A systematic approach for energy efficient building design factors optimization

Accepted Manuscript Title: A systematic approach for energy efficient building design factors optimization Author: Jun Xu Jin-Ho Kim Hiki Hong Junemo Koo PII: DOI: Reference:

S0378-7788(14)01073-1 http://dx.doi.org/doi:10.1016/j.enbuild.2014.12.022 ENB 5569

To appear in:

ENB

Received date: Revised date: Accepted date:

26-7-2014 27-9-2014 11-12-2014

Please cite this article as: J. Xu, J.-H. Kim, H. Hong, J. Koo, A systematic approach for energy efficient building design factors optimization, Energy and Buildings (2014), http://dx.doi.org/10.1016/j.enbuild.2014.12.022 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Experimental design was used to set relations between loads and design factors.

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Highlights

Pareto front lines were obtained for possible optimum points by genetic algorithm.

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System factors of building active parts affects passive part optimum design.

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Building active and passive parts should be optimized at once in a coupled manner.

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A systematic approach for energy efficient building design factors optimization

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Jun Xua, Jin-Ho Kimb, Hiki Honga, Junemo Kooa,* Department of Mechanical Engineering, Kyung Hee University, Yongin 446-701, South Korea

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Seoul 151-904, South Korea

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Construction Technology Division, Samsung C&T Corporation,

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Abstract

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We developed a systematic methodology to minimize the building heating and cooling loads

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using experimental design and non-sorting genetic algorithm to select optimal sets of building

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design factors. The analysis of experimental design provided a ranked list of important

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through less important factors design factors affecting the building heating and cooling loads.

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The factors related to window performance were found to be most significant ones. The non-

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sorting genetic algorithm offered piecewise linear pareto front lines where the optimum

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building design factor sets for minimum heating and cooling loads lie. The results of

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experimental design analysis were statistically verified against TRNSYS simulation results. It

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was found that the ratio of the efficiencies of heating and cooling systems affected the

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optimum passive building design, hence the active and passive parts of a building should be

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considered simultaneously in a coupled manner for the optimum design of net zero energy

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buildings.

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Keywords: Building envelope; optimization; experimental design; pareto front; system factor

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1. Introduction

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The building sector accounts for about 22% of total domestic energy consumption in Korea in

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2010, and it is expected that this share would grow continuously with the improvement of life

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standard and income increase. Korean government announced a plan that every new

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residential and non-residential building should meet the requirement of net-zero energy

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consumption for the approval of construction starting from the year 2025, i.e., the new

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buildings should be Net Zero Energy Buildings (NZEBs). Architects and construction

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engineers started to find ways to confront with the reinforced energy standards, and they

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realized that they should take the following steps to meet the goal (Cho et al., [1]). As the

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first step, the building heating and cooling loads should be minimized through the optimal

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selection of the passive building design factors. Secondly, high-efficiency active building

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heating and cooling systems should be selected to pair the new building design of low loads

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to yield low energy consumption. Finally, select the techno-economically affordable

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renewable energy sources to match the lowered energy demand of the optimized building.

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There are many research articles on the optimization of the building envelope design

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and the methodology for it. Caldas et al. [2] reported the development and application of a

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Genetic Algorithm (GA) based optimization tool for the placing and sizing of the windows in

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in an office building. Malkawi et al. [3] developed a decision support evolution model using

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GA as the evolution algorithm and Computational Fluid Dynamics (CFD) as the evaluation

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mechanism. Wright et al. [4] applied multi-objective GA to identify the optimum design

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considering the building energy cost and occupants discomfort. Wetter and Wright [5]

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compared the performance of optimization algorithms, and explained the coarse convergence

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criteria as the source of the discontinuities of the cost function for the building design and

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control problems. Wang et al. [6] used life cycle cost and life cycle environment impact as

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two cost functions in the optimization of building envelope design with building orientation,

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aspect ratio, window type, window-to-wall ratio, wall type, wall layer, roof type and the

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layers of roof as factors using GA. Jaffal et al. [7] applied Design of Experiments (DOE) to

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obtain simple polynomial functions of building design factors to predict building heating

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demand. Magnier and Haghighat [8] performed optimization study on building design and

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operation considering thermal comfort and energy consumption.

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In this study, a systematic statistical method was presented to determine the set of

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building design factors to minimize the building heating and cooling loads and energy

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consumptions using the fractional factorial design method, which used a subset of all possible

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combinations of design factors to ease the burden of exhaustive number of test runs using full

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factorial design while securing the prediction accuracy (refer to Montgomery et al. [9]), to

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consider all second order interactions. The dynamic simulations of building heating and

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cooling loads were performed, and the relations between the loads and the design factors

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were obtained statistically in a polynomial equation form, with which the pareto front of the

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optimum building design factor sets was determined. The relation between the optimum

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building envelope design sets and the selection of active building heating and cooling

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systems were discussed.

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2. Theory

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2.1 Baseline building model selection

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We reviewed the design drawings of 178 buildings in Korea together with researchers and

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architects in commercial companies, and it was analyzed that the buildings were about 20 to

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40 stories and 70,000 m2 of total floor area on average, and 1,400 m2 of average floor area.

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For the recently built office buildings, the total floor area tends to range between 40,000 and

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100,000 m2. The building core usually spans about 25 – 30% of total floor area, and its

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location can affect the window-to-wall ratio to vary building heating and cooling loads.

