Reliability analysis of an energy-based form optimization of office buildings under uncertainties in envelope and occupant parameters

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Reliability Analysis of an Energy-Based Form Optimization of Office Buildings under Uncertainties in Envelope and Occupant Parameters Shuai Lu , Jingyu Li , Borong Lin PII: DOI: Reference:

S0378-7788(19)32387-4 https://doi.org/10.1016/j.enbuild.2019.109707 ENB 109707

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Energy & Buildings

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31 July 2019 18 November 2019 16 December 2019

Please cite this article as: Shuai Lu , Jingyu Li , Borong Lin , Reliability Analysis of an Energy-Based Form Optimization of Office Buildings under Uncertainties in Envelope and Occupant Parameters, Energy & Buildings (2019), doi: https://doi.org/10.1016/j.enbuild.2019.109707

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Reliability Analysis of an Energy-Based Form Optimization of Office Buildings under Uncertainties in Envelope and Occupant Parameters Shuai Lu 1, 2, 3, Jingyu Li 1, Borong Lin 4* 1 School of Architecture and Urban Planning, Shenzhen University, Shenzhen, 518060, PR China. 2 Shenzhen Key Laboratory for Optimizing Design of Built Environment, Shenzhen University, Shenzhen, 518060, PR China 3 State key Laboratory of Subtropical Building Science, South China University of Technology, Guangzhou, 510640, PR China 4 School of Architecture, Tsinghua University, Beijing, 100084, PR China * Corresponding author: Tel: (86) 13910989594; E-mail: [email protected]

Abstract: Building performance optimization is effective in finding optimal design solutions and improving the building energy efficiency, but the reliability of its results can be affected by uncertainties in the input parameters. In existing research, the reliability of building form optimization, the influence of uncertainties caused by the design procedures, and the influence of individual uncertain parameters have yet to be thoroughly explored, and thus should be better addressed. In this study, a reliability analysis is conducted on an energy-based form optimization of office buildings under uncertainties in the envelope and occupancy parameters. An optimization process involving Rhinoceros, EnergyPlus, and the genetic algorithm is first implemented. Then, parametric studies of 644 configurations involving 4 cities in different climates and 3 form variables are conducted on a medium-sized office building. The results indicate that the uncertainties in the input parameters can lead to major unreliability of the optimization results, including reductions up to 13% in energy saving achieved by optimization, decreases up to 10% in energy efficiency compared with the results before optimization, and large deviations in the optimized forms. Moreover, it was found that the uncertainty in the visual transmittance of windows is the most significant cause for the unreliability, followed by the U-value of walls, whereas the uncertainties in the occupant density and occupant schedule have a limited influence. It was also found that the impacts vary by locations and the form variables for optimization. Finally, a stochastic optimization method was raised to acquire the overall optimal design under the presence of uncertainties that reduces the risk of getting very poor performance under extreme conditions and decreases the performance dispersion in various scenarios. Keywords: Building Performance Optimization; Form Design; Building Energy Efficiency; Uncertainty Analysis; Stochastic optimization; Office Building

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1. Introduction 1.1 Research Background With the severe environmental and energy crisis and people’s growing demand for a comfortable and sustainable lifestyle, building energy efficiency has become an increasingly crucial issue in architectural design. Building performance optimization, a technique that employs optimization algorithms to generate designs based on simulation results and user-defined design objectives [1], is a powerful and efficient method to find the optimal or near-optimal design solutions compared with the conventional “trial-and-error” design methodology guided by designers’ knowledge and experience [2]. Therefore, this technique has been widely used by designers and engineers to improve the building energy efficiency, and also been intensively explored by researchers during this decade [1-4]. The reliability of the results obtained from building performance optimization depends not only on the validity of the simulation and optimization algorithms, but also on the accuracy of a number of input parameters as the boundary conditions of simulation, e.g., weather data, material properties, and occupant behaviors [5]. However, owing to lack of knowledge, design procedures, and the stochastic nature of certain parameters [6], the uncertainties of some input parameters are inevitable, and thus modelers must rely on assumptions or default values, which can significantly affect the results of building performance simulation [7]. The influence of such uncertainties can be relatively small when the aim is to compare multiple design alternatives, because the deviations can be partially neutralized as long as the values of the input parameters are consistent [6]. For design performance optimization, however, the selection and evolution of designs are much more complicated, and thus the uncertainties of the input parameters can lead to problematic results. The uncertainty problem of the input parameters is even more crucial for the optimization of building forms. As the core task of the early design stage, the design of building forms not only largely determines the appearance and aesthetics of buildings, but also plays an essential role in the building performance [8-11]. For example, Liu et al. [10] suggested that different orientations, plan proportions, and window-to-wall ratios can cause a 17% variation in energy consumption for office buildings in Tianjin. Krem et al. [11] indicated that appropriate plan layouts may lead to a 6%–32% reduction in energy consumption depending on the climate zone. Because of the importance of form design, optimizing forms to achieve desirable building energy efficiency has been an important and promising topic of building performance optimization [2, 4]. However, in the early design stage when building forms are designed, other issues such as material properties and service systems have not been fully determined yet [12]. This leads to an even higher degree of uncertainty in the input parameters for building form optimization compared with the optimization of building envelope or service systems, which are designed during the later design phases. Therefore, the reliability of energy-based building form optimization under the uncertainty problem of the input parameters should be addressed; otherwise, the validity of the optimization results may be in question.

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1.2 State of the Art 1.2.1 Developments in building performance optimization Owing to its efficiency and potential in improving the building performance and automatizing the design tasks, research in building performance optimization has been increasing rapidly during this decade [2], and building performance optimization has become a well-developed method in many aspects: 1) The general procedure of building performance optimization has been established, which usually consists of four steps, namely, defining the design tasks, defining the design objectives, performance simulation, and optimization [1-2]. 2) Major aspects of the building performance including energy efficiency, thermal comfort, daylighting, ventilation, and acoustics have been covered. For example, Ascione et al. [13], Yi et al. [14], Jin et al. [15], Suh et al. [16], Lartigue et al. [17], and Xu et al. [18] employed energy consumption (including the heating/cooling load) as the optimization objective. In addition, Lartigue et al. [17], Caldas et al. [19], Trubiano et al. [20], and Zhang et al. [21] chose daylighting performance as their optimization objective, whereas Saksela et al. [22], Bassuet et al. [23], and Robinson et al. [24] optimized the building design for the most desirable acoustics. 3) Different simulation software packages have been integrated into building performance optimization, allowing various aspects of building performance to be investigated, e.g., EnergyPlus [13-16, 25-26], Transys [27-29], Radiance [19-21], and Fluent [30-31]. Moreover, self-developed simulation algorithms based on the artificial neural network, support vector machines, and other machine learning methods have also been integrated into optimization to reduce the computational costs [32-35]. 4) Different design tasks and variables such as building forms, façades, envelopes, service systems, and landscape elements are involved in building performance optimization. For example, Yi et al. [14], Jin et al. [15], Caldas et al. [19], Zhang et al. [21], Kim et al. [30], Li et al. [34], and Kämpf et al. [36] optimized the design of building forms. Lartigue et al. [17], Chen et al. [33], Bichiou et al. [37], Varma et al. [38], and Chen et al. [39] investigated the optimal envelope design using building performance optimization, whereas façade designs were optimized in the studies by You et al. [31], Zemella et al. [35], Rapone et al. [40], and Park et al. [41]. 5) Several optimization algorithms and optimization platforms are available for architects and researchers to apply according to their demands. Commonly used optimization algorithms include the genetic algorithm [13-15, 18-24, 43], particle swarm algorithm [26, 37, 40, 42], CPLEX algorithm [44-46], and ant colony algorithm [5, 48-49], while GAMS [44-47], GenOpt [26, 29, 42-43], MATLAB [13-14, 16, 29], and Rhinoceros [15, 19-21] are among the popular optimization platforms that have their own particular advantages [2]. 1.2.2 Uncertainty of input parameters in building performance simulation There are numerous parameters that can affect a building’s performance, including parameters on weather conditions, building forms, envelopes, service systems, operation, occupant behavior, etc. [6]. Many such parameters have certain degrees of uncertainty, particularly during the form design 3

in the early design stage. The sources of such uncertainties can be classified into three categories [50-51]: 1) Uncertainty in the physical parameters. This refers to the difference between the actual value and the theoretical value of a physical property, such as the thickness, density, and thermal conductivity of the wall, roof, and floor layers. Another example is the infiltration rate, which can be higher than expected owing to poor craftsmanship or cracks in the façade. Despite the continuous improvement in quality control, certain degrees of uncertainty in the physical parameters are still inevitable. 2) Uncertainty in the design parameters. This refers to the uncertainty and variations caused by the design process. For example, during form creation in the early design stage, parameters related to the envelope (e.g., construction details and thermal conductivity of the wall, roof, and floor layers) and service systems (e.g., type and coefficient of performance (COP) of the air conditioners, the power density of lighting) are normally not decided yet [12], and thus modelers must rely on assumptions or default values when conducting building performance simulation or optimization. 3) Uncertainty in the scenario parameters. This refers to the uncertainty of the parameters that can be changed during a building’s lifetime, and thus cannot be accurately predicted in advance. Compared with the two aforementioned categories, uncertainty in the scenario parameters are more complicated and can be divided into internal and external uncertainties. Internal uncertainties are largely related to the building operation, such as the occupancy density; schedules of the occupants and equipment; setpoint temperature of the heating, ventilation, and air conditioning (HVAC); and control of the lighting, windows, shadings, and other devices. External uncertainties majorly exist in the weather data because the actual weather conditions of a building may differ from the observed weather data owing to climate change, the urban heat island effect, and other factors [6]. Due to the uncertain nature of the input parameters, results generated through deterministic simulation with one set of assumed or default input parameters are actually an arbitrary sample from possible actual scenarios of a building [6]. Therefore, performance gaps (the difference between the actual and predicted building performance) may occur [52]. The impact of uncertainties in building performance simulation has been widely investigated. For example, Daly et al. [7] suggest that more than 50% discrepancies in the predicted energy consumption occur owing to uncertainties in the cooling set-point, information and communications technology (ICT) power density, ICT usage schedule, and lighting power density. Silva et al. [53] revealed that the uncertainties of user behaviors and physical parameters cause up to a 43.5% deviation in energy consumption for residential building simulation. Bucking [54] showed that a 20.4% underestimation exists in energy consumption for a house owing to variations in energy-related occupant behavior and other factors. Gaetani et al. [55], Rezaee et al. [56], Hyun et al. [57], Heo et al. [58], Mottillo et al. [59], and Wang et al. [60] also proved and quantified the influence of uncertainties in the input parameters on the results of building performance simulation. 1.2.3 Reliability of building performance optimization Compared with building performance simulation, fewer studies on the reliability of building 4

