key: cord-0959641-kgvae33p
authors: Lin, Wenye; Georgios, Kokogiannakis
title: Development of a Bayesian based adaptive optimisation algorithm for the thermostat settings in agile open plan offices
date: 2020-10-09
journal: Energy Build
DOI: 10.1016/j.enbuild.2020.110536
sha: a8a3afa24b4f2bbd4603812d9ddebde5c5af18f9
doc_id: 959641
cord_uid: kgvae33p

The development of a Bayesian based adaptive optimisation algorithm for optimising the indoor thermostat settings in a large agile open plan office is presented. Occupant expressions of thermal dissatisfaction and indoor environmental conditions were collected using densely-placed devices over a period of approximately 19 months. A logistic regression model was employed to identify the optimal settings, using regression coefficients that were estimated using Bayesian inference. A series of optimisation scenarios with and without considering the temporal variations of occupant thermal preferences and the spatial deviation of the indoor conditions was designed and implemented to evaluate their potential benefit in terms of overall occupant thermal dissatisfaction reduction. We developed two metrics that were tailored to quantify the overall reduction of thermal dissatisfaction when using optimal air temperature and PMV thermostat settings. These two metrics represented the average reduction of overall indoor thermal dissatisfaction each time a thermostat value was updated. The results showed that it was useful to consider the temporal variations of occupant thermal preferences to reduce the overall occupant thermal dissatisfaction in the office, and that using the same approach on individual zones within the open plan office would lead to further improvements. The case study demonstrated that the optimal adaptive temperature and PMV thermostat settings led to an overall thermal dissatisfaction reduction of 1.47% and 1.21% in the whole office, respectively (as opposed to 0.25% and 0.19% when single fixed temperature-based and PMV-based thermostat settings were used). By applying the proposed adaptive optimisation algorithm on individual zones in the office, the occupant thermal dissatisfaction reductions ranged from 0.88% to 5.17% for PMV-based settings, and from 1.20% to 5.19% for temperature-based settings.

The fact that comfort at the workplace is not always achieved could result in loss of productivity of occupants, and thereby in financial and performance losses of a company or an organisation. (Kershaw and Lash 2013) . Previous attempts have been made by researchers to better understand the relationship between occupant productivity and indoor environment (Bordass et al. 1993 , Seppanen et al. 2006 , Ali et al. 2015 and Valancius et al. 2013 ). These studies demonstrated that the indoor thermal comfort was one of the key factors affecting occupant productivity, but a consensus has not been fully reached on definite approaches that would optimise operational set points for HVAC systems to take into account occupant preferences in order to maximise productivity.

To capture the thermal preferences of occupants, most of the previous studies were based on post occupancy evaluations with questionnaires and spot measurements that do not have high spatial and temporal accuracy, but nevertheless they demonstrate the importance of accounting for the preferences of occupants when operating buildings. Nowadays, with the advances in the developments of low cost sensors and low cost small computer devices (e.g. Raspberry PIs), it would be possible to record and predict in real-time knowledge the diversified needs of occupants with regard to the indoor thermal environment in order to be able to adjust the indoor microclimate in an optimum way (Jazizadeh et al. 2011 ) and avoid potential incidents of productivity loss in buildings.

To achieve such a task, it would be essential to implementing methods that use highly deployable sensing, ensure reliable data gathering and most importantly have the means to perform data processing with machine learning techniques, which could be used for obtaining adaptive, To address the demand for intelligent HVAC system control while maintaining an efficient operation, various learning frameworks have been proposed and applied by a number of researchers.

For instance, Gunay et al. (2017) developed and applied a recursive thermostat learning algorithm in commercial building controllers for private cellular office spaces. In this algorithm, the frequency of the occupant thermostat interactions was recursively approximated as a univariate discrete-time Markov logistic regression model for preferred indoor temperature set point prediction. It was found that the implementation of this algorithm rationally identified the indoor thermostat according to occupant thermal preferences, while reducing energy use by adjusting the temperature set point by office and we then designed and tested different scenarios for implementing and assessing the proposed adaptive algorithm. In Section 2, we present the method used for the development of the algorithm, while in Section 3 we provide the results of the test scenarios and a discussion in this regard.

Our overall research methodology is summarised in Fig. 1 . We developed low cost, programmable, network-based sensing and occupant feedback devices and placed them in a mechanically conditioned, large agile open plan office in Sydney, Australia, to continuously collect long-term data of indoor thermal conditions and capture the thermal preferences of occupants in regards to the localised indoor conditions. We undertook a data cleaning process, involving outlier detection for the indoor environmental data and the handling of duplicated thermal preference records that were expressed within short time frames. We then formulated indoor microclimate optimisation scenarios with the aim of minimising indoor thermal dissatisfaction of occupants by deriving the most rational thermostat settings in terms of air temperatures or predicted mean vote (PMV) values. The term "indoor thermal dissatisfaction" in this paper is used as an expression of the likelihood for the occupants to express an alternative thermal preference.

