14 Best Practices for Surrogate Based Uncertainty Quantification in. . .
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of the statistical moments, the use of sparse sampling techniques or the use of
approximations of the cost function.
The use of surrogate models, approximations of the CFD solution that can be
cheaply evaluated, has acquired importance in the last years for aerodynamic shape
optimization [4, 7], and will be explained with more detail in the following section.
14.3 Surrogate Models for Uncertainty Quantification
This section introduces the use of surrogate models for robust aerodynamic shape
optimization with special focus on Uncertainty Quantification. The benefits of
surrogate models with respect to other uncertainty quantification methods are
outlined. Finally, Gradient-Enhanced Kriging surrogate technique is shown to break
the curse of dimensionality in situations where the gradient information is cheaply
available.
14.3.1 Surrogate Models Overview
In modern engineering design problems, the use of expensive simulations makes
unfeasible the full exploration of the design space. It is not always possible to
analyze all the competing options, especially in the aerospace industry, where the
modelling of fluid dynamics through numerical methods is one of the most computationally demanding fields [4, 10]. When dealing with CFD based optimization, a
deterministic solution is already a computationally expensive approach. In case of
robust aerodynamic shape optimization, i.e. with optimization under uncertainty, the
high cost of quantifying the uncertainty in each iteration of the optimization process
makes necessary the use efficient uncertainty quantification methods, especially for
high dimensional problems.
Surrogate models, also called response surfaces or meta-models, are approximations of expensive high fidelity models that represent the physical quantity
of interest (for example, drag, weight or cost), as a function of the design or
uncertainty parameters. In the case of aerodynamic shape optimization, usually
surrogate models of the drag are built as a function of the geometrical parameters.
These continuous, multi-dimensional models based on sampled data, require of a
one-time upfront investment in order to get instant, online evaluation of the data.
Surrogate models have effectively been applied in global aerodynamic shape
optimization problems [11] following an iterative process by balancing exploitation
and exploration of the design landscape. Due to the capability of approximating the
quantity of interest, another possibility is to use surrogate models as an attractive
non-intrusive method to perform uncertainty quantification, especially in the context
of Computational Fluid Dynamics.
435
of the statistical moments, the use of sparse sampling techniques or the use of
approximations of the cost function.
The use of surrogate models, approximations of the CFD solution that can be
cheaply evaluated, has acquired importance in the last years for aerodynamic shape
optimization [4, 7], and will be explained with more detail in the following section.
14.3 Surrogate Models for Uncertainty Quantification
This section introduces the use of surrogate models for robust aerodynamic shape
optimization with special focus on Uncertainty Quantification. The benefits of
surrogate models with respect to other uncertainty quantification methods are
outlined. Finally, Gradient-Enhanced Kriging surrogate technique is shown to break
the curse of dimensionality in situations where the gradient information is cheaply
available.
14.3.1 Surrogate Models Overview
In modern engineering design problems, the use of expensive simulations makes
unfeasible the full exploration of the design space. It is not always possible to
analyze all the competing options, especially in the aerospace industry, where the
modelling of fluid dynamics through numerical methods is one of the most computationally demanding fields [4, 10]. When dealing with CFD based optimization, a
deterministic solution is already a computationally expensive approach. In case of
robust aerodynamic shape optimization, i.e. with optimization under uncertainty, the
high cost of quantifying the uncertainty in each iteration of the optimization process
makes necessary the use efficient uncertainty quantification methods, especially for
high dimensional problems.
Surrogate models, also called response surfaces or meta-models, are approximations of expensive high fidelity models that represent the physical quantity
of interest (for example, drag, weight or cost), as a function of the design or
uncertainty parameters. In the case of aerodynamic shape optimization, usually
surrogate models of the drag are built as a function of the geometrical parameters.
These continuous, multi-dimensional models based on sampled data, require of a
one-time upfront investment in order to get instant, online evaluation of the data.
Surrogate models have effectively been applied in global aerodynamic shape
optimization problems [11] following an iterative process by balancing exploitation
and exploration of the design landscape. Due to the capability of approximating the
quantity of interest, another possibility is to use surrogate models as an attractive
non-intrusive method to perform uncertainty quantification, especially in the context
of Computational Fluid Dynamics.