A stacked ensemble learning framework with logistic regression meta-learner for thermal comfort prediction

Abstract

Thermal comfort is a critical determinant of human health, well-being and productivity, and is also integral to promoting energy efficiency. The predicted mean vote is the most recognized method for estimating the average thermal experience amongst a group of individuals within built environments. However, the method's reliance on climatic parameters that are difficult and resource-intensive to measure, as well as physiological parameters that require self-reporting, introduces significant practical limitations for real-world applications. The present work aims to address these limitations by proposing a lightweight predictive framework for effective, streamlined thermal comfort classification that relies on a reduced input feature space comprising the easy-to-measure and low-cost climatic parameters of air temperature and relative humidity, and the seasonal standardized approximation for the physiological parameter of clothing insulation. Leveraging an ensemble learning architecture with random forest, k-nearest neighbours, CatBoost and multi-layer perceptron as weak learners and logistic regression as a meta-learner, the proposed framework demonstrated an overall predictive accuracy of 85.8% in estimating the average thermal experience. It adequately handled the class imbalance across thermal discomfort states, particularly those underrepresented, further underscoring its robust performance. The proposed framework could emerge as a scalable and efficient approach for estimating thermal comfort in real-world applications.

Introduction

With modern people spending almost 90% of their time indoors, including residential settings, workplaces and offices, educational institutions and commercial facilities, ensuring comfortable indoor thermal environments emerges as a cornerstone for advancing health, well-being, productivity and promoting energy efficiency.^1–2 Thermal comfort is defined as a state of mind that expresses an individual's satisfaction with the prevailing thermal conditions in ambient environments. ³ Besides the profound influence of climatic conditions on shaping this subjective experience, the intricate interplay of physiological, psychological, behavioural, socio-economic and demographical determinants also affects thermal perception.^4–6 While these inherent human determinants could serve as valuable predictors for a more precise and human-centric thermal comfort assessment, the conventional thermal comfort approaches omit them, concentrating instead on parameters obtainable through sensing devices or are minimally intrusive for self-reporting. ⁷

Prior research studies have underscored thermal comfort implications on physical and mental health, cognitive function and well-being. Thermal discomfort has been associated with adverse health effects, such as accelerated respiration and heart rate, aggravated skin disorders and increased stress levels and depression.^8–9 Ensuring comfortable thermal spaces in offices and workplaces could result in substantial productivity improvement, lower fatigue, enhance job satisfaction and long-term organizational efficiency.^10–11

In 2022, the average household across the EU allocated almost 65% of the total annual energy consumption for cooling and heating purposes emphasizing the vital connection between thermal comfort and energy efficiency in the residential sector.^12–13 Informed, proactive management strategies for optimizing the operation of heating and cooling systems under the dual objective of minimizing energy costs while maintaining comfortable thermal environments for occupants constitutes a prominent research area that bridges the gap between theoretical thermal comfort models and real-world applications. Incorporating thermal comfort as a constraint in energy optimization frameworks, such as the day-ahead scheduling of household loads and appliances, and tariff adjustments in dynamic electricity markets, holds a promising potential to advance collective sustainability goals and alleviate energy poverty.^14–17 Furthermore, the thermal comfort optimization is integral to sustainable building design, employing smart technologies and digital solutions to respond in the face of varying outdoor environmental conditions, thereby contributing to climate resilience.

To date, researchers have proposed numerous models, methods and frameworks for thermal comfort assessment in built environments, spanning from straightforward empirical approaches dedicated to capturing average thermal experiences to advanced and adaptive approaches oriented towards personalization. No single approach can be considered superior, as each distinct approach entails specific strengths and limitations. Instead, they should be evaluated based on the trade-off between predictive gains, computational overhead and model complexity in response to the specific application's requirements and context. Even simple models relying on the fundamental climatic parameters of air temperature and relative humidity can deliver adequate predictive performance under relaxed thresholds in thermal comfort assessment. Incorporating more complex, refined climatic parameters, such as air velocity and mean radiant temperature, could further enhance predictive performance. More advanced modelling approaches for thermal comfort also consider subjective personal characteristics such as physiological, psychological and behavioural, tolerance and preferences with respect to the thermal conditions, and demographics such as gender and age.^18–19

The most widely recognized and adopted model in thermal comfort studies is the predicted mean vote (PMV), introduced by P.O. Fanger in 1970.^20–21 This model produces an index ranging between $-3$ and $+3$ representing an estimate for the average thermal perception experienced amongst a group of individuals occupying an enclosed space. The predictors used from the PMV incorporate both climatic and physiological determinants, including air temperature, relative humidity, mean radiant temperature, air velocity, metabolic rate and clothing insulation. The American Society of Heating, Refrigerating and Air-Conditioning Engineers (ASHRAE) has proposed a balanced seven-point thermal sensation scale to map the PMV index into discrete thermal comfort states: a zero PMV index implies neutral thermal sensation, while positive values correspond to warm discomfort states and the negative values to cold discomfort states. ²² Intervals between adjacent comfort states on this scale are considered as grey thermal comfort zones with a common mitigation measure for this ambiguity being the introduction of tolerance margins over the scale.

Despite the widespread adoption of PMV model in thermal comfort studies, it operates under the assumptions of stable thermal environments and steady-state occupants’ response to environmental conditions that constrains its effectiveness in practical applications when these assumptions do not hold for the examined environment. Lack of personalization represents another critical limitation of the PMV model, as it overlooks the idiosyncrasies and stochasticity inherent in human nature that give rise to diverse thermal responses instead of a uniform average one amongst a group of individuals. The standard effective temperature (SET) model developed by Gagge et al. ²³ in 1980 aimed to provide a more physiologically-oriented estimation for thermal comfort extending beyond the traditional PMV approach by quantifying thermal comfort based on a heat balance model of the human body. This model expresses the temperature of a standard reference room, i.e., a room under the assumptions that the relative humidity is $50\mathrm{\%}$ , the air velocity is $0.1$ m/s and the air temperature is equal to the mean radiant one, and in which an occupant would experience the same heat loss from the skin and respiratory tract as in the actual environment.

While both PMV and SET models have advanced the mechanistic understanding of human thermal comfort, their reliance on steady-state assumptions, population averages and hard-to-measure physiological parameters limits their practical usage in real-time and personalized applications. To address these limitations, data-driven approaches have been proposed, compensating for these shortcomings by directly learning the intricate, nonlinear relationships between environmental, physiological, psychological, behavioural and other contextual variables in response to subjective thermal experiences. Such methods enable: (i) real-time inference using sensed information and data streams; (ii) personalization by incorporating individual-specific characteristics or and human feedback loops; and (iii) adaptability as models can be retrained or adjusted to account for the temporal and contextual variability in the ambient environment. This mechanistic-to-data-driven transition emerges as a promising pathway towards more precise, scalable and human-centric assessment of thermal comfort in dynamic built environments.

Recent advancements in artificial intelligence (AI) and machine learning (ML) have transformed the thermal comfort domain shifting from static, model-driven approaches to data-driven, adaptive ones.^24–25 These methods leverage advanced modelling paradigms and algorithms to process large volume of sensed data collected from the humans surroundings, enabling personalized recommendations, optimizing the operation of cooling and heating systems, and reinforcing energy efficiency objectives. The integration of AI-enabled thermal comfort models into Building Management Systems emerges as a promising pathway to enhance occupants’ satisfaction while achieving substantial reduction in energy and operational costs, and advance sustainability through predictive modelling and intelligent decision-making. ²⁶ Additionally, these systems can facilitate long-term climate adaptability, making buildings more resilient to environmental fluctuations and contributing to broader energy conservation goals. ²⁷

The selection of PMV as the underlying thermal comfort model for the presented study was grounded in three main pillars. First, the PMV is a benchmark model confined to international standards and guidelines and the most widely used in prior research studies, which ensures that the results from the present study are compatible with recognized frameworks in the thermal comfort domain and comparable with prior research works. Second, the PMV is incorporated as an easy-to-obtain input parameter or is reasonably estimated from measurable ones unlike approaches relying on subjective, behavioural or psychological personal characteristics. Third, the PMV model is more flexible and generalizable compared to adaptive and human-oriented ones, thus serving as a cornerstone for integration with ML and optimization frameworks in real-world applications.

The motivation behind this approach was to deliver a lightweight and cost-effective predictive framework for PMV estimation, which formulated as a classification task adhering to the mapping of PMV index to discrete thermal sensation states as expressed in ASHRAE 55 standard. This framework leverages a reduced input space compared to the one used in deterministic PMV approach, including climatic parameters that are easy and readily measurable without requiring any specialized or costly instrumentation along with an estimation for the physiological parameter of clothing insulation with a minimal trade-off in predictive accuracy.

The main contributions of the presented study are summarized as follows:

Undertaking a comprehensive sensitivity analysis on the deterministic PMV model to reveal the most influential climatic and physiological parameters through assessing linear and non-linear dependencies, monotonic relationships, information-sharing metrics and ensemble-based permutation importance.

