Keywords

1 Introduction

As a new design method, the parametric design method has achieved considerable development in recent years [1, 2]. More and more researcher pay attention on the parametric optimization of buildings based on building energy performance in recent years. Tuhus-Dubrow [3] studied the building energy consumption through different climatic conditions and different types of variables. He also studied the genetic algorithm for different building types and variables. By genetic algorithm research, it is found that the rectangular building plane and the trapezoidal building plane have the lowest cycle energy consumption under the five different climatic conditions. Gou [4] and Bre [5] did the sensitivity analysis of the variables in building energy optimization respectively. Jin [6] optimized the energy consumption level of a free-form building with few constraints. Zhang [7] optimized the energy efficiency of the specific classroom type of the school classroom, and different types of classrooms were set as discrete variables.

In 1943, McCulloch and Pitts established the first artificial neural networks model (ANNs-model). In the 1980s, Hopfield successfully applied ANNs-model to the optimization problems. Today, the ANNs technology have been widely used in function approximation, expert systems, artificial intelligence, and optimization problems [8].

Recent studies have shown that research on building energy performance based on ANNs technology can achieve outstanding results [9,10,11]. Among them, in the field of building energy performance, Zemella [9] used ANNs-model to optimize building façades. Ayata [11] used the ANNs technology to predict the natural ventilation of buildings.

2 Research Method

2.1 Research Objectives

The research objective is to improve the overall energy performance level of office buildings in Wuhan during the operation phase, so the research objective is to minimize \( E_{A} \). The unit is kw · h/m2.

The total annual energy consumption (\( E_{A} \)) of office buildings is included: 1. annual energy consumption of building cooling system (\( E_{C} \)), 2. annual energy consumption of building heating system (\( E_{H} \)), 3. annual energy consumption of building lighting system (\( E_{L} \)), 4. annual energy consumption of building electronic equipment (\( E_{E} \)). This study will calculate \( E_{A} \) through 8760 simulation iteration. Because the electronic equipment in office buildings is mainly computers, the turning on and off is only related to the schedule of users. Therefore, it is hardly to change \( E_{E} \) by changing the design variables. \( E_{A} \) of the office building in this research is obtained by Eq. 1.

$$ E_{A} = E_{C} + E_{H} + E_{L} $$
(1)

The integral electric drive chiller has been chosen as the cooling source equipment of the air conditioning system in this study. Its performance coefficient (\( SCOP_{T} \)) follow the “Design Standard for energy efficiency of public buildings GB50189-2015” and is set as 2.50. \( A \) is the total floor area of the building. The annual cooling energy consumption \( E_{C} \) is obtained by Eq. 2, and the annual cumulative cooling power consumption (\( Q_{C} \)) is the simulation result by EnergyPlus.

$$ E_{C} = \frac{{Q_{C} }}{{A*SCOP_{T} }} $$
(2)

The gas boiler has been chosen as the heat source equipment for the heating system in this study. According to the “Design Standard for energy efficiency of public buildings GB50189-2015”, the overall efficiency of the heating system (\( \eta_{2} \)) was set to 0.75 and the coal consumption for power generation (\( q_{2} \)) is 0.36 kgce/kWh, the standard natural gas value (\( q_{3} \)) is set to 9.87 kWh/m3, and the conversion coefficient (\( \upphi \)) of natural gas and standard coal was set to 1.21 kgce/m3. \( A \) is the total floor area of the building. The annual heating energy consumption \( E_{H} \) can be obtained by Eq. 3, and the annual cumulative heating power consumption (\( Q_{H} \)) is the simulation result by EnergyPlus.

$$ {E_H} = \frac{Q_H}{{A*{\eta_2}{q_3}{q_2}}}\upphi $$
(3)

The open-type luminaires have been chosen as the indoor lighting system in this study. According to the “Standard for lighting design of buildings GB 50034-2013”, its efficiency (\( \eta P \)) was set to 0.75. \( A \) is the total floor area of the building. The annual lighting energy consumption \( E_{L} \) can be obtained by Eq. 4, and the annual cumulative lighting power (\( Q_{L} \)) is the simulation result by EnergyPlus.

$$ E_{L} = \frac{{Q_{L} }}{{A*\eta_{P} }} $$
(4)

2.2 Research Method

This study focuses on the effects of different design variables on \( E_{A} \) of office building in Wuhan. The study first established a parametric platform between design variables and building energy simulation software. An approximate model is established by the RBF-ANNs technology. The approximate model is optimized by the MIGA algorithm to search the elite cases of design variables. The research analyzed the elite cases of the design variables in the optimization. By K-means cluster analysis of the elite cases, the study could locate the optimal benchmark of each variable.

