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Optimization for Whole Building Energy Simulation Method in Facade Design.

INTRODUCTION

Building facade has a major impact on building energy demand and there is great potential for building facade to reduce energy demand through the parameter change, such as window-to-wall ratio (WWR), glazing type, fixed exterior shading, and solar heat gain control strategies (Zelenay 2011, Carmody 1996). These parametric studies often used in design processes involve changing one parameter, while leaving others constant. However, these processes can potentially miss important interactive effects (Andersen 2004). One way to find a global optimal solution is to use enumerative search methods where each possible parameter setting is combined with one another. When applying the simulation process in an architectural setting, the conventional building energy simulation process is too time-consuming because of the great potential solutions. Also, due to the complicated interaction of parameter variables, simulation users rarely know how to choose input parameter settings that lead to optimal performance of a given system.

The objective of this study is to propose an optimization method which can be used by architects with basic knowledge in building energy simulation and optimization algorithm. The method proposed is a genetic algorithm that provides a ranking of facade design strategies and parameters with a total energy cost result based on triple objectives - heating load, cooling load and lighting load. Our goal is to propose a method to evaluate the total energy cost for heating, cooling and lighting energy demand. For the optimization method, we chose a genetic algorithm which can find the optimal solutions for the problem, i.e. the solutions that lead to the best compromise among antagonistic objectives. These results could help architects with decision-making for early design stage. In this application, the variables are the grid dimensions of the windows and the depth of the shading system.

OVERVIEW AND BACKGROUND

The term "building optimization" here refers to a method that uses algorithms to find the optimal solutions of simulation parameter settings for architecture design. The goal is to find the optimum for the minimum total energy cost using much less simulation time than the approach of comparing each possible parameter setting with one another.

The optimization approaches could be classified as either discrete or continuous parameter optimization methods. Discrete parameters methods are typically used for facade design problems because continuous parameters are almost non-existent in facade design. These discrete parameters may include window dimension, construction material, insulation thickness, glazing types (SHGC, U-value), etc. In contrast, continuous parameter methods do not use fixed numbers for the parameter setting for building shape or dimension such as the window-to-wall ratio, building orientation, or compactness. Comparatively, optimization methods using discrete parameters are more suitable to solve building facade design problems.

Genetic algorithms are unconstrained search methods that were originally designed to optimize a single criterion as represented by the fitness of each individual in the population. It uses the evolutionary concept of natural selection to converge on an optimal solution over many generations GAs (Goldberg 1989). It could solve complicated problems using evolutionary principles to find optimal solutions (Leu 1999). Several comparative studies related to discrete parameters optimization have been discussed in former research: genetic algorithm, particle swarm, and sequential search methods. The GA method was found to be more efficient than the sequential search and particle swarm optimization when several parameters are considered in the optimization. The advantage of GA method is especially valuable when the cost function becomes more expensive to evaluate. The efficiency of GAs increases as the size of the search space increases (Tuhus-Dubrow 2009, Wetter 2004). Genetic algorithm has many practical uses, including the optimization of building shape (Wang 2006, Ourarghi 2006) and building HVAC (Mossolly 2009).

OPTIMIZATION METHODOLOGY

Model description

The example building is a single office room model (area of 5.27m^2 (56.7ft^2)) located in the University of Michigan, Ann Arbor, Michigan. The model is oriented with its main facade to the south. The south facade has a window with both vertical and horizontal shading systems on it. Figure 1 shows the dimensions and illustration of the room. An idealised HVAC system was used to control temperatures in the upper and lower room zones; the heating set point was 20[degrees]C and the cooling set point was 26[degrees]C, with night setbacks of 10[degrees]C and 30[degrees]C. The heat exchange through outdoor air is not considered in this case. The zone had internal gains of 10W/m2 for lights. The zone has artificial lighting controls with a 500 lux illuminance set point facing the ceiling. The set point is located at a point 0.85m (2.79ft) height and lm from the south facade. Data used to compute the model is given in Table 1.

