Publications

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This paper discusses the handling and treatment of uncertainties corresponding to relatively few data samples in experimental characterization of random quantities. The importance of this topic extends beyond experimental uncertainty to situations where the derived experimental information is used for model validation or calibration. With very sparse data it is not practical to have a goal of accurately estimating the underlying variability distribution (probability density function, PDF). Rather, a pragmatic goal is that the uncertainty representation should be conservative so as to bound a desired percentage of the actual PDF, say 95% included probability, with reasonable reliability. A second, opposing objective is that the representation not be overly conservative; that it minimally over-estimate the random-variable range corresponding to the desired percentage of the actual PDF. The performance of a variety of uncertainty representation techniques is tested and characterized in this paper according to these two opposing objectives. An initial set of test problems and results is presented here from a larger study currently underway.

This paper presents some statistical concepts and techniques for refining the expression of uncertainty arising from: a) random variability (aleatory uncertainty) of a random quantity; and b) contributed epistemic uncertainty due to limited sampling of the random quantity. The treatment is tailored to handling experimental uncertainty in a context of model validation and calibration. Two particular problems are considered. One involves deconvolving random measurement error from measured random response. The other involves exploiting a relationship between two random variates of a system and an independently characterized probability density of one of the variates.

This report explores some important considerations in devising a practical and consistent framework and methodology for utilizing experiments and experimental data to support modeling and prediction. A pragmatic and versatile 'Real Space' approach is outlined for confronting experimental and modeling bias and uncertainty to mitigate risk in modeling and prediction. The elements of experiment design and data analysis, data conditioning, model conditioning, model validation, hierarchical modeling, and extrapolative prediction under uncertainty are examined. An appreciation can be gained for the constraints and difficulties at play in devising a viable end-to-end methodology. Rationale is given for the various choices underlying the Real Space end-to-end approach. The approach adopts and refines some elements and constructs from the literature and adds pivotal new elements and constructs. Crucially, the approach reflects a pragmatism and versatility derived from working many industrial-scale problems involving complex physics and constitutive models, steady-state and time-varying nonlinear behavior and boundary conditions, and various types of uncertainty in experiments and models. The framework benefits from a broad exposure to integrated experimental and modeling activities in the areas of heat transfer, solid and structural mechanics, irradiated electronics, and combustion in fluids and solids.

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This paper1 explores some of the important considerations in devising a practical and consistent framework and methodology for working with experiments and experimental data in connection with modeling and prediction. The paper outlines a pragmatic and versatile "real-space" approach within which experimental and modeling uncertainties (correlated and uncorrelated, systematic and random, aleatory and epistemic) are treated to mitigate risk in modeling and prediction. The elements of data conditioning, model conditioning, model validation, hierarchical modeling, and extrapolative prediction under uncertainty are examined. An appreciation can be gained for the constraints and difficulties at play in devising a viable end-to-end methodology. The considerations and options are many, and a large variety of viewpoints and precedents exist in the literature, as surveyed here. Rationale is given for the various choices taken in assembling the novel real-space end-to-end framework. The framework adopts some elements and constructs from the literature (sometimes adding needed refinement), rejects others (even some currently popular ones), and adds pivotal new elements and constructs. Crucially, the approach reflects a pragmatism and versatility derived from working many industrial-scale problems involving complex physics and constitutive models, steady-state and time-varying nonlinear behavior and boundary conditions, and various categories of uncertainty in experiments and models. The framework benefits from a broad exposure to integrated experimental and modeling activities in the areas of heat transfer, structural mechanics, irradiated electronics, and combustion in fluids and solids.2.

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This paper discusses implications and appropriate treatment of systematic uncertainty in experiments and modeling. Systematic uncertainty exists when experimental conditions, and/or measurement bias errors, and/or bias contributed by post-processing the data, are constant over the set of experiments but the particular values of the conditions and/or biases are unknown to within some specified uncertainty. Systematic uncertainties in experiments do not automatically show up in the output data, unlike random uncertainty which is revealed when multiple experiments are performed. Therefore, the output data must be properly 'conditioned' to reflect important sources of systematic uncertainty in the experiments. In industrial scale experiments the systematic uncertainty in experimental conditions (especially boundary conditions) is often large enough that the inference error on how the experimental system maps inputs to outputs is often quite substantial. Any such inference error and uncertainty thereof also has implications in model validation and calibration/conditioning; ignoring systematic uncertainty in experiments can lead to 'Type X' error in these procedures. Apart from any considerations of modeling and simulation, reporting of uncertainty associated with experimental results should include the effects of any significant systematic uncertainties in the experiments. This paper describes and illustrates the treatment of multivariate systematic uncertainties of interval and/or probabilistic natures, and combined cases. The paper also outlines a practical and versatile 'real-space' framework and methodology within which experimental and modeling uncertainties (correlated and uncorrelated, systematic and random, aleatory and epistemic) are treated to mitigate risk in model validation, calibration/conditioning, hierarchical modeling, and extrapolative prediction.

