Evaluation of a Class of Simple and Effective Uncertainty Methods for Sparse Samples of Random Variables and Functions

Romero, Vicente J.; Bonney, Matthew S.; Schroeder, Benjamin; Weirs, V. Gregory

doi:10.2172/1409725

Cited by 3 publications

(13 citation statements)

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“…Finally, if the model predictions are to be used to support estimation of small "tail" probabilities of response for robust/reliable design or safety/risk analysis, the sample results from the LHS sets in 2 would be processed in a different way. This is demonstrated in recent investigations in [26,[47][48][49] on 16 diversely shaped distributions and tail probability magnitudes from 10 À5 to 10 À1 . Reliably conservative and efficient estimates of small tail probabilities are obtained.…”

Section: Averaging Equally Legitimate Tis To Reduce Chances Of Extremmentioning

confidence: 63%

“…We now consider the uncertainty processing and interpretation of the pressure failure results. If dealing with multiple but few stress-strain curves for only one material, then appropriate uncertainty treatment has been established and confirmed in the series of papers and reports [24][25][26][27]. The approach recognizes that the stress-strain curves are discrete realizations with no readily identifiable parametric relationship between them.…”

Section: Uncertainty Processing and Interpretation Of Failure Pressurmentioning

confidence: 99%

“…Investigations in [26,31,32] have concluded 95/90 TIs to be preferable to many other UQ methods tried or critically assessed for estimating, from very sparse sample data, conservative but not overly conservative bounds on the central 95% of response. The other methods tried or critically evaluated include bootstrapping [33], optimized four-parameter Johnson-family distribution fit to the response samples [34], nonparametric kernel density estimation specifically designed for sparse data [35], nonparametric cubic spline PDF fit to the data based on maximum likelihood [36], and Bayesian sparse-data approaches [37].…”

Section: Uncertainty Processing and Interpretation Of Failure Pressurmentioning

confidence: 99%

“…Although derived for Normal populations, 95/90 TIs will span the central 95% ranges of many other sparsely sampled PDF types with reasonable/useful odds or confidence. For instance, 89% of 144 PDFs (including highly skewed and multimodal highly non-Normal distributions) studied in [25][26][27] had empirical confidence levels of 75% or greater with 95/90 TIs and N = 4 random samples. From studies in [26] on several representative PDFs, it is projected that 90% of the 144 PDFs would have confidence levels > 85% with 95/95 TIs and N = 4.…”

Section: Uncertainty Processing and Interpretation Of Failure Pressurmentioning

confidence: 99%

“…For instance, 89% of 144 PDFs (including highly skewed and multimodal highly non-Normal distributions) studied in [25][26][27] had empirical confidence levels of 75% or greater with 95/90 TIs and N = 4 random samples. From studies in [26] on several representative PDFs, it is projected that 90% of the 144 PDFs would have confidence levels > 85% with 95/95 TIs and N = 4. 1 These average or expected confidence levels decline slowly as the number of samples increases.…”

Section: Uncertainty Processing and Interpretation Of Failure Pressurmentioning

confidence: 99%

See 4 more Smart Citations

Propagating Stress-Strain Curve Variability in Multi-Material Problems: Temperature-Dependent Material Tests to Plasticity Models to Structural Failure Predictions