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In this study, the impacts of the alteration of building design factors on building

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heating and cooling loads were analyzed for a representative floor of a reference building of

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exterior core. Analyzing the energy consumptions of each floor in the existing buildings,

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about 85% of total energy consumption occurred in the floors of reference type. Although the

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loads varied with the use of each floor such as lobby, restaurant, and office, the reference

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floor was selected as the office floor since most part of the office building was used for the

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purpose, and the reference building was assumed as a collection of multiples of office floor.

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There were usually mechanical rooms in the top floor, so that no special investigation was

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performed for the top most floor. Due to the limitation of the design factor number allowed

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and the difficulty to set the levels of design factors for DOE, the common design factors

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considered in the previous studies such as floor area (FA), building orientation (OR), ceiling

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height (CH), aspect ratio (AR), plenum height (PH), window-to-wall ratio (WWR), wall

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insulation (WI), window insulation (WDI), Solar Heat Gain Coefficient (SHGC) and air

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leakage (ACR) were selected for the current study. Although the shading could affect

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seriously the loads, it was not considered in the current study due to the difficulty of handling

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it as an example. Table 1 represents the specifications of the reference building together with

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the considered building design factors and levels of alteration in Table 2. The reference levels

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of building design factors were selected to comply with the latest Korean national standard

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and government guideline. In case of window-to-wall ratio, there was a guideline for the

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design of energy efficient building from Korean government [12] not to exceed 60%.

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Considering the area of the exposing core wall, the upper level of the value was assigned as

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52%. The schedules for people, heating/cooling, and lighting were set according to ASHRAE

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90.1-2004 standard. For the equipment schedule, which was not provided in ASHRAE 90.1-

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2004 standard, the hourly operation schedule for large office in the commercial reference

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building models of national building stock [11] was used. Seoul data in TMY2 weather file

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format were used as the reference weather. The floor was decomposed into four neighboring

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thermal zones (Office 1, Office 2, Office 3, and Office 4) plus an air-conditioned core zone as

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shown in Fig. 1, and a plenum space over them.

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2.2 Experimental design

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Solving an engineering problem means to find accurate functional relations between outputs

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and factors of a product or a process, and use them to design and improve the products or to

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refine and optimize the processes. The outputs represent the dependent variables, heating and

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cooling loads of a building in this study, where factors mean independent design variables

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like FA, OR, CH, AR, PH, WWR, WI, WDI, SHGC, and ACR, and levels of a factor are the

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different values of the factor considered. In this study, we try to find the optimum sets of

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levels of effective passive building design factors to yield minimum building heating and

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cooling loads. In pursuit of the functional relations between building heating/cooling loads

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and design factors, multiple trial experiments were performed, and the results were analyzed.

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Experimental design, or DOE is a systematic methodology to prepare and analyze the trial

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runs using analysis of variance (ANOVA).

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A simple approach to find the functional relation is one factor at a time design (OFAT). With OFAT, the level of only one factor varies while levels of the other factors are

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fixed for a run. This method could not analyze the interaction between factors, which is the

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variation of impact of a factor with the alteration of levels of other factors, hence OFAT

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could not be used for optimization. Full factorial design is a method to investigate the effects

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of all combination of factors on the outputs. The advantage of the method over OFAT is that

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it can consider the interaction effects of two or more factors. The disadvantage of the model

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is the exponential growth of the required number of runs to do the analysis with the increase

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of factors to consider. For example, if the number of factors considered is two with two

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levels, the total number of runs for full factorial design is four, i.e., 22, which is manageable.

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It increases to 1024, i.e., 210, if the number of factors increases to 10, and it may be beyond

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the ability in terms of time and ability to perform the experiments and analyze the results.

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Generally, the interactions of more than two factors are statistically insignificant, if any, it is

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very hard to interpret physically, so that they are usually neglected. The sum of the main

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effects, i.e., the effect of factors, and the second order interaction effects, i.e., the interaction

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between two factors, comprises the functional relation between factors and outputs. Using the

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principles of experimental design, confounding and orthogonality, the higher order

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interaction terms could be confounded into the remaining main and interaction effects, and

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the number of runs required to analyze the function relation could be reduced. This method is

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called as fractional factorial design. In this study, the functional relations between the

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building heating/cooling loads and the building design factors are investigated by virtue of

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fractional factorial design. Once the sets of trials to analyze the relation are prepared by

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experimental design, the commercial dynamic building energy simulation program, TRNSYS

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[18], estimated the heating and cooling loads of the buildings with the design factors. The

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functional relation between the building heating/cooling loads and building design factors

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were analyzed, and the polynomial form of the relations shown in Eq. (1) were obtained

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using the DOE package in the open-source statistics software, R[19].

Y  c0   ci X i  i 1

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c

jk j 1,k  j 1,

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X j Xk

(1)

where X and Y represent the level or value of each design factor and the output value

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respectively, and c’s and N are the coefficients of terms in the polynomial and the number of

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the design factors considered. The letters i, j and k are dummy index. The second and third

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terms in Eq. (1) present the main and second order interaction effects of the design factors on

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the output.

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We avoided the overfitting problem by pooling the statistically insignificant terms to

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yield the highest prediction determination coefficient, or prediction R2. With the resultant

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polynomials, the optimum combinations of the building design factors to yield the minimum

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building heating/cooling loads were searched by adopting the multi-criterion optimization

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algorithm, Non Sorting Genetic Algorithm II (NSGA-2), provided by R.

