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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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 explores various frameworks to quantify and propagate sources of epistemic and aleatoric uncertainty within the context of decision making for assessing system performance relative to design margins of a complex mechanical system. If sufficient data is available for characterizing aleatoric-type uncertainties, probabilistic methods are commonly used for computing response distribution statistics based on input probability distribution specifications. Conversely, for epistemic uncertainties, data is generally too sparse to support objective probabilistic input descriptions, leading to either subjective probabilistic descriptions (e.g., assumed priors in Bayesian analysis) or non-probabilistic methods based on interval specifications. Among the techniques examined in this work are (1) Interval analysis, (2) Dempster-Shafer Theory of Evidence, (3) a second-order probability (SOP) analysis in which the aleatory and epistemic variables are treated separately, and a nested iteration is performed, typically sampling epistemic variables on the outer loop, then sampling over aleatory variables on the inner loop and (4) a Bayesian approach where plausible prior distributions describing the epistemic variable are created and updated using available experimental data. This paper compares the results and the information provided by different methods to enable decision making in the context of performance assessment when epistemic uncertainty is considered.

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There is currently sparse literature on how to implement systematic and comprehensive processes for modern V&V/UQ (VU) within large computational simulation projects. Important design requirements have been identified in order to construct a viable 'system' of processes. Significant processes that are needed include discovery, accumulation, and assessment. A preliminary design is presented for a VU Discovery process that accounts for an important subset of the requirements. The design uses a hierarchical approach to set context and a series of place-holders that identify the evidence and artifacts that need to be created in order to tell the VU story and to perform assessments. The hierarchy incorporates VU elements from a Predictive Capability Maturity Model and uses questionnaires to define critical issues in VU. The place-holders organize VU data within a central repository that serves as the official VU record of the project. A review process ensures that those who will contribute to the record have agreed to provide the evidence identified by the Discovery process. VU expertise is an essential part of this process and ensures that the roadmap provided by the Discovery process is adequate. Both the requirements and the design were developed to support the Nuclear Energy Advanced Modeling and Simulation Waste project, which is developing a set of advanced codes for simulating the performance of nuclear waste storage sites. The Waste project served as an example to keep the design of the VU Discovery process grounded in practicalities. However, the system is represented abstractly so that it can be applied to other M&S projects.

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The objective of the U.S. Department of Energy Office of Nuclear Energy Advanced Modeling and Simulation Waste Integrated Performance and Safety Codes (NEAMS Waste IPSC) is to provide an integrated suite of computational modeling and simulation (M&S) capabilities to quantitatively assess the long-term performance of waste forms in the engineered and geologic environments of a radioactive-waste storage facility or disposal repository. To meet this objective, NEAMS Waste IPSC M&S capabilities will be applied to challenging spatial domains, temporal domains, multiphysics couplings, and multiscale couplings. A strategic verification and validation (V&V) goal is to establish evidence-based metrics for the level of confidence in M&S codes and capabilities. Because it is economically impractical to apply the maximum V&V rigor to each and every M&S capability, M&S capabilities will be ranked for their impact on the performance assessments of various components of the repository systems. Those M&S capabilities with greater impact will require a greater level of confidence and a correspondingly greater investment in V&V. This report includes five major components: (1) a background summary of the NEAMS Waste IPSC to emphasize M&S challenges; (2) the conceptual foundation for verification, validation, and confidence assessment of NEAMS Waste IPSC M&S capabilities; (3) specifications for the planned verification, validation, and confidence-assessment practices; (4) specifications for the planned evidence information management system; and (5) a path forward for the incremental implementation of this V&V plan.

This paper compares three approaches for model selection: classical least squares methods, information theoretic criteria, and Bayesian approaches. Least squares methods are not model selection methods although one can select the model that yields the smallest sum-of-squared error function. Information theoretic approaches balance overfitting with model accuracy by incorporating terms that penalize more parameters with a log-likelihood term to reflect goodness of fit. Bayesian model selection involves calculating the posterior probability that each model is correct, given experimental data and prior probabilities that each model is correct. As part of this calculation, one often calibrates the parameters of each model and this is included in the Bayesian calculations. Our approach is demonstrated on a structural dynamics example with models for energy dissipation and peak force across a bolted joint. The three approaches are compared and the influence of the log-likelihood term in all approaches is discussed.

