Linking BIM and Design of Experiments to balance architectural and technical design factors for energy performance

Automation in Construction 86 (2018) 33–43

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Automation in Construction journal homepage: www.elsevier.com/locate/autcon

Linking BIM and Design of Experiments to balance architectural and technical design factors for energy performance

MARK

⁎

Arno Schluetera, , Philipp Geyerb a b

Architecture and Building Systems, Institute of Technology in Architecture (ITA), ETH Zürich, Switzerland Architectural Engineering Division, Faculty of Engineering Science, KU Leuven, Belgium

A R T I C L E I N F O

A B S T R A C T

Keywords: Design of Experiments (DoE) Building information modeling (BIM) Dynamic simulation Distributed simulation Building retrofit Retrofit design strategies

To transform the existing energy systems towards renewable energy sources, buildings need to use less energy, use energy more efficiently and harness local renewable energy sources. For the design of energy-efficient buildings, building energy simulation of varying sophistication is commonly employed. Types of simulations range from simple, static calculations to sophisticated dynamic simulation. Especially for building retrofit many assumptions on construction, material etc. have to be taken, which increases the uncertainty of simulation results. In conjunction with simulation, methods of Building Performance Optimization are increasingly employed. They are able to identify best performing designs however do not provide insights on the mechanisms and interdependencies of the different design factors, which are most valuable to make informed design decisions. We present a methodology that aims to provide a better understanding and create knowledge about the influence and interactions of different architectural and technical design factors on building energy performance of a specific design task. For this purpose, we introduce Design of Experiments (DoE) in an integrated design workflow using the Design Performance Viewer (DPV) toolset, combining Building Information Modeling (BIM), distributed dynamic simulation and statistical analysis of the extensive simulation results. The experiments created using the methodology allow to identify the strength of effects and interactions of different design factors on selected performance indicators. We apply the methodology on an office retrofit case, introducing a factor scatterplot for result visualization, development and comparison of retrofit strategies. We further evaluate its potential to identify high performing strategies while balancing architectural and technical factors and their impact on energy performance.

1. Introduction Worldwide, buildings consume 32% of the global final energy and 25% greenhouse gas emissions (GHG) [1]. To transform the existing energy systems towards renewable energy sources and thus to meet the ambitious emission goals set by many countries and organizations such as the European Union [2], future buildings will need to use less energy, use energy more efficiently and harness local renewable energy sources. Compared to the existing building stock, the annual rate of new and retrofitted buildings in Europe, however, is low. In Germany and Switzerland, for example, retrofit rates stagnate at a low level of around 1–2% [3]. Studies claim that this is due to insufficient information, low cost-effectiveness of measures and regulatory constraints that make it challenging to find the appropriate solution [4]. To identify effective retrofit measures, building energy simulation is employed, sometimes during design, most often however afterwards in order to comply to energy codes. Such simulations range from norm-

based steady-state calculations to sophisticated dynamic building energy simulations. Due to missing information about the building itself, they are often based on a variety of assumptions, simplifications and educated guesses. Whereas simulation data can easily be produced, knowledge and understanding about the effects and interactions of different parameters is often lacking. The objective of this work is therefore to develop a methodology and computational toolset to identify the influence and interactions of architectural and technical design factors on building energy performance and thus to derive strategic knowledge for the designer rather than just numerical results. For this purpose, we link Building Information Modeling (BIM), which is used to create and store the necessary data and information, and Design of Experiments (DoE), an established and successful methodology used in engineering disciplines and industry. DoE is a method that uses simulation experiments and applies statistical analysis to obtain information on effects and interactions between different factors, aiming at the least number of experiments necessary. To embed DoE

⁎⁎

Corresponding author at: Stefano-Franscini Platz 1, CH 8093 Zürich, Switzerland. E-mail address: [email protected] (A. Schlueter).

https://doi.org/10.1016/j.autcon.2017.10.021 Received 10 January 2017; Received in revised form 29 September 2017; Accepted 25 October 2017 0926-5805/ © 2017 Elsevier B.V. All rights reserved.

Automation in Construction 86 (2018) 33–43

A. Schlueter, P. Geyer

optimization approaches which provide results optimized for certain criteria, however little insight or understanding about the mechanisms behind.

into the design process, we employ the Design Performance Viewer (DPV), a toolset that allows establishing a workflow from a Building Information Model (BIM) to parametric simulation, results collection and statistical analysis. The paper is structured as follows: First, we provide an overview on existing approaches of parametric design and environmental simulation for sustainable building design. Next, we introduce DoE as a method and its previous application for building performance. In Section 3 we outline the integration of DoE into the Design Performance Viewer toolset to establish a DoE workflow based on a BIM. This workflow is exemplified in Section 4 using an office retrofit case study, identifying a range high-performing yet unique retrofit strategies. Section 5 summarizes and discusses the methodology whereas Section 6 concludes and provides an outlook on future developments.