Implementating a hyperparameter optimization and a performance evaluation for random forest (RF), k-nearest neighbours (kNNs), CatBoost and multi-layer perceptron (MLP) weak learners in classifying PMV into thermal comfort categories under a reduced input feature space.

Proposing a stacked ensemble learning model in which a logistic regression (LR) meta-learner aggregates the predictions of diverse weak learners, yielding an accurate and reliable thermal comfort classification of $\cong 88\mathrm{\%}$ while mitigating the limitations of individual models.

Literature review

This section presents prior research findings and conclusions from studies with similar scope and objectives as the present work. Particular emphasis was placed on the research outcomes concerning the most critical and influential determinants for data-driven estimation of thermal comfort along with the predictive performance attained from different ML classification models and algorithms. This exploration informed the present work with valuable insights on effective methodological approaches for indirect, data-driven estimation of thermal comfort and allowed the comparison of the predictive outcomes from the present with those attained earlier.

Most studies identified climatic conditions as the dominant factors influencing thermal comfort when data-driven approaches are applied in mechanically ventilated built environments, with the air temperature, relative humidity, airspeed and solar radiation emerging as the most critical ones. ²⁸ These findings are consistent with PMV model that incorporates a similar set of climatic parameters for thermal comfort estimation. In naturally ventilated built environments, outdoor climatic conditions of air temperature and relative humidity also affect the occupants’ thermal experience underscoring the importance for incorporating outdoor conditions as additional predictors in thermal comfort models. ²⁹ Doing so offers a more nuanced understanding on the cumulative effect of external climatic conditions on thermal comfort levels, enabling a more comprehensive and holistic approach on estimating thermal comfort. Also, demographic attributes such as age, gender and ethnicity shape an individual's thermal perception and response to thermal conditions and lead to variations in comfort preferences across different population groups.^30–32 The building envelope exerts an indirect influence on thermal comfort shaping the baseline level, with well-designed envelopes acting as thermal barriers that protect interior from direct solar radiation, reduce glare, enhance natural ventilation and mitigate external heat gains. ³³

As discussed, two dominant approaches are identified in thermal comfort studies: model-driven and data-driven ones. The model-driven approaches employ deterministic, physics-based models to formulate the heat transfer between the human body and the surrounding environment using either refined variations of the PMV model or simulations through computational fluid dynamics (CFD).^34–37 The data-driven approaches leverage AI/ML to process sensed measurements collected through IoT and smart devices enabling a dynamic and evolving learning process that uncover patterns and dependencies underlying in an individual's thermal responses and corresponding predictors, moving beyond generalization.

Luo et al. ³⁸ evaluated nine different ML algorithms in predicting thermal comfort utilizing data from the ASHRAE DB II, the most comprehensive data collection with experimental recordings from multiple research studies in the thermal comfort domain. The RF resulted in optimal performance surpassing even the more sophisticated MLP model attaining an accuracy of $63.6\mathrm{\%}$ when incorporated a reduced input space with air temperature, relative humidity and clothing insulation as predictors, while including additional climatic and physiological predictors marginal predictive gains of around $2.6\mathrm{\%}$ were achieved. Chaudhuri et al. ³⁹ also employed a RF model to distinguish between broad thermal comfort classes using physiological parameters as main predictors. Although the model achieved an accuracy around $90\mathrm{\%}$ , the reliance on broad categorical classes should be acknowledged, especially in comparison with models capable of predicting narrower classifications. The superior performance of RF model was further showcased by Huang et al. ⁴⁰ benchmarking it against LR and support vector machines (SVM) in estimating the passengers thermal comfort in vehicles, resulting in an $R^2=0.65$ for thermal comfort classification over the seven point scale.

Xiong and Yao ⁴¹ applied the non-parametric kNN algorithm to devise informed personalized strategies for air-conditioning achieving an accuracy of $88.31\mathrm{\%}$ in thermal comfort prediction. The same algorithm was also employed by Aparicio-Ruiz et al. ⁴² under a similar research context for supporting decision-making in setting the optimal temperature in cooling and heating systems and achieved a predictive accuracy of $93\mathrm{\%}$ for cool, $89\mathrm{\%}$ for neutral and $97\mathrm{\%}$ for warm thermal comfort states. Salleh and Saripuddin ⁴³ developed a kNN-based thermal comfort monitoring system for commercial buildings in hot-humid climates that yielded an accuracy of $73\mathrm{\%}$ that significantly outperformed the $43\mathrm{\%}$ accuracy of the PMV model. Applying the same method in temperate climates, the accuracy fell to $18\mathrm{\%}$ , falling short of the PMV model that achieved $35\mathrm{\%}$ accuracy, indicating limitations on outside hot-humid conditions.

Park and Park ⁴⁴ used a hybrid learning framework with convolutional neural network (CNN) and SVM models, using CNN for feature extraction and SVM as the final thermal comfort predictor, achieving $95\mathrm{\%}$ accuracy with an improvement of $13\mathrm{\%}$ over the standalone CNN model. Wu et al. ⁴⁵ proposed an ensemble learning approach leveraging the bagging technique, which improved the model's stability by training multiple model variants on different sub-sets to predict multiple thermal comfort indices. This approach overperformed compared to PMV and other classification approaches, including an ANN. The robust performance of ensemble learning approaches on thermal comfort predictions was further demonstrated by Bai et al. ⁴⁶ resulting in an average improved performance improvement of $15.99\mathrm{\%}$ as the training data increases compared to $12.99\mathrm{\%}$ observed in traditional models like decision trees, kNN and ANN. Amongst the ensemble methods tested in classroom environments, deep cascade forest (DCF) and RF achieved consistently superior results, with DCF resulting in the highest weighted F1-score of $98.72\mathrm{\%}$ for predicting individual's thermal preference during summer.

Methodology

Architecture of the ensemble learning framework for PMV estimation

Figure 1 illustrates the high-level architectural design of the proposed ensemble learning framework to deliver estimations for the thermal comfort category using a reduced set of easy-to-measure and low-cost climatic parameters and an approximation for the physiological parameter of clothing insulation. The ASHRAE Global Thermal Comfort Database II was utilized as the core data collection serving modelling purposes and underwent critical preliminary, sequential steps to pre-process, explore and transform raw data. These steps were grouped under a unified structural block component representative of the data preparation procedure prior to modelling with the clean, processed data collection allocated to training and validation sub-sets for models training and validation. Each weak learner was fitted on the same training sub-set with their parameters being optimally configured using grid search cross-validation (CV). The individual predictions from weak learners were aggregated using two different ensemble approaches; a soft-voting scheme and a stacked scheme with a LR as meta-learner.

Figure 1.

The high-level architecture of the proposed stacking ensemble learning framework for thermal comfort classification.

The selection of the specific weak learners was based on their distinct, complementary advantages and particular effectiveness in capturing diverse patterns and dependencies within data leveraging distinct modelling paradigms that mitigates limitations and potential biases inherent to individual state-of-the-art models. The kNN model is a non-parametric model with strong capabilities in uncovering local similarities and intricate patterns that makes it particular effective in approximating similar thermal comfort states that arise from proximities in the input feature space. The RF is an ensemble technique aggregating the predictions from multiple decision trees and demonstrates particular robustness in noise and overfitting. Besides being a powerful approach for capturing non-linear and complex dependencies, its collective intelligence offers significant added-value in discriminating thermal comfort states with enhanced stability and reliability. For both kNN and RF models, prior research studies underscored their superior performance in thermal comfort classification problems.^38–43 The MLP is a feedforward neural network adept in learning intricate patterns in high-dimensional data through multiple hidden layers and non-linear activation functions. Unlike tree- and distance-based models that performing partitioning and exploring local similarities, the MLPs perform global function approximation that enables them capturing non-additive effects amongst features. In ensemble learning, MLPs are integral components, typically implemented with lightweight architectures to balance predictive gains against computational overhead. Prior studies also demonstrated the effectiveness of deep learning approaches on thermal comfort prediction.^44–46 The CatBoost is an advanced gradient boosting algorithm for classification problems that constructs sequential decision trees with each iteration correcting the error of its predecessor. Incorporating ordered boosting and exhibiting efficient handling of categorical features, CatBoost is regarded as one of the most robust approaches for classification when categorical features are included in the input space.

Data collection

The ASHRAE Global Thermal Comfort Database II ⁴⁷ was the core data foundation utilized in the present work for training and validation of each individual weak learner and the stacked meta-learner. It represents the most comprehensive data compilation in the thermal comfort domain including a total of 107,436 recordings collected from 66 on-field studies that conducted between 1979 and 2016 worldwide. A rich feature set was included, comprising, amongst other, studies metadata, indoor and outdoor climatic conditions at different spatial and temporal resolutions, occupants demographics and their physiological parameters of metabolic rate and clothing insulation, their subjective responses on the thermal comfort, acceptance and preferences, region, climate zones and seasons, operation of heating, cooling and ventilation systems, building structural characteristics and PMV. The heterogeneous recordings collected from thermal comfort studies across diverse built environments, regions, seasons, climate zones and occupant groups constitutes a predominant factor for selecting this compilation as the core material for modelling, since it captures significant contextual variability that promotes generalization.