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3. Results and discussion

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According to Montgomery et al. [9], designed experiments are employed sequentially. The

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first experiment with a complex system of many design variables is often a screening

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experiment designed to determine most important ones to reduce the number of experiments

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by dropping the insignificant factors. Then, subsequent refined experiments are performed to

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set the functional relations how the variables affect the objective functions. Finally, the

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optimization of design variables is performed to yield the optimum outputs from the derived

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functions.

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3.1 Analysis of screening experiment results

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As the first step, screening experiments were performed to have a ranked list of important

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through unimportant factors and to filter out ineffective design factors. In screening

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experiments, only main effects are considered, and all interaction effects are confounded and

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not analyzed. Table 3 shows the outputs and design factors considered in the screening

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experiment. The peak heating and cooling loads as well as the annual heating and cooling

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loads were considered as the outputs in the experiments. Stars and dots represent the

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significant levels of the design factors on the outputs in Table 3. It was found that the design

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factors related to the window performance and air leakage had significant impact on the

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building energy loads, whereas the building area aspect ratio was statistically analyzed to be

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ineffective. Afterwards the level of aspect ratio was fixed at that of the baseline model, and

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the effect of its alteration was not further studied. The number of factors became nine.

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3.2 Analysis of Fractional factorial experiments

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We paid special attention to have the resolution V (refer to NIST/SEMATECH e-Handbook

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of Statistical Methods [20] for details of the definition) for the design of our fractional

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factorial experiments, so that we could test and analyze the effects of all second order

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interaction effects. The fractional factor experiments needed dynamic building energy

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simulation for 128 sets of building designs, which is only a quarter of the number of trials

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needed for full fraction experiments. The results were analyzed statistically to obtain the

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functional relations between building cooling/heating loads and building design factors as

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well as to compare the importance of design factors on the loads. The final functional

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relations were determined after pooling the insignificant terms into error terms. Table 4 lists

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the coefficients in Eq. (1) for heating and cooling loads. Figure 2 compares the fittings of

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functional relations and dynamic simulation outcomes for the cases considered in the

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experimental design. The red lines in the figures represent the exact line. The fittings showed

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good match for both cooling (R2prediction=0.994) and heating (R2prediction=0.956) loads.

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Figures 3(a) and 4(a) present the comparison of the main effects of building design

factors on building heating and cooling loads. The horizontal axis represents the variation in

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levels of each design factor, and the vertical axis shows the loads. The numbers -1 and +1

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represent lower and upper levels of design factors. The steeper the slope is, the more

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significant the impact of the design factor is. WDI was found to be the most important design

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factor for heating load, which was followed by ACR, WWR, FA, and SHGC. It was found

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that SHGC, WDI, ACR, and WWR were the important design factors affecting cooling load.

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Overall, the design factors related to window performance and air leakage were analyzed to

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be significant.

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Figures 3(b) and 4(b) are interaction effects plots. The blanks in the plots mean that

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the interaction effects in the blanks are insignificant and pooled into error terms. The

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interaction effects are important when the slopes of two lines in each plot deviate more each

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other. The interaction effect between WDI and WWR is determined to be the most important

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one for the building heating load. The impact of the interaction effect between WDI and

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WWR on heating load is shown in the graphs (5, 3) and (3, 5) in Fig.3 (b). The four points in

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the (5, 3) and (3, 5) graphs are identical, where the impact of WDI shift on the heating load at

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different levels of WWR is shown in the graph (5, 3), whereas the impact of WWR shift at

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different WDI is in the graph (3, 5). The impact of WDI change is stronger at the upper level

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of WWR (=52%), and that of WWR is stronger at the upper level of WDI (=2.84 W/m2K).

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The lowest heating load is found at the lower levels of both WDI and WWR. The interaction

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effect between FA and WDI is another example of important one, which is shown in the

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graphs (3, 1) and (1, 3). The impact of window insulation alteration is more significant for the

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case of smaller floor area, since the portion of the surface area, or the heat transfer area

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covered by window increases with the decrease in floor area. The lowest heating load

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condition is observed at the upper level of FA (=2000 m2) and the lower level of WDI (=0.75

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W/m2K). For cooling load, the interaction between SHGC and WWR is the most important,

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and the one between FA and SHGC follows in significance. We could easily guess the

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physical meaning of some interaction effects, but it would be hard to estimate quantitatively

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the impact without using experimental design. For some other interaction effects, it was hard

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to interpret the direct relation between the two factors, where experimental design helped to

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estimate the impacts quantitatively.

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The half normal plots for the loads in Figs. 3(c) and 4(c) compare the significance of main and interaction effects together. The absolute effects are estimated to be double the

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coefficient of each effect. The impacts of interaction effects are comparable to those of main

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effects, and cannot be neglected in the following optimization process.

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3.3 Determination of pareto front for optimization

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Seeking the optimum building design to minimize the building heating and cooling loads is

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not easy, because some design factors affect in the opposite manner on each load. From Figs.

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3(a) and 4(a), the alteration to the lower level of WDI helps to decrease heating load, whereas

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it increases the cooling load. The higher SHGC decreases the heating load, while it increases

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the cooling load. The impact of each factor varies with the alteration of other factors, i.e.,

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interaction effect which makes even harder to select proper sets of design factors to minimize

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total energy loads. The main and interaction effects of all design factors on both heating and

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cooling loads should be considered together at once in determining the proper building

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design.

