Multi-objective optimization of building envelope in different climate zones in China based on BP-NSGA-Ⅱ under the future climate

. Global warming has an impact on building performance, and it is very important to explore the optimization of building performance under future climate change conditions. The study generates 2050s typical meteorological year (TMY) data of different cities (Harbin, Beijing, Shanghai, Shenzhen) representing the future climate. Taking energy consumption, thermal comfort, and initial investment cost as the objective function, the Back Propagation (BP) neural network and non-dominated sorting genetic algorithm (NSGA-Ⅱ ) were used to optimize the key parameters of the building envelope of representative cities in different climate regions of China and to obtain the Pareto curve. The final solution is obtained by the weighted sum method (WSM). The results show that, except for the type of windows, the optimal configuration of the building envelope in each city is different. Compared with the results of reference buildings, the final results of each city reduces energy consumption by 14.5~24.0 % and improves thermal comfort by 23.8~34 % when the initial investment cost increases by 27.0~35.3 %. The method proposed in this paper has reference significance for the optimization of building envelope in different climatic regions of China under the future climate.


Introduction
With the rapid development of the economy, the problem of energy shortage has become increasingly prominent [1,2]. The energy consumption of the construction field accounts for more than one-third of the global final energy consumption. The IEA expects global floor space to grow by 75 percent over the next 30 years, with 80 percent of that growth coming from emerging markets and developing economies [3]. As a large developing country in China, building energy efficiency has become an important part of implementing the national sustainable development strategy [4]. In addition, the Sixth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC) points out that the global surface temperature in the first 20 years of the 21st century has increased by 0.99 °C (0.84 ~ 1.10 °C ) compared with that in the period from 1850 to 1900 [5], which is bound to have an impact on building energy consumption.
Scholars have done a lot of research on the simulation of building performance under climate change. Tootkaboni et al. [6] analyzed the energy performance of residential buildings in Milan, Italy under climate change, and concluded that heating demand decreased by 30.9 % and cooling demand increased by 255.1 %. Liu et al. [7] developed future meteorological data of different scenarios for Hong Kong and studied residential buildings as an example. The results showed that by the end of the century, under the representative concentration pathway 4.5 and 8.5, the percentage of indoor discomfort in the cold season is expected to increase from 21.9 % to 36.0 % and 50.4 % of TMY, respectively. The annual cooling load is expected to increase to 278.80 %. Shen [8] explored the impact of climate change on residential and office buildings in four representative cities in the United States, and the results showed that the annual energy usage of residential and office buildings in different areas would vary from -1.64 % to 14.07 % and -3.27 % to -0.12 % respectively during 2040~2049. Bamdad et al. [9] explored the potential of natural ventilation in different climatic areas in Australia under future climatic conditions. The results show that, on the basis of current climatic areas, the total climatic potential of future natural ventilation may increase by 27 % or decrease by 14.3 %.
At present, the multi-objective optimization method is widely used in building energy-saving optimization design. Naji et al. [10] conducted multi-objective optimization of the envelope components of prefabricated houses in six climate zones in Australia, and compared with the baseline, the life cycle cost of the optimal solution was reduced by 27~31 %, and the thermal discomfort hours were reduced by 6-55 %. Ascione et al. [11] proposed a new comprehensive framework to perform multi-stage and multi-objective optimization, taking into account different energy, comfort, economy, and environmental performance indicators and applied it to the design of a typical office building in Milan, Italy. The results showed that primary energy consumption, full life cycle cost, and CO 2 equivalent emissions were significantly reduced compared with the reference. Abdou et al. [12] optimized the parameters of the envelope of existing residential buildings in six climate zones in Morocco and reached a compromise among building energy consumption, thermal comfort, and cost, making it possible to realize zero energy consumption buildings in all residential buildings in Morocco. Delgarm et al. [13] carried out multi-objective optimization of building parameters for four climates in Iran. The results show that the final optimal configuration can reduce the annual total building energy consumption by 23.8~42.2 %. Reasonable selection of climatic and building parameters is very important and key to reduce building energy consumption.
At present, there are many studies on multiobjective optimization of buildings and building performance simulation under climate change conditions, but few studies consider both aspects, and no study takes into account the differences between different climatic regions in China. On the other hand, a large number of simulations have been carried out for the above research on multi-objective optimization of buildings, and the calculation cost is expensive. Therefore, this paper proposes a multi-objective optimization method for the optimal allocation of building envelope structures of representative cities in different climatic regions of China based on the BP neural network and NSGA-Ⅱ under the conditions of future climate change.