performance optimization have been conducted and they mainly investigated the influence of different optimization algorithms. For example, Si et al. [61] studied the performance of three optimization algorithms, namely, the Hooke–Jeeves algorithm, genetic algorithm II, and particle swarm optimization, in terms of the stability, robustness, validity, speed, coverage, and locality, and revealed that the Hooke–Jeeves algorithm generally results in a poorer performance. Hamdy et al. [62] investigated the performance of seven optimization algorithms (a two-phase genetic algorithm, a particle swarm optimization, a dragonfly algorithm, etc.) in terms of the convergence speed and quality of the results, and suggested that the two-phase genetic algorithm achieved higher repeatability for close-to-optimal solutions. Bamdad et al. [5] compared the ant colony optimization algorithm with the PSOHJ (hybridization of particle swarm and Hooke-Jeeves algorithms) and revealed that the former converged to solutions of similar quality with approximately 50% fewer simulations. The influence of different optimization algorithms was also investigated by Si et al. [63], Wetter et al. [64], Kampf et al. [65], and Futrell et al. [66]. Regarding the reliability problem of the building performance optimization caused by uncertainties of the input parameters, Bamdad et al. [5] optimized the energy consumption of an Australian office building under three assumptions of the lighting power density, equipment power density, occupancy density and infiltration rate, and found a deviation up to 4.8% in energy consumption owing to inaccurate assumptions. Bucking [67] revealed the influence of uncertain economic parameters in building energy optimization through Monte Carlo Simulation. Hoes [68] developed a robustness indicator to rank the Pareto solutions based on the uncertainties of user behavior. Furthermore, stochastic optimization methods were developed by researchers to acquire the overall optimal design under the uncertainties of the input parameters. For example, Cano et al. [44-45] proposed a two-stage model, followed by a multi-stage dynamic stochastic model, that provides optimal solutions regarding the building systems under uncertainties of the energy market by modeling such uncertainties using scenario trees. They further developed a new stochastic optimization framework that can take the uncertainties of potential extreme events into account and minimize the risk for the design and operation of the building systems [69]. Ramallo-González et al. [70] developed a dynamic optimization method for building energy, where the uncertain environmental parameters continuously change during the optimization process to acquire optimal solutions that are resistant to situational changes. The studies above have made significant contributions to explore the reliability problem of building performance optimization caused by the uncertainties of the input parameters; however, there are still certain aspects that can be further investigated: 1) The reliability of building form optimization under the uncertainties of the input parameters should be better addressed because form design significantly influences the building energy efficiency, and has a higher degree of uncertainty in the input parameters (as indicated in Section 1.1). In existing studies, independent variables for optimization are mainly related to the envelope and service system design (wall isolation thickness, type of windows, etc.), whereas the reliability of the optimization results remains in question when form variables are optimized. 2) The influence of the uncertainty in design parameters (as defined in Section 1.2.2.2) should be further explored, as for the form design in the early design stage, parameters related to the design tasks in later design procedures (envelopes, service systems, etc.) are normally not decided yet, and the uncertainties in such 5

parameters can significantly affect the reliability of building form optimization. In existing studies, the influence of the uncertainties in the physical parameters (e.g., the infiltration rate) and scenario parameters (e.g., the occupancy density) has been better investigated, while the uncertainties caused by the design process should be further addressed. 3) The influence of the uncertainties in individual input parameters should be better revealed. It is significant to identify those parameters whose uncertainties can largely affect the reliability of building form optimization, allowing designers to reduce the degree of uncertainty in such parameters as much as they can before starting the optimization. For other parameters, however, the efforts in reducing the uncertainty can be spared. In existing studies, the influence of uncertainties in the input parameters has been investigated together, without revealing which parameters should be given more attention.

1.3 Objectives of this research Considering the importance of building form optimization and the status of precedent investigations, this research aims to explore the reliability of energy-based form optimization of an office building under uncertainties in the input parameters. Specifically, envelope parameters and occupancy parameters are investigated, the former of which incur uncertainties in the design parameters, which are significant in form design and have not been fully investigated in existing studies, whereas the latter represent uncertainties in the scenario parameters, the importance of which has often been underestimated by modelers [6].

2. Methods 2.1 Problem Statement The energy consumption of a building consists of several sectors, which can be described as follows: 𝑓(𝑋) = 𝐸𝑕 (𝑋) + 𝐸𝑐 (𝑋) + 𝐸𝑙 (𝑋) + 𝐸𝑓 (𝑋) + 𝐸𝑝 (𝑋) + 𝐸𝑚 (𝑋)

(1)

where f() is the total energy consumption, Eh() is the energy use for heating, Ec() is the energy use for cooling, El() is the energy use for lighting, Ef() is the energy use of the fans, Ep() is the energy use of the pumps, Em() is the energy use of the interior equipment, while X is a vector of the design parameters including the form parameters, envelope properties, service systems, weather, occupant behavior, etc. The problem of optimizing building designs for the minimum energy consumption (i.e., the maximum energy efficiency) can then be stated as follows: min𝑌 𝑓(𝑌, 𝑎1 , 𝑎2 , 𝑎3 … … ) (2) where f() is the energy consumption as the optimization objective, Y is a subset vector of X containing the independent variables for optimization and represents designs within the feasible design space, while a1, a2, a3… are other elements in X and are boundary conditions of the design problem that will not be optimized. For building form optimization, which this research focuses on, Y contains the form variables for optimization, whereas a1, a2, a3… represent other input parameters. If all input parameters are precise, the optimized form (Yt) and the optimized value of energy consumption (Et = f (Yt, a1, a2, a3……)) by Optimization (2) can be regarded as the true optimal solution.

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During the form design in the early design stage, however, uncertainties in some of the input parameters are inevitable due to a lack of knowledge, design procedures, and the stochastic nature of certain parameters, so that the modelers must rely on assumptions or default values (as indicated in Sections 1.1 and 1.2.2). Supposing that a1 is an uncertain input parameter and that different modelers can assume it to be a1’, a1’’, a1’’’, etc., the optimization problem is then modeled as follows: min𝑌 𝑓(𝑌, 𝑎1 ′, 𝑎2 , … … ) (3) min𝑌 𝑓(𝑌, 𝑎1 ′′, 𝑎2 , … … ) (4) min𝑌 𝑓(𝑌, 𝑎1 ′′′, 𝑎2 , … … ) (5) …… In Optimizations (3)-(5), the optimized forms (Yapp1, Yapp2, Yapp3…) are apparent optimal forms under assumed boundary conditions, instead of the true optimal form. Under real boundary conditions (a1, a2, a3…), the energy consumption values of these apparent optimal forms are as follows: 𝐸𝑎𝑝𝑝1 = 𝑓(𝑌app1 , 𝑎1 , 𝑎2 , … … ) (6) 𝐸𝑎𝑝𝑝2 = 𝑓(𝑌app2 , 𝑎1 , 𝑎2 , … … ) (7) 𝐸𝑎𝑝𝑝3 = 𝑓(𝑌app3 , 𝑎1 , 𝑎2 , … … ) (8) …… Because Yapp1, Yapp2, Yapp3…are apparent optimal forms and may differ from the true optimal form (Yt), their energy consumptions Eapp1, Eapp2, Eapp3… can be higher than Et (i.e., lower in the energy efficiency). Such “performance gaps” are caused by the input assumptions of the boundary condition parameter a1. The higher the performance gaps are, the more influential the uncertainty of a1 is on the reliability of the building form optimization results, and vice versa. For comparison, supposing that Y0 is a base form, its energy consumption E0 under real boundary conditions can be calculated as follows: 𝐸0 = 𝑓(𝑌0 , 𝑎1 , 𝑎2 , … … ) (9) The energy efficiency improvement achieved through optimization with a precise input of the boundary conditions can be quantified through the following improvement ratio:

𝑃𝑡 =

𝐸0 −𝐸𝑡

(10)

𝐸0

Similarly, the energy efficiency improvement achieved through optimization with the assumed inputs of the boundary conditions can be defined as follows:

𝑃𝑎𝑝𝑝1 = 𝑃𝑎𝑝𝑝2 = 𝑃𝑎𝑝𝑝3 =

𝐸0 −𝐸𝑎𝑝𝑝1 𝐸0 𝐸0 −𝐸𝑎𝑝𝑝2 𝐸0 𝐸0 −𝐸𝑎𝑝𝑝3 𝐸0

(11) (12) (13)

…… The performance gaps caused by the assumed inputs of the boundary condition parameter a1 are then quantified based on the following performance gap ratios: 𝑃𝑔𝑎𝑝1 = 𝑃𝑎𝑝𝑝1 − 𝑃𝑡 (14) 𝑃𝑔𝑎𝑝2 = 𝑃𝑎𝑝𝑝2 − 𝑃𝑡 (15) 7

𝑃𝑔𝑎𝑝3 = 𝑃𝑎𝑝𝑝3 − 𝑃𝑡

(16)

…… It is clear that the higher the performance gap ratios are, the more influence the uncertainty of a1 has, and the less reliable the results of the building form optimization are under the uncertainty of a1, and vice versa. In addition to the energy efficiency, architects care a lot about the forms that are acquired through optimization. Therefore, it should also be revealed whether major deviations in the forms can be caused by the uncertainties in the boundary condition parameters. Supposing that y1, y2…yn are the form variables (i.e., Y= (y1, y2…yn)), the true optimal form (Yt) and the apparent optimal forms (Yapp1, Yapp2, Yapp3…) can be written as follows: 𝑌𝑡 =(𝑦1t , 𝑦2𝑡 … … 𝑦𝑛𝑡 ) (17) 𝑌𝑎𝑝𝑝1 =(𝑦1app1 , 𝑦2𝑎𝑝𝑝1 … … 𝑦𝑛𝑎𝑝𝑝1 ) (18) 𝑌𝑎𝑝𝑝2 =(𝑦1app2 , 𝑦2𝑎𝑝𝑝2 … … 𝑦𝑛𝑎𝑝𝑝2 ) (19) 𝑌𝑎𝑝𝑝3 =(𝑦1app3 , 𝑦2𝑎𝑝𝑝3 … … 𝑦𝑛𝑎𝑝𝑝3 ) (20) …… Then, the deviation caused by the uncertainty of the boundary condition parameter a1 can be quantified based on the normalized Euclidean distance between the true optimal form and the apparent optimal forms [61]:

𝐷𝑓1 = √∑𝑛𝑖=1(

𝑦𝑖𝑎𝑝𝑝1 −𝑦𝑖𝑡 2 ) 𝑈𝑖 −𝐿𝑖

(21)

𝐷𝑓2 = √∑𝑛𝑖=1(

𝑦𝑖𝑎𝑝𝑝2 −𝑦𝑖𝑡 2 ) 𝑈𝑖 −𝐿𝑖

(22)

𝐷𝑓3 = √∑𝑛𝑖=1(

𝑦𝑖𝑎𝑝𝑝3 −𝑦𝑖𝑡 2 ) 𝑈𝑖 −𝐿𝑖

(23)

…… where Ui and Li are the upper and lower limits of the form variable yi, respectively. The distances are normalized so that deviations in different variable domains are comparable. It is clear that the higher the distances are, the larger the deviations caused by the uncertainty in a1, and vice versa.

2.2 Methodology In order to explore the reliability of the energy-based form optimization of office buildings under uncertainties in the envelope parameters and occupancy parameters, a base case is first established (Section 2.3), and the form variables (as independent variables for optimization), optimization objective function, and uncertain boundary condition parameters are then defined (Section 2.4). An optimization process is next implemented (Section 2.5), followed by parametric studies that define configurations with different inputs of the boundary condition parameters, locations, and optimization variables. The optimized forms under each configuration are then acquired (Section 2.6). Finally, the performance gaps and form deviations caused by uncertainties in each boundary condition parameter under different configurations are calculated (Section 2.7).

