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Smart Building Thermal Management: A Data-Driven Approach Based on Dynamic and Consensus Clustering

School of Economics, Fujian Normal University, Fuzhou 350117, China
Department of Mathematical Sciences, University of Essex, Colchester CO4 3SQ, UK
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Sustainability 2023, 15(21), 15489;
Submission received: 3 October 2023 / Revised: 20 October 2023 / Accepted: 27 October 2023 / Published: 31 October 2023
(This article belongs to the Special Issue Risk Analysis and Decision Making for Sustainable Development)


A customized and cost-effective building thermal control system is critical for accommodating thermal performance differences within the building, as well as satisfying the individual thermal comfort needs of occupants. Moreover, incorporating a building indoor thermal simulation procedure into the thermal control system can reduce the necessity of installing various expensive sensors (e.g., wearable sensors for personal thermal comfort management) in individual offices, as well as the requirement of extensive computing facilities without rendering the control performance, resulting into more sustainable building operations. An important step in achieving the above-mentioned goal is understanding how different offices/rooms behave differently given the same outdoor weather conditions. This study proposes a smart building indoor thermal profiling system to identify underlying physical factors that affect thermal performance in different seasons and to track dynamic cluster trajectories of considered offices to suggest indoor thermal optimization strategies. A consensus-based clustering approach is adopted to robustly cluster offices into different groups based on their hourly indoor temperature profiles for different seasons. Experimental results showed that our proposed approach could effectively discover more indoor thermal patterns in the buildings and is able to identify distinct dynamic cluster trajectories across four seasons (i.e., eight distinct dynamic trajectories in our case study). The data-driven analysis conducted in this study also indicated promising applications of the proposed smart building indoor thermal profiling system in effectively guiding the design of customized thermal control strategies for buildings. It also suggested that the proposed approach could be applied to a wide range of other applications, such as customized building energy management, energy pricing, as well as the economic benefit analysis of building retrofits and design.

1. Introduction

The building sector contributes to nearly 40% of total carbon emissions [1], leading to global warming, which poses a significant global challenge [2]. In addition, the energy consumption of buildings (e.g., office/public buildings) is the largest contributor, accounting for around 50% of the overall energy consumption in the world [3]. The thermal control systems installed in these buildings are designed to reduce energy consumption and carbon emissions, as well as to provide residents with enhanced thermal comfort where HVAC systems are popular options for optimizing the thermal comfort of building occupants. A thermostat transmits information about the temperature of a room throughout a building to a central heating or cooling system, which adjusts the temperature in that area accordingly. The indoor thermal comfort of a building, however, is also determined by its physical characteristics, such as its floor level and the surrounding environment. For complex built environments, it may be difficult for a thermal control system to effectively optimize thermal comfort and maximize energy efficiency simultaneously, especially for buildings with multiple types of offices. Furthermore, continuous monitoring of room temperatures may not always be feasible due to the high cost of installing thermostats in each room.
There are a few studies considering thermal comfort as part of their building and environment management models [4,5,6,7]. In addition, the impact of thermal comfort on different occupants, such as elderly people and university students, was studied in [8,9]. Recent studies have also examined individual/personalized thermal comfort and the underlying HVAC control systems (e.g., personalized HVAC systems) utilizing various sensor technologies and taking into account personal thermal comfort and ambient environments [10,11,12,13,14]. Most of these studies assess the potential impact as a consequence of technological changes without taking into account the influence of physical factors and external dynamic environments. Furthermore, the use of sensors around occupants to enable personalized comfort management may pose challenges to the occupant’s living experience and privacy. Moreover, personalized thermal comfort systems entail individual learning systems for each office, which can be prohibitively expensive in large buildings. Thus, a less intrusive and more cost-effective solution that accounts for thermal differences among different offices is needed.
Motivated by the above analysis, in this paper, we propose a dynamic and consensus clustering-based indoor thermal profiling system for customized building thermal control. The system investigates the relationship between physical information (e.g., floor area, floor level, etc.) of offices and their thermal behaviors within each cluster over different seasons, and analyzes the dynamic cluster trajectory of individual offices throughout the year to identify optimal indoor thermal control strategies. Customized building thermal control strategies could be derived and, therefore, recommended to the building operator/manager. The main contributions of this paper are summarized as follows.
  • We developed a data-driven indoor thermal profiling system based on dynamic and consensus clustering, which is important for understanding differences in building thermal performance among individual offices over different seasons. To the best of our knowledge, the proposed system is the first of its kind in the building simulation research community. The proposed system could bring significant benefits, such as facilitating customized building thermal control strategies and enabling robust and cost-effective building energy management among many others.
  • A consensus clustering approach with a dynamic clustering structure is developed for the proposed system, which enables the identification of different thermal behaviors during different seasons and the change of behaviors over different seasons.
  • The developed system takes advantage of the cost-effective building indoor thermal simulation instead of installing costly monitoring sensors (a much better scalability for large-scale analysis), and establishes the links between building physical factors (e.g., floor level, floor area, orientation) and indoor thermal performance.
  • The developed system is tested on a hypothetical 7-story office building consisting of 84 offices. Extensive experiment results, analysis, and managerial insights are provided.
The rest of the paper is organized as follows: Section 2 provides a review of related studies. Section 3 details the proposed four-layer system framework. Section 4 presents the results and discusses the practical implications of results and their potential wider applications. Section 5 concludes the paper and discusses future research directions.