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The big blue triangle in Fig. 5 represents the coordinate of heating and cooling load of the baseline building estimated by TRNSYS simulation. The black circles show heating

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and cooling loads of 128 building designs considered in the fractional factorial experiments

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for the 9 factors. The pareto front, the green lines in Figs. 5(a) and (b), to minimize both

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heating and cooling loads of buildings simultaneously were determined using the functional

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relations from the experimental design by NSGA-2 in R. The dashed lines indicate 95%

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confidence intervals estimated from the regression analysis. The lines connecting nine vertex

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from A’ to J’ in Fig. 5(b) consist of the pareto front, where particular design factors vary in

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each segment while others are fixed. Table 5 shows the formula of linear regression analysis

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as well as the main varying design factors in each segment. In the segment AB, WI and PH

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levels increase resulted in the increase of heating load, while lowering cooling load. In the

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following segment, the level of CH increased. The change of effective factors divided the

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pareto front into different segments. The diamonds are the results of TRNSYS simulations for

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the inflection points (A-J) of the pareto front, and the segmented straight lines connecting

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them are the new pareto front from the dynamic simulations. The window performance

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related factors, i.e., WDI and SHGC, as well as OR, did not vary along the pareto front line

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fixed at 2.84 W/m2K, 0.2, ‘W’ respectively, which could be explained by the fact that the

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cooling load of the building is higher than the heating load. The variation of the changing

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design factors along the pareto front line is listed in Table 6.

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3.4 Consideration of directional design alteration

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Since the window performance related design factors have significant impact on the loads, we

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seek a possibility of further optimization by allowing the alteration of WDI, SHGC and

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WWR in different directions. The total number of factors increased to 18, because the three

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design factors were allowed to vary in four directions. New fractional factorial experiments

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were designed considering 512 different building designs to derive the functional relations

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between the loads and the 18 design factors, which is a huge save over the full factorial

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design because it would require 262,144 different building designs to simulate.

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The lists of coefficients for the functional relations are omitted because the relations

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contain 106 and 84 terms for heating and cooling loads respectively, and make too long lists.

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Figure 6 compares the fittings of the functional relations with the TRNSYS simulation results

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for the design sets in the experimental design. The prediction determination coefficients were

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0.972 for heating and 0.942 for cooling. Figure 7 shows the pareto front as well as validation

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against the TRNSYS simulation results. The regression formula and the variation of design

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factors are presented in Table 7, and the levels of design factors at the inflection points are

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listed in Table 8. OR, SHGC in all directions, and WWR of south and west sides were kept at

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lower level (=25%), while the WDI in all directions was at upper level (OR=‘W’, SHGC=0.2,

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WWR_S=WWR_W=25%, WDI=2.84 W/m2K) for all cases on the pareto front line. The

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predicted pareto front line and the TRNSYS simulation results for the inflection points

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showed good agreement within the statistical confidence interval. The line connecting the

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inflection points from the TRNSYS simulation was defined as the new pareto front line to use

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in the optimum selection of HVAC systems in the following section. Figure 8 compares the

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pareto fronts obtained from 9 and 18 factor design cases. There was no difference between

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the two pareto fronts statistically considering the large confidence intervals, while we sought

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improvement by allowing directional variation of window performance. Although the

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optimum condition for the WWR_N was found to be at upper level while WWR in other

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directions were at the lower level, the window area in the north surface was very small due to

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the existence of the core unit, which made insignificant improvement over the 9 factor case.

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3.5 Implication for HVAC systems

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Huang and Franconi [21] introduced the concept of system and plant factors to indicate the

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ratio between the building heating or cooling load and the actual energy consumed by the

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system and plant to meet the loads, and they reported that the factors could vary in quite wide

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ranges. They also informed that the typical values are around 0.44 for heating and 0.79 for

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cooling. The total heat and cooling energy consumption is the sum of energy consumption for

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heating and cooling as in Eq. (2),

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TEC  HEC  CEC

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(2)

where TEC, HEC and CEC stand for total, heating and cooling energy consumptions

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respectively. Considering the system factors for heating and cooling system, the total energy

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consumption could be rewritten as Eq. (3) in terms of heating and cooling loads.

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 cooling HL  heating

(3)

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Then the y-intercept represents the multiplication between cooling system factor and total

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energy consumption. For a given set of system factors, the total energy consumption could be

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minimized when the line of slope -cooling/heating touches the pareto front line with the

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minimum y-intercept. Figure 9 shows examples of determination of optimum building design

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for different system factor ratios. For typical values of heating and cooling system factors in

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Huang and Franconi [21], the optimum building design set is found to be A in Table 8. If the

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system factor ratios are 0.56 and 0.17, the optimum design set changes to C and H

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respectively. For different sets of heating and cooling systems of different system factor ratio,

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the optimum building design to minimize total energy consumption changes. Recalling the

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fact that the pareto front line is a piecewise linear straight line from the results of

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experimental design analysis, each inflection points of pareto front line works as the optimum

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building design sets according to different range of the system factor ratio. The relation

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between the range of system factor ratio and the optimum building design is shown in Table

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9. This result give us an important message that the optimum building design varies with the

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selection of heating and cooling systems, hence the active and passive parts of a building

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should be considered simultaneously in a coupled manner for the optimum design for net-

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zero energy buildings.