Data preparation and pre-processing

The ASHRAE Global Thermal Comfort Database II has incomplete recordings due to the different experimental designs and sensing instrumentation used across the contributed research studies. Out of 107,436 recordings, 52.2% corresponded to missing values for the target variable of PMV, instead of PMV, self-reported thermal sensations and preferences were collected to determine thermal comfort in almost half of these studies. Entries with missing values for the target variable were left out from the original data collection in the absence of contribution for the subsequent modelling resulting in a reduced data collection of 51,354 recordings. In this reduced collection, air temperature was the only PMV parameter that was fully recorded reflecting both its central role in shaping thermal experiences and its relative ease and low-cost measurement. For mean radiant temperature detected, 37,990 $(74.0\text{\%})$ were missing values, for air velocity 15,518 $(30.2\text{\%})$ and for relative humidity 6799 $(13.2\text{\%})$ .

To impute the missing values for mean radiant temperature and air velocity, their corresponding measurements captured at different heights above the floor were utilized, and in particular those obtained at heights of 0.6 m and 1.1 m above the floor, omitting those obtained at 0.1 m to ensure that the replacements reflect the climatic conditions to which the human body is directly exposed. A hierarchical substitution approach was applied for missing values imputation, prioritizing measurements at 1.1 m above the floor and if not available, measurements at 0.6 m were used instead. Following this, the number of missing values was reduced to $21,799(42.4\mathrm{\%})$ for the mean radiant temperature and $3006(5.9\mathrm{\%})$ for the air velocity. Measurements at different heights above the floor were not available for relative humidity, thus no imputation process was performed for this climatic parameter.

Another important step in the data preparation and pre-processing phase is the identification of invalid and potential outliers. The invalid values represent those falling outside the plausible ranges of a specific parameter, such as negative values for the physiological parameters of metabolic rate and clothing insulation, or for the climatic parameters of air velocity and relative humidity. The outliers represent measurements underlying at the distribution tails and substantially deviating from the typical ranges, however, are plausible. Although no invalid measurements identified in the reduced data collection probably attributable to a prior data curation from contributors, multiple measurements were treated as outliers following a defensible strategy that structured upon two main pillars: domain-based thresholds for each specific PMV parameter and fundamental statistical approaches commonly used in ML pipelines.

The ASHRAE 55 standard documents explicit thresholds and valid ranges for both climatic and physiological parameters when these are incorporated as input features in the PMV model to ensure that the thermal comfort estimation would range between $-3$ and $+3$ . In particular, air temperature should range between $10\circ \text{C}$ and $30\circ \text{C}$ , relative humidity between $10\mathrm{\%}$ and $90\mathrm{\%}$ , air velocity between $0.0$ m/s and $0.2$ m/s, metabolic rate between $0.8$ and $2.0$ met, and clothing insulation between $0.0$ clo and $1.5$ clo, while boundaries for mean radiant temperature are not explicitly specified. Constraining to these defined thresholds of ASHRAE 55 standard, a total of $9,012$ recordings were removed as outliers from which $7,678(14.7\mathrm{\%})$ corresponded to air velocity, 1059 $(2.0\mathrm{\%})$ to clothing insulation, 374 (0.7%) to metabolic rate, and 53 (0.1%) to relative humidity. No recordings exclusions were applied for air temperature.

The most conservative and defensive statistical approaches for handling outliers in ML problems are z-score and Tukey's interquartile range (IQR) rule, with IQR rule representing the most common, interpretable and transparent one. Retaining outliers in training and validation datasets could distort estimation of the model's parameters, introduce model bias, inflate error metrics and constraint models generalization. Although the IQR rule typically defines as outliers those values ranging outside the $\pm 1.5\times IQR$ , the present work adopted an even more conservative strategy for outliers recognizing that such values may correspond to underrepresented yet realistic extreme thermal discomfort states. The adjusted yet defensive range for outliers was defined at $\pm 3.8\times IQR$ ensuring that the $\approx 99.5\mathrm{\%}$ of the normally distributed data would be preserved and the sample size for extreme warm and cold discomfort states would not be reduced more than $2.5\mathrm{\%}$ . Following the outlier's removal, a total of 708 recordings were left out constituting the data compilation for the subsequent training and validation, denoted as $\mathcal{D}$ , comprising $|\mathcal{D}|=42,984$ recordings. Out of the $708$ removed recordings, $572$ corresponded to metabolic rate, $114$ to air temperature and $83$ to mean radiant temperature.

Let ${\mathbf{\text{x}}}_i$ denote an input vector with the full set of PMV parameters where $x_i^{t_a}$ represents air temperature, $x_i^{tr}$ mean radiant temperature, $x_i^{rh}$ relative humidity, $x_i^{av}$ air velocity, $x_i^{cl}$ clothing insulation and $x_i^{mr}$ metabolic rate. Let $y_i=[-3,+3]\in \mathbb{R}$ denote the PMV corresponding to the input vector ${\mathbf{\text{x}}}_i$ . The collection $\mathcal{D}$ following the data preparation and pre-processing procedures is presented in Equations (1) and (2) with $*$ denoting missing values.

$$\begin{array}{rl}{\mathbf{\text{x}}}_i& =(x_i^{t_a},x_i^{tr},x_i^{rh},x_i^{av},x_i^{cl},x_i^{mr})\in (\mathbb{R}\cup \{*\}{)}^6\end{array}$$

(1)

$$\begin{array}{rl}\mathcal{D}& =\{({\mathbf{\text{x}}}_i,y_i){\}}_{i=1}^{|\mathcal{D}|}\end{array}$$

(2)

Data exploration

The initial step of the data exploration was to confirm the heterogeneity amongst the ASHRAE Global Thermal Comfort Database II recordings with respect to diverse regional, seasonal and climate contexts, which provides the essential foundation for robust modelling and supports further generalization rather than adapting to narrow contextual characteristics of specific studies. The most recordings originated from studies conducted in Asia $(33.43\mathrm{\%})$ and Europe $(32.08\mathrm{\%})$ with North America $(17.93\mathrm{\%})$ , Oceania $(7.68\mathrm{\%})$ , South America $(6.87\mathrm{\%})$ and Africa $(2.01\mathrm{\%})$ delivering smaller contributions. The summer $(39.32\mathrm{\%})$ and winter $(34.97\mathrm{\%})$ seasons dominated the data compilation with autumn $(13.73\mathrm{\%})$ and spring $(11.99\mathrm{\%})$ seasons contributing less. In total, 19 climate zones were represented in the data compilation amongst which the largest shares corresponded to the hot-summer Mediterranean $(21.66\mathrm{\%})$ and humid sub-tropical $(16.63\mathrm{\%})$ climate zones. From the Köppen perspective for climate classification, the most prevalent climate was temperate (59.17%) followed by tropical $(16.77\mathrm{\%})$ , arid $(15.15\mathrm{\%})$ and continental $(8.91\mathrm{\%})$ . The majority of recordings corresponded to office spaces $(66.04\mathrm{\%})$ followed by classrooms $(15.24\mathrm{\%})$ , multi-family houses $(12.08\mathrm{\%})$ , senior centres $(2.00\mathrm{\%})$ and undefined $(4.64\mathrm{\%})$ .

Further exploration of descriptive statistics and distributional characteristics for the indoor climatic conditions of air temperature, relative humidity, mean radiant temperature and air velocity in $\mathcal{D}$ delivered valuable insights on the environmental drivers for the PMV model. The average indoor air temperature was $23.2\circ \text{C}$ with a standard deviation of $2.3\circ \text{C}$ and a median of $23.1\circ \text{C}$ . With a difference of $0.1\circ \text{C}$ between the mean and median values, the air temperature distribution was fairly symmetric, supported by the low Pearson's skewness coefficient of $0.13$ . The first and the third quartiles at $Q_1=22.0\circ \text{C}$ and $Q_3=24.4\circ \text{C}$ yielded an $IQR=2.4\circ \text{C}$ providing additional evidence for the limited minimal skewness in distribution. The mean radiant and air temperatures exhibited similar descriptive statistics measures, with mean radiant temperature resulting in an average of $23.6\circ \text{C}$ with $2.5\circ \text{C}$ standard deviation and a median of $23.5\circ \text{C}$ which also suggested a fairly symmetric distribution with a Pearson's skewness coefficient of $0.12$ . The first and third quartiles at $Q_1=22.2\circ \text{C}$ and $Q_3=24.9\circ \text{C}$ yielded an $IQR=2.5\circ \text{C}$ similar to the one determined for air temperature. The close alignment between mean radiant and air temperature distributional characteristics reflected balanced conditions in the ambient environment, where convective and radiative heat exchanges were relative consistent. An average relative humidity of $45.0\mathrm{\%}$ with standard deviation of $14.2\mathrm{\%}$ was observed and a median of $44.6\mathrm{\%}$ , with the minimal difference of $0.4\mathrm{\%}$ between the central tendency measures indicating also a highly symmetrical distribution corresponding to a Pearson's skewness coefficient of $0.08$ . The first and third quartiles at $Q_1=33.9\text{\%}$ and $Q_3=55.5\text{\%}$ reflected moderate variance with half of the observations falling within the acceptable relative humidity boundaries for comfortable indoor spaces as reflected in ASHRAE 55 standard. The average air speed was 0.08 m/s with a standard deviation of 0.05 m/s corresponding to a coefficient of variation around $62.5\mathrm{\%}$ indicative of substantial dispersion. With the first and third quartiles positioned at $Q_1=0.04\text{; m}/\text{s}$ and $Q_3=0.1\text{; m}/\text{s}$ with a median of 0.07 m/s, low air flows predominate occasional increased ones attributable to different ventilation strategies.

