Multifidelity Uncertainty Propagation for Optimization Under Uncertainty

2012 ◽  
Author(s):  
Leo Wai-Tsun Ng ◽  
Dinh Bao Phuong Huynh ◽  
Karen Willcox
Keyword(s):  
Uncertainty Propagation ◽  
Optimization Under Uncertainty

Comparative Analysis of Methodologies for Uncertainty Propagation and Quantification

2017 ◽  
Author(s):  
Alessandra Cuneo ◽  
Alberto Traverso ◽  
Shahrokh Shahpar
Keyword(s):  
Engineering Design ◽  
Polynomial Chaos ◽  
Epistemic Uncertainty ◽  
Uncertainty Propagation ◽  
Computational Cost ◽  
Computational Effort ◽  
Optimization Under Uncertainty ◽  
Design Parameters ◽  
Test Case ◽  
Aleatory And Epistemic Uncertainty

In engineering design, uncertainty is inevitable and can cause a significant deviation in the performance of a system. Uncertainty in input parameters can be categorized into two groups: aleatory and epistemic uncertainty. The work presented here is focused on aleatory uncertainty, which can cause natural, unpredictable and uncontrollable variations in performance of the system under study. Such uncertainty can be quantified using statistical methods, but the main obstacle is often the computational cost, because the representative model is typically highly non-linear and complex. Therefore, it is necessary to have a robust tool that can perform the uncertainty propagation with as few evaluations as possible. In the last few years, different methodologies for uncertainty propagation and quantification have been proposed. The focus of this study is to evaluate four different methods to demonstrate strengths and weaknesses of each approach. The first method considered is Monte Carlo simulation, a sampling method that can give high accuracy but needs a relatively large computational effort. The second method is Polynomial Chaos, an approximated method where the probabilistic parameters of the response function are modelled with orthogonal polynomials. The third method considered is Mid-range Approximation Method. This approach is based on the assembly of multiple meta-models into one model to perform optimization under uncertainty. The fourth method is the application of the first two methods not directly to the model but to a response surface representing the model of the simulation, to decrease computational cost. All these methods have been applied to a set of analytical test functions and engineering test cases. Relevant aspects of the engineering design and analysis such as high number of stochastic variables and optimised design problem with and without stochastic design parameters were assessed. Polynomial Chaos emerges as the most promising methodology, and was then applied to a turbomachinery test case based on a thermal analysis of a high-pressure turbine disk.

Occupant Restraint System Design Under Uncertainty Using Analytical Uncertainty Propagation Via Metamodels

2005 ◽  
Author(s):  
Yan Fu ◽  
Ruichen Jin
Keyword(s):  
System Design ◽  
Complex Analysis ◽  
Uncertainty Propagation ◽  
Optimization Under Uncertainty ◽  
Computational Time ◽  
Restraint System ◽  
Support Design ◽  
Analytical Uncertainty ◽  
Occupant Restraint System ◽  
Analysis Models

The effectiveness of using Computer Aided Engineering (CAE) tools to support design decisions is often hindered by the enormous computational demand of complex analysis models, especially when uncertainty is considered. Approximations of analysis models, also known as “metamodels”, are widely used to replace analysis models for optimization under uncertainty. However, due to the inherent nonlinearity in occupant responses during a crash event and relatively large numbers of uncertain variables and responses, naive application of metamodeling techniques can yield misleading results with little or no warning from the algorithms which generate the metamodels. Furthermore, in order to improve the quality of metamodels, a relatively large number of design of experiments (DOE) and comparatively expensive metamodeling techniques, such as Kriging or radial basis function (RBF), are necessary. Thus, sampling-based methods, e.g. Monte Carlo simulations, for obtaining the statistical quantities of system responses during the optimization loop may still be inefficient even for these metamodels. In recent years, analytical uncertainty propagation via metamodels is proposed by Chen et al. 2004, which provides analytical formulation of mean and variance evaluations via a variety of metamodeling techniques to reduce the computational time and improve the convergence behavior of optimization under uncertainty. An occupant restraint system design problem is used as an example to test the applicability of this method.

scholarly journals Deep Neural Network and Polynomial Chaos Expansion-Based Surrogate Models for Sensitivity and Uncertainty Propagation: An Application to a Rockfill Dam

Water ◽  
2021 ◽  
Vol 13 (13) ◽  
pp. 1830
Author(s):  
Gullnaz Shahzadi ◽  
Azzeddine Soulaïmani
Keyword(s):  
Polynomial Chaos ◽  
Complex Structure ◽  
Uncertainty Propagation ◽  
Surrogate Models ◽  
Polynomial Chaos Expansion ◽  
Soil Parameters ◽  
Chaos Expansion ◽  
Rockfill Dam ◽  
Parametric Studies ◽  
The Impact

Computational modeling plays a significant role in the design of rockfill dams. Various constitutive soil parameters are used to design such models, which often involve high uncertainties due to the complex structure of rockfill dams comprising various zones of different soil parameters. This study performs an uncertainty analysis and a global sensitivity analysis to assess the effect of constitutive soil parameters on the behavior of a rockfill dam. A Finite Element code (Plaxis) is utilized for the structure analysis. A database of the computed displacements at inclinometers installed in the dam is generated and compared to in situ measurements. Surrogate models are significant tools for approximating the relationship between input soil parameters and displacements and thereby reducing the computational costs of parametric studies. Polynomial chaos expansion and deep neural networks are used to build surrogate models to compute the Sobol indices required to identify the impact of soil parameters on dam behavior.

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