This document discusses using design of experiments to optimize the energy consumption of a 3-story office building in New Delhi. It involves 4 phases: 1) An experimental setup identifies 26 design variables and runs 352 simulations. 2) ANOVA identifies significant variables affecting lighting/cooling energy. 3) Response surface models are developed and validated via Latin hypercube sampling. 4) Optimization techniques like genetic algorithms are applied to minimize lifecycle costs and energy use, identifying optimal designs. The methodology shows design of experiments can efficiently screen variables and create surrogates that optimize building design faster than simulation alone.

1. Contents
 Introduction
 What is Design Of Experiments ?
 Problem statement
 Methodology
 ANOVA Study
 System Modelling
 Model Validation and Optimization
 Experimental Setup
 Results
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2. Introduction
 It is generally recognized that direct use of main design data model is as
unifying agent in the design process. In return, this tends to force a
clarification of the process and a reduction in time.
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3. What is Design Of Experiments (DOE) ?
• It is a branch of applied statistics and a
powerful data collection and analysis tool that
can be used in a variety of experimental
situations like determining the effect of a
desired response, identifying important
interactions when experimenting one factor at
a time, etc...
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4. Problem statement
Space cooling using air conditioning and lighting are the main source of
energy consumptions in buildings in hot climates, but a typical
optimization analysis for a project like this can take years to iterate over 20
design variables each with three parametric levels, making it
computationally intensive.
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5. Methodology
To overcome this issue, an approach is proposed using a combination of
experimental design techniques (Fractional Factorial Design and Response
Surface Methodology) which are faster than a simulation model.
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6. Variables
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7. Variables Definition
 Visible Light Transmission (VLT): It is a measurement of the amount of light in the visible portion
of the spectrum that passes through the glass.
 Window U-Value: is a measure of the rate at which heat transfers through the window itself.
 Overhang Depth: Fin Depth:
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8. Variables
 Initial independent Variable: 26 design variables
 352 simulation runs were automated using VBA EnergyPlus batch file taking 9.5 hours on an
Intel® Core™ i7-2670QM processor.
 FFD : resolution V design, main effects and the two factor interactions.
 Dependent variable : Annual Cooling and lighting Energy consumption
 Design-Expert® software is used for the FFD, Box-Behnken RSM design and ANOVA..
 Some Control Variables:
 The equipment EUI is 58 kWh/(m2·yr)
 Air-conditioning set points are assumed to be 22 °C – 27 °C
 The structural material for the base case is taken as concrete
 Daylighting controls are used in each zone to reduce the lighting energy consumption
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9. ANOVA Study
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10. ANOVA Result
 For the lighting energy response variable. ( For All zone)
o Window VLT for each facade
o WWR for each facade
o and the interactions involving them
o explain more than 80% of the total variance
 For the cooling energy response variable. ( For All zone)
o WWR window for each facade
o SHGC for each facade,
o window U-value
o and wall insulation
o roof ρ and roof insulation are also important for zone 3.
o These variables and the interactions involving them : 80% of the total variance
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11. Results
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12. System Modelling
• Various methods can be used to model system behavior
• Artificial Neural Networks (ANN) & Support Vector Machines (SVM) are most
commonly used Machine Learning models for building design.
• ANN & SVM require a lot of experience and knowledge which limits the modelling
of building design
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13. System Modelling
• Response Surface Modelling (RSM) is easier to use, doesn’t require training and
can be of sufficient accuracy if an adequate model is selected thus, RSM can
increase the application of system modelling in building design
• After FFD is used to screen the variables, the significant ones are used for RSM
using a more complicated design that can capture non linear effects using 3 levels
to increase the accuracy while maintaining a reasonable number of trials
• Box Behnken or Central Composite Design can used for RSM of the different
responses (lighting energy response, zones 1&2, zone 3 cooling energy responses)
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14. Responses RSMs
Response Surface Models for the different responses using the screened variables
are:
• Annual lighting energy for each zone=
𝑓 (𝑉𝐿𝑇 − 𝑁, 𝑉𝐿𝑇 − 𝐸, 𝑉𝐿𝑇 − 𝑊, 𝑉𝐿𝑇 − 𝑆, 𝑊𝑊𝑅 − 𝑁, 𝑊𝑊𝑅 − 𝐸, 𝑊𝑊𝑅 − 𝑊, 𝑊𝑊𝑅 − 𝑆)
• Annual cooling energy for zone 1 and zone 2 =
𝑓 (𝑆𝐻𝐺𝐶 − 𝑁, 𝑆𝐻𝐺𝐶 − 𝐸, 𝑆𝐻𝐺𝐶 − 𝑊, 𝑆𝐻𝐺𝐶 − 𝑆, 𝑊𝑊𝑅 − 𝑁, 𝑊𝑊𝑅 − 𝐸, 𝑊𝑊𝑅 − 𝑊, 𝑊𝑊𝑅
− 𝑆 , 𝑊𝑖𝑛𝑑𝑜𝑤 𝑈 − 𝑣𝑎𝑙𝑢𝑒, 𝑊𝑎𝑙𝑙 𝑖𝑛𝑠𝑢𝑙𝑎𝑡𝑖𝑜𝑛)
• Annual cooling energy for zone 3=
𝑓 (𝑆𝐻𝐺𝐶 − 𝑁, 𝑆𝐻𝐺𝐶 − 𝐸, 𝑆𝐻𝐺𝐶 − 𝑊, 𝑆𝐻𝐺𝐶 − 𝑆, 𝑊𝑊𝑅 − 𝑁, 𝑊𝑊𝑅 − 𝐸, 𝑊𝑊𝑅 − 𝑊, 𝑊𝑊𝑅
− 𝑆 , 𝑊𝑖𝑛𝑑𝑜𝑤 𝑈 𝑣𝑎𝑙𝑢𝑒, 𝑊𝑎𝑙𝑙 𝑖𝑛𝑠𝑢𝑙𝑎𝑡𝑖𝑜𝑛, 𝑅𝑜𝑜𝑓 𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑣𝑒 𝑐𝑜𝑎𝑡𝑖𝑛𝑔, 𝑅𝑜𝑜𝑓 𝑖𝑛𝑠𝑢𝑙𝑎𝑡𝑖𝑜𝑛)
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15. Box Behnken Design for RSM
Form the table showing trials required for Box Behnken
Design:
• For 8 variables ( lighting response): 113 runs performed.