Romero¹,

Black²,

Orient³

et al. 2020

Engineering Failure Analysis

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This chapter presents a practical methodology for characterizing and propagating the effects of temperature-dependent material strength and failure-criteria variability to structural model predictions. The application involves a cylindrical canister ("can") heated and pressurized to failure. Temperature dependence and material sample-to-sample stochastic variability are inferred from very limited experimental data of a few replicate uniaxial tension tests at each of seven temperatures spanning the 800°C temperature excursion experienced by the can, for each of several stainless steel alloys that make up the can. The load-displacement curves from the material tests are used to determine effective temperature-dependent stress-strain relationships in ductile-metal plasticity models used in can-level model predictions. Particularly challenging aspects of the problem are the appropriate inference, representation, and propagation of temperature dependence and material stochastic variability from just a few experimental data curves at a few temperatures (as sparse discrete realizations or samples from a random field of temperature-dependent stress-strain behavior), for multiple such materials involved in the problem. Currently unique methods are demonstrated that are relatively simple and effective. 1 references [1-7] describes aspects of the associated activities, including experiments, modeling and simulation, code and calculation verification, and advanced model validation and uncertainty quantification (UQ) methods.The modeling and verification, validation, and uncertainty quantification (VVUQ) activities were performed under a multiyear "abnormal thermalmechanical breach" (T-M breach) task [1] of a Predictive Capability Assessment Project (PCAP) in the Verification & Validation (V&V) subelement of the U.S. Dept. of Energy Advanced Simulation and Computing (ASC) program. The goal of the PCAP T-M breach task was to assess the error and quantify the uncertainty in modeling the thermal-chemical-mechanical response and weld-related breach failure of sealed canisters ("cans") weakened by high temperatures and pressurized by heat-induced pyrolysis of foam. The planned outcome of the PCAP T-M breach task was to measure improvements in prediction accuracy over time as the models and computer platforms became more capable.The Sandia Weapon System Engineering and Assessment Technology Campaign (WSEAT) program supported the project by conducting material characterization tests and validation experiments [2] (see Figure 1). This partnership provided an opportunity to develop a fully integrated process from design of experiments through model validation assessment, with uncertainty reduced as much as possible and propagated through the process.Breach failures were expected to occur, and in the tests, they did occur, at the circumferential perimeter (laser) weld that joins the top lid to the can sidewalls. This is because the weld thickness is significantly less than the can lid and sidewalls (see Figure 2), and the tests/cans of...

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Section: Averaging Equally Legitimate Tis To Reduce Chances Of Extremmentioning

confidence: 63%

Section: Uncertainty Processing and Interpretation Of Failure Pressurmentioning

confidence: 99%

Section: Uncertainty Processing and Interpretation Of Failure Pressurmentioning

confidence: 99%

Section: Uncertainty Processing and Interpretation Of Failure Pressurmentioning

confidence: 99%

Section: Uncertainty Processing and Interpretation Of Failure Pressurmentioning

confidence: 99%

See 3 more Smart Citations

Propagating Stress-Strain Curve Variability in Multi-Material Problems: Temperature-Dependent Material Tests to Plasticity Models to Structural Failure Predictions

Romero¹,

Black²,

Orient³

et al. 2020

Engineering Failure Analysis

Self Cite

View full text Add to dashboard Cite

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Bootstrapping and Jackknife Resampling to Improve Sparse-Sample UQ Methods for Tail Probability Estimation

Jekel

Romero

2019

ASME 2019 Verification and Validation Symposium

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Tolerance Interval Equivalent Normal (TI-EN) and Superdistribution (SD) sparse-sample uncertainty quantification (UQ) methods are used for conservative estimation of small tail probabilities. These methods are used to estimate the probability of a response laying beyond a specified threshold with limited data. The study focused on sparse-sample regimes ranging from N = 2 to 20 samples, because this is reflective of most experimental and some expensive computational situations. A tail probability magnitude of 10−4 was examined on four different distribution shapes, in order to be relevant for quantification of margins and uncertainty (QMU) problems that arise in risk and reliability analyses. In most cases the UQ methods were found to have optimal performance with a small number of samples, beyond which the performance deteriorated as samples were added. Using this observation, a generalized Jackknife resampling technique was developed to average many smaller subsamples. This improved the performance of the SD and TI-EN methods, specifically when a larger than optimal number of samples were available. A Complete Jackknifing technique, which considered all possible sub-sample combinations, was shown to perform better in most cases than an alternative Bootstrap resampling technique.

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Discrete-Direct Model Calibration and Propagation Approach Addressing Sparse Replicate Tests and Material, Geometric, and Measurement Uncertainties

Romero

2018

SAE Technical Paper Series

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Evaluation of a Class of Simple and Effective Uncertainty Methods for Sparse Samples of Random Variables and Functions

Cited by 3 publications

References 0 publications

Propagating Stress-Strain Curve Variability in Multi-Material Problems: Temperature-Dependent Material Tests to Plasticity Models to Structural Failure Predictions

Propagating Stress-Strain Curve Variability in Multi-Material Problems: Temperature-Dependent Material Tests to Plasticity Models to Structural Failure Predictions

Bootstrapping and Jackknife Resampling to Improve Sparse-Sample UQ Methods for Tail Probability Estimation

Discrete-Direct Model Calibration and Propagation Approach Addressing Sparse Replicate Tests and Material, Geometric, and Measurement Uncertainties

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