2.2. Design of Experiments Design of Experiments (DoE) has been established and successfully applied in various fields and industries, such as product design and development [15], chemical [16] and software engineering [17]. A number of comprehensive textbooks exist [18–20]; therefore the general methodology is outlined here only in brief. As part of the application, we exemplify each methodological step for the case study. The general concept of DoE is to create a series of real or simulated experiments on a system or system model under observation. In each experiment, one or multiple of its design parameters are changed and the impact on the system or model behavior is evaluated. Which parameters are changed and how they are changed is defined using an experiment plan. The aim is to obtain as much information as possible using the least amount of experiment runs, as experiments are costly in terms of physical setups or computational effort. The behavior of the system based on the parameter changes is observed using a set of outputs. In the context of DoE, the outputs can be referred to as the ‘performance indicators’, the design parameters as the ‘factors’ and their value settings as factor ‘levels’. To analyze the impact of each factor on the system and its interactions with other factors, every factor combination would need to be tested and therefore would require an experiment. Due to the large amount of possible combinations this is an effort often infeasible in terms of time and costs. DoE offers a range of methods - referred to as experiment plans or design tables - to reduce the amount of necessary experiment runs to achieve as precise information as possible with the smallest number of experiments. The type of plan used depends on the experiment's objective. Finding the optimal design table, i.e. the least amount of experiments that is necessary to depict the systems behavior correctly has been subject to intense research. Using a set of statistical evaluation methods on the resulting experiment data, the impact, effect and interactions of the factors in relation to a chosen performance indicator is evaluated. The results of the experiments can be used to formulate a mathematical surrogate model, also called a metamodel in engineering disciplines [26,27].

2. Background The field of parametric building modeling and simulation and related methods of data analysis and optimization constitutes the relevant background of this paper. Additionally, we briefly review the method of Design of Experiments and its application to buildings. 2.1. Building energy performance optimization A large body of research exists that couples parametric building modeling, environmental simulation and optimization. The study of Gero et al. [5] and the Building Design Advisor [6] represent early, integrated design approaches combining multiple analysis and visualization tools. Caldas and Norford [7] utilize genetic algorithms to search for optimized environmental design solutions, focusing on façade configurations. Janssen [8] explores balancing heat losses of the envelope and potential heat gains through openings using evolutionary approaches. Turrin et al. [9] use genetic algorithms for the design of passive solar roofs. Heiselberg et al. [10] apply sensitivity analysis to identify the most important design parameters of a sustainable building design. Related to cooling in office buildings, Breesch and Janssens [11] utilize uncertainty and sensitivity analysis to predict the performance of free cooling using building energy simulation. More recently, multiobjective optimization techniques increasingly assist in performancedriven building design already at the conceptual stage [12,13], addressing energy, exergy, lifecycle cost and other domains. A study by Attia et al., which also provides an extensive review on building performance optimization, highlights a consensus on the general usefulness of building performance optimization tools to achieve energy efficient buildings [14]. The study also mentions shortcomings as perceived by experts in the field such as uncertainty of simulation model input, low trust in results and low interoperability for exchange between different applications. In practical application, a range of available tools link parametric building modeling to environmental analysis, such as Autodesk Vasari or Design Builder, which uses EnergyPlus as simulation engine. Additionally, a range of plugins for similar purposes exist, such as DIVA, Honeybee or Ladybug for Rhinoceros. Both tools and plugins mainly focus on building geometry, materials and resulting heating/ cooling load calculations, which are delivered as numerical results. Rather than to base design decisions on numerical simulation and optimization results only, we advocate to use a performance-driven design workflow including DoE as a method to obtain an understanding of the nature and impact of design parameters, their interdependencies and trends, and thus to be able to build knowledge within a specific design context. Such a workflow can be automated; the interpretation however requires the judgement of the expert. The focus on knowledge rather than data constitutes the main difference to the aforementioned

2.2.1. Application for building energy performance DoE has only rarely been applied in a building context. Chlela et al. [21] and Jaffal et al. [22] present the application of the DoE methodology for selected design parameters of new low energy buildings, targeting thermal performance. The focus of their work is on the exploration of various existing design tables that reduce the amount of simulation runs to derive a polynomial metamodel. Describing the mean and maximum error of the resulting metamodels as the main outcome and key evaluation criterion, the work focuses rather on the technical aspects of applying a DoE methodology for a new building design in general than on its qualitative outcome and applicability for retrofit designs. More recently, DoE in combination with dynamic energy simulation has been applied to identify factors for cooling loads on a residential building [23], and similarly, for deriving a metamodel for heating and cooling of low energy housing in Morocco [24]. For the simulation of new buildings, the selection of factors for the experiments is only restricted by the simulation capabilities whereas for building retrofit, the choice of factors and factor levels is constrained by the condition of the existing building and the available design options. As it is not possible to alter factors such as location, orientation or basic construction, the balancing of the remaining factors is even more important.