2.3 Base Model A three-story rectangular medium office building is defined as the base model in this research for further investigation (Figure 1). The form is derived from a benchmark model of the US 8

Department of Energy [71], with an area of 1,600 m2 on each floor and an aspect ratio of 1.5625 (i.e., 50 m in length and 32 m in width). It has one core thermal zone and four perimeter thermal zones on each floor, and the depth of each perimeter zone is 4 m. The floor height is 4 m, the ceiling height is 3 m, and the window-to-wall ratio (WWR) of each façade is 0.33 (i.e., 1.32m high bar windows). The orientation is north-south facing. Parameters of the envelope, service systems, occupancy, and schedules are set the same as the recommended values for the simulation of office buildings by the Standard for Green Performance Calculation of Civil Buildings of China [72], and are in line with the Design Standard for Energy Efficiency of Public Buildings of China [73]. The U-Values of the building envelope are as follows: walls and ground, 0.35 W/(m2 × K); roof, 0.25 W/(m2 × K); and windows, 2.0 W/(m2 × K). The visual transmittance of the windows is 0.6. The power densities of the lighting and equipment are 10 and 15 W/m2, respectively, whereas the occupant density is 10 m2/person. The hourly schedules for the occupants, lighting, and equipment are shown in Figure 2, while for the perimeter zones, the lighting is under continuous dimming control together with daylighting, and the target illuminance is 300 lux. The set-point temperatures for heating and cooling are 20 °C and 26 °C, whereas the comprehensive COP for heating and cooling are 1.8 and 2.6. The air infiltration rate (ACH) is 0.3 h-1, and the ventilation rate is 30 m3/h per person.

Figure 1. Base model used in this research

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Figure 2. Hourly schedules for occupants, lighting, and equipment

2.4 Variable Definition Because this research focuses on building form optimization, three form variables are selected as independent variables for optimization, (i.e., variables that are evolved during optimization to achieve optimal values of the optimization objective), namely, the aspect ratio (AR), window-to-wall ratio (WWR), and orientation (OR). These form variables can define possible variations of the base model (Figure 3), and their ranges and descriptions are as shown in Table 1. For comparable results, other form characteristics including the floor area, floor height, and ceiling height are fixed to the same values as the base model. Table 1. Form variables as independent variables for optimization Variable

Range

Aspect Ratio (AR)

[1,6.25]

Window-to-Wall Ratio (WWR) Orientation (OR)

[0.1, 0.75]

[0,180)

Description Ratio of length to width. 1 stands for square (length=width=40m). 6.25 stands for a plan as narrow as 2 structural grids (16m in width) Ratio of window area to wall area. 0.1 stands for 0.4m-high bar windows. 0.75 stands for 3m-high French windows that reach ceiling Angle between building orientation and the north. 0 stands for north facing. 90 stands for west facing. [180, 360) excluded for symmetry.

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a) AR=4, WWR=0.15, OR=60

b) AR=1, WWR=0.5, OR=150

Figure 3. Two examples of possible variations of the base model

The optimization objective is to minimize the annual total end-use energy consumption of the building, which includes energy for heating, cooling, lighting, fans, pumps, and office equipment, so that the form with the optimal building energy efficiency can be found. In order to investigate the influence of uncertainty in the envelope and occupancy parameters on the building form optimization, four parameters related to envelope and occupancy are selected as the uncertain boundary conditions of optimization (not independent variables for optimization), namely, the U-Value of the walls, the visible transmittance of the window glazing, the occupant density, and the occupant schedule. These four parameters are not only crucial sources of the uncertainty in buildings [50], but also have important and widely proven impacts on the building energy efficiency and its simulation [6-7, 74-76]. The U-value of the walls is responsible for the amount of the conduction heat transfer through the building envelope, changing the heating/cooling load and the thermal response of zones, and thus influencing the building energy consumption. The visible transmittance of window glazing controls the quantity of daylight penetrating into the interior space, changing the amount of artificial lighting needed to maintain a desirable illuminance level and thus influencing the energy consumption for lighting. The occupant density and the occupant schedule define the pattern of occupant presence, while the metabolic heat produced by occupants impacts the building's energy consumption by increasing the internal heat gain. Thus, the energy consumption of buildings is influenced by the occupant density and the occupant schedule. The range of each parameter is based on codes, standards, and previous surveys of office buildings in China and around the world, and is set to be as wide as realistically possible, so that the influence of the uncertainty in these parameters can be thoroughly revealed. The range of the U-value of the walls differs in different climate zones, to remain in line with the building codes [73], while ranges for the remaining three parameters are the same for all places. The ranges and descriptions of these four parameters are listed in Table 2, and variations in the occupant schedules are shown in Figure 4. Other boundary conditions of optimization are fixed to the same values as the base model. Table 2. Envelope and occupancy parameters as uncertain boundary conditions of optimization Parameter

Ranges

Description 11

SC: Severe Cold Zone (e.g., Harbin), C: Cold Zone (e.g., [0.10,0.38] (SC);

Beijing), HSCW: Hot-Summer Cold-Winter Zone (e.g.,

U-Value of walls

[0.15,0.5] (C);

Shanghai), HSWW: Hot-Summer Warm-Winter Zone (e.g.,

(U-Val)

[0.25,1] (HSCW);

Shenzhen). Upper limits based on requirements in different

[0.25,1.5] (HSWW)

climate zones in [73], lower limits based on settings in precedent research in similar climate zones [5, 7, 33, 77-78]

Visible Transmittance of Windows (Tvis) Occupant Density (OcDens, people/m2)

[0.4, 0.85]

[0.05, 0.25]

Occupant Schedule

5 types (S1-S5), see

(OcSche)

Figure 4 for details

Lower limit based on requirements in [73], upper limit corresponds to clear glazing unit [79] Upper limit based on requirement in [80], lower limit based on surveys in [81]. S1 is recommended schedule in [72], S2-S3 change start time of office hours, S4-S5 change length of office hours, all based on surveys in [81]

a) S1, S2 and S3

b) S1, S4 and S5 Figure 4. Variations of occupant schedules

12

2.5 Optimization Process Optimization in this research is implemented by integrating Rhinoceros (3D modeling software), Grasshopper (a graphic programming plugin to Rhinoceros), DIVA (a plug-in to Grasshopper that calls EnergyPlus) [82], EnergyPlus (widely used simulation software for building energy based on the state space method) [83-84] and Galapagos (an optimization engine based on the genetic algorithm) [85]. A parametric model is first established in Rhinoceros and Grasshopper, which can generate various designs based on the base case and the form variables (as defined in Table 1). The energy consumption of the designs is then calculated using EnergyPlus through DIVA. EnergyPlus is employed here as it is the most commonly used simulation software for building energy optimization [2], and thus ensures the representability of this research. Moreover, its accuracy has been addressed in the literature [86-87] and its advantages include the ability to calculate the conduction transfer for short time steps and the ability to analyze the 3D conduction transfer [88-89]. Finally, Galapagos is used here to find the optimal design with the minimized annual total end-use energy consumption using the genetic algorithm. The genetic algorithm is employed here due to its high efficiency and repeatability in achieving close-to-optimal solutions with a good diversity compared with other optimization algorithms [61-62], as well as its widespread use in building performance optimization [2]. The settings for the genetic algorithm are shown in Table 3. As this research focuses on the reliability problem caused by uncertainties in the boundary conditions, the settings are much higher than recommended to eliminate the reliability problem caused by the optimization algorithm. All optimization cases are conducted on a workstation (CPU: Xeon E5-2640V4; Memory: 64GB; Graphic: Quadro M5000 16G). Table 3. Settings for the genetic algorithm Description

Parameter

Value

Population Size

50

Population of the 1st generation

250

Reproduction probability

10%

By default

Crossover probability

75%

By default

Maximum generation number

100

Much more than recommended (4 times the number of independent variables [90-91]) to ensure valid results Much more than recommended (2 times of the population size [85]) to avoid getting stuck in a local optimum

Much more than recommended (50 generations [85]) to ensure the preciseness of the results

2.6 Parametric Study A parametric study is conducted to represent the possible configurations under uncertainties of the envelope and occupancy parameters. 644 configurations are defined (as listed in Table 4, with the U-value of walls specified in Table 5), which cover the possible values of each boundary condition parameter (as defined in Table 2, boundary condition parameters that are not specified are fixed to the same values as the base model). Moreover, four major Chinese cities in different climate zones (listed in Table 5) and seven possible combinations of form variables for optimization (one form variable, two form variables or three form variables, form variables that are not used for optimization are fixed to the same values as the base model) are also involved to deliver more comprehensive results. Each configuration can represent one set of true boundary conditions. As 13

indicated in Section 2.1, to reveal the performance gaps and form deviations caused by the uncertainty in one boundary condition parameter, the optimal forms under possible assumptions of the particular boundary condition parameter are needed to serve as apparent optimal forms. For example, to reveal the performance gap and form deviation caused by the uncertainty in occupant density for the case H1D1 (actual occupant density is 0.05, in Harbin, with 3 form variables for optimization), the optimal forms of H1D2, H1D3, H1D4, H1D5 and H1D6 are also needed as the apparent optimal forms for comparison. Therefore, to reveal the performance gaps and form deviations caused by the uncertainty of each boundary condition parameter under various scenarios, 644 optimization cases with all configurations defined are conducted to acquire optimal forms under each configuration.

Optimization Variables

Location

Table 4. Configurations for the parametric study U-Value of Walls (U-Val, See Table 5 for details) U1

U2

U3

U4

U5

U6

Visible Transmittance of Windows (Tvis) 0.4

0.49 0.58

0.67

0.76 0.85

Occupant Density (OcDens, people/m2) 0.05 0.09

0.13 0.17 0.21 0.25

Occupant Schedule (OcSche, See Fig. 4 for details) S1

S2

S3

S4

S5

AR+WWR H1U1 H1U2 H1U3 H1U4 H1U5 H1U6 H1T1 H1T2 H1T3 H1T4 H1T5 H1T6 H1D1 H1D2 H1D3 H1D4 H1D5 H1D6 H1S1 H1S2 H1S3 H1S4 H1S5 +OR Harbin (H)

AR+WWR H2U1 H2U2 H2U3 H2U4 H2U5 H2U6 H2T1 H2T2 H2T3 H2T4 H2T5 H2T6 H2D1 H2D2 H2D3 H2D4 H2D5 H2D6 H2S1 H2S2 H2S3 H2S4 H2S5 AR+OR

H3U1 H3U2 H3U3 H3U4 H3U5 H3U6 H3T1 H3T2 H3T3 H3T4 H3T5 H3T6 H3D1 H3D2 H3D3 H3D4 H3D5 H3D6 H3S1 H3S2 H3S3 H3S4 H3S5

WWR+OR H4U1 H4U2 H4U3 H4U4 H4U5 H4U6 H4T1 H4T2 H4T3 H4T4 H4T5 H4T6 H4D1 H4D2 H4D3 H4D4 H4D5 H4D6 H4S1 H4S2 H4S3 H4S4 H4S5 AR

H5U1 H5U2 H5U3 H5U4 H5U5 H5U6 H5T1 H5T2 H5T3 H5T4 H5T5 H5T6 H5D1 H5D2 H5D3 H5D4 H5D5 H5D6 H5S1 H5S2 H5S3 H5S4 H5S5

WWR

H6U1 H6U2 H6U3 H6U4 H6U5 H6U6 H6T1 H6T2 H6T3 H6T4 H6T5 H6T6 H6D1 H6D2 H6D3 H6D4 H6D5 H6D6 H6S1 H6S2 H6S3 H6S4 H6S5

OR

H7U1 H7U2 H7U3 H7U4 H7U5 H7U6 H7T1 H7T2 H7T3 H7T4 H7T5 H7T6 H7D1 H7D2 H7D3 H7D4 H7D5 H7D6 H7S1 H7S2 H7S3 H7S4 H7S5

AR+WWR B1U1 B1U2 B1U3 B1U4 B1U5 B1U6 B1T1 B1T2 B1T3 B1T4 B1T5 B1T6 B1D1 B1D2 B1D3 B1D4 B1D5 B1D6 B1S1 B1S2 B1S3 B1S4 B1S5 +OR Beijing (B)

