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Towards Improved Thermal Comfort Predictions and
Building Energy Savings: Bayesian Modelling of Indoor
Environmental Design Conditions
by
Sarah Crosby
A TH ES IS S UB MI TT ED I N PARTIAL FULFILLMENT
OF T HE R EQ UI RE ME NT S FO R TH E DE GR EE O F
Doctor of Philosophy
in
TH E FACULTY OF GRADUATE AND POSTDOCTOR AL
STUDIES
(Mechanical Engineering)
The University of British Columbia
(Vancouver)
January 2023
© Sarah Crosby, 2023
The following individuals certify that they have read, and recommend to the Fac-
ulty of Graduate and Postdoctoral Studies for acceptance, the thesis entitled:
Towards Improved Thermal Comfort Predictions and Building Energy
Savings: Bayesian Modelling of Indoor Environmental Design Condi-
tions
submitted by Sarah Crosby in partial fulfillment of the requirements for the degree
of Doctor of Philosophy in Mechanical Engineering.
Examining Committee:
Dr. Adam Rysanek, Professor, School of Architecture and Landscape Architecture,
UBC
Supervisor
Dr. Steven Rogak, Professor, Mechanical Engineering, UBC
Co-Supervisor
Dr. Sheryl Staub-French, Professor, Civil Engineering, UBC
University Examiner
Dr. Amanda Giang, Professor, Institute for Resources, Environment and Sustain-
ability, UBC
University Examiner
Dr. Elie Azar, Professor, Civil and Environmental Engineering, Carleton Univer-
sity
External Examiner
Additional Supervisory Committee Members:
Dr. Naomi Zimmerman, Professor, Mechanical Engineering, UBC
Supervisory Committee Member
ii
Abstract
The judgment of thermal comfort is a cognitive process that is influenced, not only
by measurable indoor environmental conditions but also by less tangible aspects of
an occupant’s well-being and overall satisfaction. Recent studies have examined
the multi-domain nature of thermal comfort to bridge the performance gap between
model-predicted and measurements of thermal comfort. This thesis seeks to inform
a well-known research gap with respect to standard models of thermal comfort: that
seminal data-informed models have not always accurately predicted true thermal
comfort observations from independent field studies. This thesis presents a novel
approach that involves the use of Bayesian inference to predict thermal comfort
as a function of both thermal and non-thermal metrics of indoor environmental
quality.
Bayesian regression was performed on a large field dataset to investigate whether
perceived thermal comfort can be attributed in a measurable and/or significant
manner to one or several non-thermal parameters of indoor environmental qual-
ity. Posterior results revealed that higher CO2concentrations are independently
correlated with lower incidences of thermal satisfaction in open-plan offices. At
indoor temperatures of 23.5 ◦C, the probability of an occupant feeling thermally
iii
satisfied at measured CO2levels of 550 ppm was 0.62 [0.54 - 0.69, 95% CrI]. This
decreased to 0.28 [0.17-0.42, 95% CrI] at 750 ppm. Further, this is the first work
to demonstrate that predictions of thermal comfort can be improved upon adding
measurements of indoor CO2concentrations.
The new data-driven thermal comfort model is integrated into a building en-
ergy model framework to predict occupants’ thermal satisfaction based on thermal
indoor environmental conditions and ventilation rates. Four different post-COVID-
19 occupancy schedules were investigated to reflect and compare different occu-
pancy profiles for post-COVID-19 hybrid work models. The simulation results
showed that it might be possible to increase the ventilation rates with minimal
building heating energy demand increase while maintaining the levels of occu-
pants’ thermal comfort. This thesis presented a solution for building managers that
have been under pressure to increase the current amounts of fresh air to lower the
risk of spreading the COVID-19 virus, and other diseases, indoors.