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Fig. 1. The design performance viewer toolset.

debugging and a testing harness for automated validation of geometric design alternatives were developed and included. To integrate DoE as a methodology, the toolset was extended by an automated zoning algorithm for fast identification of thermal zone affiliations, parallel computing capabilities for multiple simulations and a connection to the ‘R’ software package [33] for simulation results data analysis and results visualization.

The aforementioned examples address the design of new buildings and focus on the technical application of DoE for building simulation. This work aims to move beyond in order to advocate the use DoE in a performance-driven design workflow for creating understanding and knowledge about the impact of retrofit measures, their interactions and the identification of optimal retrofit strategies.

3. Linking BIM and Design of Experiments using the DPV toolset 3.1. DoE design process We use and extend the Design Performance Viewer (DPV) toolset (Fig. 1) for performance-driven building design under development since 2008. It facilitates an integrated and bi-directional link between a Building Information Model, using Autodesk Revit as BIM editor, and

The methodology proposed can be structured in several procedural steps (Fig. 2) that begin with the establishment of a Building Information Model (BIM) as the design database. In terms of geometry, the model contains all structural elements of the envelope and interior walls and floors. Also included is the volume and cubature of the neighboring buildings that may cast shadows onto the building. For material and construction experiments, an external database can be accessed, containing a variety of materials and construction prototypes. Internal gains for people, lighting and electrical appliances can be scheduled and set according to Swiss Norm SIA 2024 [34]. To allow for a high resolution for performance-driven design using DoE it is necessary to be able to distinguish between different thermal zones to run zone-specific dynamic simulations. We have developed a thermal zoning algorithm to automatically extract thermal zones, their boundaries such as walls, windows and roofs and their neighboring relation to other zones. It uses a zone box, which is a three-dimensional object that is placed inside the building geometry in the BIM modeler and represents a zone or part of a zone. Rays are cast from the center of the zone box in all directions and update the zone affiliation of the first surface hit by each ray. A building surface's zone affiliation is stored as an attribute in the BIM which also can be manually changed. A building surface has at least one zone affiliation – the default zone. To ensure correct simulation, special care has to be taken to ensure that each building surface is affiliated with at most two zones before serializing the internal model to an EnergyPlus IDF file for simulation. This requires splitting up surfaces by their zone affiliations, into sub-surfaces with at most two affiliated zones.

• Energy/exergy simulation and analysis [25], • Dynamic building energy simulation using EnergyPlus [26], • Multi-scale building and urban energy co-simulation linking EnergyPlus and CitySim [27], • Scientific workflow management for defining custom simulation workflows [28], and Roundtrip data exchange between a Building Information Model •

and a Building Energy Model using a service oriented architecture [29].

The DPV addresses designers and engineers that are accustomed to software tools for modeling and simulation as part of the design process. Case studies have shown its applicability in a performance-driven design process [26,30,31]. A key feature of the toolkit is, unlike many existing tools, the bi-directionality from design model to simulation/ visualization and back, rendering the usual export-import processes between tools, which are prone to data loss and errors, unnecessary. One of the core components of the DPV which has gained popularity among researchers and developers in the field is the Revit Python Shell (RPS) [32]. To keep a fast and intuitive workflow, a variety of techniques were developed such as knowledge-based defaults, material and construction databases and others. To aid the designer in validating the model for correct simulation input, a semantic viewer for visual 35

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runs’ feature. This allows generating the different simulations according to the chosen experiment setup. 4. Experiment methodology and execution In the following section, we describe the methodology and exemplify its application using the DPV toolset on a case study of a recently retrofitted office building. 4.1. Case study building Finished in 1971, the building belongs to an original part of a campus ensemble worthy of preserving (Fig. 3). Maintaining its exterior appearance was stated as one of the key design objectives, therefore the possible retrofit options were limited and had to be negotiated well. As a case it is typical for many office buildings built in the 60′s and 70′s all over Europe with high energy consumption that need to be retrofitted. For the simulation a long-term averaged weather data file of Zurich was used. The average annual air temperature is 7.9 °C. During the winter months of December, January and February the average monthly air temperature is 0 °C, 1.0 °C and 0.2 °C, respectively. The freestanding office building contains 2226 m2 of office space on four levels, totaling in 8200 m3 of heated volume. For simulation and parametric control, the volume is partitioned into 22 thermal zones that are either corner zones facing two directions, intermediate zones facing one direction or core zones that have no boundary to the outside. All internal loads are set and scheduled according to typical office occupation and operation schedules provided by the Swiss Norm SIA. The floor area per person is 20m2, the lighting load installed is 8 W/m2, and the load by appliances is 2.15 W/m2. The building structure consists of a concrete core and slabs that are supported by concrete columns, providing a large amount of thermal mass. The façade, which is still in its original condition, is made of aluminum sandwich panels filled with thin insulation. The original glazing has been replaced once in 1989 by double glazing. The window-to-wall ratio over the entire building is approximately 50%. The building systems for heating, cooling and ventilation were idealized for load calculation. Measured heating end use energy data was used to validate the simulation model. Data was available from a period of six years before the retrofit and one full year after. Both the measurement and the simulation results were normalized using averaged 10-year heating degree days from 2001 to 2010 for Zurich, Switzerland [36]. For the base case, a normalized average annual building heating end use energy of 72.7 kWh/m2a was measured over a period of six years before the retrofit. The normalized heating end use energy of the base case simulation, using the factor levels that represent the original state of the building, is 72.9 kWh/m2a, which constitutes a 0.3% difference. The measured and normalized annual heating energy consumption of the first full year after retrofit was 67.3 kWh/m2a. The simulation of the