Different optimisation scenarios with the considerations of temporal and/or spatial factors were designed and implemented according to the thermal preference records collected from occupants. In the optimisation process, Bayesian ordered logistic regression was utilised as the tool to identify the optimal HVAC thermostat settings in each optimisation scenario. Finally, we compared the results using different optimisation scenarios and provided recommendations for the optimal operational setting of the agile open plan office. 

The office space that was occupied by ARUP in Sydney CBD up until October 2018 is used for the data collection part of the study (Fig. 2) . The majority of the space has a typical for a commercial CBD office open plan layout with permanently closed high performance tinted windows. The office has a floor area of approximately 2700 m 2 and workstations for approximately 375 staff members.

The HVAC system was scheduled to operate between 7:00 and 18:00 on weekdays and the required set point temperature, as reported by the Facility Managers, was aimed to be approximately 23°C

throughout the year. In addition, and as noted in Fig. 2 , most office employees do not have pre-allocated working desks, but could instead use any of the desks on the south side of the office area. Similarly, the area on the north side of the office where employees had traditionally their own allocated desks, was also converted to a flexible agile space within a short period from the start of our study. The indoor environmental sensors and occupant feedback devices that were developed and used in this study comprised of a number of low cost Arduino sensors linked to a Raspberry PI unit (Fig.   3) . Fig. 2 also shows the ID numbers of the devices, and the 21 locations where these devices were placed in the office space. Most devices were placed in the open plan office area, except for device the devices were placed on working desks of occupants (at a height of around 0.6 m for non-adjustable desks, i.e. the height recommended by ISO Standard 7726 for sitting occupants). We collected the following environmental parameters that were relevant to this paper with each device: 1) dry bulb air temperature (T air ); 2) relative humidity (RH); 3) black globe temperature (T b ); 4) air velocity (v air ).

The corresponding sensor characteristics are summarised in Table 1 . The black globe temperature was measured by globes with a relatively small diameter (40 mm) in order to determine the mean radiant temperature according to ISO 7726 (1998). These sensors were calibrated both in lab and on-site by undertaking repetitive measurements with a testo 480 150mm globe probe instrument, and their offsets were defined and accounted for in our calculations. All data from the sensors were collected at 5-minute intervals and were wirelessly sent and stored in a secure SQL database. We have included in our analysis data collected for a bit more than 1.5 years, from 01/03/2017 to 11/10/2018. Three push buttons were integrated on each device to obtain instant occupant feedback in relation to the indoor environmental conditions (see Fig. 3 ). We labelled two of these buttons as "Want Warmer" and "Want Cooler", and the third button was labelled as "Too noisy" because noise was reported informally by the occupants to be an important issue for the open plan office. However, the findings from the occupant responses with regard to noise remain outside the scope of this paper.

In this way, an expression of dissatisfaction (a mild complaint or a preference) with regard to the occupants' thermal environment is indirectly logged, and can be compared with the above-mentioned collected indoor thermal data. To avoid causing unnecessary burden to the office employees, reminders to press the buttons were not sent and it was left up to the occupants' discretion to use the available buttons. This means that the typical "neutral" response from the occupants was not collected in this study and that there were often occupants who were unaware of the available push buttons.

Thermal comfort is also affected by the clothing levels and the metabolic rates of occupants, however, these are often two variables that an HVAC controller can never monitor. Instead, knowledge of the expected ranges of these values can be pre-set in a controller (or in a predictive model) based on the expected use of the building spaces.

The collected indoor environmental data and the occupant thermal preference responses during the air conditioning hours on weekdays were therefore analysed and used to develop suitable optimisation algorithms for the HVAC thermostat settings of this agile open plan office space.

The collection of high resolution spatial and temporal data in this study resulted in the development of large useful datasets. However, the large datasets might suffer from outliers due to the failure of the sensing and occupant feedback devices or errors introduced by external stimulations.

Procedures were therefore put in place to clean up the recorded indoor environmental data, to identify and eliminate the outliers, and to replace/impute the missing values due to outlier elimination (see Fig. 1 ).