In the thermal simulation, the chamber is assumed to have heating load, cooling load and artificial lighting load which to keep illuminance of 500 lux on the work plane. No mechanical ventilation exists in the office room. The suggested optimization process will be applied by running the dynamic daylight simulation program Daysim, which implemented the daylight coefficients method (Tregenza 1983). The simulation results for artificial lighting control from Daysim then will be imported in a professional dynamic simulation program TRNSYS (Klein 1976), which is very reliable for building thermal energy simulations, in order to get the annual energy demand for the office room. The annual energy cost could be achieved based on the annual energy demand for heating, cooling and lighting.

Variables

The variables of the problem are the ones that strongly impact the objective-functions, i.e. the dimensions of the window grids (discrete variables) and the depth of the shading system (continuous variables).

Therefore two facade design optimization strategies were considered in the present study: (1) change the number of grids (the length and width for each window grid) while keeping the total window area of the south facade, (2) change the depth of shading system on the south facade.

Table 2 presents the parameter variables for the width, height and depth for the studied model. The total possibilities of different combination of the three dimensions are 4000 (10x20x20), which means architects should run at least 4000 simulations to get the optimal solution during conventional design process.

Objective-functions

The objective of this article is to propose a methodology for simultaneously optimizing energy cost for heating, cooling and lighting load. For this, the objective-function [C.sub.total] has been developed. We have chosen to characterize the total energy cost [C.sub.total] with the functions [Q.sub.heat], [Q.sub.cool] and [Q.sub.light], representing the heating, cooling and lighting energy load, respectively. They were evaluated with TRNSYS 17. The heating system is a boiler which uses natural gas. The cooling system is a heat pump with a COP of 3. The price of gas ([C.sub.gas]) in Ann Arbor in 2013 is 0.474$ per 100 cubic feet (CCF) and the price of electricity ([C.sub.elec]) is 0.155$ per kilowatt hour (kWh). Therefore, the total annual energy cost of simulated building is:

[C.sub.total] = [Q.sub.heat] * [C.sub.gas] +([Q.sub.cool]/COP) * Celec + [Q.sub.light] * [C.sub.elec] (1)

The selection of the objective-function dealing with daylight depends on the building function. In this case study, the model was supposed to be a single office room. Therefore, the occupants were using the room during the daytime from 8am to 5pm. We try to increase the duration of daylight during daytime therefore the occupant could enjoy natural light during while reducing artificial lighting energy demand. The optimization criterion for daylight was Illuminance E, the luminous flux incident on a surface per unit area. When E was higher than a threshold 500 lux, it was considered high enough not to require artificial lighting, and then the artificial light is turned off. The evaluation of this objective-function is performed with Daysim. Daysim is a daylighting analysis software that uses the Radiance algorithms to calculate annual indoor illuminance profiles based on a weather climate file.

Illuminance sensor set point was computed at the height of 0.85 m that corresponds to a standard desk's height, at 1 m distance from the south wall. Facade with 20 different shading depths were modeled. The Width is 0.45m (1.48ft), Height is 0.6m (1.97ft); Depth changes from 0.20m (0.66ft) to 0.01m (0.033ft) (0.01m (0.033ft) change per group). In this study, the time-step for the illuminance computation was 5 minutes and for thermal simulation with TNRSYS was 1 h. The same weather date file was used for both the thermal and daylight simulations. The resulting file of illuminances was used to determine the control of artificial light. When the illuminance on the sensor is over 500 lux, the light is turned off; otherwise, it is turned on. Figure 2 shows the Qheat, Qcool and Qlight versus shading depth for the whole year.

This figure confirms that the variables impart a monotonous characteristic to the objective-function. When the depth of the shading system goes down, there will be more solar heat gain in the room, therefore the heating load goes down and the cooling load goes up.

When the depth of the shading system goes down, there will be more daylight in the room and the artificial lighting load also goes down. It's worth pointing out that the artificial lighting load depends on the lighting control in this case. When Illuminance E is below 500 lux, the light is turned on; otherwise, it is turned off. Though for some cases there may be a lot of daylight in the room during the whole year, it doesn't mean the Illuminance E will be high enough to turn off the artificial light every day. Therefore the change of lighting load is not the same as heating load. Therefore the artificial lighting load is not always going down when the shading depth is smaller. When artificial lighting is turned on, there will be more indoor heat gain through the heat released by the bulb, the heating load and cooling load are then influenced consequently. This make the problem more complicated.