iv
Lay Summary
Prior studies have suggested that occupants who are generally satisfied with many
non-thermal indoor environmental conditions are more likely to be satisfied with
thermal conditions as well. This thesis takes advantage of the emerging awareness
in research on the multidomain nature of thermal comfort and presents a novel
approach to investigate whether perceived thermal comfort can be attributed in a
measurable and/or significant manner to one or several non-thermal indoor envi-
ronmental quality parameters. Posterior results suggested that predictions of ther-
mal comfort can be improved by adding measurements of indoor CO2concentra-
tions. Building energy simulation results revealed that it may be possible to in-
crease the ventilation rates with minimal building heating energy demand increase
while maintaining the levels of thermal comfort. This thesis presents a solution for
building managers that have been under pressure to increase the current amounts
of fresh air to lower the risk of spreading the COVID-19 virus.
v
Preface
This dissertation is an original intellectual product of the author, Sarah Crosby.
This dissertation is an integration of published manuscripts in scholarly jour-
nals and conference proceedings as follows. Manuscripts are slightly modified for
the dissertation formatting style and coherence.
Various results from chapters 2, 3, 4, and 5 of this dissertation have been pre-
sented as oral presentations at Comfort at the Extremes (CATE) 2022 Conference,
Indoor Air 2022 Conference, Healthy Buildings America 2021 conference, ACM
BuildSys 2021 conference, Building Simulation (BS21) 2021 conference, IBPSA
eSIM 2020 conference, IAQVEC 2019 conference.
A version of Chapter 2 has been published [Crosby, S., Newsham, G., Veitch,
J., Rogak, S., Rysanek, A. (2019). “Bayesian Inference of Thermal Comfort: Eval-
uating the Effect of “Well-Being” on Perceived Thermal Comfort in Open-Plan
Offices”, IOP Conference Series: Materials Science and Engineering, vol. 609,
No. 4, p. 042028, September 2019. doi:10.1088/1757-899X/609/4/042028]. This
author completed all the analytical work and all the data analysis and wrote the
manuscript under the supervision of Dr. Adam Rysanek. Dr. Guy Newsham and
Dr. Jennifer Veitch contributed in providing the COPE field IEQ dataset and re-
vi
viewing the manuscript. Dr. Steven Rogak contributed in the paper’s revisions
phases. A version of Chapter 2 has also been published [Crosby, S., Rysanek, A.
(2020).“Correlations between thermal satisfaction and non-thermal conditions of
indoor environmental quality: Bayesian inference of a field study of offices”, Jour-
nal of Building Engineering,35, 102051. doi:10.1016/j.jobe.2020.102051]. This
author completed all the analytical work and all of the data analysis and wrote the
manuscript under the supervision of Dr. Adam Rysanek.
A version of Chapter 3 has been published [Crosby, S., Rysanek, A. (2022).
“Predicting thermal satisfaction as a function of indoor CO2 levels: Bayesian mod-
elling of new field data”, Building and Environment.108569, ISSN 0360-1323.
doi:10.1016/j.buildenv.2021.108569] and [Crosby, S., Rysanek, A. (2021). “Ex-
tending the Fanger PMV model to include the effect of non-thermal conditions
on thermal comfort”, In Proceedings of eSIM 2020: Building Simulation meets a
global pandemic, Vancouver, Canada] and [Crosby, S., Rysanek, A. (2021). “To-
wards Improved Thermal Comfort Predictions for Building Controls: Hierarchi-
cal Bayesian Modelling of Indoor Environmental Design Conditions”. In The 8th
ACM International Conference on Systems for Energy-Efficient Buildings, Cities,
and Transportation (BuildSys), Coimbra, Portugal.doi:10.1145/3486611.3491128].
This author completed all the experimental work and all of the data analysis and
prepared the manuscript under the supervision of Dr. Adam Rysanek.
A version of Chapter 4 has been published [Crosby, S., Rysanek, A. (2022).