Turning to the descriptive statistics and distributional characteristics of the physiological parameters, the average and the median metabolic rate was $1.24$ met with a standard deviation of $0.19$ met. The first and the third quartiles at $Q_1=1.13$ met and $Q_3=1.29$ met suggested a narrow $IQR=0.16$ met with low variance. This pattern indicated sedentary to light activity levels for the majority of subject engaged. The mean and median clothing insulation were nearly identical, and, in particular, $0.69$ clo and $0.68$ clo, with a standard deviation of $0.24$ clo, suggesting a highly symmetrical distribution. The first and third quartiles at $Q_1=0.51$ met and $Q_3=0.80$ yielded an $IQR=0.29$ clo reflecting that most subjects wore light to medium clothing ensembles within the typical comfort range.

As shown in Figure 2, with a mean PMV of $-0.21$ and a median of $-0.22$ , the distribution of thermal comfort was centred around the neutral thermal comfort state with a slight tendency cooler thermal states. The standard deviation of $0.65$ corresponded to $10.8\mathrm{\%}$ of the full thermal scale indicating moderate dispersion and under the empirical rule, about $68\mathrm{\%}$ of the PMV values fall within $[-0.86,+0.44]$ . The first and third quartiles at $Q_1=-0.62$ and $Q_3=0.20$ yielded an $IQR=0.82$ and confirmed that half of the PMV values are between slightly cool and slightly warm conditions. With the median closer to the $Q_1$ , the PMV exhibited a mild bias towards cooler sensations.

Figure 2.

A boxplot representing the distributional characteristics of the PMV values.

Frequency analysis in PMV revealed a significant decrease in samples as the thermal experience diverges from neutral towards thermal discomfort states. A total of $23,931$ samples $(55.52\mathrm{\%})$ corresponded to neutral thermal comfort state, whereas $12,464$ samples $(28.92\mathrm{\%})$ represented slightly cold and $5,220$ samples $(12.11\mathrm{\%})$ slightly warm thermal discomfort. The remaining samples corresponded to the cold and warm thermal comfort states comprising 2.64% and 0.81% of the total samples, respectively. A critical assumption was made by merging the two most extreme thermal discomfort states due to their limited representation in the original dataset. This scarcity is neither an anomaly of the specific dataset, which is the most recognized one in the thermal comfort studies and comprises samples from research studies conducted under diverse contexts and conditions, nor resulted following the outliers’ removal. Instead, it is an inherent limitation of thermal comfort studies owing to occupants’ natural tendency to remain near neutral thermal experiences. The most common and robust mitigation strategy is therefore to merge the two most extreme discomfort states for warm and cold discomfort reclassifying the standard seven-point thermal scale into a more compact five-point scale. Table 1 summarizes the mapping of this mitigation strategy for class imbalance in the extreme thermal discomfort states.

Table 1.

The mapping of thermal comfort states original to merged states for the extreme thermal discomfort states.

Original thermal comfort state	Merged thermal comfort state	Target class (encoded value)
Cold	Cold discomfort	−2
Cool
Slightly cool	Slightly cold discomfort	−1
Neutral	Neutral	0
Slightly warm	Slightly warm discomfort	+1
Warm	Warm discomfort	+2
Hot

Sensitivity analysis

A sensitivity analysis was conducted aiming to assess the influence of each specific climatic and physiological parameter on the deterministic PMV model that combined linear and monotonic dependencies, measures for the shared information and rankings for the predictive contributions as derived from feature importance.

Although PMV is a deterministic function using climatic and physiological parameters as inputs, the correlation analysis could provide valuable insights on how its empirical variations aligns with individual parameters and measures how sensitive is PMV to each specific parameter from a statistical perspective. Pearson's correlation coefficient r was computed to measure the strength for linear correlations underlying between PMV parameters and itself. Spearman's rank correlation coefficient $\rho$ was computed to quantify monotonic dependencies between PMV parameters and itself. Both measures identified strong linear and monotonic associations between the climatic parameters of air and mean radiant temperatures with PMV under the Evan's interpretation for Pearson's and Spearman's coefficients. In particular, the air temperature attained an $r=0.69$ , $\rho =0.64$ , and the mean radiant temperature an $r=0.70$ , $\rho =0.66$ . Based on the inherent inclusion of air temperature in mean radiant temperature, potential linear dependencies between these two climatic parameters were further explored. These parameters exhibited a very strong linear relationship according to the Evan's interpretation with an $r=0.86$ , $95\mathrm{\%}$ confidence interval $(CI)$ of $CI=[0.858,0.863]$ and $p<0.001$ . The air temperature alone explained around $74\mathrm{\%}$ of the total variance in mean radiant temperature with a $VIF\cong 3.9$ indicating moderate multicollinearity between these two parameters. Given these statistical insights suggesting redundancy and recognizing that the mean radiant temperature is hard to be measured with standard sensing instrumentation limiting the model's effectiveness in practical applications, the mean radiant temperature was omitted from the input feature space ${\mathbf{\text{x}}}_i$ . In addition, introducing an estimate for the mean radiant temperature in the input feature space for ensemble and neural network models would not deliver predictive gains due to the strong collinearity identified with the air temperature. By contrast, the physiological parameters of metabolic rate $(r=0.28,\rho =0.27)$ and clothing insulation $(r=0.24,\rho =0.26)$ exhibited weak linear and monotonic correlations of comparable magnitudes, whereas air velocity and relative humidity showed negligible associations with $|r|<0.10,|\rho |<0.10$ .

The sensitivity analysis was further extended to explore the absolute $(MI)$ and normalized $(M{I}_{norm})$ mutual information, a measure that quantifies the amount of shared information amongst variables. The air temperature $(MI=0.53,M{I}_{norm}=1.00)$ and the mean radiant temperature $(MI=0.49,M{I}_{norm}=0.92)$ achieved the highest $MI$ scores that highlighted their dominant information contribution in PMV, corroborating the prior findings. The relative humidity followed with moderate contribution to PMV $(MI=0.30,M{I}_{norm}=0.58)$ in contrast to the negligible linear and monotonic correlations, suggesting that the underlying relationship with PMV is predominantly non-linear. Weaker yet considerable information contribution revealed for the clothing insulation $(MI=0.21,M{I}_{norm}=0.40)$ , whereas for metabolic rate and air velocity the $MI<0.10$ , indicating limited predictive strength for PMV.

The permutation analysis on climatic and physiological parameters also confirmed the dominant predictive contribution of the air temperature on PMV yielding the highest permutation importance score of $PI=1.76$ . Clothing insulation also showed an intermediate $PI=0.74$ consistent with its ranking in shared information, whereas the metabolic rate followed achieved a relatively lower $PI=0.24$ . The predictive contributions from relative humidity and air velocity on PMV were negligible as reflected to $PI<0.04$ . Figure 3 illustrates the partial dependence plots that showed clear near-linear positive effect for the air temperature (t_a) and clothing insulation (clo) parameters on PMV, while the relative humidity (rh) exhibited marginal influence consistent with its low $PI$ score.

Figure 3.

Partial dependence plots of PMV for the air temperature, relative humidity and clothing insulation parameters.

Given the consistent evidence for weak associations and predictive gains between the air velocity and PMV, it was excluded from the input feature space ${\mathbf{\text{x}}}_i$ following the same rationale as for the mean radiant temperature. A subsequent investigation evaluated potential predictive contributions from higher order and interaction terms of the remaining PMV determinants: air temperature, relative humidity, metabolic rate and clothing insulation. In general, all the cubic and squared terms were less informative compared to interaction terms with $PI<0.20$ , while interaction terms comprising air temperature resulted in the highest $PI$ scores. The highest score attained for the interaction term of air temperature and clothing insulation $(PI=0.51)$ followed by the one including air temperature and metabolic rate $(PI=0.21)$ . Standalone air temperature achieved a $PI=0.26$ and clothing insulation a $PI=0.06$ . While these interaction terms revealed considerable predictive contribution, their overall strength did not alter the feature importance hierarchy established for the standalone terms. Therefore, while interaction terms could potentially contribute to more accurate PMV estimations, their predictive effects are already captured implicitly, and thus the added value of explicitly engineered interaction terms remains limited.