Figure 3 shows an example that how the [C.sub.total] versus shading depth for the whole year. When the depth is 0.2m (0.66 ft), it has the highest cost. When the depth is 0.08m (0.26ft), 0.04m (0.13ft), 0.03m (0.10ft) and 0.02m (0.07ft), it has the lowest cost, respectively. The result shows that when the depth goes down, the total energy cost goes down. However, the optimal cost doesn't show up when the depth is smallest, but shows up occasionally when the best compromise among Qheat, Qcool and Qlight is found.

Antagonistic effects of the variables on the objective-functions

Simulation results and analysis above show that the variables (width, height and depth) can have different impact on the objective-function [C.sub.total]. The bigger the depth, the lower the daylight and solar heat gain, which can lead to minimized illuminance and cooling load, as desired. At the same time, it causes higher heating load and lighting load. The large width and height could lead to a higher solar heat gain and daylight, therefore, higher cooling load, lower heating load and lighting load. These facade parameter variables have antagonistic effects on [Q.sub.heat], [Q.sub.cool] and [Q.sub.light], therefore influence the objective-function [C.sub.total]. Only varying one parameter while leaving others constant will potentially miss important interactive effects, while parametric runs will be computationally expensive. An optimization method is therefore appropriate to solve this problem.

In the case where the number of potential solutions remains reasonably low, the determination of the set of solutions can be achieved by using enumerative search methods and doing all the simulations. However, when the number of variables and/or their range of variation are high, then optimization is more appropriate.

Optimization procedure

In the cases that the potential solutions are relatively low, the set of solutions can be achieved by repeating simulation work. While the number of variables is high, then optimization algorithm should be applied. Especially when the simulation procedure of the variable objective-functions is time-consuming (typically the cost of annual energy demand), one practical solution was to compute the objective-functions and then use optimization algorithm to find the optimal solutions.

In this case, we studied three variables: width, height and depth. Note that the parameters were nonlinear, monotonous functions that increase with the three variables, while they have antagonistic effects. Therefore, we investigated a range of 10 different widths (nonlinear), 20 different heights (nonlinear) and 20 different depths (continuous). Finally, the number of potential solutions was 4000.

Genetic algorithm is applied to get the potential solutions for the lowest annual energy cost. Once the population sizes and numbers of generations were obtained, the next step was to determine the optimal solutions among them. The algorithm spans a multi-dimensional grid in the space of the antagonistic parameters, and it evaluates the objective-functions at each grid point. The optimization procedure is as follows:

1. Generate a random population of 12 binary strings.

2. Evaluate the fitness of simulation results and carry over two best strings into the next generation.

3. Use deterministic tournament selection for adjacent pairs based on non-dominance to select ten strings for reproduction.

4. Apply uniform crossover with one mutation. This strategy creates two child strings from two parent strings by swapping individual bits.

5. Check for bitwise convergence (which occurs when all strings differ by 5% or less). If converged, keep best string and generate the 19 strings beside it at the multi-dimensional grid in the space.

6. Go to step 2.

RESULT AND DISCUSSION

Figure 4 shows the solutions made up of the genetic algorithms and the optimal solutions for each generation achieved during the optimization process. The results for a typical run show a fast decrement of the fitness during the first generations and a very slow change after approximately five generations. The results were shown for each generation, each result corresponding to a specific shading type. Each point corresponds to the lowest [C.sub.total] of its generation. The Genetic algorithm is not continuous because of the discrete variables shading dimensions. It could also be found that the lighting cost is the determinant factor in this case. Therefore, even though bringing in more daylight could increase indoor solar heat gain and cooling load during summer time, it's still a good design decision because much more cost could be saved on artificial lighting energy.

Table 4 shows a typical evolution of the best individual in each generation for seven different generations. It can be observed that after the main characteristics of the facade are found, only minor changes in size determine an improvement of the fitness.