The energy simulation software used in this study is EnergyPlus 8.1.2. Because this study is aimed at the annual energy consumption of office buildings, the study not only needs to set up a simulation model, but also needs to set the schedule of office buildings. According to “Design Standard for Energy Efficiency of Public Buildings (GB50189-2015)”, the research set the annual cooling and heating system schedule, the annual building occupancy schedule and annual ventilation system schedule. The annual interior lighting system schedule needs to be adjusted based on the natural daylight conditions. DaySim software is used to simulate the natural daylight conditions and the annual interior lighting system schedule has been set followed the DaySim simulation result [2, 13].

2.3 Multi-Island Genetic Algorithm (MIGA) and Radial Basis Functions Artificial Neural Networks (RBF-ANNs)

The variable combination optimization method used in this research is Multi-Island Genetic Algorithm (MIGA). Multi-island Genetic Algorithm (MIGA) is an improved standard genetic algorithm (SGA) [14]. Details of the MIGA algorithm settings in this study are shown in Table 1.

As an approach to reduce the complexity of the model and improve the computational efficiency, the approximate modeling method is used by more and more researchers [10, 11]. ANNs as a popular approximate modeling method, has advantages in solving highly complex function problems. ANNs is similar to biological nervous system and consist of layers of parallel basic units (called neurons) [8]. Neurons are connected to each other by a large number of weighted links through which information can enter the entire system. Basically, a neuron receives input information into ANNs’ input layer, merges the input information, performs non-linear operations in the Radial basis functions layer, and then output layer gives the final result (Fig. 1). RBF (Radial Basis Functions) ANNs is used in this research, which is one of the most commonly used artificial neural networks [10]. Details of the RBF-ANNs model settings in this study are shown in the Table 2.

The research found that the shortcomings of the RBF-ANNs are obvious: 1. When the sampling data is insufficient, the RBF-ANNs will not be able to run; 2. Because of the nonlinear mapping ability of the RBF-ANNs is determined by its basis functions and the characteristics of the basis function are mainly determined by the center of the basis function, it is difficult to reach high precision by randomly selecting points as the center points to build the RBF-ANNs model.

This study will use the random sampling (RS) and Latin hypercube sampling (LHS) methods [8] to set the variables. Then use RBF-ANNs technology to establish different approximation models based on the simulation results. Finally, the MIGA is used to optimize the design variables with the best RBF-ANNs approximate model.

At the same time, the study will use testing group to analyze the prediction error of different RBF-ANNs models [15]. The study will use the Root Mean Square Error (RMSE) method to compare the RBF-ANNs’ prediction results and the simulation results of the testing group. In this study, the accuracy threshold of the RMSE value is 15%.

$$ RMSE = \sqrt {\frac{1}{N}\sum\nolimits_{t = 1}^{N} {\left( {D_{t}^{O} - D_{t}^{P} } \right)}^{2} } $$
(5)
Table 1. MIGA algorithm setting
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Fig. 1.
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Schematic diagram for the MIGA (left) RBF-ANNs workflow chart (right)

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Table 2. RBF-ANNs setting
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3 Research Setting

Fig. 2.
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The office building model in 3D model software

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Because of the complexity of building system, researcher needs to search the design variables which have highly correlation with building energy performance. From the reference [3, 15,16,17], the study found that the four aspects of the design variables have a high correlation with building energy performance: 1. building plan (BP), 2. window shape (WS), 3. building orientation (BO), 4. building insulation thickness (BIT), 5. horizontal visor (HV) (Fig. 2).

In terms of BP, this research focused on the values of the building plane aspect ratio (A) and floor height (H). Among them, A controls the planar shape of the building, and H controls the height of the building.

In terms of WS, this study focused on the size of windows in different orientations. The design variables are window to wall ratio (WWR) on north direction (WWR-N), WWR on east direction (WWR-E), WWR on south direction (WWR-S), WWR on west direction (WWR-W) and the window height (WH).

In terms of BO, this study focused on the angle (O) between the X axis of the building plane and the East direction of the simulation software (X axis of the 3D model software).

In terms of BIT, this study focused on the roof insulation thickness (RT) and the wall insulation thickness (WT).

In terms of HV, this study set four variables for the external visors in four directions. The variables are the length of the external horizontal visors in north direction (HV-N), the length of the external horizontal visors in west direction (HV-W), the length of the external horizontal visors in south direction (HV-S) and the length of the external horizontal visors in east direction (HV-E).

The detailed of the design variables of the office building is shown in the Table 3.

Table 3. The design variables
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This study mainly focused on the design variables could be used by the architects, the setting of other variables which have an impact on building energy performance are based on “Design Standard for Energy Efficiency of Public Buildings GB50189-2015”, “Standard for lighting design of buildings GB50034—2013” and “Design standard for residential buildings of low energy consumption DB42T_559-2013”. The information of the office building is listed as boundary condition in the Table 4. The construction materials are listed in the Appendix Table 6. The annual cooling and heating system schedule, annual occupancy rate schedule and annual ventilation system schedule are followed the design standard. The annual interior lighting system schedule has been set by DaySim simulation result [12, 13].

