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J. Verif. Valid. Uncert. 2017;2(1):011001-011001-10. doi:10.1115/1.4035864.

Quantification of uncertainty in the simulation results becomes difficult for complex real-world systems with little or no experimental data. This paper describes a validation and uncertainty quantification (VUQ) approach that integrates computational and experimental data through a range of experimental scales and a hierarchy of complexity levels. This global approach links dissimilar experimental datasets at different scales, in a hierarchy, to reduce quantified error bars on case with sparse data, without running additional experiments. This approach was demonstrated by applying on a real-world problem, greenhouse gas (GHG) emissions from wind tunnel flares. The two-tier validation hierarchy links, a buoyancy-driven helium plume and a wind tunnel flare, to increase the confidence in the estimation of GHG emissions from wind tunnel flares from simulations.

Commentary by Dr. Valentin Fuster
J. Verif. Valid. Uncert. 2017;2(1):011002-011002-14. doi:10.1115/1.4035918.

Successful clinical use of patient-specific models for cardiovascular dynamics depends on the reliability of the model output in the presence of input uncertainties. For 1D fluid dynamics models of arterial networks, input uncertainties associated with the model output are related to the specification of vessel and network geometry, parameters within the fluid and wall equations, and parameters used to specify inlet and outlet boundary conditions. This study investigates how uncertainty in the flow profile applied at the inlet boundary of a 1D model affects area and pressure predictions at the center of a single vessel. More specifically, this study develops an iterative scheme based on the ensemble Kalman filter (EnKF) to estimate the temporal inflow profile from a prior distribution of curves. The EnKF-based inflow estimator provides a measure of uncertainty in the size and shape of the estimated inflow, which is propagated through the model to determine the corresponding uncertainty in model predictions of area and pressure. Model predictions are compared to ex vivo area and blood pressure measurements in the ascending aorta, the carotid artery, and the femoral artery of a healthy male Merino sheep. Results discuss dynamics obtained using a linear and a nonlinear viscoelastic wall model.

Commentary by Dr. Valentin Fuster
J. Verif. Valid. Uncert. 2017;2(1):011003-011003-12. doi:10.1115/1.4035900.

The use of spectral projection-based methods for simulation of a stochastic system with discontinuous solution exhibits the Gibbs phenomenon, which is characterized by oscillations near discontinuities. This paper investigates a dynamic bi-orthogonality-based approach with appropriate postprocessing for mitigating the effects of the Gibbs phenomenon. The proposed approach uses spectral decomposition of the spatial and stochastic fields in appropriate orthogonal bases, while the dynamic orthogonality (DO) condition is used to derive the resultant closed-form evolution equations. The orthogonal decomposition of the spatial field is exploited to propose a Gegenbauer reprojection-based postprocessing approach, where the orthogonal bases in spatial dimension are reprojected on the Gegenbauer polynomials in the domain of analyticity. The resultant spectral expansion in Gegenbauer series is shown to mitigate the Gibbs phenomenon. Efficacy of the proposed method is demonstrated for simulation of a one-dimensional stochastic Burgers equation and stochastic quasi-one-dimensional flow through a convergent-divergent nozzle.

Commentary by Dr. Valentin Fuster
J. Verif. Valid. Uncert. 2017;2(1):011004-011004-15. doi:10.1115/1.4036182.

Validation of dynamics model prediction is challenging due to the involvement of various sources of uncertainty and variations among validation experiments and over time. This paper investigates quantitative approaches for the validation of dynamics models using fully characterized experiments, in which both inputs and outputs of the models and experiments are measured and reported. Existing validation methods for dynamics models use feature-based metrics to give an overall measure of agreement over the entire time history, but do not capture the model's performance at specific time instants or durations; this is important for systems that operate in different regimes in different stages of the time history. Therefore, three new validation metrics are proposed by extending the model reliability metric (a distance-based probabilistic metric) to dynamics problems. The proposed three time-domain model reliability metrics consider instantaneous reliability, first-passage reliability, and accumulated reliability. These three reliability metrics that perform time-domain comparison overcome the limitations of current feature-based validation metrics and provide quantitative assessment regarding the agreement between the simulation model and experiment over time from three different perspectives. The selection of validation metrics from a decision-making point of view is also discussed. Two engineering examples, including a simply supported beam under stochastic loading and the Sandia National Laboratories structural dynamics challenge problem, are used to illustrate the proposed time-domain validation metrics.

Commentary by Dr. Valentin Fuster
J. Verif. Valid. Uncert. 2017;2(1):011005-011005-10. doi:10.1115/1.4036180.

A systematic approach to defining margin in a manner that incorporates statistical information and accommodates data uncertainty but does not require assumptions about specific forms of the tails of distributions is developed. A margin that is insensitive to the character of the tails of the relevant distributions (tail insensitive margin, TIM) is defined. This is complemented by the calculation of probability of failure (PoF) where the load distribution is augmented by a quantity equal to the TIM. This approach avoids some of the perplexing results common to traditional reliability theory where, on the basis of very small amounts of data, one is led to extraordinary claims of infinitesimal probability of failure. Additionally, this approach permits a more meaningful separation of statistical and engineering issues.

Commentary by Dr. Valentin Fuster
J. Verif. Valid. Uncert. 2017;2(1):011006-011006-12. doi:10.1115/1.4035716.

Component-based system simulation models are used throughout all development phases for design and verification of both physical systems and control software, not least in the aeronautical industry. However, the application of structured methods for uncertainty quantification (UQ) of system simulation models is rarely seen. To enable dimensionality reduction of a UQ problem and to thereby make UQ more feasible for industry-grade system simulation models, this paper describes a pragmatic method for uncertainty aggregation. The central idea of the proposed aggregation method is to integrate information obtained during common practice component-level validation directly into the components, and to utilize this information in model-level UQ. A generic component output uncertainty description has been defined and implemented in a Modelica library for modeling and simulation (M&S) of aircraft vehicle systems. An example is provided on how to characterize and quantify a component's aggregated output uncertainty based on the component-level bench test measurement data. Furthermore, the industrial applicability of the uncertainty aggregation method is demonstrated in an approximate UQ of an aircraft liquid cooling system simulation model. For cases when the concept of thorough UQ resulting in probability boxes is not feasible, the demonstrated approximate UQ using aggregated uncertainties is considered to be a pragmatic alternative fairly in reach for the common M&S practitioner within the area of system simulation.

Commentary by Dr. Valentin Fuster

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