# American Institute of Mathematical Sciences

September 2018, 8(3): 277-286. doi: 10.3934/naco.2018016

## Application of box-behnken design with response surface for optimizing ventilation system of underground shelter

 Center for Fluid Dynamics, College of Engineering, Universiti Tenaga Nasional (UNITEN), 43000 Kajang, Selangor, Malaysia

* Corresponding author: azfarizal.mukhtar@gmail.com

Received  February 2017 Revised  June 2017 Published  June 2018

Fund Project: The first author is supported by YTN scholarship

Ventilation shaft is one of the effective elements in natural ventilation for ensuring acceptable Indoor Air Quality (IAQ) and thermal comfort. It has been found that the opening of ventilation shaft plays a significant role in the ventilation efficiency of an underground shelter. In this study, we aim to develop a predictive ventilation rate model for a naturally-ventilated underground shelter. Computational Fluid Dynamics (CFD) was employed as a simulation tool, where the result was validated with experimental data obtained from the previous literature. Goal Driven Optimization (GDO) was used for the optimization process by considering three geometrical factors and their effects on the objective function. From this study, it is found that the predicted response surface values agree well with the CFD values and hence the predictive model is reliable.

Citation: Azfarizal Mukhtar, Ng Khai Ching, Mohd Zamri Yusoff. Application of box-behnken design with response surface for optimizing ventilation system of underground shelter. Numerical Algebra, Control & Optimization, 2018, 8 (3) : 277-286. doi: 10.3934/naco.2018016
##### References:
 [1] E. M. Barber, T. Kusuda, P. J. Reynolds and F. J. Powell, A Study of Air Distribution in Survival Shelters Using a Small-Scale Modeling Technique, Technical Report, Washington D. C., 1972. doi: 10.6028/NBS.RPT.10689. [2] C. V. Chestert, Preparing underground structures for Civil Defense, Undergr. Sp., 6 (1981), 160-165. [3] R. Daghigh, Assessing the thermal comfort and ventilation in Malaysia and the surrounding regions, Renew. Sustain. Energy, 48 (2015), 682-691. doi: 10.1016/j.rser.2015.04.017. [4] U. M. Diwekar and J. R. Kalagnanam, Efficient sampling technique for optimization under uncertainty, AIChE J., 43 (1997), 440-447. doi: 10.1002/aic.690430217. [5] E. J. Edward and W. C. Randall, The neutral zone in ventilation, Trans. Am. Soc. Heat. Vent. Eng, 32 (1926), 59-74. [6] J. C. King, Gravity Ventilation of Underground Shelters, Technical Report, Port Hueneme, California, 1965. doi: 10.21236/AD0613550. [7] Y. Li and P. Heiselberg, Analysis methods for natural and hybrid ventilation - a critical literature review and recent developments, Int. J. Vent, 1 (2003), 3-20. doi: 10.1080/14733315.2003.11683640. [8] R. H. Myers, D. C. Montgomery and C. M. Anderson-cook, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, 3$^{rd}$ edition, John Wiley and Sons Ltd, 2009. [9] W. Yu, B. Li, H. Jia, M. Zhang and D. Wang, Application of multi-objective genetic algorithm to optimize energy efficiency and thermal comfort in building design, Energy Build, 88 (2015), 3-20. doi: 10.1016/j.enbuild.2014.11.063.

