Conditional parametric ARMAX models for observed hourly heat-load dynamics in apartment buildings
Smertinas, Justinas ; Bacher, Peder and Lindström, Erik LU
(2025)
In Sustainable Cities and Society
122.
- Abstract
This paper presents a methodology for estimation of physically interpretable building energy performance characteristics such as: heat loss coefficient, azimuth angle dependent solar gain, and diurnal periodicity in heat-demand. The models are demonstrated on a case-study with hourly observations of district-heating connected apartment buildings in Denmark. The weather model inputs are obtained from re-analysis climate data, hence no local climate station is necessary. The estimates are thus achieved without directly observing internal climate of the buildings, making the applications scalable, generalizable across different building types, and less prone to errors from sensors.
Building characteristics are extracted from ARX and... (More)
This paper presents a methodology for estimation of physically interpretable building energy performance characteristics such as: heat loss coefficient, azimuth angle dependent solar gain, and diurnal periodicity in heat-demand. The models are demonstrated on a case-study with hourly observations of district-heating connected apartment buildings in Denmark. The weather model inputs are obtained from re-analysis climate data, hence no local climate station is necessary. The estimates are thus achieved without directly observing internal climate of the buildings, making the applications scalable, generalizable across different building types, and less prone to errors from sensors.
Building characteristics are extracted from ARX and ARMAX models extended via B-splines to capture non-linear effects. Interactions of the B-splines with solar radiation are used for approximating a varying solar gain factor and periodic B-splines are included to capture the diurnal effect. Same model is applied independently for each building, such that the parameter estimates can be directly compared.
The quality of estimates for solar gain and diurnal effects is substantially improved with ARMAX models compared to ARX models, as demonstrated by reduced residual autocorrelation, tighter confidence intervals, and enhanced statistical significance. The ARMAX model better captures short-term heat dynamics, resulting in more accurate and physically interpretable parameter estimates. A consistent underestimation of heat loss coefficient from ARX models was found. Lastly, it is shown how the directionality of the buildings’ facades can be linked to the solar gain estimates. The periodical diurnal characteristics are markedly different between buildings with residential and commercial uses.
(Less)
- author
- Smertinas, Justinas
; Bacher, Peder
and Lindström, Erik
LU
- organization
- publishing date
- 2025-03-15
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- ARMAX, District heating, Diurnal periodicity, Non-parametric estimation, Solar gain
- in
- Sustainable Cities and Society
- volume
- 122
- article number
- 106235
- publisher
- Elsevier
- external identifiers
-
- scopus:85218858383
- ISSN
- 2210-6707
- DOI
- 10.1016/j.scs.2025.106235
- language
- English
- LU publication?
- yes
- additional info
- Publisher Copyright: © 2025
- id
- 08dcff07-42e0-4838-a436-397edbb19e80
- date added to LUP
- 2025-04-11 16:23:04
- date last changed
- 2025-04-23 17:09:03
@article{08dcff07-42e0-4838-a436-397edbb19e80,
abstract = {{<p>This paper presents a methodology for estimation of physically interpretable building energy performance characteristics such as: heat loss coefficient, azimuth angle dependent solar gain, and diurnal periodicity in heat-demand. The models are demonstrated on a case-study with hourly observations of district-heating connected apartment buildings in Denmark. The weather model inputs are obtained from re-analysis climate data, hence no local climate station is necessary. The estimates are thus achieved without directly observing internal climate of the buildings, making the applications scalable, generalizable across different building types, and less prone to errors from sensors. </p><p>Building characteristics are extracted from ARX and ARMAX models extended via B-splines to capture non-linear effects. Interactions of the B-splines with solar radiation are used for approximating a varying solar gain factor and periodic B-splines are included to capture the diurnal effect. Same model is applied independently for each building, such that the parameter estimates can be directly compared. </p><p>The quality of estimates for solar gain and diurnal effects is substantially improved with ARMAX models compared to ARX models, as demonstrated by reduced residual autocorrelation, tighter confidence intervals, and enhanced statistical significance. The ARMAX model better captures short-term heat dynamics, resulting in more accurate and physically interpretable parameter estimates. A consistent underestimation of heat loss coefficient from ARX models was found. Lastly, it is shown how the directionality of the buildings’ facades can be linked to the solar gain estimates. The periodical diurnal characteristics are markedly different between buildings with residential and commercial uses.</p>}},
author = {{Smertinas, Justinas and Bacher, Peder and Lindström, Erik}},
issn = {{2210-6707}},
keywords = {{ARMAX; District heating; Diurnal periodicity; Non-parametric estimation; Solar gain}},
language = {{eng}},
month = {{03}},
publisher = {{Elsevier}},
series = {{Sustainable Cities and Society}},
title = {{Conditional parametric ARMAX models for observed hourly heat-load dynamics in apartment buildings}},
url = {{http://dx.doi.org/10.1016/j.scs.2025.106235}},
doi = {{10.1016/j.scs.2025.106235}},
volume = {{122}},
year = {{2025}},
}