388
P. Z. Korondi et al.
fitting of the output variable based on the observed data in multidimensional input
space.
Generally speaking, a response surface model (a.k.a. surrogate model or metamodel) is used to replace expensive numerical or physical experiments with a
computationally cheap and sufficiently accurate model. In engineering, decisions
are made on information obtained from various kinds of analyses, as pointed out by
Forrester in his book [1]. One way to get information and increase the knowledge
of a problem is to conduct experiments; however, in many cases the cost and
complexity of the experiments is so high that only a limited number, if any, of
observations is feasible. For example, in aerospace engineering, experiments can
be very expensive (e.g. extra-territorial missions) or can take a long time (e.g. run
high-fidelity simulations). Consequently, models are built to increase the knowledge
gained from the observations and to predict performance values which cannot be
directly observed.
RSMs are a valuable tool for making decisions during the life-cycle of a physical
asset or process. In early-stage design phases, RSMs can give fast and cheap
predictions about the cause–effect relationship of the design inputs and outputs.
In Robust Design Optimisation and Reliability Based Design Optimisation, RSMs
can be used to substitute expensive performance analyses to provide enough data
for statistical calculations. In operational phases, RSMs can provide additional
data, information for digital twins, operators and artificial intelligence algorithms
to facilitate the control of the process. In recent decades, engineering design
has become increasingly collaborative and multi-disciplinary. In many cases, the
parameters of an expensive numerical experiment depend on the output of one
or more other expensive numerical experiments of different disciplines. In this
context, the RSM of a numerical experiment can provide response data for input
parameter predictions of numerical solvers of other disciplines, facilitating the use
of parallel discipline analyses [2]. Moreover, RSMs are able to handle possibly noisy
experimental results.
The accuracy of RSMs can be controlled by the configuration of the RSM
algorithm; however, speed and accuracy often conflict: and a compromise has to be
made. The task of choosing the most appropriate RSM is challenging and requires
expertise.
This chapter is organised as follows. Section 12.2 introduces the pragmatical
stages and steps of the RSM construction. Section 12.3 provides a brief overview of
some selected RSMs: Least Squares Method (LSM), Radial Basis Functions (RBF),
and Kriging. Section 12.4 shows the application of the RSMs in an uncertainty
analysis of a simplified wing design problem.
For a more detailed review on RSMs see one of the following books [1, 3, 4].
P. Z. Korondi et al.
fitting of the output variable based on the observed data in multidimensional input
space.
Generally speaking, a response surface model (a.k.a. surrogate model or metamodel) is used to replace expensive numerical or physical experiments with a
computationally cheap and sufficiently accurate model. In engineering, decisions
are made on information obtained from various kinds of analyses, as pointed out by
Forrester in his book [1]. One way to get information and increase the knowledge
of a problem is to conduct experiments; however, in many cases the cost and
complexity of the experiments is so high that only a limited number, if any, of
observations is feasible. For example, in aerospace engineering, experiments can
be very expensive (e.g. extra-territorial missions) or can take a long time (e.g. run
high-fidelity simulations). Consequently, models are built to increase the knowledge
gained from the observations and to predict performance values which cannot be
directly observed.
RSMs are a valuable tool for making decisions during the life-cycle of a physical
asset or process. In early-stage design phases, RSMs can give fast and cheap
predictions about the cause–effect relationship of the design inputs and outputs.
In Robust Design Optimisation and Reliability Based Design Optimisation, RSMs
can be used to substitute expensive performance analyses to provide enough data
for statistical calculations. In operational phases, RSMs can provide additional
data, information for digital twins, operators and artificial intelligence algorithms
to facilitate the control of the process. In recent decades, engineering design
has become increasingly collaborative and multi-disciplinary. In many cases, the
parameters of an expensive numerical experiment depend on the output of one
or more other expensive numerical experiments of different disciplines. In this
context, the RSM of a numerical experiment can provide response data for input
parameter predictions of numerical solvers of other disciplines, facilitating the use
of parallel discipline analyses [2]. Moreover, RSMs are able to handle possibly noisy
experimental results.
The accuracy of RSMs can be controlled by the configuration of the RSM
algorithm; however, speed and accuracy often conflict: and a compromise has to be
made. The task of choosing the most appropriate RSM is challenging and requires
expertise.
This chapter is organised as follows. Section 12.2 introduces the pragmatical
stages and steps of the RSM construction. Section 12.3 provides a brief overview of
some selected RSMs: Least Squares Method (LSM), Radial Basis Functions (RBF),
and Kriging. Section 12.4 shows the application of the RSMs in an uncertainty
analysis of a simplified wing design problem.
For a more detailed review on RSMs see one of the following books [1, 3, 4].