Table 4. The boundary setting of the energy simulation
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4 The RBF-ANNs Optimization Process

4.1 The Comparison of RBF-ANNs Models

Before using RBF-ANNs model for the optimization process, it is necessary to check the RBF-ANNs models’ accuracy. The accuracy of the RBF-ANNs model is related to the number of sampling points and the sampling method. The research set up 4 different RBF-ANNs models through different sampling numbers (250, 500, 1000) and different sampling methods (RS and LHS method). Through a RMSE method analysis for the prediction results, the study found that:

  • The accuracy of the RBF-ANNs model is very sensitive to the number of input values. Because only 250 variable combination values are randomly sampled at Model-A, The RMSE values in all aspects exceed the threshold (15%).

  • The accuracy of the RBF-ANNs model is very sensitive to the sampling method. Because the sampling method in Model-B is random sampling and in Model-C is Latin Hyper-cube method, the RMSE values of Model-C is better than the value of Model-B. RMSE values of \( E_{A} \), \( E_{H} \), and \( E_{L} \) in Model-B is 20.264%, 16.135%, and 18.135%, respectively. RMSE values of \( E_{A} \), \( E_{C} \), \( E_{H} \), and \( E_{L} \) in Model-C is 13.319%, 9.208%, 9.28%, and 12.799%, respectively.

  • By comparing the RMSE values between Model-C and Model-D, due to more sampling values in model-D (1000 values) than values in model-C (500 values), the RMSE value of model-D (\( E_{A} \), \( E_{H} \), \( E_{L} \) is 12. 132%, 7.503%, 11.829%) is better than RMSE value of model-C (\( E_{A} \), \( E_{H} \), \( E_{L} \) is 13.319%, 9.28%, 12.799%) (Fig. 3).

    Fig. 3.
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    Residual plots of prediction results and test values for \( E_{A} \), \( E_{C} \), \( E_{H} \), and \( E_{L} \) in model-D

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4.2 RBF-ANNs Optimization Process

The research uses the selected RBF-ANNs model (model-D) as the basic model for optimization. The MIGA algorithm is used to optimize the design variables in the basic model. The MIGA algorithm settings are listed in Appendix Table 1. The optimization process of RBF-ANNs model took less than 10 min. After 60 generations of optimization, the optimization results of the RBF-ANNs model have been stabilized (Fig. 4). The study found that the lowest value of \( E_{A} \) can reach 46.44 kW · h/m2.

Fig. 4.
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The optimization history of \( E_{A} \) by MIGA algorithm and the RBF-ANNs model

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Since the single energy simulation takes nearly 10 min, and the 100 generations MIGA optimization will perform 5000 energy simulation calculations, it will take approximately 833.33 h for the MIGA optimization. On the other hand, the optimization of the RBF-ANNs model is divided into three parts: 1. Establishing an approximate model through 1000 energy simulations (166.8 h); 2. Testing the model by 150 energy simulations (25 h) 3. Optimization using the RBF-ANNs approximate model and MIGA algorithm (0.08 h). These three steps took approximately 191.88 h. In terms of time consumption, compared with using MIGA algorithm alone, RBF-ANNs model optimization will save 76.97% of time. Therefore, in terms of efficiency, the RBF-ANNs model has great advantages [8, 9, 11].

Before analyzing the variables benchmarks, the predicted value of the RBF-ANNs model needs to be tested. In this study, the 30 lowest \( E_{A} \) variable combinations in RBF-ANNs model were extracted for testing.

After running the energy simulation for the 30 lowest \( E_{A} \) variable combinations and comparing the predicted value with the actual simulation value, the study found that:

  • The \( E_{A} \) prediction value of RBF-ANNs model is lower than the simulation value, which indicates that there is a certain error between the prediction values and the simulation values. Despite the errors, the \( E_{A} \) simulation values of these 30 variable combinations are all less than 52.0 kw · h/m2.

  • Compared with the \( E_{A} \) value of the Reference Case (83.19 kw · h/m2), the energy decline has reached at least 37.5%. This shows that it is feasible to optimize building energy performance by the RBF-ANNs model [11]

  • The \( E_{C} \) prediction value of the RBF-ANNs model is consistent with the simulation value, which indicates that the prediction accuracy of the RBF-ANNs model in \( E_{C} \) is high.

  • The \( E_{H} \) prediction value of the RBF-ANNs model is consistent with the simulation value, which indicates that the prediction accuracy of the RBF-ANNs model in \( E_{H} \) is high.