Instrumented, fully coupled thermal-mechanical experiments were conducted to provide validation data for finite element simulations of failure in pressurized, high temperature systems. The design and implementation of the experimental methodology is described in another paper of this conference. Experimental coupling was accomplished on tubular 304L stainless steel specimens by mechanical loading imparted by internal pressurization and thermal loading by side radiant heating. Experimental parameters, including temperature and pressurization ramp rates, maximum temperature and pressure, phasing of the thermal and mechanical loading and specimen geometry details were studied. Experiments were conducted to increasing degrees of deformation, up to and including failure. Mechanical characterization experiments of the 304L stainless steel tube material was also completed for development of a thermal elastic-plastic material constitutive model used in the finite element simulations of the validation experiments. The material was characterized in tension at a strain rate of 0.001/s from room temperature to 800 C. The tensile behavior of the tube material was found to differ substantially from 304L bar stock material, with the plasticity characteristics and strain to failure differing at every test temperature.

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This paper applies a pragmatic interval-based approach to validation of a fire dynamics model involving computational fluid dynamics, combustion, participating-media radiation, and heat transfer. Significant aleatory and epistemic sources of uncertainty exist in the experiments and simulations. The validation comparison of experimental and simulation results, and corresponding criteria and procedures for model affirmation or refutation, take place in "real space" as opposed to "difference space" where subtractive differences between experiments and simulations are assessed. The versatile model validation framework handles difficulties associated with representing and aggregating aleatory and epistemic uncertainties from multiple correlated and uncorrelated source types, including: • experimental variability from multiple repeat experiments • uncertainty of experimental inputs • experimental output measurement uncertainties • uncertainties that arise in data processing and inference from raw simulation and experiment outputs • parameter and model-form uncertainties intrinsic to the model • numerical solution uncertainty from model discretization effects. The framework and procedures of the model validation methodology are here applied to a difficult validation problem involving experimental and predicted calorimeter temperatures in a wind-driven hydrocarbon pool fire.

The objective of this work is to perform an uncertainty quantification (UQ) and model validation analysis of simulations of tests in the cross-wind test facility (XTF) at Sandia National Laboratories. In these tests, a calorimeter was subjected to a fire and the thermal response was measured via thermocouples. The UQ and validation analysis pertains to the experimental and predicted thermal response of the calorimeter. The calculations were performed using Sierra/Fuego/Syrinx/Calore, an Advanced Simulation and Computing (ASC) code capable of predicting object thermal response to a fire environment. Based on the validation results at eight diversely representative TC locations on the calorimeter the predicted calorimeter temperatures effectively bound the experimental temperatures. This post-validates Sandia's first integrated use of fire modeling with thermal response modeling and associated uncertainty estimates in an abnormal-thermal QMU analysis.

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A very general and robust approach to solving continuous-variable optimization problems involving uncertainty in the objective function is through the use of ordinal optimization. At each step in the optimization problem, improvement is based only on a relative ranking of the uncertainty effects on local design alternatives, rather than on precise quantification of the effect. One simply asks "Is that alternative better or worse than this one?"-not "HOW MUCH better or worse is that alternative to this one?" The answer to the latter question requires precise characterization of the uncertainty- with the corresponding sampling/integration expense for precise resolution. By looking at things from an ordinal ranking perspective instead, the trade-off between computational expense and vagueness in the uncertainty characterization can be managed to make cost-effective stepping decisions in the design space. This paper demonstrates correct advancement in a continuous-variable probabilistic optimization problem despite extreme vagueness in the statistical characterization of the design options. It is explained and shown how spatial correlation of uncertainty in such design problems can be exploited to dramatically increase the efficiency of ordinal approaches to optimization under uncertainty.

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