2. Related Work

In this section, we will review related work that motivated this research. First, existing studies on building indoor thermal information simulation will be discussed, followed by existing research on indoor thermal-related factors. Finally, we will review existing approaches to indoor thermal profile modeling.

2.1. Building Indoor Thermal Information Simulation

The objective of a building simulation program is to simulate the indoor–outdoor environment associated with a target building by utilizing thermodynamic algorithms [15]. Building simulation programs can quantify the building environment for occupants, identify areas of improvement, and suggest potential solutions for the designer to maximize the energy efficiency [16]. There have been several simulation tools developed as a consequence, which are used in a variety of applications, such as the renovation of building envelopes and systems, and the control of energy-consuming equipment in buildings.
For the renovations of building envelopes and systems, Ref. [3] presented a hybrid approach integrating energy simulations and validation, orthogonal array testing, and data envelope analysis to determine the optimal method of retrofitting a building envelope to achieve energy-efficient operations. The study used DesignBuilder to analyze and simulate the energy consumption of commercial buildings and identify physical factors affecting energy efficiency for the purpose of retrofitting the building envelope. Moreover, Ref. [17] constructed two energy models and assessed the energy consumption of conventional white roofs and new green roofs using eQuest. It was found that the application of green roofs reduced the amount of electricity consumed annually for space heating and cooling. For building energy-consuming equipment control, Ref. [18] developed an HVAC model using EnergyPlus and transient system simulation tools. Combined with Simulink, an HVAC fuzzy logic controller was designed for thermal comfort management. A comparative experiment showed that the fuzzy HVAC controller was capable of reducing the non-comfort time by more than half in terms of the thermal comfort provided to building occupants. Recently, a digital twin platform was developed in [14] combining building physical spatial data from the building information model (BIM) and occupant feedback temporal data from the smartwatch-based ecological momentary assessments to inform personal thermal comfort management. Furthermore, through co-simulation with EnergyPlus and CONTAM, a coupled building model was developed in [19] to implement a control strategy for energy-consuming equipment by analyzing different air re-circulation strategies. It was found that both the energy consumption and the quality of the indoor air could be improved. The results of the above studies indicate that building simulations can assist with indoor thermal control and reduce energy consumption. In light of these facts, this paper utilizes EnergyPlus and DesignBuilder to generate a synthetic commercial building of different indoor thermal behavior patterns.

2.2. Indoor Thermal-Related Factors

The research on building thermal control has focused on analyzing interactions between the indoor thermal profile of buildings and their energy-consuming equipment to optimize energy consumption and thermal comfort. Specific observable (and monitored) variables are correlated with changes in indoor thermal conditions over various time periods (e.g., different seasons). These variables typically include indoor information (e.g., floor level, room area, room orientation) and the outdoor environment (e.g., outdoor air temperature, solar radiation rate). Different thermal profiles not only indicate that different occupants use the building in different ways, but may also indicate different comfort requirements of occupants.
In [20], 5 of the 27 factors have been incorporated into building performance simulations to model space-heating behavior, including room type, occupancy, indoor relative humidity, outdoor temperature, and time of day. Similarly, according to [21], building physical environmental variables, including outdoor temperatures, indoor relative humidity, and solar radiation, all influence occupant behavior during the heating season, illustrating the potential impact of physical environmental variables on indoor thermal profiles. Ref. [22] examined household behavior regarding the adoption of appliances with thermal control systems. They found that the floor area and the social information of residents were closely related to household behavior. In order to determine the thermal comfort profiles, Ref. [23] installed different sensors and data loggers for monitoring temperature, relative humidity, and carbon dioxide concentration in different office buildings. The study found that thermal comfort was significantly influenced by environmental indicators, the type of office, and the type of work. Moreover, Ref. [24] concluded that solar radiation, as a quasi-thermal parameter, has a direct impact on indoor thermal profile. On the other hand, Ref. [25] pointed out that an excessively complex building model would be difficult to embed in the energy system operation and control. The study selected the heating/cooling power, the outdoor temperature, and the solar radiation power to model the building’s thermal profile. Additionally, they used a parameter that represents the impact of occupant behavior to improve the model accuracy. The above studies have shown that building physical factors, such as building design or the outdoor environment, can have a significant impact on building thermal performance. Thus, this research examines the interplay between multiple building physical parameters and thermal profiles, as well as the impact of outdoor weather on the indoor thermal environment over time (e.g., in different seasons).