Fig. 2. Procedural steps of integrating DoE.

The DPV model builder is capable of reading, reducing and structuring the BIM into a valid EnergyPlus input file. Visual debugging tools help ensuring that the relevant objects are semantically correct. EnergyPlus, which is one of the most comprehensive and widespread dynamic simulation engines available, serves as simulation engine for the whole building including its construction and HVAC equipment. It is constantly validated against data of existing systems and buildings [35]. The selected design factors such as insulation type and thickness, window to wall ratio, material properties and heating/cooling inlet temperatures are parameterized in the input file using the ‘parametric

Fig. 3. Case study building (left) BIM model with DPV semantic viewer, results viewer (right).

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executed retrofit case using the factor levels that represent the retrofit conditions shows 63.75 kWh/m2a which is about a 6% difference. A detailed description of a comprehensive model/measurement calibration process for retrofit using the DPV toolset is described in [26].

•

4.2. Case study experiment definitions

•

Setting up the experiments requires the definition of performance indicators, the choice of factors and appropriate factor levels as well as choosing an appropriate experiment plan. Performance indicators are computable quantities, for example heating energy consumption, that are used as categories to describe the performance of a solution. In the context of performance-driven building design such indicators can be emissions, energy use, investment or life-cycle cost or cost-efficiency. Factors are design parameters that specify selected properties of a solution, for example the thermal resistance of a construction, the dimensions of an opening or the inlet temperatures of a heating system. Varying these factors in a coordinated manner using experiment matrices and simulating these parameter settings allows identifying their impact on the performance indicators as well as interactions between each other.

•

•

4.2.1. Performance indicator and factor definitions For the experiments, we formulate a set of strategies representing different retrofit approaches that are very different in architectural and constructive implications. These strategies are encoded as factor/level combinations and their results, respectively. To conceptualize and quantify such strategies, a thorough understanding of the effect and interactions of the relevant parameters is necessary, which will be facilitated by the methodology proposed. For the experiment, heating and cooling energy end use are chosen as performance indicators as they are most influenced by the retrofit. Site energy was chosen over source energy to compare the actual amounts of energy required to operate the building, neglecting source, generation and losses, which are beyond our control due to a centralized energy system on campus. Additional performance indicators could also be thermal comfort values such as operative interior temperature or cost-efficiency of measures. For the case study, factors and factor levels were chosen to correspond to realistic design options in context of the building case (Table 1). Level values for the base case and the executed retrofit were chosen based on available design documentation. Each factor level represents a realistic design measure, for example choosing a higher window to wall ratio means replacing the existing facade by a new one. The following factor/level combinations were chosen:

4.2.2. Assessing alternative experiment plans The efficiency, applicability and validity of the experiments relies to a large extent on the structure and resolution of the design, i.e. the experiment plan, which is expressed in the design table [20]. The plan selection and thus the sizing of the design table depends on the number of factors and the effects and interactions to be examined. In the following section, we assess different plans in context of the case study to identify the plan with the least amount of runs necessary yet still acceptable error, in case a full factorial cannot be used for reasons of computational effort. Additionally, the reduction of the number of runs changes the duration of the computation from hours to a couple of minutes, which would support a fast and iterative design workflow. To compare the performance of different table designs we first run a full factorial experiment plan to compute every possible factor and level combination. This allows to emulate any specific experiment plan including its results. Due to the exponential growth in number of experiments this is only feasible for a limited number of factors and levels. Compared to full factorial plans, fractional factorial plans use a selection of factor combinations to reduce the number of experiment runs while maintaining the information gain. Being among the most suitable approaches especially for complex computer experiments using a larger amount of factor levels [18,20], we focus on orthogonal arrays for generating suitable experiment plans. To identify a suitable fractional factorial experiment plan for the retrofit experiments, a range of plans different in generation algorithms and number of runs are compared. For the creation of the matrices, two different generators are used. One version with 128 experiments is generated using the ‘R’ Design of Experiments package including the tables prepared by Kuhfeld [37]. For comparison, additional arrays with 56, 128 and 256 experiments are created and tested using the