Generation of future meteorological documents
The article selects Harbin, Beijing, Shanghai, and Shenzhen, four representative cities in China's climate regions that need cooling and heating, which are severe cold climate, cold climate, hot summer and cold winter climate, and hot summer and warm winter climate. Based on SWERA (Solar Wind Resource Assessment) historical TMY data and future forecast monthly scale data of the A2 scenario in SRES scenario released by IPCC, the CCWorldWeatherGen tool [14] was used to generate 2050s TMY data of each city through the 'morphing' method. CCWorldWeatherGen is one of the most widely used tools for generating future meteorological documents. The A2 scenario represents the situation of unbalanced global development, sustained population growth, and slow economic development. The 'morphing' method is a statistical scaling down method proposed by Belcher et al. [15], which is mainly realized by shift, linear stretch (scaling factor), and the combination of shift and linear stretch.

Building model
According to the minimum requirements of current Chinese national standards [16], a typical office building model is established as a reference building, as shown in Fig. 1. The building area is 5040 m 2 , with a total of six floors and a floor height of 3.5 m. The building faces due north, the window-to-wall ratio (WWR) of the south and north is 0.4, and the WWR of the east and west is 0.2. See Table 1 for the details of building envelope in different cities. The air conditioning system adopts Variable Air Volume System (VAV). The occupancy density of the room is 10 m 2 /person, the lighting power density is 8 W/m 2 , the equipment power density is 15 W/m 2 , and the personnel fresh air volume is 30 m 3 / (h•person). The settings of indoor temperature, occupancy rate, lighting usage rate, equipment usage rate and fresh air operation are shown in Fig. 2.

Multi-objective optimization process
Building energy consumption, thermal comfort, and initial building investment cost are determined as the three optimization objectives of this paper. The building orientation, the thickness of the external wall insulation layer, the thickness of the roof insulation layer, window type, and window wall ratio are decision variables. The building energy consumption only considers the energy consumption of the air conditioning system. The indoor thermal comfort is expressed by the average of the absolute value of the whole building's annual PMV calculated by the Fanger model. The initial investment cost considers the initial investment related to the change of the enclosure structure. The objective function is shown in Formula (1). Decision variables and related parameters are shown in Tables 2 and 3.
Where: F 1 (x), F 2 (x), and F 3 (x) are the building energy consumption function, thermal comfort function, and initial investment cost function respectively; E is the total energy consumption of building air-conditioning system, kWh; P wi and P ri are the unit volume prices of materials for each layer of exterior wall and roof respectively. The price of Expanded Polystyrene (XPS) board is 656 Yuan/m 3 , the price of reinforced concrete is 1346 Yuan/m 3 , and the price of cement mortar is 217 Yuan/m 3 ; The price of P wi window per unit area is shown in Table 3, Yuan/m 2 ; δ wi ,δ R is the thickness of insulation layer, mm; A w , A r and A win refer to the area of exterior wall roof and window respectively, m 2 .
The flow chart of multi-objective optimization is shown in Fig. 3. Set decision variables in jEPlus, conduct Latin hypercube sampling, and then use EnergyPlus batch simulation to obtain 500 groups of data to train BP neural network in MATLAB. 500 groups of data are divided into a training set and test set according to 7:3. The number of nodes in the input layer, hidden layer, and output layer of the neural network is 8, 12, and 3 respectively. The target accuracy is set to e-6, the maximum number of iterations is 5000, and the learning rate is 0.01. Tansig and purelin functions are selected for the hidden layer and output layer respectively, and the trainlm function is used for training. The coefficient of determination (R 2 ) and the root mean square error (RMSE) is used as the evaluation indicators of the BP neural network model. The formulas are shown in Formula (2) and Formula (3). (3) Where: N is the total number of data ; yi is the simulated data ; y i is the predicted data ; y is the average of the simulated data.
The trained BP neural network is input into the NSGA-Ⅱ model as the fitness function. The population size of NSGA-Ⅱ is 50, the mutation probability is 0.2, the crossover probability is 0.9, and the maximum evolution algebra is 200. The constructed NSGA-Ⅱ model is used for optimization to obtain the Pareto front. The final optimization scheme is obtained by using the WSM. The formulas are shown in (4) and (5). The weight coefficients of energy consumption, comfort, and cost are all 1/3.
Where: F i (x) is the ith objective function; λ i is the weight coefficient, between 0 and 1; F i (x) max is the maximum value of the ith objective function; F i (x) min is the minimum value of the ith objective function.