“Towards improved thermal comfort predictions and higher energy savings: build-
ing energy model of an open-plan office based on indoor CO2 and temperature
controls”. Proceedings of Indoor Air 2022.] and [Crosby, S., Rysanek, A. “A
Novel Multi-Domain Model for Thermal Comfort which Includes Building In-
vii
door CO2 Concentrations”. Proceedings of Building Simulation 2021, Bruges,
Belgium. doi:10.26868/25222708.2021.30760]. This author completed all the an-
alytical work and all the building modelling and simulation work, and wrote the
manuscript under the supervision of Dr. Adam Rysanek.
A version of Chapter 5 has been published [Crosby, S., Rysanek, A. (2022).
“On Higher Ventilation Rates and Energy Efficiency in Post-COVID-19 Buildings:
A New Thermal Comfort Model based on Indoor CO2 Levels and Temperature”.
CATE 2022 proceeding]. This author completed all the analytical work, data anal-
ysis, and all the building modelling and simulation work, and wrote the manuscript
under the supervision of Dr. Adam Rysanek.
Ethics approval for this work was sought and received from the UBC Office of
Research Ethics (Ethics approval certificate Ref: H19-01364).
viii
Contents
Abstract.................................... iii
LaySummary ................................ v
Preface .................................... vi
Contents ................................... ix
ListofTables................................. xiv
ListofFigures ................................ xvii
ListofAbbreviations ............................ xxii
ListofSymbols................................ xxiv
Acknowledgments .............................. xxvi
Dedication ..................................xxviii
1 Introduction ............................... 1
1.1 Background............................. 1
ix
1.1.1 Identified Research Questions . . . . . . . . . . . . . . . 5
1.2 LiteratureReview.......................... 5
1.2.1 Existing Models of Thermal Comfort . . . . . . . . . . . 5
1.2.2 Bayesian Modelling of Thermal Comfort . . . . . . . . . 8
1.2.3 Multicontextual Modelling of Thermal Comfort . . . . . . 10
1.2.4 Quantifiable Correlations Between Thermal Comfort and
IEQ............................. 12
1.2.5 Model Predictive Control in Indoor Thermal Environments 15
1.3 Research Objectives, Novelty, and Thesis Outline . . . . . . . . . 16
2 Investigating Relationships Between Thermal Comfort and IEQ: First
CaseStudy ................................ 21
2.1 Introduction............................. 21
2.2 A Bayesian Framework for Thermal Comfort under Thermal and
Non-thermal IEQ Criteria . . . . . . . . . . . . . . . . . . . . . . 24
2.3 First Case Study: Field Data from the Cost-effective Open-Plan
Environment (COPE) Study . . . . . . . . . . . . . . . . . . . . 27
2.3.1 Description of Bayesian Logistic Regression Model . . . . 30
2.3.2 Description of Candidate Models . . . . . . . . . . . . . 31
2.3.3 Model Comparison and Evaluation Criteria . . . . . . . . 33
2.4 Results................................ 37
2.4.1 Initialresults ........................ 38
2.4.2 Model Checks, Comparison, and Selection . . . . . . . . 40
2.4.3 Drawing Posterior Predictions from the Models . . . . . . 47
2.5 Discussion.............................. 48
x
2.5.1 On Establishing the Null Hypothesis . . . . . . . . . . . . 48
2.5.2 On Model Comparison and Selection . . . . . . . . . . . 49
2.6 Summary of Findings . . . . . . . . . . . . . . . . . . . . . . . . 50
3 Predicting thermal satisfaction as a Function of CO2levels: Second
CaseStudy ................................ 52
3.1 Introduction............................. 52
3.2 Methods............................... 54
3.2.1 Design of UBC Field Study: Second Case Study . . . . . 54