• Window to wall ratio (RO): Aggregated over the entire building, the

•

additional insulations that would make new facade elements necessary. U-value of horizontal envelope (IH): The average u-value of the original horizontal envelope is 0.8 (level 2). Levels 1 and 3 represent different thicknesses of insulation on the roof; level 4 depicts a high standard as recommended by regulation. Solar energy transmittance (g-value) (WG): The approximate gvalue of the original vertical, glazed façade is 0.58 (level 2). Levels 1 and 3 represent glazing types with different g-values; level 4 represents a low-e coated glazing with very little energy transmittance. U-value windows (WU): The U-value of the vertical, glazed facade (glazing and frame) before the retrofit is approximately 1.55 (level 2) according to thermal imaging measurements. Level 1 represents the original state from 1971, levels 2 and 3 represent exchanging the glazing to better performing double glazing whereas level 4 means replacing the entire facade due to the use of triple glazing. Shading control (SC): The original shading (horizontal louvers) is manually controlled by the occupants. This is approximated by using 150 W/m2 of irradiance as the threshold to lower the shades (level 2). Level 1 represents the absence of external shading as 1000 W/m2 on the vertical surfaces are never reached and thus the shading is never activated. Levels 3 and 4 represent automated external shading with different controls set points.

original facade has a window to wall ratio of approximately 50%, which is depicted as level 2. Potentials measures include smaller window elements (level 1), but also larger elements (levels 3 and 4). Level 4 represents a fully glazed facade. All changes in opening ratio imply the replacement of the existing facade. U-value of vertical envelope (IV): The average u-value of the original vertical opaque facade is approximately 1.5 (level 1). Level 2 represents a minimum additional interior insulation, level 3 and 4

Table 1 Factors/levels, abbreviation, base case before retrofit and executed retrofit. Factors/levels

Short

Base Case

Exec. retrofit

Level 1

Level 2

Level 3

Level 4

Window to wall ratio (%) Thermal transmittance vertical envelope (U-value, W/m2K) Thermal transmittance horizontal envelope (U-value, W/m2K) Solar energy transmittance (g-value, −) Thermal transmittance windows (U-value, W/m2K) Shading control threshold, insolation on surface (W/m2)

RO IN IH WG WU ST

50 1.5 0.8 0.58 1.55 150

50 1.5 0.4 0.15 1.10 150

30 1.5 1.5 0.8 2.00 1000

50 0.8 0.8 0.58 1.55 150

70 0.4 0.4 0.39 1.10 100

90 0.15 0.15 0.15 0.65 50

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Concluding, the CEA 128 experiment plan requiring only 128 experiment runs can be used instead of the full factorial with acceptable deviation, which means reducing computational time to about 3% with acceptable deviation. Given appropriate parallelization [40], the DoE simulation results can be obtained in similar time as a single simulation run. 4.3. Simulation, results collection, data analysis and visualization Fig. 4. Maximum deviation of regression models for total, heating and cooling energy using different experiment plans and compared to the full factorial data.

For the visualization and analysis of the full factorial experiment results we introduce a factor scatterplot (Figs. 6 and 7). Each column of plots represents a different factor separated by the factor levels; each row shows a different performance indicator. The graph allows the interactive filtering and selection of experiments (dots on the scatterplot) showing their positioning in the solution space as well as their characteristic parameter combinations. Introducing this combined graph, different characteristics of the factors can be analyzed:

coordinate-exchange algorithm (CEA) [38]. Additionally, two random plans of 128 and 256 runs are generated, choosing factors levels at random over the design space. Fig. 4 shows the maximum deviation of functions fitted separately for each factor and type of simulation response. The design plan generated by R and the tables of Kuhfeld (WKR 128) show the worst performance probably caused by a lack of an appropriate base table for the size and levels of the experiment. Fig. 5 shows the advantage of DoE tables generated by the CEA compared to a random experiment plan (RND). The cumulative maximum error of all factors at the right of the figure is about 5 kWh/m2a lower for the CEA tables with same size than for the RND tables, which is an improvement of 25 to 30%. Furthermore, the doubling of the experiment size from 128 runs to 256 runs improves the result quality by another 4 to 5 kWh/ m2a. Therefore, as a compromise of run time and accuracy, the CEA 128 plan provides the best results. An additional qualitative criterion of how accurate a DoE plan describes the design space is the deviation of the design strategies using a DoE table from the ones selected as exemplary design strategies (Table 2). To determine the closest design strategy with distance dmin, the Euclidian distance by level steps x is determined excluding the original selected point jDoE and, in case of equal distances, the design with the least difference in the total energy consumption is selected:

• Distribution and variance: The density of the scatter shows distribution and variance of the results over the entire range. • Direction and slope: The slope of minimum values of the factor le-

vels determined by regression analysis demonstrates the positive/ negative influence and impact of the factor on the performance indicator considering the best available solutions. Using the best results xfac,min and y per factor level i, the linear regression is defined as

yi = βx fac min, i + γ + εi

where γ is the y-axis intersection and ε the error. Furthermore, the graphs allow the manual selection and exploration of retrofit strategies: As each experiment is represented with its results and factor levels, picking a desired result with a certain characteristic (for example a well performing result with an opening ratio of 50%) also shows all other related factor levels that lead to the result. This allows for the identification of favorable factor settings for the formulation of design strategies.

6

np ⎛ ⎞ dmin = min ⎜ ∑ (x full, i − xDoE , i )2 ⎟ with j j=1 ⎝ i=1 ⎠ ≠ jDoE and min(abs(Etot , j − Etot , DoE ).)

(2)

(1) 4.3.1.1. Interpretation of the results. The scatterplots can now be used to interpret the experiment results of the case study, first for heating energy as performance indicator. In the top row of Fig. 6, for example, one can observe that the higher the window to wall ratio, the larger the distribution of results but also the lower the minimum values are. This is the opposite for the vertical and horizontal insulation as well as the thermal resistance of the windows, where the higher the thermal resistance, the smaller the distribution and the heating energy consumption are. The lowering of the g-value of the glazing, as depicted in Fig. 7, results in a decrease of solar gains which causes an increase in heating energy consumption. The type of shading control, on the other hand, has little influence on the heating energy consumption. Similar to the heating energy demand, the cooling energy demand is influenced by different factors. In the bottom row of Fig. 6 one can observe that for each factor level of window to wall ratio (RO) there are solutions with zero or near-zero cooling energy consumption. The variability of the solution space however drastically increases. The higher the window to wall ratio, the larger the potential solution space and the bigger the difference between best case and worst case. As this is related to the amount of solar gains received this also holds true for the factor g-value of the glazing; the higher the g-value (WG) and thus the larger the solar gains, the higher the variability of solutions. Concerning the shading control (ST), one can observe that for heating energy the lowering of the threshold to activate the shading has nearly no effect whereas, not surprisingly, for cooling energy a strong effect on the distribution of results can be observed. Especially when the threshold is so high that the shading is never activated, the results

Fig. 5 shows the average, the minimum and the maximum deviation of the total energy consumption comparing the strategy selected from the full factorial with its closest neighbours in the DoE table. The data include tables created by the CEA, random generators (RND) and the Box-Benken-Design (BBD) [39] method with sizes from 49 to 4096. The results indicate that the use of a DoE table for selecting a design strategy instead of the full factorial causes an average error of about 10 to 15 kWh/m2a for the test case. This includes, in adverse cases, a peak error of 35 kWh/m2a for some design tables, such as the RND256. The BBD method creates the smallest tables, which is of special interest for computationally intensive experiments. In particular, the CEA 128 delivered the best result with a maximum of less than 14 kWh/m2a.

Fig. 5. Average, minimum and maximum deviation of the energy consumption in kWh/ m2a (y-axis) between the closest strategy in the DoE table and the selected strategy from the full factorial. The x-axis denotes the number of experiment runs.

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Fig. 6. Scatterplots of full factorial results per factor/level: ratio of openings (RO), vertical insulation (IV), horizontal insulation (IH).

has the strongest effect on reducing heating energy demand, followed by combinations of these factors. The strongest effect on increasing heating energy demand is caused by the g-value (WG) of the glazed facades, followed by combined factors involving the window to wall ratio (RO), g-value (WG) and insulation properties (IN, IH). For cooling energy consumption, all factors that control the solar gains (primary and secondary factors) have the strongest effect on reducing cooling energy demand. The thermal resistance of the opaque and glazed facades has only little effect. Consequently, the combination of the windows' g-value with the shading threshold show the strongest effect on increasing cooling energy demand.

show a large distribution, meaning that there are high performing solutions with very responsive external shading as well as without shading. 4.3.2. Factor effects In addition to the distribution and variance of the results, the main effect of the factors Ef on the performance indicators can be calculated using the following equation [20]:

Ef = F(max) − F(min)

(3)

where F(max) represents the average response of the factor at level 4 and F(min) the average response at level 1. An effects plot (Fig. 8) is used to display importance and magnitude of effects of single and combined factors, which have been evaluated against the maximum variation, as described above, and ranked according to their strength.