Neural network results and verification
After multiple trainings, BP neural networks of four cities have been obtained. The comparison between the simulation results of Beijing's BP neural network test set and the prediction results is shown in Fig. 6. It can be seen that the curves of prediction data and simulation data are in good agreement. R 2 and RMSE of each neural network are shown in Table 4. The simulation effect for thermal comfort is weaker than energy consumption and cost, and the worst simulation effect in Shenzhen is 0.943. In general, the high R 2 indicates that the neural network has good performance.

Multi-objective optimization results of each city
The Pareto curve is obtained through multi-objective optimization of buildings in each city, as shown in Fig. 7. The trend of Pareto curves in four cities is roughly the same. WSM was used to obtain a final solution for the optimization of the buildings of each city, as shown in Table 5 The final solution of the objective function of each city is compared with the results of the reference building, as shown in Table 6. Compared with the results of the reference building, the energy consumption of the final solution in Beijing is reduced by 21.1 %, the thermal comfort is improved by 32.4 %, but the initial investment cost is increased by 35.3 %. Since the three goals conflict with each other, it is impossible to reduce the three goals at the same time. Energy consumption in Harbin, Shanghai, and Shenzhen decreased by 23.8 %, 14.5 %, and 24.0 % respectively, thermal comfort improved by 23.8 %, 28.6 %, and 34 % respectively, and initial investment cost increased by 27.0 %, 30.0 %, and 33.9 % respectively.

Conclusion
This paper proposes a multi-objective optimization method for buildings based on BP-NSGA-Ⅱ under the conditions of future climate change and explores the optimal envelope configuration of typical office buildings in representative cities in different climatic regions of China under the three objectives of energy consumption, thermal comfort, and initial investment cost. The main conclusions are as follows: (1) Different decision variables in different cities have different solutions except for window types. The three-glass two-cavity single-Low-E hollow glass was selected by four cities. The thickness of the external wall insulation layer and roof insulation layer in Harbin is the largest, 166 mm and 241 mm respectively, and the south, north, and east window wall ratios are the minimum, both of which are 0.2. The minimum thickness of the exterior wall insulation layer in Shenzhen is 71mm, and the maximum ratio of west window to wall is 0.36. The minimum thickness of roof insulation layer in Shanghai is 129 mm. The maximum WWRs for the south, north, and east are 0.44, 0.25, and 0.49, respectiviely. The window wall ratio in the west is the minimum, 0.25.
(2) Compared with the results of reference buildings, the energy consumption of buildings in each city has decreased by 14.5~24.0 %, and the thermal comfort has improved by 23.8~34 %. As the three objectives conflict, the initial investment cost has increased by 27.0~35.3 %.