The indoor environmental data recorded by our sensing and occupant feedback device are time series data, in which the dry-bulb temperature, the relative humidity, the black globe temperature have obvious periodical characteristics. These time series data with periodical characteristics were first reassembled as a matrix containing 422 daily parameter profiles, excluding weekends, and then further divided into several sub-matrices to avoid the masking of the outlier characteristics due to different HVAC operation modes at different seasons. Each sub-matrix included 65 daily parameter profiles, which correspond to a span of around 3 months or a season, except for the last sub-matrix that had 32 daily parameter profiles. The missing values in these sub-matrices were imputed by the mean values of all values present at the corresponding time of days (i.e. "CrossMean") through "imputation" function in R package "longitudinalData", to temporarily prepare continuous time series data without missing values for outlier detection. Afterwards, the prepared time series data were decomposed into "trend", "seasonal", and "remainder" components using "seasonal decomposition of time series by Loess (STL)" (Cleveland et al. 1990 ) through the "stl" function in R package "stats". For the "remainder" component data, we used boxplots to identify the suspected outliers outside the 1.5 interquartile range (IQR) of the "remainder" component data. The outlier detection process was completed with a series of Rosner's tests (Rosner 1975 and 1983) for each indoor environment variable to verify the detection of multiple outliers from the previous stages of the cleaning process. Rosner's tests were commissioned by using the "rosnerTest" function in R package "EnvStats". Eventually, the detected outliers were treated as missing values and were imputed again using the "CopyMean" method (Genolini et al. 2013 ). Consequently, the verified outliers were replaced by the mean value of the records that were recorded at that same time of the day within a 65-day sub-matrix. It should be noted that we implemented the above outlier detection process separately for the air conditioning and the non-air conditioning hours as the error characteristics of the measured variables tended to be different during these periods.

A relatively simple data cleaning procedure was implemented for the air velocity measurements on weekdays since, as opposed to the other indoor environmental variables, the air velocity did not present clear periodical characteristics. Considering that the measured air velocity in this office hardly exceeded 0.5 m/s for the majority of the time, with the exception of devices with ID 7 and ID 28, 0.5 m/s was used as a threshold, above which the measured velocities were regarded as suspected outliers. The suspected cases were then also passed through a verification process through Ronsner's test. For the sensing devices whose measured air velocities have a boxplot whisker higher than 0.5 m/s (i.e. only for devices with ID 7 and ID 28), the air velocities above the whisker were directly regarded as outliers. The outliers identified were replaced by the median values of the air velocity measured by the corresponding sensing device. 

The objective of this study was to optimise the operational thermostat settings of an agile open plan office to better match the thermal preference responses of occupants. The key to achieving this objective was the identification of the optimal indoor microclimate parameter(s) which could minimise the occupant complaints due to thermal dissatisfaction. The optimal microclimate can be represented by a neutral air temperature, considering that this has been commonly used as the ideal setting of the HVAC system for optimal building operation. More precisely and rationally, the optimal indoor microclimate in mechanically conditioned buildings can be represented by the neutral thermal sensation (assuming pre-set values for clothing and metabolic rate), as PMV includes multiple indoor environment variables and accounts for occupant activity and clothing levels. The PMV value was calculated using the "calcPMV" function in R package "comf", which applies the same calculations as Fanger (1970) and ISO 7730 (2005). Alternative algorithms or softwares can be used to carry out the PMV calculation (d'Ambrosio Alfano 2020 and ASHRAE 2017), and a careful consideration of relative air velocity in the PMV calculation is required under high metabolic rates (d'Ambrosio Alfano 2019 and 2020). We have assumed that the optimal air temperature T opt or PMV opt can be defined as the neutral condition at which a minimal percentage of people dissatisfied (PPD) can be achieved. Accordingly, occupants would have the same probability to express a "Want Warmer" and a "Want Cooler" thermal preference under the optimal indoor microclimate conditions characterised by T opt or PMV opt , as described in Eq. (1).

(1)

where x is the indoor microclimate variable (air temperature or PMV in this study), y is the thermal preference, and P represents the probability of a thermal preference. The probability of a thermal preference can be determined by the ordered logistic regression, which was proposed by McCullagh (1980) to quantify the relationship between multiple response categories and explanatory variables, as described in Eqs.

(2) and (3).

(2)

(3)

where c k and ?? are the regression coefficients in the ordered logistic function, which in this case would correlate the input variable x (i.e. indoor air temperature or PMV) with the probability of the occupants' thermal preference (i.e. y), and K is the total number of the ordered response categories.