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4. Conclusions

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We developed a systematic methodology to minimize the building heating and cooling loads

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using experimental design and non-sorting genetic algorithm. The analysis of experimental

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design provided a ranked list of important through less important factors design factors

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affecting the building heating and cooling loads. The factors related to window performance

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were found to be most significant ones together with air leakage. The non-sorting genetic

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algorithm offered piecewise linear pareto front lines where the optimum building design of

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minimum heating and cooling loads sets lie. The results of experimental design analysis were

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statistically verified against TRNSYS simulation results. It was found that the ratio of the

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efficiencies of heating and cooling systems affected the optimum passive building design,

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hence the active and passive parts of a building should be considered simultaneously in a

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coupled manner for the optimum design for net zero energy buildings.

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design evolution: integrating genetic algorithms, CFD and visualization. Automation in

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algorithms for nonsmooth simulation-based optimization. Building and Environment 39

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(2004) 989-999. doi: 10.1016/j.buildenv.2004.01.022.

351

[6] W. Wang, R. Zmeureanu, and H. Rivard, Applying multi-objective genetic algorithms in

352

green building design optimization. Building and Environment 40 2005 1512-1525. doi:

353

10.1016/j.buildenv.2004.11.017.

354

[7] I. Jaffal, C. Inard and C. Ghiaus, Fast method to predict building heating demand based

355

on the design of experiments. Energy and Buildings, 41 (2009) 669-677.

Ac ce p

te

d

M

an

us

cr

ip t

336

Page 16 of 45

[8] L. Magnier and F. Haghighat, Multiobjective optimization of building design using

357

TRNSYS simulations, genetic algorithm, and Artificial Neural Network, Building and

358

Environment, 45 (2010) 739-746. doi: 10.1016/j.buildenv.2009.08.016.

359

[9] D. C. Montgomery, G. C. Runger and N. F. Hubele, Engineering statistics, third edition,

360

John Wiley & Sons, New York, 2003.

361

[10] S.A. Klein, TRNSYS 17-A TRaNsient SYstem Simulation Program, User Manual.

362

Volume 8: Weather Data. Solar Energy Laboratory, University of Wisconsin-Madison, URL

363

http://sel.me.wisc.edu/trnsys, 2010.

364

[11] U.S. Department of energy commercial reference building models of the national

365

building stock, NREL, 2011.

366

[12] Guideline of window system design for building energy saving, in Korean, Ministry of

367

Land, Transport and Maritime Affairs, 2012.

368

[13] ASHRAE Standard-Energy standard for buildings except low-rise residential buildings,

369

ASHRAE Inc, 2007, Atlanta.

370

[14] U.S. Department of energy infiltration modeling guidelines for commercial building

371

energy analysis, PNNL, 2009.

372

[15] Design guideline for the energy saving of public buildings in innovation city, in Korean,

373

Ministry of Land, Transport and Maritime Affairs, 2010.

374

[16] Explanation of energy saving design standard in buildings, in Korean, Korea Energy

375

Management Corporation, 2011.

376

[17] ANSI/ASHRAE/IESNA Standard -90.1 User’s manual, ASHRAE Inc, 2004, Atlanta.

Ac ce p

te

d

M

an

us

cr

ip t

356

Page 17 of 45

[18] S.A. Klein, TRNSYS 17-A Transient System Simulation Program, Solar Energy

378

Laboratory, University of Wisconsin- Madison, URL http://sel.me.wisc.edu/trnsys, 2010.

379

[19] R Core Team, R: A language and environment for statistical computing. R Foundation

380

for Statistical Computing, Vienna, Austria. URL http://www.R-project.org/, 2014.

381

[20] NIST/SEMATECH e-Handbook of Statistical Methods,

382

http://www.itl.nist.gov/div898/handbook/, accessed on July 1, 2014.

383

[21] Y. J. Huang and E. Franconi, Commercial heating and cooling loads component

384

analysis. Berkeley, CA: Lawrence Berkeley National Laboratory, 1999.

an

us

cr

ip t

377

Ac ce p

te

d

M

385

Page 18 of 45

385

Table 1. Summary of reference building Sub-categories

Location

Value

References

Seoul (Climate Zone 4) KR-Seoul-471080.tm2

[10]

1444

Air conditioned area (m2)

1019

Floor height (m)

3.9

an

Size

Floor area (m2)

Ceiling height (m)

[11]

40

[12]

0.365

[13]

2.84

[13]

0.4

[13]

Infiltration (ACH)

0.3

[14]

People(people/ m2)

0.1

[15]

Lighting(W/m2)

12

[13]

Equipment(W/m2)

16

[15]

Heating (oC)

26

[16]

Cooling (oC)

20

[16]

d

Window

te

SHGC

Internal heat gain

Set temperature

M

External wall (W/m2K) U-value(W/m2K)

Tightness

[11]

2.7

Window-to-wall ratio (%) Wall U-value

cr

Office

us

Use

ip t

Categories

Ac ce p

386

People

[17]

Heating/Cooling

[17]

Lighting

[17]

Equipment

[11]

Schedule

Page 19 of 45

387 388

Factor

Symbol

Level Low (-1)

FA

1000

Aspect ratio (-)

AR

1

Orientation

OR

South

Window-to-wall ratio (%)

WWR

Ceiling height (m)

CH

Plenum height (m)

PH

Wall insulation (W/m2K)

WI

SHGC (-)

390 391 392 393

an

2 West

2.4

2.9

0.8

1.2

0.150

0.365 [13]

0.75

2.84

SHGC

0.2

0.7

ACR

0.1

0.3 [14]

M

52 [12]

d

Ac ce p

Air leakage (ACH)

2000

25

WDI

te

Window insulation (W/m2K)