2.3. Indoor Thermal Profile Modeling

Accurately analyzing the dynamic thermal profile of buildings is the basis for utilizing thermal inertia to provide operational flexibility for energy systems. Many approaches have been proposed for modeling the thermal profile of buildings, among which unsupervised learning has been given considerable attention in recent years.
The most commonly used unsupervised learning techniques are clustering methods. Ref. [26] adopted K-means to cluster UK occupancy profiles based on the UK 2000 Time Use Survey data, and finally identified 22 occupancy clusters on weekdays and 24 occupancy clusters on weekends. Similarly, Ref. [27] utilized K-means to obtain representative electricity demand profiles for Great Britain based on hourly demand and weather data. Instead of K-means, Ref. [28] combined principle component analysis with a two-step clustering method to analyze the heating behavior in residential buildings, which can automatically select the optimal number of clusters. The experiments found that different households have different thermal comfort preferences during the same hours. Ref. [29] used five clustering methods—hierarchical, K-means, Gaussian-mixture models, fuzzy, and self-organization maps—to cluster the energy and thermal comfort for the office building. Three cluster internal validity indices were jointly used to evaluate the cluster results, and experiment results showed that fuzzy clustering is the most suitable clustering technique for thermal comfort.
On the other hand, in order to capture the time-evolving variations of indoor thermal profiles, time series clustering was used in recent studies. Ref. [30] compared K-means and time series clustering for assessing the performance of HVAC zoning and controls system in the commercial building, and it found that time series clustering performed better than K-means clustering. Moreover, Ref. [31] adopted K-shape clustering to analyze the indoor thermal profile in Brisbane, Australia, during different seasons, and experiment results showed that residents in Brisbane may be at risk of exposure to low and high temperatures during cold and warm seasons.
Although various clustering methods have been employed for indoor thermal profile modeling, the following two key points have not received sufficient attention: (1) there is no consensus on the best clustering algorithm for each indoor thermal dataset; (2) clustering analyses usually focus on a certain fixed period of time. To overcome the limitations of existing studies, a dynamic clustering structure based on consensus-based robust clustering was proposed in this study to analyze seasonal variations in thermal profiles of offices/rooms in buildings. Through the use of the proposed dynamic clustering structure, strategies can be developed to optimize indoor thermal comfort, which has a direct impact on maximizing energy efficiency and occupant productivity.

3. System Framework

3.1. Overall Framework

In this paper, we consider a hypothetical office building in northern China where the demand for HVAC energy consumption in different seasons varies. To achieve customized building thermal control, we are interested in knowing how indoor temperature changes given different outdoor weather conditions. For an office building, it is not surprising to experience different indoor thermal conditions in different offices given the same outdoor weather conditions. Therefore, this study also aims to understand the relationship between physical factors and thermal profiles of different offices in the office building over different seasons.
A graphical overview of the system is shown in Figure 1 and explained step-by-step in Section 3.2, Section 3.3, Section 3.4 and Section 3.5. Specifically, the proposed system framework contains four layers. In layer 1 (Section 3.2), the indoor thermal information simulation process collects building physical factors, as well as indoor thermal patterns and outdoor weather conditions, which are passed to layer 2. Layer 2 (Section 3.3) then segments the thermal information for each office into seasonal time series and normalizes the thermal information to prepare it for unsupervised modeling. Subsequently, layer 3 (Section 3.4) conducts the consensus-based robust clustering to find typical thermal patterns in different time periods. Finally, layer 4 analyzes the clustering profiles including their relationship with building physical factors, and constructs the dynamic indoor thermal profiles trajectory tracking route. By analyzing cluster results, key drivers that affect indoor temperatures can be identified, which can help to develop customized thermal control strategies for each office cluster.

3.2. Indoor Thermal Information Simulation

The majority of existing studies on indoor thermal variation at the office level are conducted in controlled environments with thermal cameras and other expensive equipment [32]. Instead of installing various sensors to collect data from a real-world building, building simulation is a cost-effective alternative especially useful for the planning stage, e.g., in evaluating the feasibility of different technologies/concepts, and sizing of different building components. In this paper, we adopt an EnergyPlus (for simulation) and DesignBuilder (for building 3D modeling) based building simulation model to generate the hourly temperature data in each office within the building given different outdoor weather conditions.
First, a seven-floor (ground floor to sixth floor, encoded from 1 to 7 for the quantitative analysis) conceptual office building was considered as the testing case where the 3D building was modeled in DesignBuilder (see Figure 2). Each floor has 12 office rooms, and they all lie down the west and north sides of the building (see Figure 3). The office has the same room and window dimensions at the same position on different floors.
There are nine office rooms on the west side on each floor. The office rooms positioned in the middle of the west side each have one window, with the window sizes varying from 2.75 sqr.m to 5.27 sqr.m. The office room set on both ends of the west side has two windows. The south corner office on the west side has one west-facing window with a size of 5.27 sqr.m and another south-facing window with 7.20 sqr.m. The north corner office on the west side also has one west-facing window with a window size of 4.67 sqr.m and another north-facing window with 7.20 sqr.m. The office area on the west side varies from 19.15 sqr.m to 38.68 sqr.m.
Additionally, there are 3 offices on the north side on each floor. Each office has one north-facing window with a window size of about 4.1 sqr.m. Each office also has a varying room area from 28.56 sqr.m to 32.59 sqr.m.
The physical information of offices in the simulated building is summarized in Table 1, where the detailed physical information for each office room is provided in Appendix A Table A1.
The DesignBuilder-based 3D building model was then input into EnergyPlus for thermal simulation. The default office activity schedule was applied to the associated modeled rooms while the default building regulation Part L 2013 data were applied to the construction setting of the modeled office building. HVAC systems are not included in the building model, and the indoor temperature is, therefore, only associated with building physical parameters and outside environmental parameters. After the simulation process using EnergyPlus, the whole year’s indoor thermal conditions for the modeled conceptual office building were obtained.