AR+WWR B2U1 B2U2 B2U3 B2U4 B2U5 B2U6 B2T1 B2T2 B2T3 B2T4 B2T5 B2T6 B2D1 B2D2 B2D3 B2D4 B2D5 B2D6 B2S1 B2S2 B2S3 B2S4 B2S5 AR+OR

B3U1 B3U2 B3U3 B3U4 B3U5 B3U6 B3T1 B3T2 B3T3 B3T4 B3T5 B3T6 B3D1 B3D2 B3D3 B3D4 B3D5 B3D6 B3S1 B3S2 B3S3 B3S4 B3S5

WWR+OR B4U1 B4U2 B4U3 B4U4 B4U5 B4U6 B4T1 B4T2 B4T3 B4T4 B4T5 B4T6 B4D1 B4D2 B4D3 B4D4 B4D5 B4D6 B4S1 B4S2 B4S3 B4S4 B4S5 AR

B5U1 B5U2 B5U3 B5U4 B5U5 B5U6 B5T1 B5T2 B5T3 B5T4 B5T5 B5T6 B5D1 B5D2 B5D3 B5D4 B5D5 B5D6 B5S1 B5S2 B5S3 B5S4 B5S5

WWR

B6U1 B6U2 B6U3 B6U4 B6U5 B6U6 B6T1 B6T2 B6T3 B6T4 B6T5 B6T6 B6D1 B6D2 B6D3 B6D4 B6D5 B6D6 B6S1 B6S2 B6S3 B6S4 B6S5

OR

B7U1 B7U2 B7U3 B7U4 B7U5 B7U6 B7T1 B7T2 B7T3 B7T4 B7T5 B7T6 B7D1 B7D2 B7D3 B7D4 B7D5 B7D6 B7S1 B7S2 B7S3 B7S4 B7S5

Shanghai (S)

AR+WWR S1U1 S1U2 S1U3 S1U4 S1U5 S1U6 S1T1 S1T2 S1T3 S1T4 S1T5 S1T6 S1D1 S1D2 S1D3 S1D4 S1D5 S1D6 S1S1 S1S2 S1S3 S1S4 S1S5 +OR AR+WWR S2U1 S2U2 S2U3 S2U4 S2U5 S2U6 S2T1 S2T2 S2T3 S2T4 S2T5 S2T6 S2D1 S2D2 S2D3 S2D4 S2D5 S2D6 S2S1 S2S2 S2S3 S2S4 S2S5 AR+OR

S3U1 S3U2 S3U3 S3U4 S3U5 S3U6 S3T1 S3T2 S3T3 S3T4 S3T5 S3T6 S3D1 S3D2 S3D3 S3D4 S3D5 S3D6 S3S1 S3S2 S3S3 S3S4 S3S5

WWR+OR S4U1 S4U2 S4U3 S4U4 S4U5 S4U6 S4T1 S4T2 S4T3 S4T4 S4T5 S4T6 S4D1 S4D2 S4D3 S4D4 S4D5 S4D6 S4S1 S4S2 S4S3 S4S4 S4S5 AR

S5U1 S5U2 S5U3 S5U4 S5U5 S5U6 S5T1 S5T2 S5T3 S5T4 S5T5 S5T6 S5D1 S5D2 S5D3 S5D4 S5D5 S5D6 S5S1 S5S2 S5S3 S5S4 S5S5

WWR

S6U1 S6U2 S6U3 S6U4 S6U5 S6U6 S6T1 S6T2 S6T3 S6T4 S6T5 S6T6 S6D1 S6D2 S6D3 S6D4 S6D5 S6D6 S6S1 S6S2 S6S3 S6S4 S6S5

OR

S7U1 S7U2 S7U3 S7U4 S7U5 S7U6 S7T1 S7T2 S7T3 S7T4 S7T5 S7T6 S7D1 S7D2 S7D3 S7D4 S7D5 S7D6 S7S1 S7S2 S7S3 S7S4 S7S5

Shenzhen (Z)

AR+WWR Z1U1 Z1U2 Z1U3 Z1U4 Z1U5 Z1U6 Z1T1 Z1T2 Z1T3 Z1T4 Z1T5 Z1T6 Z1D1 Z1D2 Z1D3 Z1D4 Z1D5 Z1D6 Z1S1 Z1S2 Z1S3 Z1S4 Z1S5 +OR AR+WWR Z2U1 Z2U2 Z2U3 Z2U4 Z2U5 Z2U6 Z2T1 Z2T2 Z2T3 Z2T4 Z2T5 Z2T6 Z2D1 Z2D2 Z2D3 Z2D4 Z2D5 Z2D6 Z2S1 Z2S2 Z2S3 Z2S4 Z2S5 AR+OR

Z3U1 Z3U2 Z3U3 Z3U4 Z3U5 Z3U6 Z3T1 Z3T2 Z3T3 Z3T4 Z3T5 Z3T6 Z3D1 Z3D2 Z3D3 Z3D4 Z3D5 Z3D6 Z3S1 Z3S2 Z3S3 Z3S4 Z3S5

WWR+OR Z4U1 Z4U2 Z4U3 Z4U4 Z4U5 Z4U6 Z4T1 Z4T2 Z4T3 Z4T4 Z4T5 Z4T6 Z4D1 Z4D2 Z4D3 Z4D4 Z4D5 Z4D6 Z4S1 Z4S2 Z4S3 Z4S4 Z4S5 AR

Z5U1 Z5U2 Z5U3 Z5U4 Z5U5 Z5U6 Z5T1 Z5T2 Z5T3 Z5T4 Z5T5 Z5T6 Z5D1 Z5D2 Z5D3 Z5D4 Z5D5 Z5D6 Z5S1 Z5S2 Z5S3 Z5S4 Z5S5

WWR

Z6U1 Z6U2 Z6U3 Z6U4 Z6U5 Z6U6 Z6T1 Z6T2 Z6T3 Z6T4 Z6T5 Z6T6 Z6D1 Z6D2 Z6D3 Z6D4 Z6D5 Z6D6 Z6S1 Z6S2 Z6S3 Z6S4 Z6S5

OR

Z7U1 Z7U2 Z7U3 Z7U4 Z7U5 Z7U6 Z7T1 Z7T2 Z7T3 Z7T4 Z7T5 Z7T6 Z7D1 Z7D2 Z7D3 Z7D4 Z7D5 Z7D6 Z7S1 Z7S2 Z7S3 Z7S4 Z7S5

Table 5. Cities and corresponding U-Value of walls 14

U-Value of Walls (based on Table 2) City

Latitude / Longitude

Chinese Climate Zone [73] U1

U2

U3

U4

U5

U6

Harbin (H)

45.8° N / 126.6° E

Severe Cold

0.10

0.16

0.21

0.27

0.32

0.38

Beijing (B)

39.9° N / 116.3° E

Cold

0.15

0.22

0.29

0.36

0.43

0.50

Shanghai (S)

31.2° N / 121.5° E

Hot-Summer Cold-Winter

0.25

0.40

0.55

0.70

0.85

1.00

Shenzhen (Z)

22.3° N / 114.1° E

Hot-Summer Warm-Winter

0.25

0.50

0.75

1.00

1.25

1.50

2.7 Calculation of Performance Gaps and Form Deviations Following the problem statement in Section 2.1, for each configuration defined in Table 4, the energy consumption of the base form (E0), of the true optimal form (Et), and of the apparent optimal forms (Eapp1, Eapp2, Eapp3…) are calculated using EnergyPlus. Then, the energy efficiency improvement ratios (Pt, Papp1, Papp2, Papp3…) and the performance gap ratios (Pgap1, Pgap2, Pgap3…) are calculated, as defined in Equations (10)-(16). The normalized Euclidean distances between the true optimal form and the apparent optimal forms (Df1, Df2, Df3…) are also calculated, as defined in Equations (21)-(23), to represent the form deviations. Taking configuration H1D1 (in Table 4) as an example, the base form is as defined in Section 2.3, the true optimal form is the form acquired by the optimization case H1D1, while the apparent optimal forms are the forms acquired by the optimization cases H1D1, H1D2, H1D3, H1D4, H1D5, and H1D6. The calculation results are shown in Section 3.

3. Results This section reports the results of the energy efficiency improvement by the optimization with a precise input (Pt), the performance gap caused by uncertain inputs (Pgap), the energy efficiency improvement by optimization with uncertain inputs (Papp1), and deviations in the optimized forms caused by uncertain inputs (Df). For conciseness, all form variables and uncertain input parameters are denoted using the abbreviations defined in Tables 1 and 2.

3.1 Energy Efficiency Improvement by Optimization with Precise Input The energy efficiency improvement achieved by form optimization with a precise input as compared with the base form is first presented. The Box–Whisker plot in Figure 5 shows the distribution of the improvement ratios (Pt, as defined in Equation (10)) in different locations and with different combinations of form variables for optimization. It can be seen that, in general, the energy efficiency improvement achieved by the form optimization with a precise input is remarkable for a majority of cases, and can be as high as more than 20%. This indicates the fact that the building energy performance can be largely improved by appropriate form design. The overall improvement for cases in Harbin is the highest among all locations, where the median of the improvement ratio is more than 17.5%, as long as WWR is included in the form variables for optimization (i.e., AR+WWR+OR, AR+WWR, WWR+OR, and WWR). Beijing and Shenzhen are the following locations, where the median of the improvement ratio is between 8% and 10%, as long as WWR (for Beijing) or AR (for Shenzhen) is included in the form variables for optimization, respectively. The improvement for Shanghai is lower than that in other locations, 15

where the median of the improvement ratio is below 5% for all situations. In terms of the different combinations of form variables for optimization, the improvement is minor regardless of the locations if OR is the only form variable for optimization, whereas for all other combinations, the improvement can be remarkable (median > 9%) depending on the locations.

Energy Efficiency Improvement Ratio Pt

0.20

0.15

Location harbin beijing 0.10

shanghai shenzhen

0.05

0.00 AR+WWR+OR

AR+WWR

AR+OR

WWR+OR

AR

WWR

OR

Form Variables for Optimization

Figure 5. Distribution of improvement ratios by optimization with precise input (Pt)

3.2 Performance Gap by Uncertain Input The energy performance gaps caused by the input assumptions of different uncertain boundary conditions are presented in this section. The distribution of the performance gap ratio (Pgap, as defined in Equations (14)-(16)) in different locations and with different form variables for optimization are shown in Box–Whisker plots (Figure 6). Moreover, to obtain more robust results, the one-sided one-sample t-test is conducted for each situation to examine whether the true mean of the performance gap is greater than certain numbers statistically at a confidence level of 0.95 (as statistical significance is found for most situations when comparing the performance gap with 0, t-tests using 0.01 and 0.02 as the reference values are also conducted to obtain more meaningful results) [92]. The effect size (Cohen's d, which is defined as the difference between two means in the unit of the standard deviation) for each situation is also calculated to indicate the magnitude of the effects of the uncertain boundary conditions [93]. All statistical analyses are conducted in R Studio 3.6.1 [94], and the results are shown in Table 6. It can be seen that the performance gap ratio can be as high as 13%, which indicates that remarkable reductions in energy saving that should be achieved by form optimization can be caused by the uncertainties in the boundary conditions. It is also clear that the distribution of the performance gaps differs in different locations.

