Prediction using numerical simulations, a bayesian framework for uncertainty quantification and its statistical challenge

2004 ◽  
Author(s):  
J. Glimm ◽  
Yunha Lee ◽  
K.Q. Ye ◽  
D.H. Sharp
Keyword(s):  
Numerical Simulations ◽  
Uncertainty Quantification ◽  
Bayesian Framework

Uncertainty Quantification for Multiscale Simulations1

2001 ◽  
Vol 124 (1) ◽  
pp. 29-41 ◽  
Author(s):  
B. DeVolder ◽  
J. Glimm ◽  
J. W. Grove ◽  
Y. Kang ◽  
Y. Lee ◽  
...  
Keyword(s):  
Shock Wave ◽  
Numerical Simulations ◽  
Uncertainty Quantification ◽  
Confidence Intervals ◽  
Petroleum Reservoirs ◽  
Bayesian Framework ◽  
Simulation Studies ◽  
Error Statistics ◽  
Key Issues ◽  
Leading Term

A general discussion of the quantification of uncertainty in numerical simulations is presented. A principal conclusion is that the distribution of solution errors is the leading term in the assessment of the validity of a simulation and its associated uncertainty in the Bayesian framework. Key issues that arise in uncertainty quantification are discussed for two examples drawn from shock wave physics and modeling of petroleum reservoirs. Solution error models, confidence intervals and Gaussian error statistics based on simulation studies are presented.

Virtually-Guided Certification With Uncertainty Quantification Applied to Die Casting

2018 ◽  
Author(s):  
Shantanu Shahane ◽  
Soham Mujumdar ◽  
Namjung Kim ◽  
Pikee Priya ◽  
Narayana Aluru ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Product Quality ◽  
Uncertainty Quantification ◽  
Process Parameters ◽  
High Speed ◽  
Prediction Models ◽  
Die Casting ◽  
Stochastic Variation ◽  
Complex Process ◽  
Mechanical Properties Prediction

Die casting is a type of metal casting in which liquid metal is solidified in a reusable die. In such a complex process, measuring and controlling the process parameters is difficult. Conventional deterministic simulations are insufficient to completely estimate the effect of stochastic variation in the process parameters on product quality. In this research, a framework to simulate the effect of stochastic variation together with verification, validation, and uncertainty quantification is proposed. This framework includes high-speed numerical simulations of solidification, micro-structure and mechanical properties prediction models along with experimental inputs for calibration and validation. Both experimental data and stochastic variation in process parameters with numerical modeling are employed thus enhancing the utility of traditional numerical simulations used in die casting to have a better prediction of product quality. Although the framework is being developed and applied to die casting, it can be generalized to any manufacturing process or other engineering problems as well.

Uncertainty Quantification of Flame Transfer Function under a Bayesian Framework

2018 ◽  
Author(s):  
Yixing Li ◽  
Xingjian Wang ◽  
Simon Mak ◽  
Chih-Li Sung ◽  
Jeff Wu ◽  
...  
Keyword(s):  
Transfer Function ◽  
Uncertainty Quantification ◽  
Bayesian Framework

Fluid-Structure Interaction Simulation of an Aortic Phantom with Uncertain Young's Modulus Using the Polynomial Chaos Expansion

2015 ◽  
Vol 807 ◽  
pp. 34-44
Author(s):  
Jonas Kratzke ◽  
Michael Schick ◽  
Vincent Heuveline
Keyword(s):  
Numerical Simulations ◽  
Uncertainty Quantification ◽  
Young’S Modulus ◽  
Clinical Decision Making ◽  
Polynomial Chaos ◽  
Young's Modulus ◽  
Clinical Decision ◽  
Von Mises Stress ◽  
Strong Impact ◽  
Fluid Structure

To add reliability to numerical simulations, Uncertainty Quantification is considered to be a crucial tool for clinical decision making. This especially holds for risk assessment of cardiovascular surgery, for which threshold parameters computed by numerical simulations are currently being discussed. A corresponding biomechanical model includes blood flow, soft tissue deformation, as well as fluid-structure coupling. Thereby, structural material parameters have a strong impact on the dynamic behavior. In practice, however, particularly the value of the Young's modulus is rarely known in a precise way, and therefore, it reflects a natural level of uncertainty. In this work we introduce a stochastic model for representing variations in the Young's modulus and quantify its effect on the wall sheer stress and von Mises stress by means of the Polynomial Chaos method. We demonstrate the use of uncertainty quantification in this context and provide numerical results based on an aortic phantom benchmark model.

Simulations of Die Casting With Uncertainty Quantification

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
Shantanu Shahane ◽  
Soham Mujumdar ◽  
Namjung Kim ◽  
Pikee Priya ◽  
Narayana R. Aluru ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Product Quality ◽  
Uncertainty Quantification ◽  
Process Parameters ◽  
High Speed ◽  
Prediction Models ◽  
Die Casting ◽  
Stochastic Variation ◽  
Complex Process ◽  
Mechanical Properties Prediction

Die casting is a type of metal casting in which a liquid metal is solidified in a reusable die. In such a complex process, measuring and controlling the process parameters are difficult. Conventional deterministic simulations are insufficient to completely estimate the effect of stochastic variation in the process parameters on product quality. In this research, a framework to simulate the effect of stochastic variation together with verification, validation, and uncertainty quantification (UQ) is proposed. This framework includes high-speed numerical simulations of solidification, microstructure, and mechanical properties prediction models along with experimental inputs for calibration and validation. Both experimental data and stochastic variation in process parameters with numerical modeling are employed, thus enhancing the utility of traditional numerical simulations used in die casting to have a better prediction of product quality. Although the framework is being developed and applied to die casting, it can be generalized to any manufacturing process or other engineering problems as well.

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