3.3. Indoor Thermal Information Management

To understand the typical characteristics of the obtained thermal information, we first briefly analyze the indoor temperature changes associated with different floor levels and orientations in different seasons. Figure 4 shows the average indoor temperature of offices on different floors in different seasons.
As can be observed, the ground floor has the lowest indoor temperature in spring, summer, and autumn, while it becomes the highest during the daytime in winter. Furthermore, during the transition seasons (spring and autumn), lower and middle floors (second and third floors) tend to have higher indoor temperatures. On the other hand, during summer months, the middle floors (third and fourth floors) have the highest indoor temperatures, reaching 44.01 Celsius at 17:00, while the ground floor has the coolest indoor temperature. In general, for winter months, offices on higher floors tend to be cooler (for instance, on the top floor the average room temperature at 6:00 is only 9.35 Celsius). Instead, offices on lower floors tend to be warmer in the cold season.
Based on the above seasonal segmentation, we aim to model the thermal profiles of offices in layer 3 using unsupervised learning techniques. However, it is important for these algorithms to deal with scale invariance to prioritize the shape features of the thermal patterns over amplitude features, especially for time series clustering [33,34,35]. Therefore, z-normalization was used to normalize the thermal profiles:
Z i = x i μ i s i
where Z i are the normalized values calculated for all thermal profiles x i for season i. μ i and s i represent the mean feature value and the standard deviation, respectively. For the seasonal thermal profiles, we use the mean feature value and the standard deviation over the season months. This will enable us to determine the dynamic trajectory of the indoor temperature profile under different weather conditions and seasons.
To assess the suitability for clustering before and after the z-normalization, we consider Hopkins’ statistical scores for the raw and z-normalized data in the four seasons, which are shown in Table 2. The Hopkins statistical score represents the degree of randomness in a dataset, which is calculated by comparing the sum of distances between random points in the data with the sum of distances between random points in a uniformly distributed reference set. A Hopkins score near 0.5 indicates high randomness, whereas a score near 1 (or 0) indicates high clustering (or dispersion) [36]. The results indicate that the z-normalized data produce the highest scores for all four seasons, suggesting that more meaningful clusters are present in the data set after z-normalization.

3.4. Consensus-Based Unsupervised Modeling

In layer 3, we perform clustering on the normalized seasonal indoor thermal segments. Clustering algorithms must take into account two key components, namely distance measures and prototyping functions [37]. It was demonstrated that clustering results can be unstable when only one clustering algorithm is used [38,39], and for this reason, we employ consensus-based robust clustering across multiple distance metrics and prototype combinations. Table 3 lists the clustering algorithm combinations used in this paper. Note that clustering is only one type of unsupervised learning method that could be applicable to our problem. For instance, the hierarchical Bayesian non-parametric model proposed in [40] could be considered in our future work for the problem.
The Euclidean distance [41], which approximates a one-to-one correspondence between each pair of sequences, is the most commonly used distance measure. However, for time series data (like the thermal profiles data we are considering), the distance measure needs to be invariant to specific distortions of the data to yield accurate results, which has been regarded as a limitation of the Euclidean distance [41]. Therefore, except for using the Euclidean distance, two state-of-the-art distance measures, namely the dynamic time-warping distance (DTW) [42] and the shape-based distance (SBD) [43] are also adopted in this paper to produce comprehensive similarity measures for thermal profile clustering.
To quantitatively choose the optimal number of clusters and evaluate the clustering results, three cluster validity indices (CVIs) are used in the validation process to produce robust validation results: the silhouette index, Davies–Bouldin (DB) index, and Calinski–Harabasz (CH) index. These metrics simultaneously measure the cohesion of the objects within clusters and the separation between clusters. For the silhouette index, it contrasts the average distance of objects within the same cluster to the average distance of objects in other clusters. It assumes values between −1 and 1. Cluster configurations with a higher silhouette index value are considered to be more optimal. Similarly, a higher CH index value signifies a better clustering result. In contrast, for the DB index, a lower value indicates a better clustering configuration. A more detailed description of the evaluation metrics can be found in [44,45,46].
Table 3. List of the used combination of the consensus-based clustering algorithm. DTW: dynamic time warping, SBD: shape-based distance; PAM: partition around medoids; DBA: DTW barycenter averaging.
Table 3. List of the used combination of the consensus-based clustering algorithm. DTW: dynamic time warping, SBD: shape-based distance; PAM: partition around medoids; DBA: DTW barycenter averaging.
Distance MeasuresCluster Prototypes
Euclidean DistanceK-means [47]
PAM [48]
SBDShape extraction [43]