The result of the optimization is consistent with the constraints of the model. Since the main determinant factor considered for fitness was lighting cost, the windows occupy the minimum depth and maximum width and height, improving the total daylight penetration. The results were consistent between several runs of 84 solutions, showing that the final result did not correspond to a local minimum, but to an optimized solution. Since there are a range of 10 different widths (nonlinear), 20 different heights (nonlinear) and 20 different depths (continuous), therefore totally 4000 potential solutions, the 84-simulation process shows significantly time-saving comparing with the 4000 parametric runs.

CONCLUSION

This article proposes a method to simultaneously optimize the objective-function annual total energy cost [C.sub.total]. The function is impacted by three functions [Q.sub.heat], [Q.sub.cool] and [Q.sub.light], which are strongly nonlinear and uncoupled. An appropriate way to find the solutions of this problem is to use an optimization method.

The genetic algorithm was chosen, which is appropriate for optimizing several conflicting objectives. This method has been proved to be useful for many optimization problems, enabling the determination of a set of equally optimal solutions that are helpful to make decision in early design stage. The variables of the problem are the dimensions of the window grids (discrete variables) and the depth of the shading system (continuous variables). The first step was to define the objective-function [C.sub.total] by [Q.sub.heat], [Q.sub.cool] and [Q.sub.light]. In this case, the most complex case was the one dealing with daylight. We calculated the artificial lighting load when indoor illuminance was higher than a threshold, which was 500 lux in this case. This process was conducted with the simulation program Daysim by simulating cases and proposing correlation functions giving the artificial lighting control schedule as a function of grid dimension and shading depth. Then, the set of the potential solutions was computed using TRNSYS. Lastly, the optimal solutions were calculated using the genetic algorithm.

This method offers a quick and accurate way to find the optimal solutions of the whole building energy demand problem, providing guidelines to make architectural facade design decisions more efficient. Additionally, there are several improvements that could be applied to the present method. The method can be used for many other optimization problems such as carbon emission and life cycle cost. The same study can also be performed with facades design by calculating the optimal VT, ST, and U-value in any range.

ACKNOWLEDGMENTS

The authors would like to thank Prof. Lars Junghans, Prof. Harry Giles and Prof. Mojtaba Navvab for supporting this research. The present research was developed as part of doctoral studies at the University of Michigan in 2013.

REFERENCES

Andersen, R., Christensen, C., Barker, G., Horrowitz, S., Courtney, A., Gilver, T., Tupper, K., 2004. Analysis of Systems Strategies Targeting Near-Term Building America Energy-Performance Goals for New Single-Family Homes NREL/TP 550 36920

Carmody. J., et al., Window systems for high-performance building, 2004. ASTM E903-96. 1996. Standard Test Method for Solar Absorptance, Reflectance, and Transmittance of Materials Using Integrating Spheres. Philadelphia: American Society for Testing and Materials.

Goldberg, D. E., Genetic Algorithms in Search, Optimization, and Machine Learning, 1989.

Klein, S.A., Duffie, J.A., Beckman, W.A., 1976. TRNSYS--a transient simulation program. ASHRAE Transactions 82(1):623-33.

Leu, S.S., Yang, C.H., 1999. GA based multicriteria optimal model for construction scheduling. Journal of Construction Engineering and Management 125 (6) 420-427.

Mossolly, M., Ghali, K., Ghaddar, N., 2009. Optimal control strategy for a multi-zone air conditioning system using a genetic algorithm, Energy ,34 58-66

Ourarghi, R., Krarti, M., 2006. Building shape optimization using neutral network and genetic algorithm approach, ASHRAE Transactions, 112 484-91

Tregenza, P.R., Waters, I.M., 1983. Lighting Research and Technology, vol. 15 no. 2 65-71

Tuhus-Dubrow, D., Krarti, K., 2009. Comparative Analysis of Optimization Approaches to Design Building Envelope for Residential Buildings", ASHRAE Transactions, 115 554-562.

