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Nándor Vincze Department of Applied Information Technology, Institute of Vocational Training, Adult Education and Knowledge Management, Juhász Gyula Faculty of Education, University of Szeged, Szeged, Hungary
Department of Basic Sciences, Faculty of Mechanical Engineering and Automation, John von Neumann University, Kecskemét, Hungary

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Kristóf Roland Horváth Paulinyi & Partners Ltd, Budapest, Hungary

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István Kistelegdi Department of Simulation Driven Design, Institute of Architecture, Ybl Miklós Faculty of Architecture and Civil Engineering, Óbuda University, Budapest, Hungary

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Tamás Storcz Department of Systems and Software Technologies, Institute of Information and Electrical Technology, Faculty of Engineering and Information Technology, University of Pécs, Pécs, Hungary

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Zsolt Ercsey Department of Systems and Software Technologies, Institute of Information and Electrical Technology, Faculty of Engineering and Information Technology, University of Pécs, Pécs, Hungary

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Abstract

As part of the energy design synthesis method, complex dynamic building simulation database was created with IDA ICE code for all family house building configurations for a considered problem. In this paper, the annual heat energy demand output parameter is considered to serve as basis of a building energy design investigation. The sensitivity analysis performed by Morris' elementary effect method was used. As the result of the sensitivity analysis of the output parameter, the most important input parameters can be identified, that influence the buildings' energy efficiency, that can support further building designs.

Abstract

As part of the energy design synthesis method, complex dynamic building simulation database was created with IDA ICE code for all family house building configurations for a considered problem. In this paper, the annual heat energy demand output parameter is considered to serve as basis of a building energy design investigation. The sensitivity analysis performed by Morris' elementary effect method was used. As the result of the sensitivity analysis of the output parameter, the most important input parameters can be identified, that influence the buildings' energy efficiency, that can support further building designs.

1 Family house

Design of buildings has a key role in the world's energy consumption and due to the negative environmental impacts caused by the building industry sustainable buildings frequently gain focus recently. In this relation, the process of building energy and climate responsive design represents a key factor. For energy issues see for example [1], and for nature-based solutions consider for example [2]. Unfortunately, conventional building design method in industry practice generates only one or a very limited number of concepts, based on previous experience. This is often supported by the fact, that architects consider the artistic side of design more important than complex building physics simulations and complicated mathematical models to be evaluated from the beginning of the design. Thus, when the architectural plan is ready, i.e., the building body shape together with the space organization or layout are ready as the most fundamental design features, and the technical apparatus is designed subsequently.

Energy design method [3] integrates some of these high-level engineering calculations to implement a sustainable architectural design. The method includes some heuristic building simulations, quantifying the chosen design concepts. As its extension, Energy Design Synthesis (EDS) method is a unique technique ensuring optimal buildings performing highest energy efficiency while offering best comfort. A family house geometry case was considered, where the house was constructed from 6 building blocks. First geometry generation rules were determined to generate all feasible and potentially optimal building configurations for a family house class. For these 167 configurations as accepted geometries, 5010 complex dynamic thermal simulations were performed, i.e., all the configurations were modeled and the family houses were fully generated within IDA ICE code. Please note that during the simulations two different structures including isolation as main building property were considered: one meeting the minimum standards of a family house, while the other is close to a passive house. Further, the simulations included 3 wall-window ratios and 5 orientations. From the simulation data, the annual heating energy demand as output parameter and some input parameters were selected for further investigations. Based on the results of the simulations, the most influential parameters and their dependencies were identified.

2 Sensitivity analysis

Generally, sensitivity analysis is used to identify the important parameters together with their relations, i.e., the individual importance of the selected design variables as well as their joint-effect is measured and evaluated. In other words, it is the study of how uncertainty in the output of a model can be apportioned to different sources of uncertainty in the model input. A sensitivity analysis determines the contribution of the individual design variable to the total performance of the design solution. As a result the dynamics of the variables can be investigated. Note that the effects may vary widely, therefore the order of importance is also significant. Further, individual, as well as aggregate influence occurs. For building design it is of importance, since architects will understand the underlying coherence between the input parameters of a building and its output annual energy demand. Therefore, already in the first building shape and layout design step expert decisions can be made that has direct significant influence on energy consumption sustainability.