High (+1)

us

Floor area (m2)

ip t

Table 2. List of factors and their levels

cr

389

Page 20 of 45

393

394

Heating load

◦

Cooling load

*

Peak heating load

***

AR

OR

◦

**

*

WI

*

**

WDI SHGC ACR

◦

◦

**

*

**

***

***

***

***

**

***

***

◦

O

O

***

O

O

O

O

O

O

Ac ce p

399

◦

PH

d O

398

*

**

te

Significant factors

CH

***

Peak Cooling load

WWR

cr

FA

us

Response

an

397

Table 3. Determination of significant design factors from the 20 runs screening DOE (Significance codes: ‘0’ *** ‘0.001’ ** ‘0.01’ * ‘0.05’ ◦ ‘0.1’)

M

396

ip t

395

Page 21 of 45

ip t cr

Table 4. The coefficients for the building heating and cooling loads in Eq. (1) for the fractional factorial design for 9 design factors Heating load Coefficients

Factors

Coefficients

Intercept

6.732

PH:WDI

1.508

FA:WDI

-1.894

WI:ACR

WDI:WWR

1.042

SHGC

Cooling load

Factors

Coefficients

Factors

Intercept

48.210

WWR:WI

7.716

FA:OR

4.087

WWR

-8.657

M an

Factors

us

400

27.184

FA:SHGC

14.543

WDI:SHGC

-8.224 3.0142

Coefficients

WDI:ACR

9.830

FA:ACR

-5.177

WDI:WWR

-4.889

SHGC:ACR

WDI:SHGC

-2.263

CH:WWR

7.280

SHGC:WWR

5.184

WWR:ACR

6.215

-8.487

WDI:WI

2.178

FA:WWR

--5.401

PH:WWR

2.992

11.320

FA:WDI

6.725

PH:WDI

-3.790

ed

FA:WWR

-3.381

-6.508

PH:ACR

CH:WDI

1.860

WWR

-1.911

CH:SHGC

5.218

FA:WI

1.467

FA:CH

-1.527

SHGC:OR

-2.296

FA:CH

-5.850

-3.469

PH:SHGC

4.703

ACR

SHGC:WWR

-1.395

ce pt

WDI

CH:ACR

18.740

FA:WI

ACR

-58.410

CH:SHGC

FA SHGC:ACR FA:SHGC

3.053

Ac

WWR:ACR

1.025

-15.750

2.761

PH:WWR CH FA:PH

-2.756

6.299 -4.277

-1.155

WWR:OR WDI:ACR FA WDI CH:WWR

-2.826 1.715 4.313 -2.071 4.227

CH:ACR

-5.688

SHGC

-5.825

CH:WDI

-9.222 -2.614

WI

-7.743

CH

-1.729

OR

1.437

WDI:WI

4.842

FA:PH

-4.563

401

Page 22 of 45

401

Table 5. Classification of zones on the pareto front line for 9 factor experimental design

Wall Insulation Plenum

BC

(CL)=37.2-0.909(HL)

Ceiling Height

CD

(CL)=36.7-0.588(HL)

Floor Area Ceiling Height Plenum Wall Insulation Air leakage

DE

(CL)=33.8-0.469(HL)

Wall Insulation

EF

(CL)=32.8-0.354(HL)

Ceiling Height

FG

(CL)=31.4-0.158(HL)

GH

(CL)=30.9-0.004(HL)

404

ip t

(CL)=38.0-14.190(HL)

cr

AB

HJ

403

Main varying factor

us

Regression function

d

M

an

Zone

Plenum Height

te

Ac ce p

402

(CL)=30.3-0.003(HL)

Window-to-wall ratio Window-to-wall ratio

Page 23 of 45

404 405

Table 6. Model prediction of building heating and cooling loads variation with design change

406

along the pareto front line for 9 factor experimental design

[kWh/m2yr] [kWh/m2yr]

ACR

CH

PH

WWR

[m2]

[m]

[m]

[%]

[W/m2K]

[ACH]

0.274

0.1

38.11

2000

2.5

0.9

25

B

0.03

37.31

2000

2.4

1.2

25

0.360

0.1

C

0.98

36.57

2000

2.8

1.1

25

0.360

0.1

D

6.37

33.33

1000

2.4

0.8

25

0.168

0.3

E

8.75

32.24

1000

2.4

0.8

25

0.360

0.3

F

12.70

30.82

1000

2.9

0.8

25

0.360

0.3

G

14.90

30.48

1000

2.9

1.2

25

0.360

0.3

H

20.88

30.45

1000

2.9

1.2

41

0.360

0.3

J

24.23

30.44

1000

2.9

1.2

50

0.360

0.3

Ac ce p

te

d

us

cr

0.00

M

A

407 408

WI

FA

an

Points

CL

ip t

HL

Page 24 of 45

408

Table 7. Classification of zones on the pareto front line for 18 factor experimental design Regression function

Main varying factor

AB

(CL)=37.7-0.796 (HL)

Floor Area

BC

(CL)=36.3-0.533(HL)

Floor Area Ceiling Height Wall Insulation Air leakage

CD

(CL)=33.4-0.413(HL)

Air leakage Wall Insulation

DE

(CL)=32.7-0.180(HL)

Ceiling Height

EF

(CL)=32.5-0.351(HL)

Window-to-wall ratio (N)

FG

(CL)=32.3-0.296(HL)

Ceiling Height

GH

(CL)=31.4-0.209(HL)