Feature engineering

The feature engineering involved selecting those PMV determinants with the strongest predictive contribution to construct a reduced input feature space ${{\mathbf{\text{x}}}^{\mathrm{\prime }}}_i$ for the subsequent modelling and also applying the appropriate numerical transformations and encodings on features of the reduced space to ensure compatibility with the architectural requirements of models. The feature selection was guided by results of sensitivity analysis, that revealed air temperature as the parameter with the strongest dependencies and predictive strength for PMV predictions, making its inclusion essential. Clothing insulation also demonstrated a considerable contribution as PMV predictor and was therefore incorporated into the feature set. The relative humidity showed moderate non-linear dependencies with PMV, however, given that it is an easy-to-measure, low-cost parameter it was retained in the reduced input space. Metabolic rate showed notable contribution only through the interaction term with air temperature, with its standalone predictive gains being negligible to weak. Recognizing that metabolic rate is not a directly measurable parameter with standard sensing instrumentation and requires either estimation through indirect methods or self-reporting, its inclusion would limit the framework's practicality without commensurate substantial predictive gains. Therefore, its exclusion from the reduced input space preserves both applicability and parsimony for the framework's deployment in real-world settings.

Let ${{\mathbf{\text{x}}}^{\mathrm{\prime }}}_i$ denote the input vector of the reduced feature space, then Equation (3) provides its mathematical formulation.

$$\begin{array}{r}{{\mathbf{\text{x}}}^{\mathrm{\prime }}}_i=(x_i^{t_a},x_i^{rh},x_i^{cl})\in (\mathbb{R}\cup \{*\}{)}^3\end{array}$$

(3)

Let ${\mu }^{(f)}$ represent the mean and ${\sigma }^{(f)}$ represents the standard deviation of a specific feature f. The features $x_i^{t_a}$ and $x_i^{rh}$ corresponding to the climatic parameters of air temperature and relative humidity were standardized using z-score normalization to centre their distributions around the mean and scale them to the unit variance as described in Equation (4).

$$\begin{array}{r}{x}_i^{\mathrm{\prime }(f)}=\frac{x_i^{(f)}-{\mu }^{(f)}}{{\sigma }^{(f)}}\end{array}$$

(4)

The numerical feature of clothing insulation $x_i^{cl}$ was discretized into categories adhering to the ASHRAE 55 standard, which defines representative clothing insulation values for seasonal ensembles. For summer season, the typical clothing insulation is $0.5$ clo and for winter season, $1.0$ clo. An additional transitional typical seasonal ensemble for autumn and spring is $0.75$ clo. This approximation was applied across all the clothing insulation values included in $\mathcal{D}$ capitalizing on the assigned season to each single recording. The mathematical formulation of this approximation is described in Equation (5).

$$\begin{array}{r}{x}_i^{cl}=\{\begin{array}{ll}\text{0.5},& \text{if season = summer}\\ \text{0.75},& \text{if season = {winter, autumn} }\\ \text{1.0},& \text{if season = winter}\end{array}\end{array}$$

(5)

The target variable of PMV $y_i$ was encoded into five (5) discrete thermal comfort classes as presented in Table 1. The intermediate values $y_i\notin \mathbb{Z}$ that do not directly correspond to a specific thermal comfort category were assigned based on rounding to the nearest one. The transformation is formulated as Equation (6).

$$\begin{array}{r}{y}_i=min\{\text{2,max}\{\text{ - 2,round}({\text{y}}_{\text{i}})\}\}\end{array}$$

(6)

Modelling

All the recordings containing at least one missing value for an input features ${{\mathbf{\text{x}}}^{\mathrm{\prime }}}_i$ or for the target variable $y_i$ were removed from the dataset $\mathcal{D}$ constituting the dataset ${\mathcal{D}}^{\mathrm{\prime }}$ with $|{\mathcal{D}}^{\mathrm{\prime }}|=43,102$ . Removal was preferred over imputation with estimates or statistical measures to avoid introducing additional uncertainty to predictions. The dataset ${\mathcal{D}}^{\mathrm{\prime }}$ was then partitioned into two sub-sets: the training set ${{\mathcal{D}}_t}^{\mathrm{\prime }}$ and the validation set ${{\mathcal{D}}_v}^{\mathrm{\prime }}$ using a stratified 80/20 split ratio to preserve the class distribution of ${\mathcal{D}}^{\mathrm{\prime }}$ . Let $\mathcal{C}$ denote the set of five thermal comfort classes with $c\in \mathcal{C}$ representing a specific one. The partition of ${\mathcal{D}}^{\mathrm{\prime }}$ into training $({{\mathcal{D}}_t}^{\mathrm{\prime }})$ and validation $({{\mathcal{D}}_v}^{\mathrm{\prime }})$ sub-sets is described in Equation (7) and the stratification constraint is formalized as Equation (8).

$$\begin{array}{rl}& \begin{array}{rl}{\mathcal{D}}^{\mathrm{\prime }}& ={{\mathcal{D}}_t}^{\mathrm{\prime }}\cup {{\mathcal{D}}_v}^{\mathrm{\prime }},{{\mathcal{D}}_t}^{\mathrm{\prime }}\cap {{\mathcal{D}}_v}^{\mathrm{\prime }}=\oslash \\ & \text{where }|{{\mathcal{D}}_t}^{\mathrm{\prime }}|=0.8\times |{\mathcal{D}}^{\mathrm{\prime }}|\text{and}|{{\mathcal{D}}_v}^{\mathrm{\prime }}|=0.2\times |{\mathcal{D}}^{\mathrm{\prime }}|\end{array}\end{array}$$

(7)

$$\begin{array}{rl}& \frac{|{\mathcal{D}}_t{{}^{\mathrm{\prime }}}^{(c)}|}{|{{\mathcal{D}}_t}^{\mathrm{\prime }}|}=\frac{|{\mathcal{D}}_v{{}^{\mathrm{\prime }}}^{(c)}|}{|{{\mathcal{D}}_v}^{\mathrm{\prime }}|},\mathrm{\forall }c\in \mathcal{C}\end{array}$$

(8)

Evaluation metrics

To evaluate and report the predictive performance for each individual weak learner and the overall ensemble learning framework, the four standard classification metrics were used: (i): accuracy to measure the proportion of samples classified correctly across all the thermal comfort classes; (ii): precision to measure the proportion of correctly classified samples amongst those predicted to belong to a specific thermal comfort class; (iii): recall to measure the model's ability to identify all relevant samples for a specific thermal comfort class; (iv): and F1-score to represent the harmonic mean of precision and recall, providing a balanced measure of performance. In the ${{\mathcal{D}}_v}^{\mathrm{\prime }}$ , let the number of true positives denoted as $TP$ , true negatives as $TN$ , false positives as $FP$ and false negatives as $FN$ . Let also $T{P}^{(c)}$ , $T{N}^{(c)}$ , $F{P}^{(c)}$ and $F{N}^{(c)}$ denote the corresponding counts for a specific thermal comfort class $c\in \mathcal{C}$ . Then, the standard evaluation metrics could be expressed as in Equations (9) to (12).

$$\begin{array}{rl}\text{Accuracy}& =\frac{TP+TN}{TP+TN+FP+FN}\end{array}$$

(9)

$$\begin{array}{rl}\text{Precision}& =\frac{T{P}^{(c)}}{T{P}^{(c)}+F{P}^{(c)}}\end{array}$$

(10)

$$\begin{array}{rl}\text{Recall}& =\frac{T{P}^{(c)}}{T{P}^{(c)}+F{N}^{(c)}}\end{array}$$

(11)

$$\begin{array}{rl}F1-\text{score}& =2\times \frac{\text{Precisio}{\text{n}}^{(\text{c})}\times \text{Recal}{\text{l}}^{(\text{c})}}{\text{Precisio}{\text{n}}^{(\text{c})}+\text{Recal}{\text{l}}^{(\text{c})}}\end{array}$$

(12)

To quantify uncertainty in PMV predictions, all the standard evaluation metrics were reported using the mean value together with its $95\mathrm{\%}CI$ . The $CI$ was computed using a stratified CV with 5 folds and $B=1000$ bootstrap re-samples of the fold scores in ${{\mathcal{D}}_v}^{\mathrm{\prime }}$ to approximate the sampling distribution of means. Let $m_b$ denote the mean score obtained in the bootstrap sample b, where $b=\{1,2,\dots ,B\}$ . Then the empirical distribution $\{m_b{\}}_{b=1}^B$ used to compute the two-sided percentile $CI$ is described as in Equations (13) and (14), where $Q_p$ denotes the p-th quantile of the bootstrap distribution and $\overline{m}$ the mean performance across all folds

$$\begin{array}{rl}& C{I}_{95\mathrm{\%}}=[Q_{0.025}(m_b),Q_{0.975}(m_b)]\end{array}$$

