scholarly journals Mixed Aleatory/Epistemic Uncertainty Quantification for Hypersonic Flows via Gradient-Based Optimization and Surrogate Models

2012 ◽  
Author(s):  
Brian Lockwood ◽  
Mihai Anitescu ◽  
Dimitri Mavriplis
Keyword(s):  
Uncertainty Quantification ◽  
Epistemic Uncertainty ◽  
Surrogate Models ◽  
Hypersonic Flows ◽  
Gradient Based

A Comparison of Numerical Optimizers in Developing High Dimensional Surrogate Models

2019 ◽  
Author(s):  
Yanwen Xu ◽  
Pingfeng Wang
Keyword(s):  
Gaussian Process ◽  
Process Model ◽  
Likelihood Function ◽  
Surrogate Models ◽  
Kernel Functions ◽  
Function Optimization ◽  
High Dimensional ◽  
Model Parameters ◽  
Gradient Based ◽  
Gp Model

Abstract The Gaussian Process (GP) model has become one of the most popular methods to develop computationally efficient surrogate models in many engineering design applications, including simulation-based design optimization and uncertainty analysis. When more observations are used for high dimensional problems, estimating the best model parameters of Gaussian Process model is still an essential yet challenging task due to considerable computation cost. One of the most commonly used methods to estimate model parameters is Maximum Likelihood Estimation (MLE). A common bottleneck arising in MLE is computing a log determinant and inverse over a large positive definite matrix. In this paper, a comparison of five commonly used gradient based and non-gradient based optimizers including Sequential Quadratic Programming (SQP), Quasi-Newton method, Interior Point method, Trust Region method and Pattern Line Search for likelihood function optimization of high dimension GP surrogate modeling problem is conducted. The comparison has been focused on the accuracy of estimation, the efficiency of computation and robustness of the method for different types of Kernel functions.

Uncertainty Quantification of Time-Dependent Reliability Analysis in the Presence of Parametric Uncertainty

2016 ◽  
Vol 2 (3) ◽  
Author(s):  
Zhen Hu ◽  
Sankaran Mahadevan ◽  
Xiaoping Du
Keyword(s):  
Uncertainty Quantification ◽  
Reliability Analysis ◽  
Surrogate Model ◽  
Reliability Index ◽  
Integration Method ◽  
Epistemic Uncertainty ◽  
Random Variables ◽  
Time Dependent ◽  
Data Uncertainty ◽  
State Function

Limited data of stochastic load processes and system random variables result in uncertainty in the results of time-dependent reliability analysis. An uncertainty quantification (UQ) framework is developed in this paper for time-dependent reliability analysis in the presence of data uncertainty. The Bayesian approach is employed to model the epistemic uncertainty sources in random variables and stochastic processes. A straightforward formulation of UQ in time-dependent reliability analysis results in a double-loop implementation procedure, which is computationally expensive. This paper proposes an efficient method for the UQ of time-dependent reliability analysis by integrating the fast integration method and surrogate model method with time-dependent reliability analysis. A surrogate model is built first for the time-instantaneous conditional reliability index as a function of variables with imprecise parameters. For different realizations of the epistemic uncertainty, the associated time-instantaneous most probable points (MPPs) are then identified using the fast integration method based on the conditional reliability index surrogate without evaluating the original limit-state function. With the obtained time-instantaneous MPPs, uncertainty in the time-dependent reliability analysis is quantified. The effectiveness of the proposed method is demonstrated using a mathematical example and an engineering application example.

scholarly journals Efficient Utilization of Surrogate Models for Uncertainty Quantification

PAMM ◽  
2021 ◽  
Vol 20 (1) ◽  
Author(s):  
Maria Böttcher ◽  
Ferenc Leichsenring ◽  
Alexander Fuchs ◽  
Wolfgang Graf ◽  
Michael Kaliske
Keyword(s):  
Uncertainty Quantification ◽  
Surrogate Models ◽  
Efficient Utilization

Gradient Enhanced Surrogate Models Based on Adjoint CFD Methods for the Design of a Counter Rotating Turbofan

2012 ◽  
Author(s):  
Jan Backhaus ◽  
Marcel Aulich ◽  
Christian Frey ◽  
Timea Lengyel ◽  
Christian Voß
Keyword(s):  
Fitness Function ◽  
Computational Cost ◽  
Surrogate Models ◽  
Training Data ◽  
Design And Optimization ◽  
Additional Information ◽  
Gradient Based ◽  
Reference Design ◽  
Objective Function Values ◽  
The Impact

This paper studies the use of adjoint CFD solvers in combination with surrogate modelling in order to reduce the computational cost of the optimization of complex 3D turbomachinery components. The method is applied to a previously optimized counter rotating turbofan, with a shape parameterized by 104 CAD parameters. Through random changes on the reference design, a small number of design variations are created to serve as training samples for the surrogate models. A steady RANS solver and its discrete adjoint are then used to calculate objective function values and their corresponding sensitivities. Kriging and neural networks are used to build surrogate models from the training data. To study the impact of the additional information provided by the adjoint solver, each model is trained with and without the sensitivity information. The accuracy of the different surrogate model predictions is assessed by comparison against CFD calculations. The results show a considerable improvement of the fitness function approximation when the sensitivity information is taken into account. Through a gradient based optimization on one of the surrogate models, a design with higher isentropic efficiency at the aerodynamic design point is created. This application demonstrates that the improved surrogate models can be used for design and optimization.

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