16

Energy Performance Gap Pgap

0.15

Location: HARBIN 0.10

Uncertain Parameter U−Val 0.05

Tvis OcDens

OcSche

0.00

Energy Performance Gap Pgap Ratio of Gap>3%(Void)&>5%(Solid)

AR+WWR+OR

AR+WWR

AR+OR

WWR+OR

AR

WWR

OR

0.5 (>0.03) U−Val (>0.05)

a) Harbin

0.4

0.15

(>0.03) Tvis (>0.05)

0.3

Location: (>0.03) BEIJING OcDens

0.2

(>0.05)

0.10 0.1

(>0.03) OcSche (>0.05)

0.0

Uncertain Parameter

AR+WWR+OR

AR+WWR

AR+OR

WWR+OR

AR

WWR

OR

Form Variables for Optimization

U−Val

0.05

Tvis OcDens OcSche

0.00

Pgap Energy Performance of Gap>3%(Void)&>5%(Solid) RatioGap

AR+WWR+OR

AR+WWR

AR+OR

0.5

WWR+OR

AR

WWR

OR

b) Beijing

(>0.03) U−Val (>0.05)

0.4

0.15

(>0.03) Tvis (>0.05)

0.3

Location: (>0.03) OcDens SHANGHAI

0.2

(>0.05)

0.10 0.1

(>0.03) OcSche (>0.05)

0.0 AR+WWR+OR

AR+WWR

AR+OR

WWR+OR

AR

WWR

OR

Form Variables for Optimization

Uncertain Parameter U−Val

0.05

Tvis OcDens

OcSche

Gap>3%(Void)&>5%(Solid) Gap Pofgap Energy PerformanceRatio

0.00 AR+WWR+OR

AR+WWR

AR+OR

WWR+OR

AR

WWR

OR

0.5 (>0.03) U−Val (>0.05)

c) Shanghai

0.4

(>0.03) Tvis (>0.05)

0.3 0.15

(>0.03) OcDens

0.2

(>0.05) Location: SHENZHEN (>0.03)

0.1

OcSche (>0.05)

0.10 0.0

AR+WWR+OR

AR+WWR

AR+OR

WWR+OR

AR

WWR

OR

Uncertain Parameter

Form Variables for Optimization

U−Val

0.05

Tvis OcDens

OcSche

0.00

Ratio of Gap>3%(Void)&>5%(Solid)

AR+WWR+OR

AR+WWR

AR+OR

WWR+OR

AR

WWR

OR

0.5

0.4

d) Shenzhen

(>0.03) U−Val (>0.05)

0.3

Figure 6. Distribution of the performance gap ratios (Pgap)

(>0.03) Tvis (>0.05) (>0.03) OcDens (>0.05)

0.2

17

0.1

(>0.03) OcSche (>0.05)

0.0

AR+WWR+OR

AR+WWR

AR+OR

WWR+OR

Form Variables for Optimization

AR

WWR

OR

Table 6. Results of the t-test and the effect size calculation of the performance gap ratios (P gap) U-Val P-value of t-test

Results

(reference value)

Harbin (H)

0

Beijing (B) Shanghai (S)

Effect Size

0.01 0.02

P-value of t-test (reference value) 0

OcDens Effect Size

0.01 0.02

P-value of t-test (reference value) 0

OcSche Effect Size

P-value of t-test (reference value)

0.01 0.02

0

Effect Size

0.01 0.02

AR+WWR+OR

***

0.016

***

0.114

***

0.036

**

0.014

AR+WWR

***

0

**

0.113

***

0.036 ***

0.014

AR+OR

***

0

***

0.018

**

0.01

*

0.017

WWR+OR

**

0.003

***

0.132

**

0.007

*

0.007

AR

***

0.002

**

0.005

**

0.002

0

WWR

Shenzhen (Z)

Tvis

0

0

0

0

0.004

0

0.004

0

OR

***

AR+WWR+OR

***

**

0.132

***

*** **

0.486

***

0.187

**

0.025

AR+WWR

***

***

0.131

***

*** **

0.489

***

0.192

*

0.024

AR+OR

***

0.022

***

0.031

**

0.016 ***

0.018

WWR+OR

***

0.023

***

0.491

***

0.079

0.007

AR

***

0.021

***

0.031

**

0.014

0

WWR

***

0.036

***

0.491

***

0.076

0

OR

***

0.008

***

0.003

***

0.007

0

AR+WWR+OR

***

***

0.359

***

*** **

0.447

***

0.124

**

0.097

AR+WWR

***

***

0.367

***

*** **

0.446

***

0.123 ***

0.055

AR+OR

***

0.066

***

0.256

***

0.153 ***

0.107

WWR+OR

***

0.12

***

0.419

***

0.101 ***

0.132

AR

***

0.064

***

0.254

***

0.151 ***

0.098

WWR

***

0.114

***

0.422

***

0.106 ***

0.131

OR

**

0.002

*

0.004

**

0.01

**

0.02

AR+WWR+OR

***

**

0.161

***

***

0.469

***

0.029 ***

0.018

AR+WWR

***

*

0.157

***

***

0.459

***

0.029 ***

0.021

AR+OR

***

*

0.114

***

0.203

***

0.006 ***

0.009

WWR+OR

***

*

0.147

***

0.477

***

0.021 ***

0.063

AR

***

0.113

***

WWR

***

0.079

***

OR

***

0.047

***

*** ** *** **

*** ** *** **

*** **

0

0.214 *** **

0.482

***

0.021 ***

0.032

0.098

***

0.003 ***

0.01

All t-tests are one-sided, i.e., to test if the performance gap is statistically greater than the reference value T-test significance code: p-value<0.001: ***; p-value<0.01: **; p-value<0.05: *; p-value≥0.05: (void). Effect Size: Bold indicates effect size>0.2 (<0.2: small, 0.2-0.5: medium, 0.5-0.8: large [93])

For Harbin, the performance gaps are limited, with the median below 1% for all situations. There are no gaps >5% and gaps >3% are only caused by the uncertainty of U-Val when certain combinations of form variables are optimized (AR+WWR+OR, AR+WWR, AR+OR, AR, OR). Although the t-test results indicate that the performance gap is statistically higher (p<0.05) than 0 for a majority of situations, statistical significance is not found for any situation when comparing the performance gap with 1% or 2%, and the effect size is also small (<0.2) for all situations. 18

0

For Beijing, Shanghai, and Shenzhen, the characteristics of the performance gaps are similar. In terms of the extreme cases, the performance gaps can be higher than 10% for all three cities (up to 13% for Shanghai and Shenzhen). The uncertainty of Tvis is the most crucial cause for the performance gap, with median gaps from 2% (Shanghai and Shenzhen) to 2.5% (Beijing) for situations where WWR is included in the form variables for optimization (i.e., AR+WWR+OR, AR+WWR, WWR+OR, WWR). Performance gaps approaching or larger than 10% also exist in each of the aforementioned situations. Moreover, medium effect sizes (>0.2) are found in all situations above, and t-tests indicate that the performance gap is statistically greater (p<0.01) than 2% in most of these situations (except for AR+WWR+OR and AR+WWR in Shenzhen, where the performance gap is still statistically greater (p<0.001) than 1%). In addition, the uncertainty of Tvis can also cause performance gaps as high as 5% and medium effect sizes (>0.2) for two other situations (AR+OR, AR) in Shanghai and Shenzhen. The following remarkable cause for the performance gap after Tvis is the uncertainty of U-Val, which can lead to performance gaps of approximately 2% in terms of the median for some situations in all three cities. Performance gaps higher than 5% and statistically significant excess (p<0.05 in the t-test) of the performance gap over 1% are found when AR+WWR+OR or AR+WWR is used as the form variables for optimization in all three cities. Furthermore, the performance gap is also statistically greater (p<0.05 in the t-test) than 1% for AR+OR and WWR+OR in Shenzhen, and the medium effect sizes are found for AR+WWR+OR and AR+WWR in Shanghai. The uncertainty of OcDens and OcSche, by contrast, results in much smaller performance gaps for all three cities, because the resulting highest performance gaps are only around 3% (OcDens, AR+WWR+OR and AR+WWR in Shanghai), and no statistically significant surplus of the performance gap over 1% or 2% is found for any situation. The effect size is small for all situations.

3.3 Energy Efficiency Improvement by Optimization with Uncertain Input Based on the results presented in Section 3.2, it is clear that the uncertainty of some boundary condition parameters does cause major performance gaps compared with the energy efficiency achieved by form optimization with precise boundary conditions, or in other words, reduces the amount of energy saving that can be achieved through form optimization. Nevertheless, form optimization with uncertain boundary conditions is still beneficial if the building energy efficiency of the optimized form is higher than that of the form before optimization, i.e., the base form. However, if the energy efficiency of the optimized form can be even lower than the base form, careful attention must be paid to properly control the uncertainties of the boundary conditions before conducting any form optimization. Therefore, the energy efficiency improvement achieved by form optimization with uncertain boundary conditions compared with the base form is also a crucial indicator of the reliability of building form optimization under uncertainties. The distribution of the improvement ratios (Papp, as defined in Equations (11)-(13)) in different locations and with different form variables for optimization are shown in Box–Whisker plots (Figure 7). It can be seen that the lowest improvement ratio approaches -10%, revealing that a remarkable decrease instead of an increase in energy efficiency compared with the base case may be caused by the uncertainties in the boundary conditions. The distribution of the improvement ratios also varies in different locations.

19

Energy Efficiency Improvement Ratio Papp

0.2

Location: HARBIN 0.1

Uncertain Parameter U−Val

Tvis

0.0

OcDens OcSche

Ratio Papp Energy Efficiency Improvement Ratio of Descent>3%(Void)&>5%(Solid)

−0.1 AR+WWR+OR

AR+WWR

AR+OR

WWR+OR

AR

WWR

OR

0.25

(>0.03) U−Val (>0.05)

a) Harbin 0.20

(>0.03) Tvis (>0.05)

0.15 0.2

(>0.03)

0.10

OcDens Location: (>0.05) BEIJING

0.05

(>0.03) OcSche (>0.05)

0.1 0.00 AR+WWR+OR

AR+WWR

AR+OR

WWR+OR

AR

WWR

OR

Form Variables for Optimization

Uncertain Parameter U−Val

Tvis

0.0

OcDens

OcSche

Ratio Papp Energy Efficiency Improvement Ratio of Descent>3%(Void)&>5%(Solid)

−0.1 AR+WWR+OR

AR+WWR

AR+OR

0.25

WWR+OR

AR

WWR

OR

b) Beijing

(>0.03) U−Val (>0.05)

0.20

(>0.03) Tvis (>0.05)

0.15 0.2

(>0.03)

0.10

OcDens Location: (>0.05) SHANGHAI

0.05

(>0.03) OcSche (>0.05)

0.1 0.00 AR+WWR+OR

AR+WWR

AR+OR

WWR+OR

AR

WWR

OR

Form Variables for Optimization

Uncertain Parameter U−Val Tvis

0.0

OcDens

OcSche

Ratio of Descent>3%(Void)&>5%(Solid) Energy Efficiency Improvement Ratio Papp

−0.1 AR+WWR+OR

AR+WWR

AR+OR

WWR+OR

AR

WWR

OR

Form Variables for Optimization

0.25

c) Shanghai

0.20

(>0.03) U−Val (>0.05)