4.3.3. Factor interactions In addition to identifying important effects and determining their magnitude, the interactions between effects are crucial. Interactions occur when the effect of a factor is dependent on the level of another factor. A design measure always addresses multiple factors. Understanding how these factors interact in which magnitude allows

4.3.2.1. Interpretation of the results. For the case study, the thermal resistance of the horizontal (IH), vertical (IN) and glazed facade (WU)

Fig. 7. Scatterplots of full factorial results per factor/level: solar gain (WG), window insulation (WU), shading control (SC).

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Fig. 8. Plot of absolute effects (reduction/increase in kWh/m2a) for heating (left) and cooling energy demand (right).

Fig. 9. Interaction plot for heating energy demand (kWh/m2a) (ratio of openings (RO), vertical insulation (IV), horizontal insulation (IH), solar gain (WG), window insulation (WU), shading control (SC)).

the window to wall ratio (RO) and the thermal properties of vertical opaque (IN) and transparent (WU, WG) surfaces. The levels of those factors should therefore be chosen carefully and taking the interdependencies into account. Other parameters show no or only very little interactions. For cooling energy demand, the strongest interactions can be found between the window to wall ratio (RO) and the window g-value and the shading threshold, respectively. Both findings substantiate but quantify a known relation: as the surface where heat gain/heat losses occurs increases or decreases, the thermal properties of the surface become more or less important in relation to the energy demand.

for choosing the best combination of measures by revealing factor combinations with cumulative or degrading effect. The interaction IA,B between two factors A and B can be calculated using the equation [20]

IA, B =

1 (EA, B (max) − EA, B (min) ) 2

(4)

where EA, B(max) is the effect of factor A if factor B is at level 4 and EA, B(min)is the effect of factor A if factor B at level 1. The interaction plot (Fig. 9) allows for easily identifying interactions between two factors. It plots the mean response of two factors for all occurring combinations. If the lines are parallel, no interaction is present, non-parallel and intersecting lines indicate that there is an interaction between the factors. The more non-parallel the lines are the stronger the interaction is.

4.4. Identification of retrofit design strategies Based on the results, effect and interactions, we identify different exemplary design strategies that perform above average and that each represents an exemplary retrofit approach for the given case study. A

4.3.3.1. Interpretation of the results. Using the interaction plot, the factor interactions of the case study can be interpreted (Fig. 9). For heating energy, the main factor interactions can be observed between 40

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Table 2 Factor levels for design strategies.

RO IV ICH WG WU SC Total energy demand (kWh/m2a) Total heating energy demand (kWh/m2a) Total cooling energy demand (kWh/m2a)

Wind to wall ratio Thermal transmittance vertical envelope Thermal transmittance horizontal envelope Solar energy transmittance Thermal transmittance windows Shading control threshold

A

B

C

D

F

Base Case

Executed retrofit

Maximum reduction

Executed retrofit, alt. glazing

Facade conserv.

Level

Level

Level

Level

Level

2 1

2 2

4 4

2 2

2 1

2

3

4

3

4

2 2 2 103.1 75.5

4 3 2 89.6 66.0

1 4 4 46.0 18.0

1 3 4 70.1 44.2

1 1 2 82.0 53.0

6.8

1.8

6.9

4.8

8.2

regarding the building envelope, analyzing and comparing different experimental plans. The results allow the identification of the main effects, corresponding factor level settings and their interactions. The choice of an appropriate experiment plan allows the reduction of the amount required experiments, which is especially crucial for computationally intensive simulations. We show that a small subset of 3% of the possible combination in the design space leads to results with less than 15% deviation as compared to the full factorial of the given case. The experiment plan identified is certainly specific to the case study. For statements on optimal experiments plans for groups or typologies of buildings, a larger number of cases would need to be studied. Nonetheless, we expect a similar performance of experiment plans for retrofit cases with similar design factor structures. We introduced the factor scatterplot as a visualization technique that, in its digital form, allows interactive filtering, solution tracing in different combinations of factors and performance indicators and further statistical analyses, such as linear regressions for the best solutions per level. The plot represents an effective means to identify the distribution and variability of results, impact of factors, tendencies, dependencies, factor combinations and thus the identification of wellperforming strategies. The impact of design decisions can thus not only be observed qualitatively but also quantified in terms of the impact and interdependencies of levels, allowing for a better understanding of the energetic behavior of the building and extending the flexibility in design. The designer can choose a solution (i.e. a dot) in the scatterplot and immediately observe the related factor levels, which correspond to different measures on the building envelope. As we can demonstrate on the case study, the methodology allows for the identification of differing retrofit strategies that equally yield good performance but stress different architectural or technical design factors. With this workflow, we tackle the complexity that decision makers are facing if they strive to deliver energy-efficient and sustainable building designs. There is neither one solution nor one key factor nor is a factor itself positive or negative without its context. The interdependency of factors opens a design space with large combinatorics that the decision maker often cannot overview efficiently. In this situation, we encourage decision makers to use BIM-based DoE as a tool for examining the design space efficiently. The result of such an examination and its visualization provides the decision maker with vital information to tackle the complexity and to understand, which factors are influential, which factors interact and what configurations perform well. Seeing the design space in diagrams and being able to interact with these diagrams, e.g., by selecting well performing configurations and learning how factors are configured, allows the designer to experience the design space with its dependencies between factors and

