Research Papers

Hybrid Probabilistic–Possibilistic Treatment of Uncertainty in Building Energy Models: A Case Study of Sizing Peak Cooling Loads

[+] Author and Article Information
Fazel Khayatian

Department of Architecture Built Environment
and Construction Engineering,
Politecnico di Milano,
Via Ponzio, 31,
Milano 20133, Italy
e-mail: fazel.khayatian@polimi.it

Maryam MeshkinKiya

Department of Architecture Built Environment
and Construction Engineering,
Politecnico di Milano,
Via Ponzio, 31,
Milano 20133, Italy
e-mail: maryam.meshkinkiya@polimi.it

Piero Baraldi

Department of Energy,
Politecnico di Milano,
Via Ponzio, 34/3,
Milano 20133, Italy
e-mail: piero.baraldi@polimi.it

Francesco Di Maio

Department of Energy,
Politecnico di Milano,
Via Ponzio, 34/3,
Milano 20133, Italy
e-mail: francesco.dimaio@polimi.it

Enrico Zio

Chaire Systems Science and the Energy
Fondation Electricite' de France,
Laboratoire Genie Industriel,
CentraleSupélec/Université Paris-Saclay,
Grande voie des Vignes,
Chatenay-Malabry 92290, France;
Department of Energy, Politecnico di Milano,
Via Ponzio, 34/3,
Milano 20133, Italy
e-mails: enrico.zio@centralesupelec.fr,

1Corresponding author.

Manuscript received September 5, 2017; final manuscript received March 20, 2018; published online April 30, 2018. Assoc. Editor: Athanasios Pantelous.

ASME J. Risk Uncertainty Part B 4(4), 041008 (Apr 30, 2018) (13 pages) Paper No: RISK-17-1088; doi: 10.1115/1.4039784 History: Received September 05, 2017; Revised March 20, 2018

Optimal sizing of peak loads has proven to be an important factor affecting the overall energy consumption of heating ventilation and air-conditioning (HVAC) systems. Uncertainty quantification of peak loads enables optimal configuration of the system by opting for a suitable size factor. However, the representation of uncertainty in HVAC sizing has been limited to probabilistic analysis and scenario-based cases, which may limit and bias the results. This study provides a framework for uncertainty representation in building energy modeling, due to both random factors and imprecise knowledge. The framework is shown by a numerical case study of sizing cooling loads, in which uncertain climatic data are represented by probability distributions and human-driven activities are described by possibility distributions. Cooling loads obtained from the hybrid probabilistic–possibilistic propagation of uncertainty are compared to those obtained by pure probabilistic and pure possibilistic approaches. Results indicate that a pure possibilistic representation may not provide detailed information on the peak cooling loads, whereas a pure probabilistic approach may underestimate the effect of uncertain human behavior. The proposed hybrid representation and propagation of uncertainty in this paper can overcome these issues by proper handling of both random and limited data.

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Grahic Jump Location
Fig. 1

Transformation of possibility distribution to belief function

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Fig. 2

The case-study building as modeled in designbuilder software

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Fig. 3

Zoning schema of a sample floor. Only zones labeled “Office” are considered as conditioned spaces.

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Fig. 4

Representation of climatic uncertain variables: dry-bulb temperature (top) and MCWB temperature (bottom) through probabilistic representations (solid line) and their transformation into possibilistic measures (dashed lines)

Grahic Jump Location
Fig. 5

Representation of human-dominated uncertain variables: occupant density (top), lighting power (middle) and appliance power (bottom) through probabilistic representations (solid line) and their transformation into possibilistic measures (dashed lines)

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Fig. 6

Flowchart of hybrid probabilistic–possibilistic uncertainty propagation derived from Ref. [64]

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Fig. 7

Limiting probability bounds derived from the outputs of the hybrid method by using homogeneous postprocessing

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Fig. 8

Mapping outputs from pure probabilistic (MC), hybrid (Pl,Bel) and pure possibilistic (Π,N) uncertainty treatments for 0.4% design condition

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Fig. 9

Mapping “control sample A” and “case study A” on the cumulative distributions of uncertain peak cooling loads for the 0.4% design condition. Top: pure probabilistic, middle: hybrid probabilistic–possibilistic, and bottom: pure possibilistic.

Grahic Jump Location
Fig. 10

Assigning size factors for different uncertainty representations. Top: 0.4% design condition, middle: 1% design condition, bottom: 2% design condition.




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