Sensitivity Analysis (SA) methods can be classified for example in the following way:

  1. (i)global sensitivity methods consider multiple design parameters;
  2. (ii)local sensitivity methods evaluate the output variability based on the variation of a single design parameter; and
  3. (iii)screening methods consider usually two extreme values on both sides of the standard value for selected design parameters to evaluate, which design parameters the building performance is significantly sensitive to.

Some local SA applications consider model parameters as varying inputs, and aim at assessing how their uncertainty impacts model performance [4]. Applications often apply One-At-a-Time (OAT) approach where the sample is constructed in a way that between two sampling points the influence of only one input variable is considered while all other variables remain constant; individual influences of the output variable are examined. In other words OAT design is called when only one parameter changes values between consecutive simulations, i.e., how the output value changes in case only one input variable changed and the other variables remained or considered to be constant. On the other hand, SA applications often consider interactions between the input variables also when examining the influence of the input variables on the output. In general, global SA sampling is more often performed by All-At-a-Time (AAT) approach, where all the input factors are varied simultaneously. As a consequence, the sensitivity to each input variable considers the direct influence of that factor as well as their joint influence.

It is one of the most important elements of the models to consider the distribution of the input variables. Frequently, well-known distributions describe the input variables, for example uniform, normal, lognormal, or Weibull distribution. However, in practice many variables describing the models are not continuous and their distribution cannot be described in this manner.

Here, Morris Elementary Effect (MEE) method is used [5], when the effect of the change along the adequately scale of OAT randomly selected variable is measured. This can be well applied with a larger number of variables also as a sampling based method.

If y(x1,x2,,xk) is an output parameter, depending on the x1,x2,,xk input parameters, then elementary effect corresponding to the i-th variable can be defined as Eq. (1). Note that Morris suggested p=6and=p/(2·(p1)) where the number of levels within the grid is denoted by p. However, this is suitable, where the variables are continuous, and the sampling can be based on the discretization of the continuous variables. The sensitivity measure can be defined as Eq. (2), and further instead of mean μi, the mean of the absolute value of the elementary effects μi*, introduced by [6], can be defined as given in Eq. (3). Note that r is the number of trajectories,
di(x)=y(x1,x2,,xi1,xi+Δ,xi+1,,xn)y(x1,x2,,xi1,xi,xi+1,,xn)Δ,
μi=s=1rds(i)(x)r,
μi*=s=1r|ds(i)(x)|r.

High result of the absolute expected value shows great influence of the input variable to the output. A low standard deviation means that effects are constant, namely the output is linear on this variable. High result of its standard deviation shows that there is a non-linear effect, or the interaction between the input variable and other input variables is significant. Therefore, significant parameters are depicted in the section of the μ*σ diagram, where both sensitivity measures are high. Further, if the distribution of elementary effects contains both positive and negative elements, some effects may cancel each other out, thus producing a low μ value even for an important variable. In this case the model is considered to be non-monotonic [7].

3 Applied method

The selection of the right type of the input variables is crucial from the sampling point of view. Morris method requires uniform distribution on the [0,1] interval, nevertheless in practice this cannot be fulfilled. In many cases, the variables are discrete and their distribution cannot be known. To overcome this problem, some special sampling methods are applied, and the selected method serves as the heart of the sensitivity analysis afterwards.

For example, some processes are based on the Latin hypercube sampling techniques; other are based on distance measure and uniformity. A potential solution can be the following: the levels of the parameters are given by quantiles, then in the samples the even distribution of the variables is reached; for example [8]. There the sampling is not directly done, but based on the quantile values and thus the levels of the trajectories of the Morris method appear as equal distances.

There are other processes to reach uniformity also. For example [9], which is called sampling for uniformity method, or [10], which is known as the enhanced Sampling for Uniformity method, eSU in short. This latter is used hereinafter. Note that this is a key point, since here some variables cannot be considered as continuous and in case of eSU, the sampling method defines grids that correspond to the values of the variables.

4 Model input parameters

The following total of 15 buildings' design variables was considered. As building design parameters structure, wall window ratio, and orientation were selected. Further, a set of input parameters related to the various building configurations was selected: roof surface (r), surface connected to the ground (g), balcony (b), external walls (w); together with specific edges and vertices. Further, a complex descriptor selected by the architects, namely envelope surface/Area/net floor Surface (A/S) ratio, was also considered as input variable.