M

an

us

cr

ip t

Zone

Ac ce p

HJ

410 411 412 413

te

d

409

(CL)=30.9-0.010(HL)

Plenum Height

Window-to-wall ratio (E)

414 415 416 417

Page 25 of 45

418 419 420

Table 8. Model prediction of building heating and cooling loads variation with design change

422

along the pareto front line for 18 factor experimental design

423 HL

CL

PH

WWR_N

WI

ACR

[%]

[W/m K]

[ACH]

43

25

0.36

0.1

47

25

0.36

0.1

50

25

0.15

0.3

0.8

51

0.36

0.3

0.8

52

26

0.36

0.3

WWR_E

[kWh/m yr]

[m ]

[m]

[m]

[%]

A

0.00

37.77

2000

2.4

0.8

B

2.20

35.71

1000

2.4

0.8

C

6.60

33.37

2000

2.8

0.8

D

9.73

32.09

1000

2.4

E

10.06

32.01

1000

2.5

F

10.89

31.72

1000

G

13.97

30.80

1000

H

16.41

30.30

1000

J

18.94

30.06

1000

2

25

2.6

0.8

47

25

0.36

0.3

2.9

0.8

52

26

0.36

0.3

2.9

1.2

51

25

0.36

0.3

2.9

1.2

52

48

0.36

0.3

te

d

M

an

[kWh/m yr]

2

Ac ce p

425

CH

2

2

424

FA

us

Points

cr

ip t

421

Page 26 of 45

425 426

Table 9. The relation between system factor ratio range and optimum building design set Optimum building design set

cooling/heating  0.779

A

0.764 cooling/heating  0.779

B

us

0.202  cooling/heating  0.764

C

0.182  cooling/heating  0.202

an

G

0.163  cooling/heating  0.182

M

cooling/heating0.163

J

te Ac ce p

429

H

d

428

ip t

System factor ratio (cooling/heating)

cr

427

Page 27 of 45

429

List of figures

431

Figure 1

Floor area schematics of the reference building

432

Figure 2

Comparison of the regression equation predictions with dynamic simulation results for 9 factor experimental design: (a) heating and (b) cooling load

Figure 3

Figure 4

(a) Main effects, (b) interaction effects and (c) half normal plots for building

Figure 5

an

cooling load from the fractional factorial experiments of 9 factor case

437 438

us

heating load from the fractional factorial experiments of 9 factor case

435 436

(a) Main effects, (b) interaction effects and (c) half normal plots for building

cr

433 434

ip t

430

Comparison of building heating and cooling loads of the building designs on the pareto front line against those of the baseline design and DOE design

440

points for 9 factor case: (a) comparison of the heating and cooling loads of

441

DOE design points and pareto front, and (b) enlarged view for the pareto

442

front and verification of the experimental design predictions against

443

TRNSYS simulation results

d

Figure 6

448 449 450 451

Ac ce p

447

Comparison of the regression equation predictions with dynamic simulation results for 18 factor experimental design: (a) heating and (b) cooling loads

445 446

te

444

M

439

Figure 7

Comparison of building heating and cooling loads of the building designs on the pareto front line against those of the baseline design and DOE design points for 18 factor case: (a) comparison of the heating and cooling loads of DOE design points and pareto front, and (b) enlarged view for the pareto front and verification of the experimental design predictions against TRNSYS simulation results

452

Figure 8

Comparison of the pareto front lines between 9 and 18 factor DOE analyses

453

Figure 9

Examples of determination of optimum building design sets for different

454

system factor ratios cooling/heating: (a) 0.17, (b) 0.56 and (c) 1.80

455 456

Page 28 of 45

ip t cr us M

an 458

d

Fig. 1

te

457

251658240

Ac ce p

456

Page 29 of 45

20

ip t

data exact line

0

M

5

an

10

us

15

cr

2

Modelpredictheatingload[kWh/m yr]

25

458

5

10

15

20

25

d

0

2

461

Ac ce p

460

te

Trnsysheatingload[kWh/m yr]

459

Fig. 2(a)

Page 30 of 45

ip t

55 30

35

40

45

M

30

35

an

40

us

45

cr

50

2

Modelpredictcoolingload[kWh/m yr]

60

data exact line

50

55

60

2

Trnsyscoolingload[kWh/m yr]

te

464

Fig. 2(b)

Ac ce p

463

d

462

Page 31 of 45

CH

WDI

SHGC

WWR

ACR

-1

467

1

251658240

-1

1

-1

1

-1

1

-1

1

d

Level

te

466

-1

Fig. 3(a)

Ac ce p

465

1

M

1

2

an

3

4

us

5

cr

2

Heatingload[kWh/m yr]

6

ip t

7

8

FA

Page 32 of 45

12 8

-1 4

FA

12

0

1

8

ip t

-1 4

CH

12

cr

8

-1 4

WDI

8

-1 4

SHGC

0

1

us

12

0

1

12

2

Heatingload[kWh/m yr]

0

1

8

an

-1

4

WWR

470

1

-1

1

-1

1

-1

ACR 1

1

-1

1

-1

1

Level

d

-1

te

469

251658240

-1

Fig. 3 (b)

