Net ZEB Design Processes and Tools - Modeling, Design, and Optimization of Net-Zero Energy Buildings - page 226

Fig. 4.25 Parametric analysis in Ecos (O'Brien, Athienitis, and Kesik,
2009), where lower points on the curves indicate lower annual heating and
cooling energy
4.3.4.4 Interactions
In many cases, it would be unwise to merely optimize each parameter
independently since they usually interact to some level. For instance,
O'Brien, Athienitis, and Kesik (2008) showed that the optimal south-facing
glazing area for a house with high internal gains was a third of the size
of the optimal size with low internal gains. Therefore, one can conclude
that certain parameters should be manipulated in subsets, rather than
individually. Manipulating more than several parameters simultaneously is
tedious and yields an exponentially expanding design space, as previously
illustrated in Figure 4.12 .
For the population of 30 parameters used in Ecos (O'Brien, Athienitis, and
Kesik, 2009), there are 435 (30 choose 2) two-way interactions to consider.
The current focus is on two-way interactions since higher-order interactions
are unusual (Shah, Kulkarni, and Vargas-Hernandez, 2000). One common
method to understand interactions is to create interactions plots, as is
commonly performed in the field of design of experiments (DOE) (Mason,
Gunst, and Hess, 2003). If the main effects plots are approximately linear,
interactions can be quantified using ( Eqs. 4.1 ) through ( 4.3 )