5 Results

The purpose of the sensitivity analysis here was to determine the contribution of the selected individual building design variables to the total energy performance. In other words, the order of the variables with the most influence on the annual energy demand is to be determined to support efficient or optimal building design.

Here, Morris method was considered with a level of 6, i.e., for the variable models the trajectories were moved on six levels. Note that in the literature the minimum level is 4. The calculations were based on 30 trajectories.

Table 1 demonstrates the sensitivity analysis results of the full input data; i.e., the order of the considered input variables is given according to Eq. (3). Note that the table shows clearly the difference in the interpretation of the sensitivity measures discussed earlier. The corresponding unit of the investigated annual heating energy demand is kWh/a, and therefore the unit of the sensitivity measures μ and μ* as well as the standard deviation σ have the same unit within the tables detailed below, i.e., kWh/a.

Table 1.

Order of the variables

#Parametersμi* (kWh/a)μi (kWh/a)σ (kWh/a)
1structure3,982−3,982424
2orientation725312841
3b668452694
4a_negative_edge643599588
5g541532389
6r473460410
7g_edge460457313
8window_rate378−69475
9r_positive_edge374366312
10a_positive_air_positive_vertex334318261
11r_negative_edge25433344
12g_positive_positive_vertex220203251
13a_positive_edge2004269
14a_per_s107103131
15w9812146

Table 2 demonstrates the sensitivity analysis results of the input data related to structure 1, where the minimum standards were considered as the necessary building properties, while in Table 3 is demonstrated the sensitivity analysis results of the input data related to structure 2, close to a passive house’ properties. The order of the considered input variables is given according to Eq. (3) in both cases. It is important to mention that there is only a slight difference in the order as well as in the data of the results, which can be considered as not significant and may be a result of the random generation steps. Obviously, the structure and orientation are the most important parameters. Then, variables describing the various building configurations follow for every separate study.

Table 2.

Order of the variables for structure 1

#Parametersμi* (kWh/a)μi (kWh/a)σ (kWh/a)
1orientation8343221,005
2b715515715
3a_negative_edge663609622
4g558556391
5r462454395
6g_edge458446333
7window_rate412−371390
8r_positive_edge403388342
9a_positive_air_positive_vertex343324267
10r_negative_edge28698359
11g_positive_positive_vertex221201260
12a_positive_edge20380267
13a_per_s113108144
14w9816144
Table 3.

Order of the variables for structure 2

#Parametersμi* (kWh/a)μi (kWh/a)σ (kWh/a)
1orientation708290844
2a_negative_edge639603557
3b638410655
4g583582435
5r491483422
6g_edge445445326
7r_positive_edge352345286
8window_rate319258293
9a_positive_air_positive_vertex298274230
10r_negative_edge27226361
11g_positive_positive_vertex207197212
12a_positive_edge190−39257
13a_per_s9390113
14w84−26120

The μ=±2σ/r lines were proposed originally by Morris to identify factors with dominant non-additive and/or non-linear effects; these lines are also depicted in Fig. 1. Factors, i.e., variables, above the lines in both plots are considered to have dominant interactions, while the factors under the line are almost monotonic. Similarly, the μ*σ relation is depicted in Fig. 2. Note that the small standard deviation (see the corresponding tables) indicates monotonicity in a way that the elementary effect values are almost constants. High standard deviation indicates that the relationship of the output variable, namely the annual energy demand, and the factor, namely the considered input variable, is not linear. In other words, the value of the elementary effect can be smaller or greater depending on the value of the input variable and/or the change is greatly influenced by other input variables' changes, i.e. there is an interaction between the input variables. Reference [7] suggested the following boundaries of the standard deviation per mean: 0.1, 0.5 and 1; note that 1 is depicted in Fig. 2.

Fig. 1.
Fig. 1.

Dominant variables

Citation: Pollack Periodica 19, 1; 10.1556/606.2023.00752

Fig. 2.
Fig. 2.