3.5. Dynamic Indoor Thermal Profiling

After the consensus-based unsupervised modeling, a dynamic clustering structure is adopted in layer 4 to capture seasonal/dynamic changes in the indoor thermal profiles of offices. The proposed dynamic indoor thermal profiling structure is illustrated in Figure 5.
Under the dynamic profiling structure, a separate consensus-based clustering analysis is implemented for each season. The ultimate clustering results from the dynamic clustering structure consists of two components: (1) relationship pattern between the clusters and the physical factors of each office; (2) dynamic indoor thermal profile of each office.
Specifically, the clusters for different seasons are described by testing the difference in the building’s physical factors. Since the physical factors (detailed in Table 1) can all be seen as categorical variables, the chi-square test [50] is adopted to analyze the association between the clusters and the physical factors. Then, based on cluster results for each season, the dynamic indoor thermal profile for each building can be tracked, which is a cluster trajectory for each office in the building (e.g., a cluster assignment for each room under each season). More importantly, by analyzing the dynamic cluster trajectories, the corresponding physical factors possessed by the offices in each dynamic cluster trajectory can be sketched. We highlight that the proposed dynamic indoor thermal profiling layer not only allows the investigation of different thermal behaviors but also facilitates the understanding of seasonal behavioral changes.

4. Results and Analysis

In this section, we will show the results of our proposed consensus-based clustering approach, followed by the analysis of the relationship between indoor thermal patterns and building physical factors, empowered by the consensus clustering and the chi-square test. Then, the results of the dynamic indoor thermal profile recognition are discussed. For comparison purposes, we considered the benchmark case where all-seasons data are considered simultaneously, which is the most adopted approach in existing studies. In addition, to demonstrate the benefits of our proposed consensus clustering approach, performances of individual clustering algorithms are reported and compared as part of the comparative analysis.

4.1. Cluster Validity Results

We adopt consensus-based clustering to cluster the 84 simulated offices based on their daily indoor temperature in different seasons. To serve as a baseline benchmark, we also consider the same clustering procedure based on all-seasons data (i.e., average thermal profile of the year rather than of each season) without differentiating different seasons. The optimal cluster number and cluster algorithm for each season and the whole year (all seasons) are chosen according to the majority vote from the three CVIs (silhouette, DB, and CH).
Specifically, we utilized tsclust in R for the consensus-based clustering process [37]. This package is specifically designed to handle the unique characteristics of time series data and offers a wide range of clustering algorithms and distance measures. We took advantage of the flexibility provided by tsclust to customize the clustering process according to our specific requirements. The parameter settings used in tsclust during our experiment are summarized in Table 4.
During the experiment, a random seed value (in our case, 8) was also used for reproducibility and consistency in the clustering results. We consider cluster numbers k with the range from 2 to 10. The distance measure is used to calculate the distance between time series data points, while the centroid refers to the cluster prototypes that are used to calculate the centroid for each cluster. Regarding the DTW barycenter averaging, the window.size parameter determines the size of the subsequence used for calculating the alignment path between two time series. In the experiment, a 10-h window was used to balance local patterns and the overall behavior of the time series. Figure 6 presents the visualizations of the CVIs for the cluster results in each season and the whole year (all seasons).
The CVIs offer significant insights into the quality of clustering outcomes. Table 5 compares the performance of different clustering algorithms with the optimal cluster number across different seasons and the overall year, and the best scores for each algorithm are highlighted in bold.
Dynamic time-warping clustering and shape-based clustering consistently demonstrate excellent performance across all seasons. These algorithms consistently achieve higher silhouette and CH scores, indicating superior cluster separation, while also maintaining relatively low DB indices, suggesting dense and compact cluster results.
Dynamic time-warping clustering shows remarkable performance in terms of all three CVIs across spring and summer, which highlights the effectiveness of DTW clustering in capturing temporal patterns and generating meaningful clusters in each season. Similarly, shape-based clustering can capture shape-based similarities and consistently demonstrates strong performance across autumn and winter.
In contrast, traditional clustering algorithms, such as K-means and PAM, show relatively worse performance in terms of the CVIs for each season. These two algorithms generally achieve moderate silhouette scores and CH scores across all seasons. These algorithms generally achieve moderate silhouette and CH scores but tend to have higher DB indices, indicating less distinct and less dense clusters. This may be due to their limitations in capturing the inherent temporal or shape-based patterns in the time series data.
It is worth noting that the employed consensus-based approach uses multiple distance metrics (Euclidean, DTW, SBD) and prototype methods (K-means, PAM, DBA) rather than relying on a single algorithm. This approach captures different aspects of the data and reduces the bias introduced by a single algorithm. Furthermore, it enhances the robustness and stability of the clustering process compared to studies that used only a single clustering algorithm [51,52,53,54].
Moreover, evaluating cluster validity using multiple indices (silhouette, CH, DB) enables us to assess the quality and characteristics of the clusters from different perspectives, providing a more comprehensive quantitative assessment compared to many existing studies [9,30,54].
All the CVIs vote K = 2 as the best clustering number for the indoor thermal profiles in summer and autumn. Although K = 2 is also selected as the optimal number in spring and winter, the DB index and the CH index vote different numbers for the former and the latter, respectively. The final chosen clustering algorithms and their corresponding CVIs for each season and the whole year (benchmark) are listed in Table 6.
Finally, dynamic time-warping clustering is selected to generate two clusters for the spring and summer seasons, respectively. The same choice was made for the clustering of all-year data (all seasons). The K-shape utilizing the SBD distance and the shape extraction prototype is applied to produce two clusters for the autumn and winter seasons. Figure 7 illustrates the cluster centroids for each of four seasons and the whole year (all seasons).