strategy is defined by a set of measures. As described in Section 4.2, measures are represented by factor settings. Table 2 compares the base case (strategy A), the executed retrofit (strategy B) and three alternative strategies regarding their factor levels and resulting energy performance. The retrofit strategy actually executed (B) intends to improve the envelope by exchanging the existing glazing with double layer glazing and adding insulation on the vertical surfaces. This way the existing facade and therefore the historic appearance can be maintained. Elements not visible from the street level such as the roof are fully insulated. Even though glazing with a very low g-value is used, the manual shading is kept. The maximum reduction strategy (C), as the title implies, targets maximum energy savings. Using the optimal factor levels, heating energy demand can be reduced by 75% as compared to the base case. This strategy however means high efforts on the building envelope, including the exchange of the existing aluminum facade by a new, highly insulated and triple glazed one, featuring a window to wall ratio of 90%. The factor settings of strategy (D) represent the retrofit measures realized, however with alternative glazing. Different from the actual retrofit strategy it uses standard glazing with high g-value that allows for higher solar energy transmittance and higher passive solar heat gains. These heat gains are controlled using more reactive shading devices at the exterior. This results in a reduction of heating energy demand of 42% compared to the base case before the retrofit. For the façade conservation strategy (E) the façade remains untouched; only maximum thermal insulation of the roof is applied. The heat losses through the badly insulated façade can to some extent be counterbalanced by the high thermal gains through the openings. The existing manual shading systems can control solar heat gains in summer. In practice this solution, however might lead to uncomfortable states because of overheating, as this was observed for the case study building. Already with this minimal measure, the heating energy demand can be lowered by 30% compared to the base case. 5. Discussion This work presents a methodology linking BIM and DoE to provide a better understanding of the impact and interactions of architectural and technical design factors on building performance. The methodology is integrated into the Design Performance Viewer toolset, which allows establishing a workflow from a Building Information Model (BIM) to parametric simulation, results collection and statistical analysis. Applied on the actual case study retrofit, we conducted experiments 41

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performance. This information helps decision makers to identify beneficial strategies for retrofitting that go beyond that what can be manually identified, as we have demonstrated for the case. This offers a substantial potential to reduce environmental impact and costs by efficient retrofit while maintaining flexibility in design. The proposed workflow requires BIM data as basis, which might not always be available. However, as BIM as a design environment is increasingly applied in practice for both new construction and retrofit of buildings, we believe that the proposed workflow is feasible for the informed and technically apt designer. As the workflow can be automated, we imagine that this could become a feature of the Design Performance Viewer toolset, which has successfully been applied in research practice. As for any energy simulation, the designer however needs sufficient knowledge on energy performance and related design parameters.

[3]

[4] [5] [6] [7] [8]

[9]

6. Conclusion

[10]

The approach presented in this paper suggests using a set of simulations and DoE as a methodology to build up an understanding of the impact of technical and architectural design factors rather than relying on the numerical outputs alone. Dynamic building energy simulation is known to be very sensitive to specific parameter input. Normally, especially in practice, only a single or a very few simulations are executed to assess the effectiveness of retrofit measures. This bears the risk of neglecting crucial parameters or setting their values to inappropriate levels, thus distorting the results and leading to wrong conclusions. Employing many simulations using ranges of input values instead of just a single input value better depicts the buildings' energy behavior within a bandwidth of performance, which allows trends to become more visible. Increasingly available computing power and availability of parallel computing, such as employed for this work, puts the application of DoE experiment plans into perspective as it is increasingly easy and fast to run large numbers of simulations in parallel at low cost. Nevertheless, the smaller the amount of necessary experiment runs to obtain the results, the more likely a real-time application and thus its employment in the design process is. The choice of a small experiment plan thus has both advantages and drawbacks. It provides similar performance results with acceptable error, equally provides information on effects and interactions with much less computational time, however also reduces the variety of available design solutions for the designer to choose from. As an extension of this work, the experiments could be set up more fine-grained, for example focusing on single thermal zones and their interactions. This could reveal how optimal settings for one thermal zone/orientation interacts with the settings of the adjacent zones with different use and orientation. Adding investment or lifecycle costs as a performance indicator would add an additional dimension and benefit for the application of DoE as a methodology without compromising the ease of application.

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Acknowledgements The authors would like to thank Daren Thomas for supporting the implementation of the DoE workflow.

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