Wang, W., Rivard, H., Zmeureanu, R., 2006. Floor shape optimization for green building design, Advanced Engineering Informatics, 20 363-78

Wetter, M., Wright, J., 2004. A comparison of deterministic and probabilistic optimization algorithms for nonsmooth simulation-based optimization, Building and Environment 39 - 989-999

Zelenay, K., Perepelitza, K., Lehrer, D., 2011. High-performance facades design strategies and applications in North America and Northern Europe, California Energy Commission, Publication number: CEC-500-99-013

Rudai Shan

Student Member ASHRAE

Rudai Shan is a PhD student in Building Technology, College of Architecture and Urban Planning, University of Michigan, Ann Arbor, Michigan.
Table 1. Inputs for the case study

             Parameter                     Value

             Location                Ann Arbor, MI, USA
            Orientation                    South
       Dimension of the room           2.20x2.61x1.85
               WxLxH                  (7.22x8.56x6.07)
   External opaque wall U-value        0.510 (0.090)
Artificial lighting total heat gain      100 (31.7)
          Convective part                   10%
      Heating set temperature            20 (68.0)
      Cooling set temperature            26 (78.8)

             Parameter                            Unit

             Location
            Orientation
       Dimension of the room                       m^3
               WxLxH                             (ft^3)
   External opaque wall U-value      W-m^2/K (Btu/h*ft^2*[degrees]F)
Artificial lighting total heat gain        W/m^2 (Btu/h*ft^2)
          Convective part
      Heating set temperature            [degrees]C([degrees]F)
      Cooling set temperature            [degrees]C ([degrees]F)

Table 2. Parameter variables of the studied model

Parameter variables  Width            Height            Depth

1                    0.6m (1.97ft)    0.6m (1.97ft)     0.20m (0.66ft)
2                    0.45m (1.48ft)   0.4m (1.31ft)     0.19m (0.62ft)
3                    0.36m (1.18ft)   0.3m (0.98ft)     0.18m (0.59ft)
4                    0.3m (0.98ft)    0.24m (0.79ft)    0.17m (0.56ft)
5                    0.225m (0.74ft)  0.2m (0.66ft)     0.16m (0.52ft)
6                    0.18m (0.59ft)   0.15m (0.49ft)    0.15m (0.49ft)
7                    0.15m (0.49ft)   0.12m (0.39ft)    0.14m (0.46ft)
8                    0.12m (0.39ft)   0.1m (0.33ft)     0.13m (0.43ft)
9                    0.1m (0.33ft)    0.08m (0.26ft)    0.12m (0.39ft)
10                   0.09m (0.30ft)   0.06m (0.20ft)    0.11m (0.36ft)
11                                    0.05m (0.16ft)    0.10m (0.33ft)
12                                    0.048m (0.157ft)  0.09m (0.30ft)
13                                    0.04m (0.13ft)    0.08m (0.26ft)
14                                    0.0375m (0.12ft)  0.07m (0.23ft)
15                                    0.03m (0.10ft)    0.06m (0.20ft)
16                                    0.024m (0.08ft)   0.05m (0.16ft)
17                                    0.02m (0.07ft)    0.04m (0.13ft)
18                                    0.016m (0.05ft)   0.03m (0.10ft)
19                                    0.015m (0.049ft)  0.02m (0.07ft)
20                                    0.01m (0.03ft)    0.01m (0.03ft)

Note that the parameters are defined as the number of vertical or
horizontal shading elements on the window. For example, as shown in
Figure 1, when the window is divided by three horizontal and five
vertical shading elements, the height and width of the shading element
is 0.6m (1.97ft) and 0.45m (1.48ft) respectively.

Table 4. Best individual per generation

Generation  Width            Height         Depth

1           0.36m (1.18ft)   0.4m (1.31ft)  0.07m (0.23ft)
2           0.225m (0.74ft)  0.6m (1.97ft)  0.09m (0.30ft)
3           0.3m (0.98ft)    0.2m (0.66ft)  0.07m (0.23ft)
4           0.45m (1.48ft)   0.6m (1.97ft)  0.14m (0.46ft)
5           0.45m (1.48ft)   0.6m (1.97ft)  0.08m (0.26ft)
6           0.45m (1.48ft)   0.6m (1.97ft)  0.14m (0.46ft)
7           0.45m (1.48ft)   0.6m (1.97ft)  0.08m (0.26ft)
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Date:Dec 22, 2014
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