(13)

$$\begin{array}{rl}& \overline{m}\pm \frac{1}{2}\times (Q_{0.025}(m_b),Q_{0.975}(m_b))\end{array}$$

(14)

Results and discussion

RF classifier

The RF classifier is a tree-based model with particular effectiveness in uncovering complex and non-linear dependencies and robust performance against overfitting. An RF variant comprising $n_{\text{est}}=100$ estimators, unrestricted maximum depth $d_{\text{max}}$ from a root to a leaf node, $n_{\text{split}}=2$ minimum samples to split an internal node and $n_{\text{leaf}}=1$ minimum sample required at a leaf node was used to establish the minimum performance threshold, achieving an overall accuracy of $85.2\mathrm{\%}\pm 1.3\mathrm{\%}$ and a macro average F1-score of $74.9\mathrm{\%}\pm 1.5\mathrm{\%}$ . For the neutral thermal comfort class, this baseline model attained the strongest predictive performance with a precision of $87.3\mathrm{\%}\pm 0.9\mathrm{\%}$ , a recall of $90.2\mathrm{\%}\pm 0.8\mathrm{\%}$ and an F1-score of $88.7\mathrm{\%}\pm 0.8\mathrm{\%}$ . Likewise, for the slightly warm thermal discomfort class, the baseline model also showed strong performance, as reflected to a precision of $84.0\mathrm{\%}\pm 1.1\mathrm{\%}$ , a recall of $80.5\mathrm{\%}\pm 1.2\mathrm{\%}$ and $82.2\mathrm{\%}\pm 1.1\mathrm{\%}$ F1-score. For the thermal comfort classes representing extreme warm and cold thermal discomfort states, the baseline model reported comparable precision of $\cong 80\mathrm{\%}$ but recall was substantially degraded; in particular, warm thermal discomfort state resulted in a recall of $53.7\mathrm{\%}\pm 1.4\mathrm{\%}$ and cold thermal discomfort state a recall of $44.9\mathrm{\%}\pm 1.6\mathrm{\%}$ , indicating reduced sensitivity of the baseline model towards these minority classes.

The hyperparameter space ${\mathcal{H}}_{rf}$ was explored to optimally configure the RF weak learner with respect to the F1-score metric using a grid search with a stratified 3-fold CV that focuses on parameters governing the model's complexity. The search space ${\mathcal{H}}_{rf}$ was defined as the cartesian product of $n_{\text{est}}$ , $d_{\text{max}}$ , $n_{\text{split}}$ and $n_{\text{leaf}}$ hyperparameters as described in Equations (15) and (16) with the optimal performance achieved for $n_{\text{est}}=200$ , $n_{\text{split}}=2$ , $n_{\text{leaf}}=2$ and an unrestricted $d_{max}=none$ .

$$\begin{array}{rl}& {\mathcal{H}}_{\text{rf}}=n_{\text{est}}\times d_{\text{max}}\times n_{\text{split}}\times n_{\text{leaf}}\end{array}$$

(15)

$$\begin{array}{rl}& \begin{array}{rl}{n}_{\text{est}}& =\{100,120,\dots ,400\},d_{\text{max}}=\{\text{none},1,2,\dots ,20\},\\ n_{\text{split}}& =\{2,3,\dots ,10\},n_{\text{leaf}}=\{1,2,..,5\}\end{array}\end{array}$$

(16)

Although the optimized RF exhibited marginally reduced overall accuracy compared to the baseline model, it delivered a more consistent predictive performance across the thermal comfort classes, markedly improving predictions for thermal discomfort classes at the expense of only minimal degradation in the majority class. For the neutral thermal comfort class, it achieved a precision of $91.1\mathrm{\%}\pm 1.1\mathrm{\%}$ , a recall of $83.1\mathrm{\%}\pm 1.2\mathrm{\%}$ and an F1-score of $86.9\mathrm{\%}\pm 1.1\mathrm{\%}$ . For the slightly warm thermal discomfort class, it reported a precision of $75.6\mathrm{\%}\pm 1.1\mathrm{\%}$ , a recall of $88.5\mathrm{\%}\pm 1.2\mathrm{\%}$ and an F1-score of $81.5\mathrm{\%}\pm 1.1\mathrm{\%}$ . The slightly cold thermal discomfort state resulted in an F1-score of $81.2\mathrm{\%}\pm 1.0\mathrm{\%}$ , comparable to its slightly warm counterpart that indicated symmetry in performance across opposing mild discomfort states. Τhe optimized RF achieved the most notable predictive gains for the extreme thermal discomfort states; for the cold thermal discomfort class, a precision of $57.6\mathrm{\%}\pm 1.4\mathrm{\%}$ , a recall of $70.0\mathrm{\%}\pm 1.2\mathrm{\%}$ and an F1-score of $63.2\mathrm{\%}\pm 1.3\mathrm{\%}$ were reported, while for the warm thermal discomfort class the precision was $70.0\mathrm{\%}\pm 1.1\mathrm{\%}$ , the recall was $73.1\mathrm{\%}\pm 1.1\mathrm{\%}$ and the F1-score was $71.5\mathrm{\%}\pm 1.1\mathrm{\%}$ .

The confusion matrix of Figure 4 confirmed the optimized RF model's strong ability to deliver a more balanced and consistent predictive performance relative to the baseline model. In particular, it markedly enhanced the recognition of the extreme thermal discomfort classes, with recall increasing from 45% to 70% for the cold thermal discomfort class and from 54% to 73% for the warm thermal discomfort class. Moreover, it reduced the tendency of the baseline model to misclassify mild discomfort instances into the dominant neutral thermal comfort class, thereby mitigating class imbalance effects.

Figure 4.

Comparative confusion matrices of the baseline and optimized RF weak learners.

kNN classifier

The second weak learner implemented was a kNN, a model that captures local neighbourhood structures and decision boundaries in the feature space and is particularly effective for discriminating thermal comfort states. A non-optimized variant with $k=15$ neighbours, Euclidean distance $(p=2)$ and uniform voting was developed to provide performance benchmark for this specific weak learner. The selection of $k=15$ neighbours was guided by the need for balanced model bias and variance that ensures sufficient smoothing in class boundaries while reducing sensitivity to noise. Given the multiclass nature of the thermal comfort classification problem and the class imbalance in the dataset, selecting a moderately large number of neighbours helped to stabilize predictions. The baseline model attained an overall accuracy of $75.7\mathrm{\%}\pm 1.2\mathrm{\%}$ with relatively strong performance only for the majority neutral thermal comfort class, in which reported a precision of $78.6\mathrm{\%}\pm 1.1\mathrm{\%}$ , recall of $84.5\mathrm{\%}\pm 1.1\mathrm{\%}$ , and an F1-score of $81.4\mathrm{\%}\pm 1.1\mathrm{\%}$ . For the mild thermal discomfort classes, the baseline kNN model achieved comparable performance as reflected to F1-scores $\cong 70\mathrm{\%}$ : the slightly warm thermal discomfort class reported a precision of $77.6\mathrm{\%}\pm 1.1\mathrm{\%}$ , recall of $62.6\mathrm{\%}\pm 1.3\mathrm{\%}$ , and an F1-score of $69.3\mathrm{\%}\pm 1.2\mathrm{\%}$ ; the slightly cold thermal discomfort class reported a precision of $70.5\mathrm{\%}\pm 1.1\mathrm{\%}$ , recall of $70.2\mathrm{\%}\pm 1.1\mathrm{\%}$ and an F1-score of $70.4\mathrm{\%}\pm 1.1\mathrm{\%}$ . The baseline model showed weak performance for the extreme thermal discomfort states, and in particular it achieved an F1-score of $31.4\mathrm{\%}\pm 1.7\mathrm{\%}$ for the cold discomfort and $51.5\mathrm{\%}\pm 1.5\mathrm{\%}$ for the warm discomfort classes.

