples the presiding random-function source. A simple classical statistical method, Tolerance Intervals, is tested for effectively treating sparse stress-strain curve data. The method is found to perform well on the highly nonlinear input-to-output response mappings and non-standard response distributions in the can-crush problem. The results and discussion in this paper support a proposition that the method will apply similarly well for other sparsely sampled random variable or function data, whether from experiments or models. Finally, the simple Tolerance Interval method is also demonstrated to be very economical.

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When making computational simulation predictions of multi-physics engineering systems, sources of uncertainty in the prediction need to be acknowledged and included in the analysis within the current paradigm of striving for simulation credibility. A thermal analysis of an aerospace geometry was performed at Sandia National Laboratories. For this analysis a verification, validation and uncertainty quantification workflow provided structure for the analysis, resulting in the quantification of significant uncertainty sources including spatial numerical error and material property parametric uncertainty. It was hypothesized that the parametric uncertainty and numerical errors were independent and separable for this application. This hypothesis was supported by performing uncertainty quantification simulations at multiple mesh resolutions, while being limited by resources to minimize the number of medium and high resolution simulations. Based on this supported hypothesis, a prediction including parametric uncertainty and a systematic mesh bias are used to make a margin assessment that avoids unnecessary uncertainty obscuring the results and optimizes computing resources.

When very few samples of a random quantity are available from a source distribution of unknown shape, it is usually not possible to accurately infer the exact distribution from which the data samples come. Under-estimation of important quantities such as response variance and failure probabilities can result. For many engineering purposes, including design and risk analysis, we attempt to avoid under-estimation with a strategy to conservatively estimate (bound) these types of quantities -- without being overly conservative -- when only a few samples of a random quantity are available from model predictions or replicate experiments. This report examines a class of related sparse-data uncertainty representation and inference approaches that are relatively simple, inexpensive, and effective. Tradeoffs between the methods' conservatism, reliability, and risk versus number of data samples (cost) are quantified with multi-attribute metrics use d to assess method performance for conservative estimation of two representative quantities: central 95% of response; and 10^-4 probability of exceeding a response threshold in a tail of the distribution. Each method's performance is characterized with 10,000 random trials on a large number of diverse and challenging distributions. The best method and number of samples to use in a given circumstance depends on the uncertainty quantity to be estimated, the PDF character, and the desired reliability of bounding the true value. On the basis of this large data base and study, a strategy is proposed for selecting the method and number of samples for attaining reasonable credibility levels in bounding these types of quantities when sparse samples of random variables or functions are available from experiments or simulations.

Characterizing the tails of probability distributions plays a key role in quantification of margins and uncertainties (QMU), where the goal is characterization of low probability, high consequence events based on continuous measures of performance. When data are collected using physical experimentation, probability distributions are typically fit using statistical methods based on the collected data, and these parametric distributional assumptions are often used to extrapolate about the extreme tail behavior of the underlying probability distribution. In this project, we character- ize the risk associated with such tail extrapolation. Specifically, we conducted a scaling study to demonstrate the large magnitude of the risk; then, we developed new methods for communicat- ing risk associated with tail extrapolation from unvalidated statistical models; lastly, we proposed a Bayesian data-integration framework to mitigate tail extrapolation risk through integrating ad- ditional information. We conclude that decision-making using QMU is a complex process that cannot be achieved using statistical analyses alone.

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A discussion of the five responses to the 2014 Sandia Verification and Validation (V&V) Challenge Problem, presented within this special issue, is provided hereafter. Overviews of the challenge problem workshop, workshop participants, and the problem statement are also included. Brief summations of teams' responses to the challenge problem are provided. Issues that arose throughout the responses that are deemed applicable to the general verification, validation, and uncertainty quantification (VVUQ) community are the main focal point of this paper. The discussion is oriented and organized into big picture comparison of data and model usage, VVUQ activities, and differentiating conceptual themes behind the teams' VVUQ strategies. Significant differences are noted in the teams' approaches toward all VVUQ activities, and those deemed most relevant are discussed. Beyond the specific details of VVUQ implementations, thematic concepts are found to create differences among the approaches; some of the major themes are discussed. Lastly, an encapsulation of the key contributions, the lessons learned, and advice for the future are presented.

This work examines the variability of predicted responses when multiple stress-strain curves (reflecting variability from replicate material tests) are propagated through a transient dynamics finite element model of a ductile steel can being slowly crushed. An elastic-plastic constitutive model is employed in the large-deformation simulations. The present work assigns the same material to all the can parts: lids, walls, and weld. Time histories of 18 response quantities of interest (including displacements, stresses, strains, and calculated measures of material damage) at several locations on the can and various points in time are monitored in the simulations. Each response quantity's behavior varies according to the particular stressstrain curves used for the materials in the model. We estimate response variability due to variability of the input material curves. When only a few stress-strain curves are available from material testing, response variance will usually be significantly underestimated. This is undesirable for many engineering purposes. This paper describes the can-crush model and simulations used to evaluate a simple classical statistical method, Tolerance Intervals (TIs), for effectively compensating for sparse stress-strain curve data in the can-crush problem. Using the simulation results presented here, the accuracy and reliability of the TI method are being evaluated on the highly nonlinear inputto- output response mappings and non-standard response distributions in the can-crush UQ problem.