4.2. Relationship Pattern between Seasonal Indoor Thermal Clusters and Physical Factors

Using the consensus clustering results, the chi-square test is performed to test differences in different clusters according to building physical factors (floor level, floor area, orientation) during different seasons. To serve as a benchmark, the chi-square test has also been conducted for the consensus clustering results based on the all-year data (all seasons). The detailed test results for three building physical variables are provided in Appendix B Table A2, Table A3, Table A4, Table A5 and Table A6.
Several high-level distinct patterns can be observed, which is not possible without differentiating among different seasons. In particular, the dynamic impact of physical factors on the indoor temperature in different seasons can be identified through our proposed approach. That is, a certain physical factor (e.g., floor level, floor area, or orientation) could be the main factor for one season but less important in other seasons. To be more specific, based on the chi-square test results, a statistically significant association between clusters and floor levels in the spring season is observed. For instance, cluster 1 mainly consists of offices on the ground and first floors (see Table A2). Most of the small offices are located in cluster 2, with the majority of offices located to the west. Similarly, the association between clusters and floor levels is found to be significant for the summer season with cluster 1 consisting of all the offices on the ground floor. In fact, the floor level is the dominant factor for the indoor temperature in the summer season (see Table A3). Interestingly, all three physical factors are significantly associated with the autumn season. Among the three physical factors, floor area seems to be the dominant factor with small offices primarily located in cluster 2. In addition, the physical factor of office orientation is only found to be significant for the autumn season with almost all offices in cluster 2 facing either North or West (see Table A4). For the winter season, the association between clusters and the floor levels is found to be significant with cluster 2 including all the offices on the ground floor and almost all the offices on the sixth floor (top floor) (see Table A5). In contrast, the chi-square test results based on the clustering of all-seasons data indicate only floor level is significantly associated. In particular, cluster 1 consists of offices on the ground floor and first floor only (see Table A6).
To better understand the changing patterns in clusters over different seasons and their dynamic association with different physical factors, the corresponding average physical factors are utilized to reflect common building characteristics in each cluster, as shown in Table 7. Moreover, the mean, minimum, and maximum indoor temperatures of offices within each cluster are also summarized for each of the four seasons to facilitate tracking of the dynamic cluster trajectory for each office. We can conclude from the results of clustering and the physical information of the buildings that there is a distinct characteristic associated with each cluster, as indicated in the cluster labels. In generating the cluster labels, floors are divided into three categories: low (ground to second floors, i.e., 1–3), medium (third and fourth floors, i.e., 4–5), and high (fifth and sixth floors, i.e., 6–7).
We can observe that during the spring season, cluster 1 has low floor levels, medium-sized offices, and lower indoor temperatures. In contrast, cluster 2 has medium floor levels, medium office sizes, and a higher daily indoor temperature. During the summer, cluster 1 is associated with low floor levels and a cooler indoor temperature, while cluster 2 has medium floor levels and higher indoor temperature with a maximum temperature of 42.61 Celsius. In autumn, cluster 1 has a medium floor level, a large office size, and a warmer indoor temperature, while cluster 2 has a low–medium floor level, small offices, and a cooler indoor temperature. In winter months, cluster 1 has low–medium floor level, medium floor area, and slightly higher indoor temperature, while cluster 2 has a medium floor level, a medium floor area, and a lower indoor temperature. It is also observed that the differences in average indoor temperatures in the two clusters for the autumn and winter seasons are less distinct than other seasons. To summarize, based on our approach, the clustering results over four seasons generate six distinct cluster profiles (six distinct cluster labels). In contrast, the clustering based on all-seasons data only results in two clusters (i.e., two distinct cluster labels), where cluster 1 has a low floor level, medium office area, and lower indoor temperature, and cluster 2 has a medium floor level, medium office size, and higher indoor temperature.
Based on the above analysis, we can observe distinct thermal performances and behaviors of offices in different seasons and underlying physical factors. In other words, the same offices may behave differently in different seasons, affected by different physical factors differently over time.