0.15 0.2

(>0.03) Tvis (>0.05) (>0.03) Location: OcDens SHENZHEN (>0.05)

0.10

0.05 0.1

(>0.03) OcSche (>0.05)

0.00

AR+WWR+OR

AR+WWR

AR+OR

WWR+OR

AR

WWR

OR

Uncertain Parameter U−Val Tvis

0.0

OcDens OcSche

−0.1

Ratio of Descent>3%(Void)&>5%(Solid)

AR+WWR+OR

AR+WWR

AR+OR

0.25

WWR+OR

AR

WWR

OR

d) Shenzhen

(>0.03) U−Val (>0.05)

0.20

Figure 7. Distribution of improvement ratios by optimization with uncertain input (P(>0.03) app) 0.15

Tvis (>0.05)

20

0.10

(>0.03) OcDens (>0.05)

0.05

(>0.03) OcSche (>0.05)

0.00 AR+WWR+OR

AR+WWR

AR+OR

WWR+OR

Form Variables for Optimization

AR

WWR

OR

For Harbin, major energy efficiency improvements (median around 17.5%) can still be achieved by optimization even with the uncertainties of the boundary conditions, as long as WWR is included in the form variables for optimization (i.e., AR+WWR+OR, AR+WWR, WWR+OR, WWR). For other combinations of form variables, the improvement ratios are limited, but the median values are still above 0. Moreover, there is no descent worse than 3% for any situation. Therefore, it is generally safe to employ form optimization in Harbin even under uncertainties of the boundary conditions. For Beijing and Shenzhen, the patterns of the improvement ratios are similar. The median improvement ratio is approximately 8%, as long as WWR (for Beijing) or AR (for Shenzhen) is included in the form variables for optimization respectively. For other combinations of form variables, the improvement ratios are limited, but the median values are still above 0. In Shenzhen, the worst descents of the energy efficiency are higher than 5%, but can only be caused by the uncertainty of Tvis when WWR+OR or WWR is used as the form variable for optimization, whereas for Beijing, the worst descents are around 3% and are only caused by the uncertainty of Tvis under the same two combinations of form variables. Therefore, it is also safe to employ form optimization in Beijing and Shenzhen, as long as the uncertainty of Tvis is under control when WWR+OR or WWR is used as the form variables for optimization. For Shanghai, the improvement ratio contributed by optimization with uncertainty is rather limited, with the median values of the improvement ratio below 5% for all situations. Moreover, descents around 5% and even approaching 10% are found in various situations. The uncertainty of Tvis is still the leading cause, which results in descents close to 10% (WWR+OR, WWR) or around 5% (AR+WWR+OR, AR+WWR, AR+OR, AR) for all combinations of form variables except for OR alone. The uncertainty of U-Val is the following cause and can also lead to descents approaching 10% in energy efficiency when AR+WWR+OR or AR+WWR is used as the form variables for optimization. The uncertainty of OcDens and OcSche, however, can cause no descents worse than 2%. In short, employing form optimization with uncertain Tvis or U-Val can lead to a major decrease instead of an increase in the building energy efficiency, and thus careful attention must be paid to ensure that the uncertainties in Tvis and U-Val are under control before conducting form optimization.

3.4 Deviations in Optimized Forms Due to Uncertain Input The deviations in optimized forms caused by the input assumptions of different uncertain boundary conditions are presented in this section. The normalized Euclidean distance between the true optimal form and the apparent optimal forms (Df, as defined in Equations (21)-(23)) in different locations and with different form variables for optimization are shown in Box–Whisker plots (Figure 8).

21

Distance Between Forms Df

0.6

Location: HARBIN 0.4

Uncertain Parameter U−Val 0.2

Tvis OcDens OcSche

0.0 AR+WWR+OR

AR+WWR

AR+OR

WWR+OR

AR

WWR

OR

Form Variables for Optimization

a) Harbin

Distance Between Forms Df

0.6

Location: BEIJING 0.4

Uncertain Parameter U−Val 0.2

Tvis OcDens OcSche

0.0 AR+WWR+OR

AR+WWR

AR+OR

WWR+OR

AR

WWR

OR

Form Variables for Optimization

b) Beijing

Distance Between Forms Df

0.6

Location: SHANGHAI 0.4

Uncertain Parameter U−Val 0.2

Tvis OcDens OcSche

0.0 AR+WWR+OR

AR+WWR

AR+OR

WWR+OR

Form Variables for Optimization

c) Shanghai

22

AR

WWR

OR

Distance Between Forms Df

0.6

Location: SHENZHEN 0.4

Uncertain Parameter U−Val 0.2

Tvis OcDens OcSche

0.0 AR+WWR+OR

AR+WWR

AR+OR

WWR+OR

AR

WWR

OR

Form Variables for Optimization

d) Shenzhen Figure 8. Normalized distance between true optimal form and apparent optimal forms (Df)

The pattern of the deviations in the optimized forms is rather similar to that of the performance gaps reported in Section 3.2. This is reasonable, because the more the form changes, the more likely that a major change in performance will occur. For Harbin, the deviations in optimized forms are extremely limited, with the median below 0.02 for all situations, and the largest deviation is only approximately 0.06. For Beijing, Shanghai, and Shenzhen, larger deviations are found. Similar to the performance gaps, the uncertainty of Tvis is the most significant cause for the deviations in the optimized forms for most situations, with the largest deviation up to around 0.4 for each of the three cities. The following crucial cause is also the uncertainty of U-Val, the largest deviation caused by which approaches 0.6 in Shanghai, and is around 20% in Beijing and Shenzhen. Despite the similarity, differences also exist between the pattern of deviations in the optimized forms and the pattern of the performance gaps. The uncertainties in OcDens and OcSche, which are not the major causes for the performance gaps, lead to unneglectable deviations in the optimized forms. Deviations greater than 0.2 caused by the uncertainties of OcDens and OcSche are found in 5 situations in Shanghai (AR+WWR+OR, AR+WWR, AR+OR and AR by OcDens, and AR+WWR+OR by OcSche), and 2 situations in Beijing (AR+WWR+OR and AR+WWR by OcDens). This difference in patterns is also possible because different forms may have the same or similar energy efficiency performance.

4. Discussion The results in Section 3 indicate that for a number of situations, the uncertainty of particular boundary conditions can cause major unreliability problems of the results of the energy-based form optimization of an office building, including reductions in energy saving, deterioration than the results before optimization, and deviations in the optimized forms. In reality, the uncertainties can be difficult to control due to a lack of knowledge, design procedures, or the stochastic nature of the parameters (see Section 1.2.2 for more details). Under such circumstances, designers should choose the design that maximizes the overall performance for all scenarios, or in other words, take all possible boundary conditions into account and then find an optimal design under the 23

uncertainties. A method to acquire the overall optimal design is raised in this section based on stochastic optimization [44-45, 69].

4.1 Theory Stochastic optimization refers to the methods for minimizing or maximizing an objective function when randomness is present [95], and the processes of transforming a deterministic optimization model to a stochastic model normally includes the following: 1) approximating the probability distribution of the stochastic parameters through a finite set of scenarios, 2) requiring constraints to be fulfilled for all scenarios, and 3) optimizing the mathematical expectation of the objective [45]. For the problem of energy-based building form optimization investigated in this research, supposing that due to the uncertainty of the boundary conditions, there are n possible scenarios, namely, S1, S2, S3…Sn, and the probability of each scenario is p1, p2, p3…pn, whereas the energy consumption is e1, e2, e3…en, respectively, then the expectation of the energy consumption Ee for all scenarios is as follows: 𝐸𝑒 = ∑𝑛𝑖=1 𝑝𝑖 ∗ 𝑒𝑖 (24) The expectation reflects the average energy consumption for all scenarios, and a risk measure based on the Conditional Value at Risk (CVaR) method [96] is then added in order to manage risk (i.e., very bad outcomes for some extreme scenarios). Given a confidence level α, 0 < α < 1, the Value at Risk (VaR) of the CVaR method is defined as the lowest value λ that ensures a probability lower than 1-α of obtaining a value higher than λ, i.e.: 𝑉𝑎𝑅(α) = min⁡*λ: 𝐏𝐫,𝑆|𝑒 > λ- ≤ 1 − α+, (25) where S is the scenarios and e is the energy consumption. In other words, VaR is the (1-a)-quantile of the energy consumption distribution. The VaR cannot reflect the energy consumption distribution beyond the VaR, and to overcome this problem, CVaR is defined as the conditional expectation of the values that exceed the VaR level λ and thus quantify the energy consumption in extreme scenarios: 𝐶𝑉𝑎𝑅 = 𝑬,𝑒|𝑒 > λ(26) where e is the energy consumption. Combining the average and the risk together, the optimization problem can be defined as follows: min⁡⁡(1 − 𝛽) ∗ 𝐸𝑒 + 𝛽 ∗ 𝐶𝑉𝑎𝑅 (27) where β is the risk weight that can be set by the decision-maker, and the higher the value of β is, the more risk aversion that is included. Specifically, β=0 makes the objective risk-neutral without any risk management. Following the method above, designers can acquire the overall optimal design that takes the mean and extreme cases of all scenarios into account under the uncertainty of the boundary condition parameters.

4.2 Example An example is provided to demonstrate the theoretical method based on the optimization problem defined in Sections 2.3-2.6. Three form parameters, aspect ratio (AR), window-to-wall ratio (WWR) and orientation (OR), are employed as the independent variables for optimization. Their definitions and ranges are presented in Table 1. Four envelope and occupancy parameters, U-Val, Tvis, OcDens, and OcSche, are selected as the boundary condition parameters with uncertainty, and their definitions and ranges are as shown in Table 2. For conciseness, only three possible values are considered for each uncertain parameter (Table 7), and their combinations result in 81 24

(3 × 3 × 3 × 3) possible scenarios (as S1, S2, S3…Sn defined in Section 4.1) in total, whereas the probability of each scenario (as p1, p2, p3…pn defined in Section 4.1) is regarded as equal. For stochastic optimization, α is fixed to 0.75 [45], whereas four values of β are considered, namely, 1) Risk Neutral (RN), β=0; 2) Risk Averse-Low (RAL), β=0.1; 3) Risk Averse-Medium (RAM), β=0.5; and 4) Risk Averse-High (RAH), β=0.95. For comparison, a case of deterministic optimization (DO) with only one boundary condition scenario is also conducted, and all of its boundary condition parameters are set to the median of the possible values defined in Table 7. Moreover, four major cities in different climate zones (details shown in Table 5) are also involved to obtain more comprehensive results. All optimization configurations applied herein are listed in Table 8, and the implementation of the optimization is the same as described in Section 2.5. Table 7. Possible values for each uncertain parameter Parameter

Possible Value

U-Value of walls (U-Val)

0.1, 0.24, 0.38 (Harbin); 0.15, 0.33, 0.5 (Beijing); 0.25, 0.63, 1 (Shanghai); 0.25, 0.88, 1.5 (Shenzhen)

Visible Transmittance of Windows (Tvis)

0.4, 0.63, 0.85

Occupant Density (OcDens, people/m2)

0.05, 0.15, 0.25

Occupant Schedule (OcSche)

S1, S3, S5, see Figure 4 for details

Table 8. Optimization cases conducted in the example Case Number

Location

Optimization Configuration

1

Deterministic (DO)

2

Stochastic, β=0 (RN)

3

Stochastic, β=0.1 (RAL)

Harbin (H)

4

Stochastic, β=0.5 (RAM)

5

Stochastic, β=0.95 (RAH)

6

Deterministic (DO)

7

Stochastic, β=0 (RN)

8

Stochastic, β=0.1 (RAL)

Beijing (B)

9

Stochastic, β=0.5 (RAM)

10

Stochastic, β=0.95 (RAH)

11

Deterministic (DO)

12

Stochastic, β=0 (RN)

13

Stochastic, β=0.1 (RAL)

Shanghai (S)

14

Stochastic, β=0.5 (RAM)

15

Stochastic, β=0.95 (RAH)

16

Deterministic (DO)

17

Stochastic, β=0 (RN)

18

Stochastic, β=0.1 (RAL)

Shenzhen (Z)

19

Stochastic, β=0.5 (RAM)

20

Stochastic, β=0.95 (RAH) 25

The optimal form of each configuration is acquired after the optimization. To compare the quality of the results, for each optimal form, its energy consumption in all 81 possible boundary condition scenarios is calculated respectively. For comparison between cities, the optimized energy consumption of the deterministic optimization in each city is used as the reference and all values of the energy consumption are divided by the reference value of the corresponding city. The distribution of the ratios of each optimization case is then presented in the Box–Whisker plot of Figure 9, with the energy consumption of each optimal form in the base scenario (the boundary condition scenario adopted in the deterministic optimization) shown as dots.