There were only two categories of thermal preference responses, i.e. "Want Warmer" and "Want Cooler", represented by k of 1 and 2, respectively. Thus, the probabilities for occupants expressing a "Want Warmer" or "Want Cooler" preference in the office under different air temperatures or PMV values can be determined by implementing an ordered logistic regression. Since there were only two thermal preference categories, the intersection point of the two ordered logistic regression curves would have the same probability of 50% for individual thermal preferences, and this intersection point can be considered as being the most optimal air temperature or PMV value setting for the HVAC thermostat settings.

The regression coefficients in the ordered logistic function Eq.

(2) can be estimated using Bayesian inference. Bayesian inference is a statistical inference method using Bayes' rule to determine the conditional probability of an event by updating the probabilities of estimates when more evidence related to that event is given (Gelman et al. 2013 ). Accordingly, the posterior probability density distribution of the regression coefficients (c k , β) conditioned on the observations (D) can be inferred by Eq.(4). As a consequence, regression coefficients and their standard deviation can be respectively estimated from the median and standard deviation values of their probability density distributions, as shown in Eq. (5). The above recursive Bayesian ordered logistic regression provides a recursive approach to adaptively identify the desired thermostat settings for the HVAC system based on the updated training dataset. Meanwhile, the posterior information from the Bayesian regression that was based on the previous training dataset, i.e. before updating the hypothetical thermal preference responses, is used as prior (see Fig. 4 ). It can be expected that in the recursive Bayesian inference the credible interval may experience a convergent process, however the output will remain adaptive.

Since the posterior probability density distribution tends to be analytically intractable, we 

We considered six optimisation scenarios to meet different temporal and spatial control requirements in the office, as summarised in Table 2 . Optimisation Scenarios 1-3 were designed with the objective to gain the optimal HVAC thermostat settings for the whole office without considering the indoor microclimate deviation due to spatial differences.

In detail, all the occupant thermal preference records collected were treated as a training dataset in Optimisation Scenario 1 to identify an optimal thermostat setting for the whole office. For

Optimisation Scenario 2, the same training dataset was divided into hourly sub-datasets for the air conditioning hours on weekdays (e.g. all occupant preferences expressed between 7:00 to 8:00

during the period of the study were grouped in one hourly sub-dataset, etc.). Each sub-dataset was used to facilitate the identification of optimal fixed hourly HVAC settings using Bayesian regression.

We then combined the derived hourly optimal settings into an optimal daily profile for the HVAC settings. In Optimisation Scenario 2, there were a small number of occupant thermal preference records in each hourly sub-dataset which were not enough to reliably infer an optimal thermostat setting with an acceptable credible interval through a batch Bayesian regression. For this reason, the whole set of thermal preference records during the air conditioning hours on weekdays were used as the prior information in Optimisation Scenario 2.

In Optimisation Scenario 3, as described in Section 2.3.2, a fixed number of thermal preference observations defined a moving dataset window (see Fig. 4 ) that was updated when new observations were recorded. This moving dataset window was used as the training dataset to identify the adaptive settings for the HVAC system. As opposed to the previous two optimisation scenarios, Optimisation

Scenario 3 was carried out by recursive inference (see section 2.3.2). Since there was no significant change in the occupants and occupant characteristics, and the time period investigated was not too long, the manual additional deviations (Δσ-see Eq. (5)) for the regression parameters were set to 0.

An initial dataset is required in this scenario to provide prior information for the inference of adaptive settings.

Optimisation Scenarios 4-6 were similar to Optimisation Scenarios 1-3 in terms of temporal resolution, except that they were to be implemented based on the thermal preference observations in individual areas (i.e. zones) rather than the whole office, in order to consider the existence of potential indoor deviations on the conditions of the large open plan office. (2005) and it is consistent with the typical daily wear clothing of the majority of occupants in the specific office. The pre-determined target PMV for each zone was calculated by the same rule but based on the indoor environmental variables measured in the corresponding zones. Compared to the "original" case, the indoor air conditions for the "optimal" cases after adopting the optimal HVAC thermostat settings identified from the optimisation scenarios were assumed to follow the relationship in Eq. (8).