4.3. Dynamic Indoor Thermal Profile Recognition

In order to track the dynamic cluster trajectory for the offices (i.e., track different behavior patterns in different seasons), a category summary is performed after characterizing each cluster for each season. Table 8 summarizes all cluster trajectories that exist based on clustering results over four different seasons in the previous subsection, together with the average thermal profile of each trajectory. In total, eight dynamic trajectories (DTs) were identified for the 84 simulated offices, and the characteristics of each DT can be summarized by combining the cluster labels for each season defined in Table 7. For instance, for offices following DT 1, they appear in cluster 1 (lower temperature according to Table 7) in the spring season, remain in cluster 1 (lower temperature) for the summer season but change to cluster 2 (lower temperatures) in the autumn and winter seasons. That is, the offices following DT 1 have relatively lower indoor temperature throughout the year, characterized by low floor levels and medium floor areas. The detailed offices that follow each dynamic trajectory (DT) are listed in Appendix B Table A7.
In general, there are low floor levels in both DT 1 and DT 2, with DT 1 containing medium offices and DT 2 containing large offices. Most offices that follow DTs 3, 5, and 7 are located on medium floor levels, and offices in DTs 3 and 5 have large floor areas. On the other hand, DT 7, which has the largest number of offices, is characterized by low to medium floor levels and small office sizes. Furthermore, most offices following DTs 4, 6, and 8 are located on the upper floors. In addition, those who follow DTs 4 and 6 have a medium-sized office, while those who follow DT 8 have a small-sized office.
Based on the characteristics described in each DT, the dynamic thermal behavior can be summarized, and useful managerial insights (MIs) can be gained to assist the building manager/operator in developing customized thermal control strategies:
  • MIs for DT 1. Offices following DT 1 experience lower indoor temperatures throughout the year than offices following other DTs. As these offices experience a cooler winter, thermal control decisions should be made with additional consideration for DT 1 during this period.
  • MIs for DT 2. The indoor temperature of offices following DT 2 is lower in the spring and higher from the summer to the winter. It is, therefore, necessary for the thermal control system to cool the offices that follow DT 2 during the summer months to ensure optimal comfort for the occupants.
  • MIs for DT 3. In DT 3, offices experience lower indoor temperatures during winter and spring, and higher indoor temperatures during summer and autumn. Consequently, offices following DT 3 require special attention to the thermal control system during the summer and winter months as occupants suffer from high indoor temperatures in the summer and low indoor temperatures in the winter. In addition, it expects extended operations of thermal control systems in transition seasons due to higher temperatures in the autumn and lower temperatures in the spring.
  • MIs for DT 4. In DT 4, offices experience higher indoor temperatures in the summer and lower indoor temperatures in the winter and two transition seasons (spring and autumn). As in DT 3, the thermal control system should ensure that the offices in DT 4 are maintained at a comfortable temperature throughout the summer and winter.
  • MIs for DT 5. Offices in DT 5 are generally warmer throughout the year. Similar to DT 2, DT 5 requires the thermal control system to maintain a comfortable temperature during the summer months.
  • MIs for DT 6. As in DTs 3 and 4, offices in DT 6 also experience higher indoor temperatures during the summer and two transition seasons and lower indoor temperatures during the winter. Therefore, the thermal control system in DT 6 should optimize thermal comfort for the offices during the summer and winter seasons.
  • MIs for DT 7. In offices following DT 7, the indoor temperature is lower during autumn and higher during other seasons, especially during the summer. Thermal control systems should, therefore, ensure that the indoor temperatures in DT 7 do not become excessively hot during the summer months.
  • MIs for DT 8. As with DTs 3, 4, and 6, offices in DT 8 also experience higher summer temperatures and lower winter temperatures. Therefore, the thermal control system in DT 8 should enable offices to remain comfortably cool during the summer and warm during the winter. However, DT 8 presents a unique trajectory with higher temperatures in the spring and lower temperatures in the autumn.
It can be observed that offices following DTs 3, 4, 6, and 8 experience higher summer temperatures and lower winter temperatures. Therefore, thermal control strategies can be developed in order to optimize the thermal comfort of these offices in both seasons. Moreover, offices following DTs 2, 5, and 7 require thermal comfort optimization strategies during the summer, while offices following DT 1 require thermal comfort optimization strategies during the winter. Although some DTs (e.g., DTs 3, 4, 6, 8) seem to present similar thermal behaviors in summer and winter seasons, they have distinct patterns during two transition seasons (i.e., spring and autumn). Overall, each DT presents a unique trajectory with its own characteristics, which could provide useful insights and opportunities for customized building operation and management.

