Design of Experiment

1. Presentation Content
• Introduction
• Study Objectives
• Methodology
• Case Study
1. Experiment Setup
2. GSA
3. Surrogate Modelling
4. Optimization Analyses
5. Discussion
• Conclusions

2. Introduction
Lighting
Cooling
Simulations & Variables
LCC : Lifecycle Cost
EUI : Energy Use Intensity

3. Sensitivity Analysis (SA)
can be used to find the design variables that have the
largest influence on the response variable.
Local Sensitivity Analysis (Local SA):
focuses on finding the effect of the change in
design variables around a point or the base case.
Global Sensitivity Analysis (GSA):
makes the analysis base case independent.
• Morris Method
• Fractional Factorial Design (FFD)

4. Optimization Methods
can be more effective in finding the optimal building
design after eliminating the less important variables.
GA for optimization to reduce the energy consumption in HVAC.
Full factorial design based GSA with Pareto optimization using
NSGA-II algorithm for building simulation based optimization.
Coupled EnergyPlus with GenOpt to minimize LCC for building
materials and operational energy consumption.
suggested that the direct coupling between building simulation
and optimization engine is time-consuming, and surrogate
based optimization should be studied. .
Nassif (2014)
Evins (2012)
Karaguzel (2014)
Nguyen (2014)

5. Surrogate Models
used to approximate the simulation model behavior. It
is created using a limited number of simulation runs
over the search space of interest for predicting the
simulation output.
Coupled the ANN model with GA to optimize for thermal
comfort and energy consumption.
Used response surface models to predict domestic energy use.
The application of response surface methodology (RSM) for
surrogate modelling can help to avoid using artificial
intelligence techniques which requires some knowledge. .
Magnier (2014)
Robertson (2015)
Machairas (2014)

6. Objectives of this study
• Choosing significant variables using FFD and making
an approximate model using RSM and using
optimization algorithm like GA and then testing the
validation of this model.
• Comparing the optimization obtained from this step
with GA optimization or GA after GSA optimization
both directly coupled with building simulation.
• There is a mistake in the text: “This allows the use of
RSM to fit a model with fewer variables thereby
enhancing its accuracy”.

7. Methodology
• The GSA and the SM parts
in the flowchart need to be
applied for each response
variable at a time and then
all the SMs will be used for
optimization.

8. Methodology_Continued
Equations:
• 𝑦 = 𝛼0 + 𝑖=1
𝑘
𝛼𝑖𝑥𝑖 + 𝑖≠𝑗 𝛼𝑖𝑗𝑥𝑖𝑥𝑗 + 𝜀 (1)
• 𝐸 =
𝐿𝑂 𝐿𝑂 𝐿𝑂
𝐿𝑂 𝐿𝑂 𝐻𝐼
𝐿𝑂 𝐻𝐼 𝐿𝑂
𝐿𝑂 𝐻𝐼 𝐻𝐼
𝐻𝐼 𝐿𝑂 𝐿𝑂
𝐻𝐼 𝐿𝑂 𝐻𝐼
𝐻𝐼 𝐻𝐼 𝐿𝑂
𝐻𝐼 𝐻𝐼 𝐻𝐼
(2)
• 𝑖 𝑗 𝑦𝑖𝑗 − 𝑦
2
= 𝑖 𝑛𝑖 𝑦𝑖 − 𝑦 2
+ 𝑖 𝑗 𝑦𝑖𝑗 − 𝑦𝑖
2 (3)
• 𝑦 = 𝑓 𝑥1, 𝑥2, 𝑥3 + 𝜀 (4)
• 𝑦 = 𝛽0 + 𝑖=1
𝑘
𝛽𝑖𝑥𝑖 + 𝑖=1
𝑘
𝛽𝑖𝑖𝑥𝑖
2
+ 𝑖≠𝑗 𝛽𝑖𝑗𝑥𝑖𝑥𝑗 + 𝜀
(using the method of least squares method)
(5)

9. 4 -Case study :
• 4.1 Experiment setup :
GSA, SM and GA are applied
as per the framework in
the figure.

10. 4.1 Experiment setup :
• Design-Expert® software (Stat-Ease 2014) is used
for the FFD .
• Box-Behnken RSM design and ANOVA .
• VBA programming language and MATLAB are
used for running the simulations in batch mode .
• All the computational analyses are performed on
a computer using an Intel® Core™ i7-2670QM
processor.