where i represents the index of a thermal preference record, N is the total number of the thermal preference records; subscripts org and opt represent the original and optimal cases respectively;

subscript set refers to an HVAC thermostat setting; subscript act represents the actual measured conditions around the monitoring devices at the moment of a thermal preference record when using the original HVAC thermostat setting (assuming there is a difference between original fixed setting and actual measured conditions); subscript exp represents the expected conditions when using the optimal HVAC thermostat setting after accounting for the occupant response and for the difference between the actual condition and the original HVAC setting; δ represents the difference between the optimal HVAC thermostat setting and the original HVAC setting. In addition, constraints were set for the optimal HVAC settings to remain within the 18 to 28 o C, and the -1 and 1 ranges when using air temperature and PMV as the HVAC thermostat settings, respectively. The constraint ranges of the air temperature and the PMV were only set to initiate the calculations of the conditions of the thermostat control, and therefore support the initial convergence of the Bayesian based optimal adaptive thermostat setting algorithm. For this reason, instead of using the ranges from by ASHRAE 55 In this case, the revised PPD is calculated from a revised thermal preference based PPD function from Eq. (10). The optimal PMV setting (PMV opt,set,j ) is updated based on a specific number of thermal preference records, including the thermal preference records in the training dataset (number of n j ) and the records used in the prior information (number of n prior ), depending on the optimisation scenario. It was therefore necessary to include all of the (n j +n prior ) thermal preference records in the calculation of Eq. (9). In Eq. (10), if the neutral PMV (i.e. optimal PMV setting) is 0, two ordered logistic distributions representing the thermal preferences of "Want Warmer" and "Want Cooler"

were developed, whose summation was required to approach the original PPD-PMV function in ISO 7730 (2005) . The comparison between the sum of the revised PPDs for "Want Warmer" and "Want cooler" that was calculated using Eq. (10) (when PMV opt,set,j = 0) and the original PPD calculated from ISO 7730 is presented in Fig. 5 . The corresponding RMSE from this comparison was approximately 1.12% over the PMV range from -2 to 2, which shows that this method is a reasonable approximation of the ISO 7730 PPD-PMV function. In addition, if the optimal PMV setting (PMV opt,set,j ) is not equal to 0, the "Want warmer" and "Want cooler" distributions need be shifted by the value of optimal PMV setting (as shown in Fig. 6 ). We then average the in Eq. (11) for all the optimal PMV settings to compare the impact of the optimisation scenarios in relation to the original case (i.e. the benefit from using the optimisation to better match the occupant preferences). Accordingly, provides an indicator to quantify the overall reduction of indoor thermal dissatisfaction in different optimisation scenarios, when using PMV as the HVAC thermostat setting.

(9) (10)

where J is the total number of the optimal thermostat settings, which was 1 for Optimisation Scenarios 1 and 4, 11 for Optimisation Scenarios 2 and 5, and equal to the total number of training datasets for Optimisation Scenarios 3 and 6, respectively; n prior represents the number of thermal preference records used in the inference of the prior information (it was 0 for Optimisation Scenarios 1 and 4, equal to the total number of the thermal preference records in the whole office or individual zones for Optimisation Scenarios 2 and 5, and equal to (j-1) for Optimisation Scenarios 3 and 6 when n j is set as 1); j is the index of an optimal thermostat setting (out of a total of J settings), and the subscript rev indicates the revised value. An intuitive description of the adopted method when using PMV settings is shown with an example in Fig. 6 . An optimal PMV set point (PMV opt,set,jhighlighted by the black bold solid line) can be derived using the recursive Bayesian inference every time an occupant preference is recorded, which also indirectly involved all the previous occupant preferences by using them as prior information. This derived optimal PMV at that moment of time is considered to be an improved setting for the conditions in the office based on the up-to-date occupant thermal preference records. By using this optimal PMV thermostat setting, (PMV opt,set,j ), it is assumed that the measured PMV (PMV act,i ) could be improved to an expected PMV (PCM exp,i,j ) by following the same linear relationship as that between the actual measured PMV and the original HVAC thermostat setting (i.e. PMV act,i -PMV org.set = PMV exp,i,j -PMV opt,set,j ). A revised thermal preference based PPD function (highlighted by the red and blue solid curves in Fig. 6) is revised from the thermal preference based PPD function (highlighted by the red and blue dash curves in Fig. 6 ) after taking into account the derived optimal PMV setting (PMV opt,set,j ) when an occupant preference was recorded. The neutral of the revised PPD-PMV function was considered to be the optimal PMV thermostat setting, at which the sum of PPDs is minimised based on the up-to-date occupant thermal preference responses. The corresponding revised thermal preference based PPD values of PMV act,i and PMV exp,i,j were calculated to represent the thermal dissatisfaction when using the original and optimal PMV thermostat settings, respectively. The difference of using the optimal PMV thermostat setting as compared to the original PMV setting is therefore calculated by subtracting the revised thermal preference based PPD value of PMV exp,i,j corresponding to the optimal PMV from the revised thermal preference based PPD value of PMV act,i corresponding to the optimal PMV (i.e. Fig. 6 ).