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##### References:
 [1] E. M. Barber, T. Kusuda, P. J. Reynolds and F. J. Powell, A Study of Air Distribution in Survival Shelters Using a Small-Scale Modeling Technique, Technical Report, Washington D. C., 1972. doi: 10.6028/NBS.RPT.10689. [2] C. V. Chestert, Preparing underground structures for Civil Defense, Undergr. Sp., 6 (1981), 160-165. [3] R. Daghigh, Assessing the thermal comfort and ventilation in Malaysia and the surrounding regions, Renew. Sustain. Energy, 48 (2015), 682-691. doi: 10.1016/j.rser.2015.04.017. [4] U. M. Diwekar and J. R. Kalagnanam, Efficient sampling technique for optimization under uncertainty, AIChE J., 43 (1997), 440-447. doi: 10.1002/aic.690430217. [5] E. J. Edward and W. C. Randall, The neutral zone in ventilation, Trans. Am. Soc. Heat. Vent. Eng, 32 (1926), 59-74. [6] J. C. King, Gravity Ventilation of Underground Shelters, Technical Report, Port Hueneme, California, 1965. doi: 10.21236/AD0613550. [7] Y. Li and P. Heiselberg, Analysis methods for natural and hybrid ventilation - a critical literature review and recent developments, Int. J. Vent, 1 (2003), 3-20. doi: 10.1080/14733315.2003.11683640. [8] R. H. Myers, D. C. Montgomery and C. M. Anderson-cook, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, 3$^{rd}$ edition, John Wiley and Sons Ltd, 2009. [9] W. Yu, B. Li, H. Jia, M. Zhang and D. Wang, Application of multi-objective genetic algorithm to optimize energy efficiency and thermal comfort in building design, Energy Build, 88 (2015), 3-20. doi: 10.1016/j.enbuild.2014.11.063.
Boundary conditions
Optimization parameters
Grid independence test
Validation of CFD model
Correlation matrix
Coefficient of determination
Scatter plot
Comparison between CFD and RSM
Quality of fit between predicted and observed point
Sensitivities of the three parameters for optimization
Response of two major inputs on ventilation rate
Boundary conditions for the simulation
 Domain Inlet constant velocity, 2.68 m/s at a constant temperature, 23$^0$C Domain Outlet zero pressure Domain Wall free slip wall at a constant temperature, 23$^0$C Supply Duct adiabatic, no-slip wall Exhaust Duct adiabatic, no-slip wall Heating Cable 70 $W/m^2$ Underground Shelter adiabatic, no-slip wall
 Domain Inlet constant velocity, 2.68 m/s at a constant temperature, 23$^0$C Domain Outlet zero pressure Domain Wall free slip wall at a constant temperature, 23$^0$C Supply Duct adiabatic, no-slip wall Exhaust Duct adiabatic, no-slip wall Heating Cable 70 $W/m^2$ Underground Shelter adiabatic, no-slip wall
Quantification of factor and response parameters
 Parameter Name Max $(m)$ Min $(m)$ Constraints P1 Factor Inlet Opening (D1) 0.1524 0.1016 - P2 Factor Ratio of Elbow Shaft (R/H) 2.5 0.75 R/H $\geq 0.75$ P3 Factor Outlet Opening (D1) 0.1524 0.1016 - P4 Response Ventilation Rate $(m^3/s)$ -
 Parameter Name Max $(m)$ Min $(m)$ Constraints P1 Factor Inlet Opening (D1) 0.1524 0.1016 - P2 Factor Ratio of Elbow Shaft (R/H) 2.5 0.75 R/H $\geq 0.75$ P3 Factor Outlet Opening (D1) 0.1524 0.1016 - P4 Response Ventilation Rate $(m^3/s)$ -
Candidate points generated from the screening algorithm
 Candidate Point P1 $(m)$ P2 $(m)$ P3 $(m)$ P4 $(m^3/s)$ Deviation $(\%)$ CP 1 0.1524 0.833 0.1524 0.0445 2.24 CP 2 0.1509 1.538 0.1522 0.0441 3.11 CP 3 0.1522 1.172 0.1506 0.0439 3.53
 Candidate Point P1 $(m)$ P2 $(m)$ P3 $(m)$ P4 $(m^3/s)$ Deviation $(\%)$ CP 1 0.1524 0.833 0.1524 0.0445 2.24 CP 2 0.1509 1.538 0.1522 0.0441 3.11 CP 3 0.1522 1.172 0.1506 0.0439 3.53
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