3.2.2 Hierarchical Bayesian logistic Regression Model . . . . . 63
3.2.3 Model Comparison and Evaluation of Fitness . . . . . . . 67
3.3 Results................................ 69
3.3.1 Outcomes of UBC Field Study . . . . . . . . . . . . . . . 69
3.3.2 Correlation Analysis . . . . . . . . . . . . . . . . . . . . 72
3.3.3 Regression Results . . . . . . . . . . . . . . . . . . . . . 76
3.3.4 Model Comparison, Selection, and Validation Checks . . . 78
3.3.5 Drawing Posterior Predictions from the Models . . . . . . 80
3.4 Discussion.............................. 83
3.4.1 Similarities and Differences between the COPE and UBC
datasets........................... 83
3.4.2 Evidence in Support of the Bayesian Regression Models . 86
3.4.3 Comparison to Results from First Case Study . . . . . . . 87
4 Building Energy Model of an Office Space based on Indoor CO2and
TemperatureControls.......................... 90
4.1 Introduction............................. 90
xi
4.2 Proposing a New Predictive Thermal Comfort Model for Building
Controls............................... 91
4.2.1 Model Validation . . . . . . . . . . . . . . . . . . . . . . 94
4.3 Developing a New Building Energy Model . . . . . . . . . . . . . 95
4.3.1 Simulated HVAC System and Control Strategy . . . . . . 97
4.4 Building Simulation Results and Discussion . . . . . . . . . . . . 99
5 Increasing Ventilation Rates and Energy Efficiency in Post-COVID-
19Buildings ............................... 103
5.1 Introduction............................. 103
5.2 Post-COVID-19 Occupancy Schedules . . . . . . . . . . . . . . . 105
5.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . 106
5.4 Summary of Findings . . . . . . . . . . . . . . . . . . . . . . . . 113
5.4.1 Limitations of Approach . . . . . . . . . . . . . . . . . . 114
6 Conclusions, Contributions, and Recommendations for Future Work 116
6.1 Overview .............................. 116
6.2 Conclusions, Contributions, and Limitations . . . . . . . . . . . . 116
6.2.1 On the Correlations Between Thermal Comfort and Non-
thermal Metrics of IEQ . . . . . . . . . . . . . . . . . . . 117
6.2.2 On the Root Causes and Significance of Observed Corre-
lations Between CO2Concentrations and Thermal Comfort 119
6.2.3 On the Universality of the Findings . . . . . . . . . . . . 122
6.2.4 On the Implementation of the New Predictive Model in
Building Control Systems . . . . . . . . . . . . . . . . . 124
6.3 Limitations, Implications and Recommendations for Future Work 125
xii
List of Tables
Table 2.1 Summary of the buildings studied in the ’COPE’ database . . . 28
Table 2.2 List of cases evaluated for generating models of p(S)and p(D)33
Table 2.3 Scores of WAIC and LOO-CV for the p(S)models, with Null
hypothesis shown in red . . . . . . . . . . . . . . . . . . . . . 43
Table 2.4 Scores of WAIC and LOO-CV for the p(D) models, with Null
hypothesis shown in red . . . . . . . . . . . . . . . . . . . . . 43
Table 3.1 Summary of the COPE and UBC field study buildings; all UBC
building are located in Vancouver, BC, Canada . . . . . . . . . 55
Table 3.2 IEQ sensors mounted on the UBC and COPE carts . . . . . . . 58
Table 3.3 Observational and manual data collected . . . . . . . . . . . . 62
Table 3.4 List of candidate models of predicted thermal satisfaction, p(S),
as a condition of different thermal (F)and non-thermal (W)
parameters , p(S|F,W).T=indoor air temperature; R= in-
door relative humidity; V=indoor air velocity; C=indoor CO2
concentrations; P=partition height; N= ambient noise levels;
L=lighting intensity. . . . . . . . . . . . . . . . . . . . . . . . 68
xiv
Table 3.5 ELPD PSIS-LOO scores of models trained on the COPE, UBC,
and COPE+UBC datasets. The Null hypothesis is shown in red. 80