μ*σ relation of the variables

Citation: Pollack Periodica 19, 1; 10.1556/606.2023.00752

Figure 3 corresponds to monotonicity, the variables on the μ*=|μ| line are monotone, and the variables close to the line can be considered to be almost monotone. It is also worth mentioning that in both cases the indicators define the same monotonicity and non-linearity as well as interaction between the variables.

Fig. 3.
Fig. 3.

Monotonicity of the variables

Citation: Pollack Periodica 19, 1; 10.1556/606.2023.00752

6 Conclusions

The sensitivity measures μ and μ* of the study presented show that the structure is inevitable the most influential parameter, when considering the energy performance. When considering this parameter the μ*=|μ| equality holds, this means that its relationship to the output variable is monotone. Moreover, due to its minimal standard deviation this relationship can be considered as linear. Note that the method discussed in the paper applies a technique where in general the samples are randomly selected. Therefore, those input parameters that have the most influence on the output are identified; moreover, these parameters remain with multiple runs. In other words, the model is robust. The model screens the most important and the negligible variables in the considered building annual heating energy model. For more than half of the variables, the model showed a monotonic or close to monotonic effect on the annual heating energy demand input variable, which may be important information during design.

Acknowledgements

This work was partially supported by the 2019-2.1.11-TÉT Bilateral Scientific and Technological Cooperation.

Many thanks for Drs. Yogesh Khare and Rafael Muñoz-Carpena for development of the Matlab/Octave packages for Morris' Elementary Effect methods using enhanced Sampling for Uniformity.

References

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    J. Chitale, Y. Khare, R. Muñoz-Carpena, G. S. Dulikravich, and C. Martinez, “An effective parameter screening strategy for high dimensional models,” in Proceedings on ASME International Mechanical Engineering Congress and Exposition, vol. 7, Tampa, Florida, USA, Nov. 3–9, 2017, Art no. V007T09A017.

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  • [1]

    M. S. Albdour, B. Baranyai, and M. M. Shalby, “Overview of whole-building energy engines for investigating energy-related systems,” Pollack Period., vol. 18, no. 1, pp. 3641, 2022.

    • Search Google Scholar
    • Export Citation
  • [2]

    Q. He and A. Reith, “Using nature-based solutions to support urban regeneration: A conceptual study,” Pollack Period., vol. 17, no. 2, pp. 139144, 2022.

    • Search Google Scholar
    • Export Citation
  • [3]

    B. Baranyai, B. Póth, and I. Kistelegdi, “Planning and research of smart buildings and constructions with the ‘Energy design Roadmap’ method,” Pollack Period., vol. 8, no. 3, pp. 1526, 2013.

    • Search Google Scholar
    • Export Citation
  • [4]

    F. Pianosi, K. Beven, J. Freer, J. W. Hall, J. Rougier, D. B. Stephenson, and T. Wagener, “Sensitivity analysis of environmental models: A systematic review with practical workflow,” Environ. Model. Softw., vol. 79, pp. 214232, 2016.

    • Search Google Scholar
    • Export Citation
  • [5]

    M. D. Morris, “Factorial sampling plans for preliminary computational experiments,” Technometrics, vol. 33, no. 2, pp. 161174, 1991.

    • Search Google Scholar
    • Export Citation
  • [6]

    F. Campolongo, J. Cariboni, and A. Saltelli, “An effective screening design for sensitivity analysis of large models,” Environ. Model. Softw., vol. 22, no. 10, pp. 15091518, 2007.

    • Search Google Scholar
    • Export Citation
  • [7]

    D. G. Sanchez, B. Lacarrière, M. Musy, and B. Bourges, “Application of sensitivity analysis in building energy simulations: Combining first- and second-order elementary effects methods,” Energy Build, vol. 68, pp. 741750, 2014.

    • Search Google Scholar
    • Export Citation
  • [8]

    A. Saltelli, M. Ratto, T. Andres, F. Campolongo, J. Cariboni, D. Gatelli, M. Saisana, and S. Tarantola, Global Sensitivity Analysis. The Primer. John Wiley & Sons, Ltd, 2007.

    • Search Google Scholar
    • Export Citation
  • [9]

    Y. P. Khare, R. Muñoz-Carpena, R. W. Rooney, and C. J. Martinez, “A multi-criteria trajectory-based parameter sampling strategy for the screening method of elementary effects,” Environ. Model. Softw., vol. 64, pp. 230239, 2015.