The hyperparameter space ${\mathcal{H}}_{knn}$ was explored to find the optimal configuration for the kNN weak learner with respect to the F1-score using a grid search with a stratified 3-fold CV. The search space ${\mathcal{H}}_{knn}$ was defined as the cartesian product of neighbour's number k, distance metric d and weight function w as described in Equations (17) and (18). The optimal performance was achieved for $k=5$ neighbours with $d=\text{Euclidean}$ distance metric and $w=uniform$ weight function yielding an identical overall accuracy of $75.7\mathrm{\%}\pm 1.2\mathrm{\%}$ .

$$\begin{array}{rl}& {\mathcal{H}}_{knn}=k\times d\times w\end{array}$$

(17)

$$\begin{array}{rl}& \begin{array}{rl}k& =\{2,3,\dots ,25\},d\in \{\text{Euclidean and Minkowski}\},\\ w& \in \{uniform,distance\}\end{array}\end{array}$$

(18)

Even the optimized kNN model exhibited an identical overall accuracy compared to the baseline model, it provided an enhanced predictive performance across the thermal comfort classes with the fewer samples, as also presented in Figure 5, sharing a common observation with the RF weak learner. In addition, it attained a strong performance in the dominant neutral thermal comfort class with a recall of $93\mathrm{\%}$ .

Figure 5.

Comparative confusion matrices of the baseline and optimized kNN weak learners.

Figure 6.

Comparative confusion matrices of the baseline and optimized CatBoost weak learners.

Figure 7.

The confusion matrix for the fine-tuned MLP weak learner.

CatBoost classifier

The third weak learner implemented was a CatBoost, a model with particular effectiveness dealing robustly with imbalanced data distributions, which is advantageous for thermal comfort classification. The performance benchmark for this weak learner established using a minimal model configuration with $n_{\text{iter}}=100$ boosting iterations that demonstrated an overall accuracy of $82.0\mathrm{\%}\pm 1.0\mathrm{\%}$ . For the neutral thermal comfort class, the baseline model attained the strongest predictive performance with a precision of $92.5\mathrm{\%}\pm 0.9\mathrm{\%}$ , a recall of $79.9\mathrm{\%}\pm 1.2\mathrm{\%}$ and an F1-score of $85.7\mathrm{\%}\pm 1.1\mathrm{\%}$ , and the mild discomfort thermal states followed with similar F1-scores of around $80\mathrm{\%}$ . Notably, the baseline CatBoost achieved enhanced predictive gains for the extreme warm thermal discomfort class, resulted in an F1-score of $75.8\mathrm{\%}\pm 1.2\mathrm{\%}$ , which was significantly higher than the corresponding ones observed at the non-optimized variables of RF and kNN. For the extreme cold thermal discomfort class, the baseline CatBoost showed weak performance, yielding an F1-score of $62.0\mathrm{\%}\pm 1.3\mathrm{\%}$ .

The hyperparameter space ${\mathcal{H}}_{cb}$ was constructed to search the optimal configuration for the CatBoost weak learner using also a stratified grid search with 3-fold CV. The search space comprised the cartesian product of boosting iterations $n_{iter}$ , learning rate l and maximum tree depth $d_{max}$ as described in Equations (19) and (20). The optimal performance attained for $n_{iter}=600$ , $l=0.2$ and $d_{split}=7$ reporting an overall accuracy of $86.3\mathrm{\%}\pm 1.2\mathrm{\%},$ a marginally higher accuracy by $1.3\mathrm{\%}$ than the baseline CatBoost model.

$$\begin{array}{rl}& {\mathcal{H}}_{cb}=n_{iter}\times l\times d_{max}\end{array}$$

(19)

$$\begin{array}{rl}& n_{iter}=\{100,150,\dots ,800\},l\in \{0.01,0.05,0.1,0.2\},\\ & d_{max}=\{3,4,\dots ,7\}\end{array}$$

(20)

The optimized CatBoost resulted in an overall accuracy of $83.5\mathrm{\%}\pm 1.0\mathrm{\%}$ and a macro average F1-score of $81.9\mathrm{\%}\pm 1.1\mathrm{\%}$ , with the confusion matrix of Figure 6 presenting the recall scores for all the thermal comfort classes. It demonstrated particular effectiveness in the majority class with a precision of $96.8\mathrm{\%}\pm 0.7\mathrm{\%}$ , recall of $87.0\mathrm{\%}\pm 0.9\mathrm{\%}$ and an F1-score of $91.6\mathrm{\%}\pm 0.8\mathrm{\%}$ . A strong performance was also observed for the classes representing mild thermal discomfort states: for the slightly warm thermal discomfort, it attained a precision of $77.2\mathrm{\%}\pm 1.1\mathrm{\%}$ , a recall of $95.2\mathrm{\%}\pm 0.7\mathrm{\%}$ and an F1-score of $85.3\mathrm{\%}\pm 0.9\mathrm{\%}$ . For the slightly cold thermal discomfort, a precision of $83.3\mathrm{\%}\pm 1.0\mathrm{\%}\text{was; attained}$ , a recall of $88.6\mathrm{\%}\pm 1.0\mathrm{\%}$ and an F1-score of $85.9\mathrm{\%}\pm 1.0\mathrm{\%}$ . Similar to the baseline model, the optimized CatBoost variant demonstrated notable performance in extreme warm thermal discomfort classes, yielding a precision of $77.4\mathrm{\%}\pm 1.1\mathrm{\%}$ , a recall of $85.4\mathrm{\%}\pm 1.0\mathrm{\%}$ , and an F1-score of $81.2\mathrm{\%}\pm 1.0\mathrm{\%}$ . On the contrary, while the F1-score for the extreme cold thermal discomfort was substantially lower, and in particular $65.7\mathrm{\%}$ , it showed improved performance compared to the optimized variant of kNN.

MLP classifier

A feedforward neural network also incorporated as weak learner in the ensemble learning framework to provide significant benefits related to capturing nonlinear relationships and complex feature interactions beyond those modelled by tree- and distance-based weak learners. The hyperparameter space ${\mathcal{H}}_{mlp}$ was constructed to find the optimal hyperparameters for the MLP using a stratified grid search with 3-fold CV. This search space comprised the hidden layer size $n_h$ with single-layer architectures of $\{50,100,150\}$ neurons and two-layer architectures of $(50,50)$ and $(100,50)$ neurons, activation functions $f_a=\{relu,tanh\}$ , regularization strength $a=\{0.0001,0.001,0.01\}$ and $l_r=\{adaptive,constant\}$ learning rates. Considering the predictive accuracy in response to the computational overhead, a balanced MLP architecture was adopted with a single hidden layer of $n_h=100$ neurons, $a=0.001$ , $f_a=relu$ , and $l_r=constant$ .

The MLP weak learner showed a strong predictive performance across all the thermal comfort states besides the extreme cold thermal discomfort class, as illustrated in Figure 7. For the neutral thermal comfort class, it attained a precision of $95.7\mathrm{\%}\pm 0.6\mathrm{\%}$ , a recall of $97.3\mathrm{\%}\pm 0.6\mathrm{\%}$ and an F1-score of $95.5\mathrm{\%}\pm 0.6\mathrm{\%}$ . For the slightly cold thermal discomfort class, it reported a precision of $89.9\mathrm{\%}\pm 0.7\mathrm{\%}$ , a recall of $87.3\mathrm{\%}\pm 0.8\mathrm{\%}$ and an F1-score of $88.6\mathrm{\%}\pm 0.8\mathrm{\%}$ . For the slightly warm thermal discomfort class, it reported a precision of $86.7\mathrm{\%}\pm 0.9\mathrm{\%}$ , a recall of $89.7\mathrm{\%}\pm 0.9\mathrm{\%}$ and an F1-score of $88.6\mathrm{\%}\pm 0.9\mathrm{\%}$ . These results converge to demonstrate the consistently strong performance across the neutral and slightly deviating thermal comfort states, indicating reliable detection of mild thermal conditions. In contrast, for the extreme thermal discomfort states the model exhibited weaker performance with opposing patterns. Specifically, while the extreme cold thermal discomfort class attained a relatively high precision of $82.7\mathrm{\%}$ , its recall fell markedly to $47\mathrm{\%}$ . Conversely, for the extreme warm thermal discomfort class, the model reached perfect recall but at the expense of a much lower precision of $53\mathrm{\%}$ . These results highlighted the model's difficulty in balancing sensitivity and specificity when detecting minority classes associated with extreme thermal conditions.

Ensemble learning

Two ensemble learning paradigms were adopted and evaluated exploiting their strong capacity to improve predictive robustness by aggregating the strengths of multiple individual classifiers and mitigating the weaknesses of individual models. Within the proposed ensemble framework, both bagging and boosting were already represented through RF and CatBoost weak learners, respectively, complemented by kNNs and a neural network to ensure algorithmic diversity. While bagging and boosting alone enhanced predictive accuracy compared to single learners, their formulation is typically restricted to a single family of models. By contrast, the proposed stacked architecture integrates heterogeneous learners through a meta-learner, enabling complementary strengths across tree-based, distance-based and neural network architectures to be combined.

The first learning approach employed was a soft voting scheme in which the predicted class probabilities of the four individual weak learners were averaged and the class with the highest aggregated probability was selected as the final prediction. This simple yet effective aggregation rule leverages the collective confidence from diverse modelling paradigms, thus reducing the variance and improving the predictive stability. The second learning approach utilized was a stacked ensemble with a meta-learner, where predictions from the individual base learners served as input features, enabling the meta-learner to identify complex relationships and dependencies amongst the individual predictions of weak learners and yielding enhanced performance and more flexible decision boundaries, particularly for minority classes.