1 Fig. 6 Example of using the adopted method to quantify the potential benefit from the optimisation of thermostat settings using PMV as 2 thermostat setting. The black bold solid line represents the optimal PMV thermostat setting which is updated when an occupant preference is 3 recorded; the grey solid line represents the historical optimal PMV thermostat settings; the black dashed line represents the original PMV 4 thermostat setting; the red and blue solid curves represent the revised thermal preference based PPD functions for the optimal PMV setting when 5 an occupant preference is recorded; and the red and blue dashed curves represent the original revised thermal preference based PPD functions for 6 an original PMV setting of 0; the blue colour is for "Want Warmer" thermal preference, and the red colour is for "Want Cooler" thermal 7 preference.

When temperature was instead used as a parameter for developing the thermostat setting strategy, 9 we developed a function ( ), as described in Eq. (12), to calculate the mean differences of thermal Similar to that of using PMV thermostat settings, an optimal set point air temperature can be 30 derived using the recursive Bayesian inference every time an occupant preference is recorded. In this 31 way, the difference of using the optimal temperature thermostat setting as compared to the original 32 temperature setting can be calculated (i.e. gi,j(Tact,i)-gi,j(Texp,i,j)). 2. It can be seen from Fig. 8a and b that the indoor air temperatures tended to be relatively low 

When the proposed optimal fixed air temperature thermostat setting was adopted, the potential preference records in the training dataset. After 9:00am, the optimal temperature setting became 149 more reliable with a narrower 95% credible interval, and the highest optimal temperature setting of 150 24.6 o C was calculated for the hour between 12:00 -13:00.

By adopting the optimal daily temperature profile settings, the overall thermal dissatisfaction Fig. 12 presents the optimal daily PMV profile settings for the HVAC system. Throughout the air 166 conditioning hours on weekdays, the optimal PMV settings spanned from -0.01 to 0.12, and had 167 relatively narrow 95% credible interval. By using the optimal daily PMV profile settings, the Table 3 . The sensitivity of the resulted optimal PMV to the size of the dataset was 199 also verified through a series of batch Bayesian regressions and the results are also summarised in 200   Table 3 . Bayesian ordered logistic regression. The missing part before the individual temperature setting 211 curve is due to the use of the first 60% of the thermal preference observations in the initial dataset 212 window for regression coefficient initialisation. It can be seen that the optimal adaptive temperature 213 thermostat settings fluctuated over the monitoring period, ranging from 19.4 to 25.5 o C. The 95% 214 credible interval was relatively wide at the beginning, but converged gradually with the recursive 215 process After around December 2017, the optimal adaptive temperature settings were higher than the 216 optimal fixed temperature setting identified in Section 3.2.1 (i.e. 23.5°C). Fig. 14 also shows an 217 enlarged section of the variation of the optimal adaptive thermostat setting over a short period from 218 around 21 st to 24 th of May 2018 together with thermal preference records of that period. It can be 219 seen that the optimal thermostat temperature setting is updated every time a "Want Cooler" 220 ("Response 1" and "Response 2" in Fig. 14) and a "Want Warmer" response is recorded ("Response 221 3" and "Response 4" respectively).

The overall reduction of the thermal dissatisfaction that was calculated as benefit from the interval of the optimal adaptive temperature setting ranged from 0.47% to 5.42%, whose mean value 233 was 2.95% and higher than that of 2.39% (i.e. mean value of the range from 0.78% to 4.0%) for 234 Optimisation Scenario 2. The main reason for this improvement is that, as opposed to using a fixed 235 optimal temperature (Optimisation Scenario 1) or an optimal daily temperature profile (Optimisation

Scenarios 2) as the thermostat setting, Optimisation Scenario 3 adaptively adjusted the optimal 237 temperature setting, thereby better matching the overall occupant thermal preferences dynamically. The open plan office was partitioned into 4 clusters (see Table 4 ). The devices with IDs 7, 18, 28, The optimal daily temperature and PMV profile thermostat settings were identified for Zones 1 299 and 2, respectively, as shown in Fig. 16 . As Fig. 16a shows, the optimal hourly temperature settings interval for the optimal temperature settings between 7:00 and 9:00 were constrained above 18 o C to 303 overcome issues caused by the small number of thermal preference records during the early hours of 304 the morning. From Fig. 16b , it can be seen that the optimal PMV profile settings of Zone 1 was 305 above than that of Zone 2 over the air conditioning hours, demonstrating that the occupants in Zone 1 306 tended to prefer a slightly warmer indoor environment compared to that in Zone 2. By adopting the 307 optimal daily temperature profile settings per zone, the overall thermal dissatisfaction reduction 308 calculated by Eq. (14) can in this case reach 3.83% and 1.68% for Zones 1 and 2, respectively. These 309 reductions were higher than the reductions calculated in the optimal fixed temperature thermostat 310 settings case in these zones. Besides, the benefits from deriving an optimum daily PMV profile for 311 the thermostat settings were calculated by Eq. (11) as 0.28% and 1.09% for Zones 1 and 2, 312 respectively. These results for the optimal PMV profile settings in individually controlled zones were 313 approximately the same as those of the optimal fixed PMV thermostat settings in these zones (i.e.