11. 4.1 Experiment setup :

12. 4.2 GSA
• For the 26 design variables with their ranges
as shown in Table 1, the FFD chosen for GSA is
a resolution V design. This resolution V design
can estimate the main effects and the two
factor interactions. A total of 352 simulation
runs based on this design were automated
using VBA, calling the EnergyPlus batch file for
each simulation taking 9.5 hours on an Intel®
Core™ i7-2670QM processor.

13. 4.2 GSA
• Table A1 shows the
values of the design
variable for three out
of 512 runs for GSA
for the case study.

14. 4.2 GSA
• ANOVA table in Table A2 shows the significant effects and the contribution of
these effects in explaining the variance in response, i.e. cooling energy for zone 3.

15. 4.2 GSA
• Figure 3 shows the design variables that have
the most significant effects for the lighting
energy GSA. Window VLT, WWR for each
facade and the interactions involving them
explain more than 80% of the total variance in
the model for the lighting energy response
variable. The results are similar for each zone

16. 4.2 GSA

17. 4.2 GSA
• Figure 4 shows that WWR and window SHGC for each
facade, window U-value and wall insulation are
significant in explaining the cooling energy for each of
the three zones. Additionally, roof ρ and roof insulation
are also important for zone 3. These variables and the
interactions involving them explain more than 80% of
the total variance in cooling energy. Figure 4 also
shows that WWR-N and SHGC-N are among the most
important design variables for the three zones for the
GSA for cooling energy. Roof ρ is the most important
design variable for the zone 3 cooling energy GSA.

18. 4.2 GSA

19. A surrogate model (SM) can be used to approximate the
simulation model behavior. It is created using a limited
number of simulation runs over the search space of interest
“significant Variables” from GSA
for predicting the simulation output.
Box-Behnken RSM designs are used in Design-Expert® for
the creation of SMs for lighting energy and cooling energy
for the three zones.
These designs use three levels for each factor, taking the lower, the
middle and the upper limit from the range of the design variables in
Table 1 “Experiment Setup”.
(ANN)- Artificial Neural Network
(RSM)-Response Surface Modelling
Surrogate Modelling “SM”

20. SM
113 simulation - Lightening energy response
161 simulation - Cooling Energy response
For zone 1 &2
193 simulation - Cooling Energy response
for zone 3
2 Response & DOE Study one response at a time
For zone 3 cause their is other significant variables that doesn’t shown in zone
1 & 2 “ INS-R”

21. Box-Behnken

22. Validation of SMs
Latin hypercube sampling and Monte
Carlo sampling are each used to
generate 125 test cases for the
lighting and cooling energy SMs for
the three zones since the number of
design variables is large.
the predicted and simulated results for the lighting and
cooling energy for the three zones for the 250 test cases.

23. shows the Box
and Whisker Plot for the percentage error for the lighting
and the cooling energy prediction. The error for the lighting
energy for all the zones is kept together as it is similar for all the zones.
The prediction error is on the positive side for the lighting energy prediction and on the negative side for the
cooling energy prediction but is within 10%.
These results validate the effectiveness of the SMs.

24. Optimization analyses
By using GA “Genetic Algorithm”
Or any algorithm doing optimization
In this case 1000 experiment has been done to get optimum design
Tuning around optimum solution that we get from GA to get suitable solution
that serve the objective of study
In our case lower the better.

25. Discussion
• EnergyPlus + FFD + RSM.
• If error is greater than 10%, then Central Composite
Design can be used for building SMs.
• There is a mistake: “Another strategy to reduce the
error can be to create an SM with fewer design
variables”.
• To create the SM it needs 1000 simulation runs.

26. Discussion_cont.
• SMs make it faster to reach the optimum design.
• Using GSA generates better solutions even in the use of GA only.
• Working the what-if scenario analysis around the optimal solution using
SM is faster.
• GSA can be done in parallel with GA directly on the simulation, but GA
cannot be done in parallel with simulation.
Limitations:
• All the variables in this paper were used in only two levels, but it is
accepted to only decide the significant variables.
• For the sensitive objectives, small deviation in the variables will cause a
large change in the response, the SMs will be less useful.

27. Conclusion
• The obtained SMs can be used for mass housing projects with checking
the validation of these models in each case.