Table 4.1 Maximum a posteriori estimates (MAPE) of each model param-
eter for p(S|T,C)model with 95% Credible intervals (CrI) . . 92
Table 4.2 Simulation results: Monthly heating energy demand [KWh/m2]
for 36 scenarios of indoor air temperature setpoint and indoor
CO2setpoint........................... 100
Table 5.1 Daily occupancy schedules used to scale the internal heat gain
and indoor CO2production rates . . . . . . . . . . . . . . . . 105
Table 5.2 Monthly heating energy demand [KWh/m2] for 36 scenarios
of indoor air temperature setpoint and indoor CO2setpoint for
schedule 1 ‘post-COVID-19’, (3 days/week, 100% full capacity) 107
Table 5.3 Monthly heating energy demand [KWh/m2] for 36 scenarios
of indoor air temperature setpoint and indoor CO2setpoint for
schedule 2 ‘post-COVID-19’, (5 days/week, 50% full capacity) 107
Table 5.4 Monthly heating energy demand [KWh/m2] for 36 scenarios
of indoor air temperature setpoint and indoor CO2setpoint for
schedule 3 ‘post-COVID-19’, (5 days/week, 60% full capacity) 108
Table 5.5 Comparison between the percentage increase in monthly heat-
ing energy demand for both scenarios of increasing the ventila-
tion rates for the four investigated occupancy schedules . . . . 109
Table A.1 UBC field dataset- Part 1-I . . . . . . . . . . . . . . . . . . . 143
Table A.2 UBC field dataset- Part 1-II . . . . . . . . . . . . . . . . . . . 144
xv
Table A.3 UBC field dataset- Part 1-III . . . . . . . . . . . . . . . . . . . 145
Table A.4 UBC field dataset- Part 1-IV . . . . . . . . . . . . . . . . . . . 146
Table A.5 UBC field dataset- Part 2-I . . . . . . . . . . . . . . . . . . . 147
Table A.6 UBC field dataset- Part 2-II . . . . . . . . . . . . . . . . . . . 148
Table A.7 UBC field dataset- Part 2-III . . . . . . . . . . . . . . . . . . . 149
Table A.8 UBC field dataset- Part 2-IV . . . . . . . . . . . . . . . . . . . 150
Table A.9 UBC field dataset- Part 3-I . . . . . . . . . . . . . . . . . . . 151
Table A.10 UBC field dataset- Part 3-II . . . . . . . . . . . . . . . . . . . 152
Table A.11 UBC field dataset- Part 3-III . . . . . . . . . . . . . . . . . . . 153
Table A.12 UBC field dataset- Part 3-IV . . . . . . . . . . . . . . . . . . . 154
Table A.13 UBC field dataset- Part 4-I . . . . . . . . . . . . . . . . . . . 155
Table A.14 UBC field dataset- Part 4-II . . . . . . . . . . . . . . . . . . . 156
Table A.15 UBC field dataset- Part 4-III . . . . . . . . . . . . . . . . . . . 157
Table A.16 UBC field dataset- Part 4-IV . . . . . . . . . . . . . . . . . . . 158
Table A.17 UBC field dataset- Part 5-I . . . . . . . . . . . . . . . . . . . 159
Table A.18 UBC field dataset- Part 5-II . . . . . . . . . . . . . . . . . . . 160
Table A.19 UBC field dataset- Part 5-III . . . . . . . . . . . . . . . . . . . 161
Table A.20 UBC field dataset- Part 6-I . . . . . . . . . . . . . . . . . . . 162
Table A.21 UBC field dataset- Part 6-II . . . . . . . . . . . . . . . . . . . 163
Table A.22 UBC field dataset- Part 6-III . . . . . . . . . . . . . . . . . . . 164
Table A.23 UBC field dataset- Part 6-IV . . . . . . . . . . . . . . . . . . . 165
Table C.1 UBC field IEQ study- Survey questions-Part 1 . . . . . . . . . 200
Table C.2 UBC field IEQ study- Survey questions-Part 2 . . . . . . . . . 201
Table C.3 UBC field IEQ study- Survey questions-Part 3 . . . . . . . . . 202
xvi
List of Figures
Figure 2.1 A Bayesian Network for the proposed thermal satisfaction mod-
elling framework which incorporates both thermal and non-
thermal parameters of indoor environmental quality . . . . . . 26
Figure 2.2 Proportion of thermal satisfaction responses received as a frac-
tion across all buildings . . . . . . . . . . . . . . . . . . . . . 29
Figure 2.3 Probability distributions of IEQ thermal parameters (F) across
