Chapter 12
Response Surface Methodology
Péter Zénó Korondi , Mariapia Marchi , and Carlo Poloni
Abstract Response Surface Methods (RSMs) are statistical and numerical models
that approximate the relationship between multiple input variables and an output
variable. This chapter introduces the methodology and its importance for engineering design optimisation. The basic steps to build RSMs and validate the model
accuracy are explained. An overview of three classical methods (Least Squares,
Radial Basis Functions, and Kriging) is provided. A simple wing structure design
optimisation problem is used to illustrate the different phases of the response surface
methodology and its application to design optimisation. This example also includes
the case of noisy data.
Keywords Response surface method · Radial basis function · Kriging ·
Surrogate model · Quality indicators · Design optimisation
12.1 Introduction
Response Surface Methodology refers to statistical and numerical techniques to
model the relationship between multiple input variables and an output variable. A
Response Surface Method (RSM) can be considered as a multidimensional surface
P. Z. Korondi ()
ESTECO SpA, Trieste, Italy
Department of Engineering and Architecture, University of Trieste, Trieste, Italy
e-mail: korondi@esteco.com
M. Marchi
ESTECO SpA, Trieste, Italy
e-mail: marchi@esteco.com
C. Poloni
Department of Engineering and Architecture, University of Trieste, Trieste, Italy
ESTECO SpA, Trieste, Italy
e-mail: poloni@units.it; poloni@esteco.com
© Springer Nature Switzerland AG 2021
M. Vasile (ed.), Optimization Under Uncertainty with Applications to Aerospace
Engineering, https://doi.org/10.1007/978-3-030-60166-9_12
387
Response Surface Methodology
Péter Zénó Korondi , Mariapia Marchi , and Carlo Poloni
Abstract Response Surface Methods (RSMs) are statistical and numerical models
that approximate the relationship between multiple input variables and an output
variable. This chapter introduces the methodology and its importance for engineering design optimisation. The basic steps to build RSMs and validate the model
accuracy are explained. An overview of three classical methods (Least Squares,
Radial Basis Functions, and Kriging) is provided. A simple wing structure design
optimisation problem is used to illustrate the different phases of the response surface
methodology and its application to design optimisation. This example also includes
the case of noisy data.
Keywords Response surface method · Radial basis function · Kriging ·
Surrogate model · Quality indicators · Design optimisation
12.1 Introduction
Response Surface Methodology refers to statistical and numerical techniques to
model the relationship between multiple input variables and an output variable. A
Response Surface Method (RSM) can be considered as a multidimensional surface
P. Z. Korondi ()
ESTECO SpA, Trieste, Italy
Department of Engineering and Architecture, University of Trieste, Trieste, Italy
e-mail: korondi@esteco.com
M. Marchi
ESTECO SpA, Trieste, Italy
e-mail: marchi@esteco.com
C. Poloni
Department of Engineering and Architecture, University of Trieste, Trieste, Italy
ESTECO SpA, Trieste, Italy
e-mail: poloni@units.it; poloni@esteco.com
© Springer Nature Switzerland AG 2021
M. Vasile (ed.), Optimization Under Uncertainty with Applications to Aerospace
Engineering, https://doi.org/10.1007/978-3-030-60166-9_12
387