Response Surface Modeling for Design Space Exploration of Embedded Systems - Multi-objective Design Space Exploration of Multiprocessor SoC Architectures - page 79

Fig. 4.3 Typical usage of a
Response Surface Model

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Observations
Interpolation
Regression

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4.2.2 Design of Experiments

The training data used for identifying the parameters w is fundamental for creating
reasonably accurate prediction models. Of course, the set should be limited given the
simulation time needed to gather these data. The literature on RSM calls for a system-
atic Design of Experiments (DoE) [ 17 ] to identify the most suitable configurations
with which the RSM can be trained. Design of Experiments is a discipline that has
had a very broad application across natural and social sciences and encompassed a set
of techniques whose main goal is the screening and analysis of the system behavior
with a small number of simulations. Each DoE plan differs in terms of the layout of
the selected design points in the design space. Several design of experiments have
been proposed in the literature so far. Among the most used DoEs for training RSMs
we can find:
￿ Random DoE . Design space configurations are picked up randomly by following

a Probability Density Function (PDF).

￿ Full Factorial DoE . In statistics, a factorial experiment is an experiment whose

design consists of two or more parameters, each with discrete possible values or
“levels” and whose experimental units take on all possible combinations of these
levels across all such parameters. Such an experiment allows studying the effects
of each parameter on the response variable, as well as the effects of interactions
between parameters on the response variable. The most important full-factorial
DoE is called 2-level full factorial, where the only levels considered are the
minimum and maximum for each parameter.

￿ Central Composite DoE . A Central Composite Design is an experimental design

specifically targeted to the construction of response surfaces of the second order
(quadratic) without requiring a three-level factorial.

It is important to note that, while factorial and central composite DoE layouts require
a fixed number of points, the Random DoE can have a varying number of design
points. In this topic, we will leverage Random DoE for validating the proposed RSMs.