Ensemble learning using soft voting scheme

The predictive performance of the soft voting scheme was first evaluated using samples included in the validation set ${{\mathcal{D}}_v}^{\mathrm{\prime }}$ with the corresponding recall scores presented in the confusion matrix of Figure 8. Achieving an overall accuracy of $85.0\mathrm{\%}\pm 1.1\mathrm{\%}$ and a macro-average F1-score of $82.3\mathrm{\%}\pm 1.1\mathrm{\%}$ , the results confirmed the inherent limitation of this ensemble approach: while it delivered more consistent predictions and balanced performance across the thermal comfort classes, the simple predictions aggregation failed to leverage class-specific strengths of individual weak learners. The soft voting scheme revealed a particular effectiveness in identifying samples in the majority neutral thermal comfort class with a precision of $95.5\mathrm{\%}\pm 0.6\mathrm{\%}$ and a recall of $91.7\mathrm{\%}\pm 0.8\mathrm{\%}$ . Furthermore, for mild thermal discomfort classes, the soft voting scheme attained comparable performance, and in particular, it achieved an F1-score of $87.3\mathrm{\%}\pm 1.0\mathrm{\%}$ for the slightly cold and $87.9\mathrm{\%}\pm 0.9\mathrm{\%}$ for the slightly warm classes. For the extreme thermal discomfort classes, the soft voting scheme showed limited predictive gains, failing to surpass the performance of the best individual weak learner for each class. The model resulted in an F1-score of $76.9\mathrm{\%}\pm 1.2\mathrm{\%}$ for the warm thermal discomfort state, while for the cold state dropped to an even lower F1-score of $65.6\mathrm{\%}\pm 1.4\mathrm{\%}$ .

Figure 8.

The confusion matrix for the soft voting scheme.

To further examine the robustness of the soft voting scheme, additional validation was performed under both 5-fold and 10-fold CV, presenting the results with $95\mathrm{\%}$ CI. Under 5-fold CV, it demonstrated an overall accuracy of $84.9\mathrm{\%}$ with $CI:[84.7\mathrm{\%},85.4\mathrm{\%}]$ , while under 10-fold CV, it resulted in an overall accuracy of $85.2\mathrm{\%}$ with $CI:[84.8\mathrm{\%},85.3\mathrm{\%}]$ , both overlapping with the reported accuracy of $85.0\mathrm{\%}\pm 1.1\mathrm{\%}$ in ${{\mathcal{D}}_v}^{\mathrm{\prime }}$ . The stability of the soft voting scheme was also reflected in the recall scores: cold thermal discomfort state attained recall scores of $65.4\mathrm{\%}$ with $CI:[64.7\mathrm{\%},66.3\mathrm{\%}]$ and $65.6\mathrm{\%}$ with $CI:[64.9\mathrm{\%},66.1\mathrm{\%}]$ under 5- and 10-fold CV, respectively. The slightly cold thermal discomfort class attained recall scores of $76.9\mathrm{\%}$ with $CI:[75.4\mathrm{\%},77.2\mathrm{\%}]$ and $75.9\mathrm{\%}$ with $CI:[74.5\mathrm{\%},76.7\mathrm{\%}]$ under 5- and 10-fold CV, respectively. The slightly warm thermal discomfort class achieved recall scores of $91.0\mathrm{\%}$ with $CI:[90.6\mathrm{\%},91.2\mathrm{\%}]$ and $91.1\mathrm{\%}$ with $CI:[90.8\mathrm{\%},91.2\mathrm{\%}]$ under 5- and 10-fold CV, respectively. The neutral thermal comfort class exhibited a recall of $91.8\mathrm{\%}$ with $CI:[91.4\mathrm{\%},92.0\mathrm{\%}]$ and $92.1\mathrm{\%}$ with $CI:[91.3\mathrm{\%},92.0\mathrm{\%}]$ under 5- and 10-fold CV, respectively. Although predictive improvements were limited, the soft voting scheme highlighted the potential of lightweight ensemble methods that prioritize consistency and computational efficiency over complexity.

Ensemble learning using LR as meta-leaner

LR was selected as the meta-learner due to its simplicity, interpretability and low variance make it particularly well suited for stacking frameworks. The meta-learners operating on the out-of-fold predictions of the base learners using more complex models such as XGBoost, LightGBM or SVR at this stage risks overfitting to these predictions rather than effectively integrating them. By contrast, LR provides a stable linear combination of the base models’ outputs, ensuring that the improvements in predictive performance are due to the diversity of the weak learners rather than the complexity of the meta-learner. This design choice is consistent with best practices in ensemble learning, where a simple, regularized meta-model is often preferred to achieve robust generalization.

The predictive performance of the stacked ensemble approach with LR as meta-learner was first evaluated using the samples included in the validation set ${{\mathcal{D}}_v}^{\mathrm{\prime }}$ with the corresponding recall scores presented in the confusion matrix of Figure 9. Although the stacked ensemble approach achieved an overall accuracy of $85.8\mathrm{\%}\pm 0.9\mathrm{\%}$ , similar to that obtained in the soft voting scheme, the stacked ensemble demonstrated superior predictive ability across both majority and minority thermal comfort classes. Notably, substantial improvements were observed in the extreme thermal discomfort states: recall for the cold state was increased from 62.9% to 90.2%, and for the warm state from 71.2% to 96.8%. Additional gains were also achieved in the slightly warm state, where recall rose from 91.4% to 94.2%. These improvements were accompanied by a moderate reduction in recall for the neutral and slightly cool states, which nevertheless remained at effective levels of identification.

Figure 9.

The confusion matrix for the stacked ensemble with LR as meta-learner.

Importantly, this behaviour remained consistent under both 5-fold and 10-fold CV attaining an overall accuracy of $85.2\mathrm{\%}$ with $CI:[84.9\mathrm{\%},85.5\mathrm{\%}]$ and $88.5\mathrm{\%}$ with $CI:[87.8\mathrm{\%},89.2\mathrm{\%}]$ under 5- and 10-fold CV. For the extreme cold thermal discomfort class, the recall score achieved was $89.9\mathrm{\%}$ with $CI:[89.5\mathrm{\%},90.4\mathrm{\%}]$ and $90.2\mathrm{\%}$ with $CI:[76.1\mathrm{\%},78.3\mathrm{\%}]$ under 5- and 10-fold CV, while for the extreme warm thermal discomfort class, the recall scores were $97.0\mathrm{\%}$ with $CI:[96.6\mathrm{\%},97.3\mathrm{\%}]$ and $97.3\mathrm{\%}CI:[97.0\mathrm{\%},97.5\mathrm{\%}]$ , respectively. The stacked ensemble exhibited also consistent performance for the neutral thermal comfort class with recall score of $86.8\mathrm{\%}$ with $CI:[86.6\mathrm{\%},87.4\mathrm{\%}]$ and $87.2\mathrm{\%}$ with $CI:[86.9\mathrm{\%},87.4\mathrm{\%}]$ under 5- and 10-fold CV.

Conclusion

As highlighted in this paper, thermal comfort plays a vital role in improving occupants’ satisfaction, health, well-being and productivity in enclosed spaces while supporting energy-efficient operations in built environments. Conventional thermal comfort assessment methods often depend on models that require either challenging-to-measure environmental parameters or self-reported personal thermal factors, which can be subjective and unreliable. This study has developed an innovative, data-driven approach to assessing an individual's thermal comfort state through an ensemble learning framework. The framework utilized an LR meta-learner to aggregate predictions from four diverse base learners, RF, kNN, MLP and CatBoost, achieving an accuracy exceeding $85\mathrm{\%}$ in predicting thermal comfort states. The primary advantage of this model lies in its reliance on only two easily measurable environmental variables, air temperature and relative humidity, eliminating the need for specialized equipment or complicated data acquisition processes. This approach also differentiates from traditional models, such as the PMV and SET, which require the measurement of hard-to-measure or highly variable environmental parameters like air velocity and globe temperature. Moreover, this model considers solely the personal thermal factor of clothing insulation, while traditional models also require the metabolic rate, which must be either self-reported or obtrusively measured through wrist wearables. Furthermore, the framework has been trained and evaluated on the most extensive database of thermal comfort recordings from diverse climate zones, building types, geographical regions and seasons, ensuring its scalability and adaptability to various situations and contexts. Future work should focus on incorporating personalized information into the framework to create more tailored and precise models that account for individual occupants’ unique thermal comfort preferences and characteristics. This would entail integrating demographic attributes, personal preferences and other individual factors to more accurately capture the variability in thermal comfort across diverse users. Additionally, the framework should be extended to accommodate multi-occupant environments, enabling its performance to be thoroughly evaluated in more complex and dynamic real-world scenarios.