• For 10 variables ( for zones 1 and 2 for cooling response):
161 runs performed.
• For 12 variables ( for zone 3 for cooling response): 193
runs performed.
The results are used to fit a regression model which is then
validated
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16. Model Validation
• Various methods can be used to assess the quality of a model such as (runs plot,
normal probability plot, Box& Whisker plot ..etc)
• Latin hybercube is a sampling method that is often used construct computer
experiments
• Monte carlo is a class of computational algorithms that rely on repeated random
sampling to obtain numerical values
• Latin hypercube sampling and Monte Carlo sampling are each used to generate
125 test cases for the lighting and cooling energy of the three zones
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17. Model Validation
• Results obtained from the
models and simulation runs
at the sampled test cases are
compared as follows:
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18. Model Validation
• Box and Whisker plots are represented for the models
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19. Optimization
• Single objective function: minimizing lifecycle cost (LCC) of the building
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20. Optimization
• The objective function is
optimized by Genetic
Algorithms (GA) on Matlab
• Total 1000 simulation runs
are compared for 3 cases
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21. Optimization
• Multi objective functions: to minimize LCC and energy use intensity (EUI).
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22. Discussion Summary
• This paper discussed energy consumption minimization in buildings by defining the optimum
settings for the independent variables affecting the consumption.
• Two main significant variables affecting the energy consumption in buildings are lighting and
cooling energies
• Design of Experiments was chosen over “building simulation-based optimization” because
these analyses require a large number of simulations to find the optimal building designs and
hence, they may not be viable as they are computationally intensive
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23. Discussion Summary
• The methodology is illustrated for a 3-storey office building in
for New Delhi.
• Each floor has two blocks of 9 X 9 X 3 .
• This area on each floor is considered as a thermal zone and is
centrally air-conditioned.
• This leads to three zones on three floors with air-conditioning
• Sequence of work is categorized in 4 main phases.
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24. Phase 1: experimental set-up
• Choosing 26 independent variables.
• Identifying the domain for each variable.
• Performing FFD (fractional factorial design) with 352 runs.
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25. Phase 2: Modelling
• Running ANOVA
• Results show:
1) 8 significant variables affecting the lighting energy.
2) 10 significant variables affecting the cooling energy of zones 1 & 2.
3) 12 significant variables affecting the cooling energy of zone 3.
• BOX Behnken design used on variables that don’t satisfy normality criteria
• Eliminating least significant variables
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26. Phase 3: Validation using Surrogate Models
• For validation purposes a surrogate model is used which in this case is an RSM
design
• Performing ANOVA to output the surface model function
• Do some refinements in order to improve the adequacy checks
• Compare the results with previously constructed model
• Iterate till the error percentage is less than 10%
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27. Phase 4: Optimization
• Optimization techniques are performed on the refined response equation
• Best response is identified.
• Best solution is selected
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28. Criticism
• Very large fractionation is performed which definitely impacted the accuracy of the results
negatively.
• Significance of variables are assessed based on contribution to the total SS, it would have been
better if it was assessed against a certain confidence interval
• The model only used two levels of each of the design variables which assume a monotonic
relationship of the design variables with the response. A non-linear relationship might have been
better. However, 2-levels models save a lot of time in screening variable at the beginning.
• Despite the fact that Surrogate models such as RSM saves a lot of computational time, they
sometimes are not very useful with sensitive objective functions because any small deviation
would result in a great reduction in the optimum.
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29. Conclusion
• Design of experiments is proved to be time and cost effective by highlighting the significant variables and screening non-
significant variables at low cost and time by performing fractional factorial designs.
• FFD screens the most important design variables for which the SMs are created.
• The SMs are orders of magnitude faster than the simulation model by approximating the simulation model behavior.
• This model helps in achieving the best solution as well as the minimum computational time as compared to other cases.
“The optimization with GA using these SMs leads to quick analyses of single- and multi-objective optimization , resulting in a
better solution than GA directly coupled to the simulation model.”
• The model is set only one time and can be fit to be used for many objectives.
“The SMs developed through this analysis can be used for mass housing projects for a given climate by architects or other
building industry professionals, who do not have a background in building simulation.”
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30. References
• Alvarez LF (2000). Design optimization based on genetic
programming. PhD Thesis, University of Bradford, UK.
• Deb K (2001). Multi-Objective Optimization Using Evolutionary
Algorithms. Chichester, UK: John Wiley & Sons.
• Dhariwal J, Banerjee R (2015).Building simulation based optimization
through design of experiments. Paper presented at 2nd IBPSAItaly
Conference (BSA2015), Bozen-Bolzano
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