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There is an increasing need to assess the performance of high consequence systems using a modeling and simulation based approach. Central to this approach are the need to quantify the uncertainties present in the system and to compare the system response to an expected performance measure. At Sandia National Laboratories, this process is referred to as quantification of margins and uncertainties or QMU. Depending on the outcome of the assessment, there might be a need to increase the confidence in the predicted response of a system model; thus a need to understand where resources need to be allocated to increase this confidence. This paper examines the problem of resource allocation done within the context of QMU. An optimization based approach to solving the resource allocation is considered and sources of aleatoric and epistemic uncertainty are included in the calculations.

Accurate material models are fundamental to predictive structural finite element models. Because potting foams are routinely used to mitigate shock and vibration of encapsulated components in electro/mechanical systems, accurate material models of foams are needed. A linear-viscoelastic foam constitutive model has been developed to represent the foam's stiffness and damping throughout an application space defined by temperature, strain rate or frequency and strain level. Validation of this linear-viscoelastic model, which is integrated into the Salinas structural dynamics code, is being achieved by modeling and testing a series of structural geometries of increasing complexity that have been designed to ensure sensitivity to material parameters. Both experimental and analytical uncertainties are being quantified to ensure the fair assessment of model validity. Quantitative model validation metrics are being developed to provide a means of comparison for analytical model predictions to observations made in the experiments. This paper is one of several recent papers documenting the validation process for simple to complex structures with foam encapsulated components. This paper specifically focuses on model validation over a wide temperature range and using a simple dumbbell structure for modal testing and simulation. Material variations of density and modulus have been included. A double blind validation process is described that brings together test data with model predictions.

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A detailed model validation study has been initiated to assess model predictions of foam encapsulated components. A bottom-up experimental approach has been used to first characterize the foam material, and then characterize foam/component interaction within increasingly complex systems. This paper presents a summary of the model validation approach at component and benchmark levels and details specific issues identified at the subsystem validation level. Specifically, manufacturing process issues were identified in the hardware which precluded continued validation. A summary of the modal data is given and the issues relating to the manufacturing process are discussed.

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The constitutive behavior of mechanical joints is largely responsible for the energy dissipation and vibration damping in weapons systems. For reasons arising from the dramatically different length scales associated with those dissipative mechanisms and the length scales characteristic of the overall structure, this physics cannot be captured adequately through direct simulation of the contact mechanics within a structural dynamics analysis. The only practical method for accommodating the nonlinear nature of joint mechanisms within structural dynamic analysis is through constitutive models employing degrees of freedom natural to the scale of structural dynamics. This document discusses a road-map for developing such constitutive models.

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Dynamic thermography is a promising technology for inspecting metallic and composite structures used in high-consequence industries. However, the reliability and inspection sensitivity of this technology has historically been limited by the need for extensive operator experience and the use of human judgment and visual acuity to detect flaws in the large volume of infrared image data collected. To overcome these limitations new automated data analysis algorithms and software is needed. The primary objectives of this research effort were to develop a data processing methodology that is tied to the underlying physics, which reduces or removes the data interpretation requirements, and which eliminates the need to look at significant numbers of data frames to determine if a flaw is present. Considering the strengths and weakness of previous research efforts, this research elected to couple both the temporal and spatial attributes of the surface temperature. Of the possible algorithms investigated, the best performing was a radiance weighted root mean square Laplacian metric that included a multiplicative surface effect correction factor and a novel spatio-temporal parametric model for data smoothing. This metric demonstrated the potential for detecting flaws smaller than 0.075 inch in inspection areas on the order of one square foot. Included in this report is the development of a thermal imaging model, a weighted least squares thermal data smoothing algorithm, simulation and experimental flaw detection results, and an overview of the ATAC (Automated Thermal Analysis Code) software that was developed to analyze thermal inspection data.

This report describes the underlying principles and goals of the Sandia ASCI Verification and Validation Program Validation Metrics Project. It also gives a technical description of two case studies, one in structural dynamics and the other in thermomechanics, that serve to focus the technical work of the project in Fiscal Year 2001.

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