allbuildings........................... 29
Figure 2.4 Probability distributions of IEQ non-thermal well-being (W)
parameters across all buildings . . . . . . . . . . . . . . . . . 30
Figure 2.5 Probability p(D|F,W)and p(S|F,W), with thin blue lines in-
dicating individual sample traces, solid red lines indicate mean
predicted value from all traces, dashed red bands indicate the
standard error of traces, grey bars indicate the probability dis-
tribution of each independent parameter as observed in the
COPE dataset, and black dashed centre lines are the mean val-
uesofobservations....................... 39
xvii
Figure 2.6 Odds Ratio of posterior traces of non-thermal (W) IEQ param-
eters for p(D)(on the left) and p(S)(on the right) Bayesian
Models with prior distributions displayed in red . . . . . . . . 41
Figure 2.7 Posterior predictive distributions of p(S)for different quantiles
of field observations. . . . . . . . . . . . . . . . . . . . . . . 45
Figure 2.8 Posterior predictive distributions of p(D)for different quantiles
of field observations. . . . . . . . . . . . . . . . . . . . . . . 46
Figure 2.9 p(S)models posterior predictive showing the effect of each
non-thermal parameter on the relationship between operative
temperature and thermal satisfaction; mean and standard devi-
ation of predictions shown (Unless otherwise specified, R=30%,
V=0.08 m/s,T=M=Operative temperature) . . . . . . . . . . 48
Figure 3.1 IEQ sensor cart developed for the UBC study . . . . . . . . . 59
Figure 3.2 Researchers beginning the process of collecting IEQ sensors
measurements at a participant’s workstation; shortly after be-
ginning the automatic data collection process, the researchers
move at least 2m away from the sensor cart . . . . . . . . . . 63
Figure 3.3 Network diagram of hierarchical logistic regression model for
p(S|T,C)............................ 65
Figure 3.4 UBC field study measured IEQ metrics and comparison with
COPE study outcomes . . . . . . . . . . . . . . . . . . . . . 70
Figure 3.5 UBC field study survey responses and comparison with COPE
studyoutcomes......................... 71
Figure 3.6 UBC field study survey responses-Part I . . . . . . . . . . . . 72
xviii
Figure 3.7 UBC field study survey responses-Part II . . . . . . . . . . . 73
Figure 3.8 T-test evaluating overall statistical differences between COPE
and UBC datasets (only parameters shared by both datasets are
shown) ............................. 74
Figure 3.9 Kendall-τbcorrelation analysis of subjective data collected in
COPEstudy........................... 75
Figure 3.10 Kendall-τbcorrelation analysis of subjective data collected in
UBCstudy ........................... 76
Figure 3.11 Kendall-taubcorrelation heatmaps of subjective and measured
data in COPE and UBC studies . . . . . . . . . . . . . . . . . 77
Figure 3.12 Pearson correlation heatmaps of physical measured IEQ data
in the COPE and UBC studies . . . . . . . . . . . . . . . . . 78
Figure 3.13 Posterior predictions of the probability of thermal satisfaction
p(S|T,W)............................ 79
Figure 3.14 ELPD PSIS-LOO scores for each candidate model, normalized
around the scores for each dataset’s Null hypothesis, p(S|T);
solid lines depict the standard errors of the mean scores . . . . 81
Figure 3.15 Posterior predictions of ’thermally satisfied’ occupants as a
function of indoor air temperature and CO2concentrations (COPE
and UBC datasets combined) . . . . . . . . . . . . . . . . . . 82
Figure 3.16 Posterior probabilities of the effect of different CO2levels on
the relationship between thermal satisfaction p(S)and opera-
tivetemperature ........................ 83
xix
Figure 4.1 Posterior traces of the p(S|T,C)model parameters (