Energy Consumption (Ratio to Reference)

1.6

1.4

Optimization Configuration DO

1.2

RN RAL RAM RAH Base Scenario

1.0

0.8

Harbin

Beijing

Shanghai

Shenzhen

Location

Figure 9. Distribution of the energy consumption of each optimization configuration

It can be seen that for Harbin, the distributions of different optimization configurations generally remain the same. This is reasonable, as the influence of the uncertain boundary condition parameters is very limited for Harbin (as indicated in Sections 3.2 and 3.4), so deterministic optimization that ignores the uncertainties of the boundary conditions can yield results similar to stochastic optimization. For the remaining three cities, remarkable changes in the distributions can be found in different optimization configurations. For the base scenario alone (shown by the dots in Figure 9), the energy consumption acquired by the deterministic optimization is lower than that by the stochastic optimization, but for extreme scenarios, the energy consumption of the stochastic optimization is much lower, regardless of the degree of risk aversion. Moreover, the dispersion of the energy consumption distribution is also reduced by stochastic optimization, and thus the result is more robust in multiple scenarios. This proves the effectiveness of stochastic optimization in providing a more reliable optimal design when uncertainty is present. For different configurations of stochastic optimization, as the degree of risk aversion increases, the energy consumption of extreme scenarios decreases, thereby reducing the risk of getting very poor results. However, the overall energy consumption (including the median) increases, especially for RAM and RAH, 26

which is the downside of a higher risk aversion. Therefore, designers should balance the importance of the average and extreme energy consumption, and choose the value of β according to the specific requirements of their design problem.

5. Conclusion Herein, a reliability analysis of energy-based form optimization of office buildings under uncertainties in four parameters related to the envelope and occupancy is conducted based on parametric studies on a medium office building. A possible method to acquire the overall optimal design under the presence of uncertainties is also raised. Several conclusions can be drawn from this research: 1) Uncertainties in the boundary condition parameters can lead to major unreliability problems of the results of energy-based form optimization of office buildings, including reductions up to 13% in energy saving achieved by optimization, descents up to 10% in energy efficiency compared with the results before optimization, and deviations in the optimized forms with normalized distances up to 0.6. 2) The uncertainty in the visual transmittance of window glazing is the most significant cause for the unreliability in the results of the form optimization, and can lead to reductions around 10% in energy saving in Beijing, Shanghai and Shenzhen, and descents approaching 10% in comparison with the results before optimization in Shanghai. The uncertainty in the U-value of the walls is the following cause, whereas the influence of the uncertainties in the occupant density and occupant schedule is minor. 3) The influence of uncertainties in the boundary conditions varies in different locations and form variables for optimization. In Harbin, the influence is limited, without any reduction >5% in energy saving or descent >3% compared with the results before optimization, while in Beijing, Shanghai, and Shenzhen, the influence is more remarkable. The influence is generally large when WWR is included in the form variables for optimization (AR+WWR+OR, AR+WWR, WWR+OR, WWR), while if OR alone is the form variable for optimization, no reductions >3% in energy saving or descents >3% compared with the results before optimization are found under all situations. 4) Stochastic optimization is an effective method for acquiring the optimal design when the uncertainty cannot be resolved, as the risk of getting very poor performance under extreme conditions, and the performance dispersion in various scenarios, are both smaller compared with the traditional deterministic optimization.

Acknowledgments We gratefully thank the National Science Foundation of China (Grant No. 51708355, 51825802), 27

State Key Laboratory of Subtropical Building Science (Grant No. 2019ZB14), Key Laboratory of Ecology and Energy-saving Study of Dense Habitat (Tongji University), Ministry of Education (Grant No. 2019030103) and the Research Start-up Project for New Teachers of Shenzhen University (Grant No. 2018072, 2018076) for funding this work.

Author Contribution Statement

Shuai Lu: Conceptualization; Methodology; Software; Formal analysis; Investigation; Data Curation; Writing - Original Draft; Visualization; Funding acquisition Jingyu Li: Software; Validation; Formal analysis; Investigation; Data Curation; Visualization Borong Lin: Conceptualization; Methodology; Validation; Resources; Data Curation; Writing - Review & Editing; Supervision; Project administration; Funding acquisition

Conflict of interest statement None

28

References [1] [2]

[3] [4]

[5] [6] [7]

[8] [9] [10] [11] [12] [13]

[14] [15] [16]

[17] [18] [19] [20]

[21]

Nguyen A, Reiter S, Rigo P. A review on simulation-based optimization methods applied to building performance analysis. Appl Energy, 2014, 113: 1043–58. Shi X, Tian Z, Chen W, Si B, Jin X. A review on building energy efficient design optimization from the perspective of architects. Renewable and Sustainable Energy Reviews, 2016, 65: 872–884. Huang Y, Niu J. Optimal building envelope design based on simulated performance: history, current status and new potentials. Energy and Buildings, 2016, 117: 387-398. Tian Z, Zhang X, Jin X, Zhou X, Si B, Shi X. Towards adoption of building energy simulation and optimization for passive building design: A survey and a review. Energy and Buildings, 2018, 158: 1306-1316. Bamdad K, Michael CE, Guan L, Bell J. Building energy optimization under uncertainty using ACOMV algorithm. Energy and Buildings, 2018, 167: 322-333. Hensen J, Lamberts R. Building performance simulation for design and operation. Spon Press, 2011. Daly D, Cooper P, Ma Z. Understanding the risks and uncertainties introduced by common assumptions in energy simulations for Australian commercial buildings. Energy and Buildings, 2014, 75, 382-393. Markku J. IEA-BCS ANNEX 30, Bringing simulation to application, Subtask 2: Design process analysis, Final report. 1998. Hemsath TL, Bandhosseini KA. Sensitivity analysis evaluating basic building geometry ' s effect on energy use. Renewable Energy, 2015, 76: 526-538. Liu L, Wu D, Li X, Hou S, Liu C, Jones P. Effect of geometric factors on the energy performance of high-rise office towers in Tianjin, China. Building Simulation, 2017: 1-17. Krem M, Simi T. Structural configuration and building energy performance. Journal of Architectural Engineering, 2013, 19: 29–40. Torcellini PA, Ellis PG. Early-phase design methods. Center for Buildings and Thermal Systems at National Renewable Energy Laboratory (NREL), 2006. Ascione F, Bianco N, Stasio C, Mauro G, Vanoli G. A new methodology for cost-optimal analysis by means of the multi-objective optimization of building energy performance. Energy and Buildings, 2015, 88: 78–89. Yi Y, Malkawi A. Optimizing building form for energy performance based on hierarchical geometry relation. Automation in Construction, 2009, 18(6): 825-833. Jin, JT, Jeong JW. Optimization of a free-form building shape to minimize external thermal load using genetic algorithm. Energy and Buildings, 2014, 85: 473–482. Suh J, Park S, Kim D. W. Heuristic vs. meta-heuristic optimization for energy performance of a post office building. In: Proceedings of the 12th conference of international building performance simulation association, 2011. Lartigue B, Lasternas B, Loftness V. Multi-objective optimization of building envelope for energy consumption and daylight. Indoor Built Environ, 2013, 0 (0):1–11. Xu J, Kim J, Hong H, Koo J. A systematic approach for energy efficient building design factors optimization. Energy and Buildings, 2015, 89: 87–96. Caldas L, Santos L. Painting with light: An interactive evolutionary system for daylighting design. Building and Environment, 2016, 109: 154-174. Trubiano F, Ozkan A, Roudsari MS et al. Building simulation and evolutionary optimization in the conceptual design of a high-performance office building. Proceedings of the Building Simulation Conference, 2013. Zhang L, Zhang L, Wang Y. Shape optimization of free-form buildings based on solar radiation gain and space efficiency using a multi-objective genetic algorithm in the severe cold zones of China. Solar Energy, 2016, 132: 38–50. 29

[22]

[23] [24]

[25]

[26]

[27]

[28] [29]

[30]

[31]

[32]

[33] [34] [35] [36] [37] [38] [39]

[40] [41]

[42]

Saksela K, Botts J, Savioja L. Optimization of absorption placement using geometrical acoustic models and least squares. Journal of the Acoustical Society of America, 2015, 137, 274–280. Bassuet A, Rife D, Dellatorre L. Computational and optimization design in geometric acoustics. Building Acoustics, 2014, 21: 75–86. Robinson P, Siltanen S, Lokki T, Savioja L. Concert hall geometry optimization with parametric modeling tools and wave-based acoustic simulations. Building Acoustics, 2014, 21: 55–64. Ochoa E, Aries C, van Loenen J, etal. Considerations on design optimization criteria for windows providing low energy consumption and high visual comfort. Appl Energy, 2012, 95(2): 238–45. Salvatore C, Lorenzo P, Paolo Z. Optimization by discomfort minimization for designing a comfortable net zero energy building in the Mediterranean climate. Adv Mater Res, 2013, 689: 44–8. Magnier L, Haghighat F. Multi objective optimization of building design using TRNSYS simulations, genetic algorithm, and artificial neural network. Build Environ, 2010, 45(3):739–46. Chantrelle P, Lahmidi H, Keilholz W, et al. Development of a multi criteria tool for optimizing the renovation of buildings. Appl Energy, 2011, 88 (4): 1386–94. Asadi E, da Silva G, Antunes H, et al. A multi-objective optimization model for building retrofit strategies using TRNSYS simulations, Gen Opt and MATLAB. Build Environ, 2012; 56: 370–8. Kim J, Yi YK, Malkawi AM. Building Form Optimization in Early Design Stage to Reduce Adverse Wind Condition, Using Computational Fluid Dynamics. 12th Conference of International Building Performance Simulation Association, at Sydney, Australia, 2011. You W, Qin M, Ding W. Improving building facade design using integrated simulation of daylighting, thermal performance and natural ventilation. Building Simulation, 2013, 6(3): 269-282. Chan TS, Chang YC, Huang JH. Application of artificial neural network and genetic algorithm to the optimization of load distribution for a multiple-type-chiller plant. Building Simulation, 2017, 10(5): 711-722. Chen X, Yang H. A multi-stage optimization of passively designed high-rise residential buildings in multiple building operation scenarios. Applied Energy, 2017, 206: 514-557. Li Z, Chen H, Lin B, Zhu Y. Fast bidirectional building performance optimization at the early design stage. Building Simulation, 2018, 11(4): 647-661. Zemella G, March DD, Borrotti M. Optimized design of energy efficient building facades via Evolutionary Neural Networks. Energy and Buildings, 2011, 43(12):3297-3302. Kämpf JH, Robinson D. Optimisation of building form for solar energy utilization using constrained evolutionary algorithms. Energy and Buildings, 2010: 42(6): 807-814. Bichiou Y, Krarti M. Optimization of envelope and HVAC systems selection for residential buildings. Energy and Buildings, 2011, 43(12): 3373–82. Varma P, Bhattacharjee B. Building envelope optimization using simulated annealing approach. In: Proceedings of the 2nd BSO conference; 2014. Chen KW, Janssen P, Schlueter A. Multi-objective optimization of building form, envelope and cooling system for improved building energy performance. Automation in Construction, 2018, 94, 449-457. Rapone G, Saro O. Optimisation of curtain wall facades for office buildings by means of PSO algorithm. Energy and Buildings, 2012, 45:189–96. Park CS, Augenbroe G, Sadegh N. Real-time optimization of a double-skin façade based on lumped modeling and occupant preference. Building and Environment, 2004, 39(8): 939-948. Karaguzel O, Zhang R, Lam K. Coupling of whole-building energy simulation and multi-dimensional numerical optimization for minimizing the life cycle costs of office 30

