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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 (