Prediction and Uncertainty in Computational Modeling of Complex Phenomena: A Whitepaper

Trucano, Timothy Guy

doi:10.2172/3503

Cited by 8 publications

(10 citation statements)

References 29 publications

(27 reference statements)

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“…Uncertainties in the operating scenarios (atmospheric state, vehicle flight conditions, controls, etc. -namely aleatoric uncertainties 16 ) were typically characterized using Gaussian probability distributions and propagated through the computational model using brute-force Monte Carlo sampling. In spite of the demonstrated success of this approach, there is a need to reduce the cost and effort involved in calibrating the computational models to allow a more comprehensive exploration of the design space and to extend the performance threshold closer to the operability limits by reducing excessively conservative use of the safety factors, while demonstrating reliability to expected variations in the operation of the vehicles.…”

Section: A Risk Quantificationmentioning

confidence: 99%

Risk Assessment of Scramjet Unstart Using Adjoint-Based Sampling Methods

et al. 2012

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We demonstrate an adjoint based approach for accelerating Monte Carlo estimation of risk, and apply it to estimating the probability of unstart in a SCRamjet engine under uncertain conditions that are characterized by various Gaussian and non-Gaussian distributions. The adjoint equation is solved with respect to an objective function that is used to identify unstart and the adjoint solution is used to generate a linear approximation to the objective function. This linear surrogate is used to divide the uncertain input parameters into three different strata, corresponding to safe operation of the engine, uncertain operation and unstart. The probability of unstart within these strata is very different and as a result, stratified sampling significantly increases the efficiency of the risk assessment procedure by reducing the variance of the estimator. Using this technique, the Monte Carlo method was demonstrated to be accelerated by a factor of 5.4.

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Section: A Risk Quantificationmentioning

confidence: 99%

Risk Assessment of Scramjet Unstart Using Adjoint-Based Sampling Methods

et al. 2012

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“…Different ways of classifying uncertainties in model prediction are seen in the literature (Apostolakis 1994;Trucano, 1998;Hazelrigg, 1999;Oberkampf et al, 1999). In this work we assume that that the computational error has been satisfactorily resolved or eliminated through "verification" (Oberkampf and Trucano, 2000).…”

Section: The Bayesian Procedures For Model Predictionmentioning

confidence: 99%

A Design-Driven Validation Approach Using Bayesian Prediction Models

Chen

Xiong

Tsui

et al. 2007

Journal of Mechanical Design

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“…Different ways of classifying uncertainties in model prediction are seen in the literature (Apostolakis 1994;Trucano, 1998;Hazelrigg, 1999;Oberkampf et al, 1999 (Easterling and Berger, 2002) and Bayesian approaches. The fundamental difference between the two is that the former draws confidence intervals of prediction based on statistical data analysis, while the latter assumes that the model parameters themselves are random and follow a prior distribution, specified based on model builder/designers' prior knowledge.…”

Section: Uncertainties In Model Prediction and The Mathematical Framementioning

confidence: 99%

Some Metrics and a Bayesian Procedure for Validating Predictive Models in Engineering Design

Chen

Xiong

Tsui

et al. 2006

Volume 1: 32nd Design Automation Conference, Parts a and B

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Even though model-based simulations are widely used in engineering design, it remains a challenge to validate models and assess the risks and uncertainties associated with the use of predictive models for design decision making. In most of the existing work, model validation is viewed as verifying the model accuracy, measured by the agreement between computational and experimental results. However, from the design perspective, a good model is considered as the one that can provide the discrimination (good resolution) between design candidates. In this work, a Bayesian approach is presented to assess the uncertainty in model prediction by combining data from both physical experiments and the computer model. Based on the uncertainty quantification of model prediction, some design-oriented model validation metrics are further developed to guide designers for achieving high confidence of using predictive models in making a specific design decision. We demonstrate that the Bayesian approach provides a flexible framework for drawing inferences for predictions in the intended but may be untested design domain, where design settings of physical experiments and the computer model may or may not overlap. The implications of the proposed validation metrics are studied, and their potential roles in a model validation procedure are highlighted. general term of design validation metric k number of design candidates space INTRODUCTIONWith rapid increase of computational capability, modeling and simulation based design has been increasingly used for designing new engineering systems. However, it remains a challenge on assessing the risks and uncertainties associated with the use of predictive models in engineering design. Even

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Prediction and Uncertainty in Computational Modeling of Complex Phenomena: A Whitepaper

Cited by 8 publications

References 29 publications

Risk Assessment of Scramjet Unstart Using Adjoint-Based Sampling Methods

Risk Assessment of Scramjet Unstart Using Adjoint-Based Sampling Methods

A Design-Driven Validation Approach Using Bayesian Prediction Models

Some Metrics and a Bayesian Procedure for Validating Predictive Models in Engineering Design

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