[43]

[44]

[45]

[46] [47]

[48] [49]

[50] [51]

[52]

[53] [54]

[55]

[56] [57]

[58] [59] [60]

[61] [62]

buildings. Build Simul, 2014, 7(2): 111–21. Murray S, Walsh B, Kelliher D, O’Sullivan D. Multi-variable optimization of thermal energy efficiency retrofitting of buildings using static modelling and genetic algorithms: a case study. Build Environ, 2014, 75: 98–107. Emilio L. Cano, Javier M. Moguerza, Tatiana Ermolieva and Yuri Ermoliev, "Energy efficiency and risk management in public buildings: strategic model for robust planning", Computational Management Science, 11(1), pp. 25-44, 2014. Emilio L. Cano, Javier M. Moguerza and Antonio Alonso-Ayuso, "A multi-stage stochastic optimization model for energy systems planning and risk management", Energy and Buildings, 110(1), pp. 49-56, 2016. Sameti M, Haghighat F. Optimization approaches in district heating and cooling thermal network. Energy and Buildings, 2017, 140, 121-130. Zhang R, Nie Y, Lam KP, Biegler LT. Dynamic optimization based integrated operation strategy design for passive cooling ventilation and active building air conditioning. Energy and Buildings, 2014, 85, 126-135. Bamdad K, et al. Ant colony algorithm for building energy optimization problems and comparison with benchmark algorithms, Energy and Buildings. 154 (2017) 404–414. Bamdad K, et al. Building energy optimization using artificial neural network and ant colony optimization, in: Proceedings of the Australasian Building Simulation Conference, Australia, 2017. Hopfe C, Hensen J. Uncertainty analysis in building performance simulation for design support. Energy and Buildings, 2011: 43(10): 2798-2805. Hopfe C. Uncertainty and sensitivity analysis in building performance simulation for decision support and design optimization, PhD thesis, Technische Universiteit Eindhoven, The Netherlands, 2009. Menezes AC, Cripps A, Bouchlaghem D, Buswell R. Predicted vs. actual energy performance of non-domestic buildings: using post-occupancy evaluation data to reduce the performance gap, Applied Energy, 2011, 97: 355-364. Silva S, Ghisi E. Uncertainty analysis of user behavior and physical parameters in residential building performance simulation. Energy and Buildings, 2014, 76: 381-391. Bucking S, Zmeureanu R, Athienitis A. A methodology for identifying the influence of design variations on building energy performance. Journal of Building Performance Simulation, 2014, 7(6):411-426. Gaetani I, Hoes PJ, Hensen JLM. On the sensitivity to different aspects of occupant behavior for selecting the appropriate modelling complexity in building performance predictions, J. Build. Perform. Simul. 2016, 10: 1–11. Rezaee R. Assessment of uncertainty and confidence in building design exploration, Artif. Intell. Eng. Des. Anal. Manuf. 2015, 29(4): 429–441. Hyun SH, Park CS, Augenbroe G. Uncertainty and sensitivity analysis of natural ventilation in high-rise apartment buildings. in: Proceedings of the Building Simulation, Beijing, China, 2007. Heo Y, Choudhary R, Augenbroe GA, Calibration of building energy models for retrofit analysis under uncertainty, Energy and Buildings. 2012, 47: 550–560. Mottillo M, Sensitivity analysis of energy simulation by building type, ASHRAE Transactions, 2001, 107: 722–732. Wang L, Mathew P, Pang X. Uncertainties in energy consumption introduced by building operations and weather for a medium-size office building. Energy and Buildings, 2012, 53: 152–158. Si B, Tian Z, Jin X, Zhou X, Shi X. Performance indices and evaluation of algorithms in building energy efficient design optimization[J]. Energy, 2016, 114:100-112. Hamdy M, Nguyen AT, Hensen JLM. A performance comparison of multi-objective optimization algorithms for solving nearly-zero-energy-building design problems[J]. Energy and Buildings, 2016, 121: 57-71. 31

[63] [64]

[65]

[66]

[67] [68]

[69]

[70]

[71]

[72]

[73] [74]

[75]

[76] [77]

[78]

[79] [80] [81] [82] [83]

Si B, Tian Z, Jin X, Zhou X, Shi X. Ineffectiveness of optimization algorithms in building energy optimization and possible causes. Renewable Energy, 2019, 134: 1295-1306. Wetter M, Wright J. A comparison of deterministic and probabilistic optimization algorithms for nonsmooth simulation-based optimization. Build Environ, 2004, 39(8): 989-999. Kampf JH, Wetter M, Robinson D. A comparison of global optimization algorithms with standard benchmark functions and real-world applications using EnergyPlus. J Build Perform Simul, 2010, 3(2):103-120. Futrell BJ, Ozelkan EC, Brentrup D. Optimizing complex building design for annual daylighting performance and evaluation of optimization algorithms, Energy and Buildings, 2015, 92: 234–245. Bucking S. Optimization under economic uncertainty using a net zero energy commercial office case study, ASHRAE Transactions, 2016, 122: 444–454. Hoes P. Optimizing building designs using a robustness indicator with respect to user behavior. in: Proceedings of the 12th Conference of International Building Performance Simulation Association, Sydney, 2011. Cano, L. E, Moguerza, M. J, Ermolieva, Tatiana, Yermoliev, Yurii (2017). “A strategic decision support system framework for energy-efficient technology investments.” TOP, 25(2), 249-270, 2017. Ramallo-González AP, Blight TS, Coley DA. New optimization methodology to uncover robust low energy designs that accounts for occupant behavior or other unknowns, J. Build. Eng. 2015, 2: 59–68. Deru M, Field K, Studer D, Benne K, Griffith B, Torcellini P, et al. Commercial reference building models of the national building stock. February 2011. Available from: http://www.nrel.gov/docs/fy11osti/46861.pdf. Ministry of Construction (MOC) of China. JGJ/T 449-2018, Standard for Green Performance Calculation of Civil Buildings. Beijing: China Architecture & Building Press, 2015. Ministry of Construction (MOC) of China. GB50189-2015, Design standard for energy efficiency of public buildings. Beijing: China Architecture & Building Press, 2015. Granadeiro V, Correia JR, Leal VM, Duarte JP. Envelope- related energy demand: A design indicator of energy performance for residential buildings in early design stages. Energy and Buildings, 2013, 61: 215–223. Delzendeh E, Wu S, Lee A, Zhou Y. The impact of occupants’ behaviors on building energy analysis: A research review. Renewable and Sustainable Energy Reviews, 2017, 80, 1061-1071. Haldi F, Robinson D. The impact of occupants' behavior on building energy demand. Journal of Building Performance Simulation, 2011, 4: 323-338. Junghans L, Darde N. Hybrid single objective genetic algorithm coupled with the simulated annealing optimization method for building optimization. Energy and Buildings, 2015, 86: 651-662. Danielski I, Nair G, Joelsson A. Heated atrium in multi-storey apartment buildings, a design with potential to enhance energy efficiency and to facilitate social interactions. Building and Environment, 2016, 106: 352-364. Jin Q, Overend M. Sensitivity of façade performance on early-stage design variables. Energy and Buildings, 2014, 77: 457-466. Ministry of Construction (MOC) of China. JGJ67-2006, Design code for office building. Beijing: China Architecture & Building Press, 2015. Zhang Q, Research of operation and usage energy model and energy simulation method in office building. Tsinghua University, 2014. Jakubiec AJ, Reinhart CF. DIVA 2.0: integrating daylight and thermal simulations using Rhinoceros 3D, daysim and energyplus, Proc. Build. Simul., 2011, 20(11): 2202-2209. U.S. Department of Energy. EnergyPlus™ Version 9.2.0 Documentation: EnergyPlus 32

[84] [85] [86]

[87]

[88] [89] [90]

[91]

[92] [93] [94] [95] [96]

Essentials. https://energyplus.net/documentation. U.S. Department of Energy. EnergyPlus™ Version 9.2.0 Documentation: Engineering Reference. https://energyplus.net/documentation. Galapagos users’ manual. https://ieatbugsforbreakfast.wordpress.com/2011/07/31/ongetting-lucky-in-higher-dimensions/. Ceylan, H. T., and G. E. Myers. 1980. Long-time Solutions to Heat Conduction Transients with Time-Dependent Inputs. ASME Journal of Heat Transfer, Volume 102, No. 1, pp. 115-120. Ouyang, K., and F. Haghighat. 1991. A Procedure for Calculating Thermal Response Factors of Multi-layered Walls–State Space Method. Building and Environment, Vol. 26, No. 2, pp. 173-177. Seem, J. E. 1987. Modeling of Heat Transfer in Buildings, Ph.D. Thesis, University of Wisconsin, Madison, WI. Strand, R. K. 1995. Heat Source Transfer Functions and Their Application to Low Temperature Radiant Heating Systems, Ph.D. Thesis, University of Illinois, Urbana, IL. Chen S, Montgomery J, Bolufé-Röhler A. Measuring the curse of dimensionality and its effects on particle swarm optimization and differential evolution. Appl. Intell. 2015, 42(3): 514–526. Mauro GM, Hamdy M, Vanoli GP, Bianco N, Hensen JL. A new methodology for investigating the cost-optimality of energy retrofitting a building category. Energy Build. 2015, 107: 456–478. Lehmann EL, Romano JP, Testing Statistical Hypotheses, Springer New York, New York, NY, 2005, http://dx.doi.org/10.1007/0-387-27605-X. Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Hillsdale, NJ: Lawrence Earlbaum Associates. R. Core Team, R: A Language and Environment for Statistical Computing, Vienna, Austria (2016) https://www.R-project.org/. Wright JD. International Encyclopedia of the Social & Behavioral Sciences, 2nd Edition. Elsevier, 2015. T. Rockafellar, S. Uryasev, Optimization of conditional value-at-risk. J. Risk 2(3) (2000) 21–41.

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