Ac ce p

468

M

0

4

8

12

0

1

Page 33 of 45

WDI

2.0

*

1.5

*

WWR

WDI:WWR

FA

cr

*

1.0

* WDI:ACR * FA:WDI * SHGC

us

* CH WDI:SHGC * FA:WWR *CH:WDI

* * SHGC:WWR CH:ACR *WWR:ACR

0

1

an

*

* SHGC:ACR * FA:SHGC * WDI:PH * ACR:WI * FA:ACR * CH:WWR * WDI:WI * ACR:PH * FA:CH * FA:WI * CH:SHGC ** WWR:PH FA:PH

2

M

0.0

0.5

half-normal scores

*

ACR

ip t

*

3

4

5

6

absolute effects

473

d te

472

251658240

Fig. 3(c)

Ac ce p

471

Page 34 of 45

CH

WDI

SHGC

WWR

WI

ACR

OR

ip t

46 -1

476

1

-1

251658240

1

-1

1

-1

1

-1

1

-1

1

-1

1

d

Level

te

475

-1

Fig. 4 (a)

Ac ce p

474

1

M

36

38

an

40

42

us

44

cr

2

Coolingload[kWh/m yr]

48

50

FA

Page 35 of 45

30

45

-1 FA 1

30

45

-1 WDI 1

cr

2

Coolingload[kWh/m yr]

ip t

30

45

-1 CH 1

30

45

-1 SHGC 1

30

an

45

-1 WI 1

-1

1

-1

1

-1

1

-1

1

-1

1

-1

1

-1

1

d

Level

te

479

1

-1 OR 1

Fig. 4(b)

Ac ce p

478

-1

M

45

30

45

-1 ACR 1

30

477

us

30

45

-1 WWR 1

Page 36 of 45

2.5

*

WDI

ACR

WWR SHGC:WWR

cr

1.5

* * *

FA:SHGC

FA WDI:SHGC * WDI:WWR *WIOR * FA:WWR * FA:WDI * CH:SHGC * SHGC:OR * SHGC:PH * * WWR:OR * WDI:ACR * CH:WWR * CH:ACR * WWR:WI FA:OR * SHGC:ACR * WWR:ACR * WWR:PH * WDI:PH ** FA:WI * CH FA:CH CH:WDI ** WDI:WI ** FA:PH

*

2

us an

0.0

0

4

M

1.0

*

0.5

half-normal scores

*

SHGC

ip t

2.0

*

6

8

10

12

14

te

481

251658240

Fig. 4(c)

Ac ce p

480

d

absolute effects

Page 37 of 45

65

ip t

55

5

10

15

M

0

an

30

35

40

us

45

cr

50

2

Coolingload[kWh/m yr]

60

baseline DOE design points(9 factors) Trnsys(9 factors) Pareto-front(9 factors)

20

25

30

2

Heatingload[kWh/m yr]

d

484

Fig. 5(a)

te

483

251658240

Ac ce p

482

Page 38 of 45

38

A' A Trnsys(9 factors) Pareto-front(9 factors) Confidence interval(9 factors)

B' B

34

cr

2

Coolingload[kWh/m yr]

36

ip t

C'C

D

us

D' E

32

E'

G

F'

30

G'

5

10

15

H'

M

0

an

F

20

HJ'

25

J

30

2

Heatingload[kWh/m yr]

d

Fig. 5(b)

te

486

251658240

Ac ce p

485

Page 39 of 45

ip t

15 0

M

0

an

5

us

10

cr

2

Modelpredictheatingload[kWh/m yr]

data exact line

5

10

15

20

2

Trnsysheatingload[kWh/m yr]

d

Fig. 6(a)

te

488

251658240

Ac ce p

487

Page 40 of 45

60

ip t 35

40

M

35

an

40

us

45

cr

50

2

Modelpredictcoolingload[kWh/m yr]

55

data exact line

45

50

55

2

Trnsyscoolingload[kWh/m yr]

491 492 493 494 495 496 497 498

d

Fig. 6(b)

te

490

251658240

Ac ce p

489

Page 41 of 45

cr

ip t

60 50

us

45

an

40

0

M

30

35

2

Coolingload[kWh/m yr]

55

baseline DOE design points(18 factors) Trnsys(18 factors) Pareto-front(18 factors)

5

10

15

20

2

Heatingload[kWh/m yr]

d

Fig. 7(a)

te

500

251658240

Ac ce p

499

Page 42 of 45

ip t

Trnsys(18 factors) Pareto-front(18 factors) Confidence interval(18 factors) B

36

38

A' A

34

cr

2

Coolingload[kWh/m yr]

B'

32

D

E F D'E' F'

an

G

us

C C'

H

G'

0

M

30

H'

5

10

15

J

J'

20

2

503

te

502

251658240

Fig. 7(b)

Ac ce p

501

d

Heatingload[kWh/m yr]

Page 43 of 45

28

an

30

ip t

us

32

34

cr

2

Coolingload[kWh/m yr]

36

38

Trnsys(9 factors) Trnsys(18 factors) Pareto-front(9 factors) Pareto-front(18 factors) Confidence interval(9 factors) Confidence interval(18 factors)

5

10

15

M

0

20

25

2

Heatingload[kWh/m yr]

507

d

506

Fig. 8

te

505

251658240

Ac ce p

504

Page 44 of 45

A

ip t

36

B

34

cr

2

Coolingload[kWh/m yr]

Inflection points(18 factors) Pareto-front(18 factors) Case a(18 factors) Case b(18 factors) Case c(18 factors)

32

D

E F

us

C

30

an

G

5

10

M

0

H J 15

20

2

Heatingload[kWh/m yr]

510 511 512

d

Fig. 9

te

509

251658240

Ac ce p

508

Page 45 of 45