Optimisation Scenario 4 in Section 3.5.2). In addition, compared to the optimised settings for the 315 whole office without zoning (i.e. Optimisation Scenario 2 in Section 3.3), using the optimal daily 316 temperature and PMV profiles for each zone tended to be more effective in reducing the overall As in Optimisation Scenario 3, parametric studies were carried out for Zones 1 and 2 to identify 326 the suitable initial dataset window size. While the results of these parametric studies are not included 327 in the paper for brevity, the initial dataset window size with narrow 95% credible interval was set to 328 include 80% of the total number of the thermal preference records in both zones (i.e. 228 and 151 329 responses for Zones 1 and 2 respectively).

The adaptive thermostat temperature and PMV settings were identified and are shown in Fig. 17 .

It can be seen that the optimal adaptive HVAC temperature settings for Zone 1 experienced 332 significant fluctuating trends from 22.7 to 28.0 o C, compared to that for Zone 2 that ranged between 333 21.8 to 28.0 o C (Fig. 17a) thermal dissatisfaction enhancement of 0.25% and 1.03% for Zones 1 and 2, respectively) and the 358 optimal daily PMV profile settings in Optimisation Scenario 5 (0.28% and 1.09% for Zones 1 and 2, 359 respectively), the overall thermal dissatisfaction reduction in this optimisation scenario was 360 improved. It can also be seen that the zoned approach in this optimisation scenario provided a higher 361 reduction of thermal dissatisfaction (weighted mean thermal dissatisfaction reduction of 2.09%, even 362 when the thermal dissatisfaction reduction for Zones 3 and 4 were assumed to be 0) compared to that 363 using the optimal adaptive PMV settings for the whole office (i.e. 1.21% in Optimisation Scenario 3 364 in Section 3.4). The simplest scenario was to identify and use an optimal fixed setting in the HVAC system for 386 the whole office, without considering the temporal and spatial aspects at all. Due to its simplicity, the 387 scenario presented an almost negligible potential to reduce the thermal dissatisfaction of occupants 388 (thermal dissatisfaction reduction less than 0.3% for both optimal temperature and PMV thermostat 389 settings). The small benefit from this scenario was due to the fact that the optimal thermostat settings such implementation, the following pseudo-code in Table 7 was developed for the identification of 412 the adaptive optimal HVAC settings (Optimisation Scenario 6). 413 Table 7 Implementation pseudo-code for the identification of the adaptive optimal HVAC settings. Collect microclimate data and thermal preference observations in a zone, and carry out data cleaning; 3 Implement batch Bayesian inference ordered logistic regression using Eqs (2) -(4) based on the thermal preference records collected in the zone; 4

Check the range of the 95% credible interval, if not acceptable change the size of the initial data set D 1 and go to Algorithm Line 3; else: identify the proper size of D 1 : 5

For (z Z) 6

Initialise D 1 ; 7 Implement batch Bayesian inference ordered logistic regression using Eqs (2) -(4)； 8

Calculate static characteristics of the regression coefficients c k and β using Eq.(5); 9

Identify initial optimal setting using Eq. (1); 10

For (j J) 11

Update training dataset D j according to Eq. (7) 12 Implement recursive Bayesian inference ordered logistic regression using Eqs (2), (3) and (6); 13

Calculate static characteristics of the regression coefficients c k and β using Eq.(5); 14