  • The \( E_{L} \) prediction value of the RBF-ANNs model is significantly different from the simulation value. Due to the simulation of \( E_{C} \) and \( E_{H} \) does not take into account the changing schedule, the RBF-ANNs model can well establish the nonlinear equations between the variables and the simulation results. On the other hand, since the \( E_{L} \) simulation needs to consider the effect of natural daylight on the annual interior lighting system schedule, there is a more complicated nonlinear relationship between the variables and the \( E_{L} \) simulation results. This complex relationship is the main reason for the low accuracy of the RBF-ANNs model \( E_{L} \) prediction (Fig. 5).

    Fig. 5.
    figure 5

    Comparison of 30 RBF-ANNs model prediction values and simulation values

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4.3 Analysis the Optimization Results

Prior to analysis the benchmark of variable values, the study screened the optimization results. The study selected 47.0 kw · h/m2 as the \( E_{A} \) threshold value for the screening process. the study found that 214 cases in the RBF-ANNs model optimization process met the screening requirements, and these cases will become the elite cases for k-means cluster analysis. The research found that the cases that met the requirements were mainly concentrated after the 80th generation. This proved that the optimization combined MIGA with the RBF-ANNs model for the office building energy performance was successful.

The study compared the different energy aspects of the elite cases in the MIGA optimization process and found that the proportions of different energy aspects in the elite cases are roughly same. The proportion is consistent with the high temperature and high humidity climate in Wuhan summer [18]. Due to the largest proportion in \( E_{A} \) is \( E_{C} \), it is found that the most effective way to improve office building energy performance in Wuhan is to reduce \( E_{C} \).

4.4 K-means Cluster Analysis

Clustering is a machine learning technique that is considered to be one of the most effective data mining processes and the most commonly used algorithm for building energy analysis is K-means clustering [19]. The K-means clustering would be used in this research for finding the benchmarks of variables (Fig. 6).

Table 5. The final cluster centers for the elite cases
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Table 6. Building material setting
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Fig. 6.
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Comparison chart of each design variable cluster centers

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The study sets the number of clusters in K-means clustering analysis to 5 separately for the optimization. From Table 5, the study found that cluster 2 in RBF-ANNs cluster analysis has 118 elite cases, and cluster 5 has 70. These two clusters account for 87.8% of all elite cases in RBF-ANNs model optimization. It means that the value of each design variable in these two clusters represents the benchmarks of each design variable in RBF-ANNs model optimization.

5 The Conclusion

The research chooses the cluster centers in the RBF-ANNs optimization as the benchmarks. The study found that:

In terms of building aspect ratio, due to the large proportion of \( E_{L} \) in \( E_{A} \) and great optimization potential for \( E_{L} \), the study found that the north-south facade of the building should be as long as possible,, which will help the sun enter into the building. Since the value range of A in this study is 1.2 to 5.0, the study believes that within this range, the north-south facade can be as long as possible.

In terms of building height, as the increase of H will increase the building volume, which will increase \( E_{C} \) and \( E_{H} \), the building floor height should be as small as possible in an acceptable range.

In terms of building orientation, due to the large proportion of \( E_{L} \) in \( E_{A} \) and great optimization potential for \( E_{L} \), the value of O should be considered how to increase the length of the south-facing facade as much as possible. When the value of A is about 4.9 and O is between 10° and 14°, the diagonal of the building rectangle will be perpendicular to the south direction, so that the length of the south facade will be the largest. This would let more natural light enter into the building, and \( E_{L} \) would be the smallest.

In terms of the thickness of the building insulation, the research found that the thickness of the roof insulation is between 0.20 and 0.22, and the thickness of the wall insulation is between 0.25 and 0.28. Although the maximum value in the variable range has not been taken, the two thickness have high values.

In terms of WWR, the study found that the value of WWR-W is the smallest and should not exceed 0.4, the value of WWR-N and WWR-E should not be greater than 0.5, and the value of WWR-S is the largest and should not below 0.7. In general, the WWR of office buildings in Wuhan should consider façade direction. The value of WWR should be small in all directions except south façade.

In terms of building window height, the study found that the value is about 1.8 m. This shows that the building needs a high window height. Because the WWR value in west and east is generally low, a higher W-H value will make the building’s east-west window opening style be high and narrow, which will help east-west shading.

In terms of HV, the research found that the value of HV-N is the smallest, and should not exceed 0.7 m. This is because there is no natural light from the north direction, so it is not necessary to block sunlight by a long visor. Due to the east-west window opening style is high and narrow, there is no need too much horizontal visor for shading, so the value of HV-W is between 0.7 m to 1.0 m. Due to the value of WWR-E is about 0.5, larger than the value of WWR-W, the value of HV-E is larger than the value of HV-W, is between 1.2 m to 1.4 m. Although the WWR-S value is larger than 0.7, due to the large proportion of \( E_{L} \) in \( E_{A} \) and great optimization potential for \( E_{L} \), the value of HV-S is not too large, is between 0.7 m to 1.0 m.