A new approach to estimate discretization error for multidisciplinary and multidirectional mesh refinement

Rangavajhala, Sirisha; Sura, Venkata S.; Mahadevan, Sankaran; Hombal, Vadiraj

doi:10.2514/6.2011-1926

Cited by 2 publications

(2 citation statements)

References 22 publications

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“…Furthermore, since the errors in 4 sd p along the dome vary in magnitude spatially, it would be beneficial to use a more flexible error model, such as a Gaussian process model, in more practical applications. 26 Figure 9 and Table 8 The deterministic errors are useful for assessing the accuracy of the nominal model predictions, however this is a stochastic problem and error alone does not provide a statistical assessment of the confidence in the model prediction. Therefore, the most important step in this model uncertainty framework is to validate the models by assessing the confidence.…”

Section: Figure 5 Bayes Network For Calibrating Model Inputs and Errmentioning

confidence: 99%

Error Quantification and Confidence Assessment of Aerothermal Model Predictions for Hypersonic Aircraft

Smarslok¹,

Culler²,

Mahadevan³

2012

53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials ConferenceSelf Cite

34
1
16
0

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Assessing prediction confidence and enabling its use as a decision-making metric for autonomous model fidelity selection is essential to the USAF's vision of a 'Digital Twin' as a viable approach for condition-based fleet management by tail number. Significant strides have been made in modeling complex interactions of the multi-physics, fluid-thermalstructural coupling applicable to hypersonic flow conditions. However, validation of these models remains a challenge due to limited experimental data for hypersonic conditions. This research addresses quantifying errors and assessing the confidence in aerodynamic pressure and heating predictions for a spherical dome protruding from a flat ramp. Wellcharacterized aerothermal test data from hypersonic wind tunnel experiments are used to calibrate uncertain model parameters and quantify errors through Bayesian techniques. A Bayesian hypothesis testing-based confidence metric is employed to compare the accuracy in various model predictions. A model selection study is performed for 1 st -, 2 nd -, and 3 rd -order piston theories. The results showed that the greatest confidence in model predictions does not necessarily correspond to the highest-order model. NomenclatureB = Bayes factor C = Bayesian hypothesis testing-based confidence metric D = diameter of the spherical dome e = model error H = height of the spherical dome M = Mach number p = aerodynamic pressure q = dynamic pressure (ρU 2 /2) Q = aerodynamic heat flux R eq = equivalence ratio (fuel-to-air ratio divided by stoichiometric fuel-to-air ratio) S = main effect sensitivity index S T = total effect sensitivity index T = temperature w = transverse panel displacement x = model prediction, location along dome y = observed data β = oblique shock angle relative to freestream ϕ = uncertain input parameters γ = ratio of specific heats µ = mean π = probability density function 2 θ = panel inclination angle to freestream ρ = density σ = standard deviation Subscripts aw = adiabatic wall e = edge of boundary layer i = variable index, position along spherical dome true = true value of x pred = model prediction of x w = wall, aerodynamic surface 1 = freestream flow 3 = flow at the leading edge of panel 4 = flow at location of interest along the panel Superscripts fp = flat plate sd = spherical dome * = flow properties evaluated at Eckert's reference temperature

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Section: Figure 5 Bayes Network For Calibrating Model Inputs and Errmentioning
confidence: 99%

Error Quantification and Confidence Assessment of Aerothermal Model Predictions for Hypersonic Aircraft
Smarslok¹,
Culler²,
Mahadevan³
2012
53rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials ConferenceSelf Cite
34
1
16
0
View full text Add to dashboard Cite

show abstract

“…Ostoich et al looked at the heat flux into a spherical dome protuberance on a flat plate model, calculated from high-fidelity, fully compressible Navier-Stokes equations without turbulence model and compared the results to experimental data and lower-order methods [15,16]. Rangavajhala et al investigated the discretization error associated with multidisciplinary analyses caused by mesh sizes and mismatch of disciplinary meshes [17]. These efforts underscore the importance of understanding the uncertainty in a coupled aerothermoelastic model; however, many questions remain about the significant sources of uncertainty and how to assess the confidence in multi-physics model predictions.…”

Section: Introductionmentioning
confidence: 99%

Quantifying Confidence in Model Predictions for Hypersonic Aircraft Structures
Smarslok¹
2015
2
0
0
0
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Lack of confidence in structural response and life predictions of a vehicle exposed to combined extreme environments has consistently prevented the USAF from fielding affordable, reliable, and reusable hypersonic space access platforms. Significant strides have been made in modeling complex interactions of the multi-physics, fluid-thermal-structural coupling applicable to hypersonic flow conditions. However, validation of these models remains a challenge due to limited experimental data for hypersonic conditions. This research addresses fundamental and critical issues in quantifying uncertainty and assessing the confidence in model predictions of hypersonic structural response through a systematic framework. The first year of this research focused on identifying and developing the components of the model uncertainty framework for aerodynamic pressure and heating predictions, including global sensitivity analysis, Bayesian model calibration, and validation metric comparison. The second year emphasized effectively integrating information into the coupled system through segmented Bayesian model calibration. The final year brought together model discrepancy in aerodynamic pressure calibrated from aerothermal experiments with nonlinear structural dynamic reduced order models to investigate the uncertainty and sensitivity in coupled aeroelastic response (i.e., flutter and limit cycle oscillation). ix Approved for public release; distribution unlimited. Approved for public release; distribution unlimited. 1.1 Uncertainty Quantification and Model Prediction Confidence Assessment Quantifying the confidence in model prediction consists of two intertwined, yet distinct, activities: uncertainty quantification (UQ) and verification and validation (V&V). The science of uncertainty quantification for numerical simulations (i.e., the quantitative characterization and reduction of uncertainties) has origins dating back to the early-1990's. However, over the past decade there has been a surge in multiple research communities towards formalizing and generalizing the process. Thus, there are now multiple descriptions and implementations of the UQ and V&V processes that are all similar in their objectives, but different in their details. Due to the nature of UQ and V&V research, it is necessary to establish terminology and research scope. Uncertainty is inherent in all computational model predictions due to imperfect knowledge and physical variability in the system, model order reduction, assumptions and approximations, and the limited experimental data available for model calibration and validation. This is especially the case for compliant structures in hypersonic environments due to the complex and poorly-understood loading and the coupled multi-physics nature of the fluidthermal-structural interaction. Physical variability is incorporated in fluid-thermal-structural models through variations in material properties, geometry, boundary conditions, and load interactions. The aerothermoelastic model prediction also has both model-for...

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A new approach to estimate discretization error for multidisciplinary and multidirectional mesh refinement

Cited by 2 publications

References 22 publications

Error Quantification and Confidence Assessment of Aerothermal Model Predictions for Hypersonic Aircraft

Error Quantification and Confidence Assessment of Aerothermal Model Predictions for Hypersonic Aircraft

Quantifying Confidence in Model Predictions for Hypersonic Aircraft Structures

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