Identify the optimal setting using Eq. (1); 15 j=j+1 and go to Algorithm Line 10 16 z =z+1 and go to Algorithm Line 5 *Note: z is the zone index (all symbols were defined in the previous sections and in nomenclature). indoor conditions. To compare the importance of the temporal aspects, we designed and evaluated an 422 optimal fixed thermostat setting, an optimal daily profile thermostat setting, and an optimal adaptive 423 thermostat setting. The importance of the spatial aspect was evaluated by zoning the office space and 424 implementing the above three different optimisation scenarios (fixed, daily profile and adaptive) 425 based on the occupant thermal preferences and indoor conditions in individual zones. Two artificial 426 metrics were developed and utilised to assess the impact of these optimisation scenarios when using 427 air temperature and PMV as reference thermostat metrics, respectively.. 428 We found that the Bayesian-based adaptive optimisation algorithm can result into reduced 429 thermal dissatisfaction of occupants when taking the real-time temporal variation of occupant 430 thermal preferences into account. For the non-zoning scenarios, the adaptive optimisation 431 outperformed, in some cases marginally, the cases that had optimal fixed and optimal daily profile 432 thermostat settings. Using the two developed metrics to represent thermal dissatisfaction reductions 433 for temperature and PMV based settings, the adaptive optimisation resulted in the overall reduction 434 of the thermal dissatisfaction of 1.47% and 1.21% respectively, slightly higher than that of the fixed 435 optimal thermostat setting optimisation. 436 We also found that the occupant thermal dissatisfaction can be further reasonably reduced by 437 taking the spatial deviation of indoor climate into account. The adaptive optimisation algorithm that 438 considers both, the temporal and spatial differences between the occupant thermal preferences, can 439 result in overall occupant thermal dissatisfaction reductions in a zone of up to 5.19% when using the 440 resulted optimal adaptive temperature settings and of up to 5.17% when using the resulted optimal 441 adaptive PMV settings. 

Energy efficiency index as an indicator for measuring building energy performance: a review

The effect of physical environment comfort on 455 employees' performance in office buildings: a case study of three public universities in Malaysia

Thermal environment conditions for human occupancy

A comfort-based approach to smart heating 460 and air conditioning

Learning personalized 463 thermal preferences via Bayesian active learning with unimodality constraints

User and occupant controls in office buildings

Building Design, Technology and Occupant Well-being in Temperate Climates

STL: a seasonal-trend 467 decomposition procedure based on loess

Fifty years of Fanger's equation: Is 469 there anything to discover yet?

Model: Reliability, Implementation and Design of Software for Its Calculation

Energy performance of buildings -ventilation for buildings -Part 1: 475 Indoor environmental input parameters for design and assessment of energy performance of 476 buildings addressing indoor air quality, thermal environment, lighting and acoustics -Module M1-6

Energy performance of buildings -ventilation for buildings -Part 2: 479 Interpretation of the requirements in EN 16798-1 -Indoor environmental input parameters for design 480 and assessment of energy performance of buildings addressing indoor air quality, thermal 481 environment, lighting and acoustics (Module M1-6)

Thermal comfort analysis and applications in environmental engineering

Bayesian Data Analysis

Copy Mean: a new method to impute 487 intermittent missing values in longitudinal studies

Occupancy-based zone-climate control for 489 energy-efficient buildings: complexity vs. performance

Development and 491 implementation of a thermostat learning algorithm

Real-time occupant feedback and environmental learning framework for collaborative thermal 495 management in multi-zone, multi-occupant buildings

Making recursive Bayesian inference accessible

The American Statistician

Ergonomics of the thermal environment -instruments for measuring 499 physical quantieies', ISO/TC 159/SC 5 Ergonomics of the physical environment

Ergonomics of the thermal environment -analytical determination and 501 interpretation of thermal comfort using calculation of the PMV and PPD indices and local thermal 502 comfort criteria

Continuous sensing of occupant 504 perception of indoor ambient factors

Open spaces, supple bodies? Considering the impact of agile working on 506 social work office practices

Clustering by means of medoids', Statistical Data Analysis 508 Based on the L Norm

The effect of agile workspace and remote 510 working on experiences of privacy, crowding and satisfaction

Investigating the productivity of office workers to quantify the 512 effectiveness of climate change adaptation measures

A Bayesian approach for probabilistic 514 classification and inference of occupant thermal preferences in office buildings

Inference of thermal preference profiles for 517 personalized thermal environments with actual building occupants

Implementation of a self-tuned 520

HVAC controller to satisfy occupant thermal preferences and optimize energy use

A variation focused cluster analysis strategy to identify typical 523 daily heating load profiles of higher education buildings

Regression Models for Ordinal Data

On the Detection of Many Outliers

Percentage Points for a Generalized ESD Many-Outlier Procedure

Effect of temperature on task performance in office 530 environment

Stan modeling language user's guide and reference manual

Learning occupants' indoor comfort temperature through a Bayesian 535 inference approach for office buildings in United States

Influence of indoor air temperature variation on office work 538 performance

Productivity and employee satisfaction in flexible workplaces

A data-driven method to describe 543 the personalized dynamic thermal comfort in ordinary office environment: From model to 544 application

Wireless sensor network based monitoring 546 system for a large-scale indoor space: data process and supply air allocation optimization

The authors would like to thank Arup for funding this study under the Arup Global Research