    • Search Google Scholar
    • Export Citation
  • [10]

    J. Chitale, Y. Khare, R. Muñoz-Carpena, G. S. Dulikravich, and C. Martinez, “An effective parameter screening strategy for high dimensional models,” in Proceedings on ASME International Mechanical Engineering Congress and Exposition, vol. 7, Tampa, Florida, USA, Nov. 3–9, 2017, Art no. V007T09A017.

    • Search Google Scholar
    • Export Citation
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Computer Science Applications 616/792 (22nd PCTL)
Software 344/404 (14th PCTL)
Scopus
SNIP
0.861

2021  
Web of Science  
Total Cites
WoS
not indexed
Journal Impact Factor not indexed
Rank by Impact Factor

not indexed

Impact Factor
without
Journal Self Cites
not indexed
5 Year
Impact Factor
not indexed
Journal Citation Indicator not indexed
Rank by Journal Citation Indicator

not indexed

Scimago  
Scimago
H-index
12
Scimago
Journal Rank
0,26
Scimago Quartile Score Civil and Structural Engineering (Q3)
Materials Science (miscellaneous) (Q3)
Computer Science Applications (Q4)
Modeling and Simulation (Q4)
Software (Q4)
Scopus  
Scopus
Cite Score
1,5
Scopus
CIte Score Rank
Civil and Structural Engineering 232/326 (Q3)
Computer Science Applications 536/747 (Q3)
General Materials Science 329/455 (Q3)
Modeling and Simulation 228/303 (Q4)
Software 326/398 (Q4)
Scopus
SNIP
0,613

2020  
Scimago
H-index
11
Scimago
Journal Rank
0,257
Scimago
Quartile Score
Civil and Structural Engineering Q3
Computer Science Applications Q3
Materials Science (miscellaneous) Q3
Modeling and Simulation Q3
Software Q3
Scopus
Cite Score
340/243=1,4
Scopus
Cite Score Rank
Civil and Structural Engineering 219/318 (Q3)
Computer Science Applications 487/693 (Q3)
General Materials Science 316/455 (Q3)
Modeling and Simulation 217/290 (Q4)
Software 307/389 (Q4)
Scopus
SNIP
1,09
Scopus
Cites
321
Scopus
Documents
67
Days from submission to acceptance 136
Days from acceptance to publication 239
Acceptance
Rate
48%

 

2019  
Scimago
H-index
10
Scimago
Journal Rank
0,262
Scimago
Quartile Score
Civil and Structural Engineering Q3
Computer Science Applications Q3
Materials Science (miscellaneous) Q3
Modeling and Simulation Q3
Software Q3
Scopus
Cite Score
269/220=1,2
Scopus
Cite Score Rank
Civil and Structural Engineering 206/310 (Q3)
Computer Science Applications 445/636 (Q3)
General Materials Science 295/460 (Q3)
Modeling and Simulation 212/274 (Q4)
Software 304/373 (Q4)
Scopus
SNIP
0,933
Scopus
Cites
290
Scopus
Documents
68
Acceptance
Rate
67%

 

Pollack Periodica
Publication Model Hybrid
Submission Fee none
Article Processing Charge 900 EUR/article
Printed Color Illustrations 40 EUR (or 10 000 HUF) + VAT / piece
Regional discounts on country of the funding agency World Bank Lower-middle-income economies: 50%
World Bank Low-income economies: 100%
Further Discounts Editorial Board / Advisory Board members: 50%
Corresponding authors, affiliated to an EISZ member institution subscribing to the journal package of Akadémiai Kiadó: 100%
Subscription fee 2023 Online subsscription: 336 EUR / 411 USD
Print + online subscription: 405 EUR / 492 USD
Subscription Information Online subscribers are entitled access to all back issues published by Akadémiai Kiadó for each title for the duration of the subscription, as well as Online First content for the subscribed content.
Purchase per Title Individual articles are sold on the displayed price.

 

Pollack Periodica
Language English
Size A4
Year of
Foundation
2006
Volumes
per Year
1
Issues
per Year
3
Founder Akadémiai Kiadó
Founder's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Publisher Akadémiai Kiadó
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 1788-1994 (Print)
ISSN 1788-3911 (Online)

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