4.4. Discussion

In light of the above analysis, we can conclude that there are different physical factors contributing to thermal differences among offices in different seasons. Furthermore, the dynamic cluster trajectory of the offices provides valuable guidance for designing customized building climate control strategies. Although we considered a case study focusing on different rooms/offices within a single building, it is worth mentioning that the proposed method can be readily extended or easily modified to other different built environment settings at different spatial-temporal scales such as examining behaviors of different types of buildings or a group of buildings. When performing the analysis for a group of different types of buildings simultaneously (e.g., a district or city level), we could consider extending the current simulation model by including more building physical factors (e.g., building material, insulation, etc.) to account for the difference between buildings.
Moreover, the above promising results can also be applied to other relevant applications, such as for the building energy management/energy pricing and accounting for economic benefits of building retrofits. As for the former, based on the customized data-driven building’s indoor thermal profiles, customized HVAC control and the energy management approach can be developed for each office/each group of offices, considering the differences in thermal performance. It is also possible to consider customized energy pricing and demand response management strategies in similar application scenarios (e.g., for a group of buildings) to manage the energy costs. For the latter, it can be achieved by using the developed clustering-based indoor thermal performance profiling system, allowing different building retrofit plans to be evaluated through simulations on a group of rooms/buildings rather than on individual rooms/buildings, which can then be incorporated into an economic benefit analysis to obtain the optimal building retrofit plan. According to the above, the proposed smart building indoor thermal profiling system can lead to promising computational benefits, as the consensus-based clustering method can significantly reduce the number of simulations required, which is particularly useful for large and complex buildings and big data scenarios.

5. Conclusions

This paper proposes an indoor thermal profiling system for smart buildings that is useful for customized thermal control in buildings. Firstly, a building simulation model based on EnergyPlus is developed to simulate the thermal conditions of individual offices under various outdoor weather conditions. Secondly, the simulated thermal conditions are segmented and normalized based on the different seasons throughout the year. To capture different building thermal behaviors in different seasons, the consensus-based robust clustering approach is applied to cluster individual offices into different groups. By analyzing clustering results with accompanying building physical information, we are able to identify underlying factors that can explain the observed thermal performance behaviors, which is an important step toward developing a fully automated customized building climate control system. Moreover, the dynamic cluster trajectories of the simulated 84 offices are summarized to provide valuable guidance for designing different building climate control strategies for different times of the year. The promising results shown in our experimental analysis will inspire future directions of our work; we aim to further develop and extend our proposed methodological framework to other areas, such as customized building energy management, energy pricing, and economic benefit analysis of building retrofits and design. For instance, different thermal behaviors of offices (assuming multiple companies/organizations share the same building in this example) can be taken into account when offering different energy tariffs to different companies/organizations by the load serving entity (LSE), to incentivize the best energy use behaviors, such as reducing emissions and energy bills. Another potential area of our proposed framework is to study the potential impact of different building retrofit designs on indoor thermal behavior in order to evaluate its impact on overall energy efficiency.

Author Contributions

Conceptualization, H.C., S.D. and F.M.; Methodology, H.C., S.D. and F.M.; Validation, H.C. and S.D.; Investigation, H.C., S.D. and F.M.; Writing—original draft, H.C. and S.D.; Writing—review & editing, F.M. All authors have read and agreed to the published version of the manuscript.


This research received no external funding.

Data Availability Statement

Not applicable.

Conflicts of Interest

The authors declare no conflict of interest.

Appendix A. Detailed Physical Information of Office Rooms

Table A1. Detailed physical information of office rooms.
Table A1. Detailed physical information of office rooms.
Room NumberFloor LevelOrientationFloor Area (m 2 )
Office1Ground floorSouth-West Corner38.68
Office2Ground floorWest19.15
Office3Ground floorWest19.15
Office4Ground floorWest22.78
Office5Ground floorWest22.78
Office6Ground floorWest27.04
Office7Ground floorWest27.04
Office8Ground floorWest34.22
Office9Ground floorNorth-West corner34.22
Office10Ground floorNorth32.59
Office11Ground floorNorth31.5
Office12Ground floorNorth28.56
Office13First floorSouth-West Corner38.68
Office14First floorWest19.15
Office15First floorWest19.15
Office16First floorWest22.78
Office17First floorWest22.78
Office18First floorWest27.04
Office19First floorWest27.04
Office20First floorWest34.22
Office21First floorNorth-West corner34.22
Office22First floorNorth32.59
Office23First floorNorth31.5
Office24First floorNorth28.56
Office25Second floorSouth-West Corner38.68
Office26Second floorWest19.15
Office27Second floorWest19.15
Office28Second floorWest22.78
Office29Second floorWest22.78
Office30Second floorWest27.04
Office31Second floorWest27.04
Office32Second floorWest34.22
Office33Second floorNorth-West corner34.22
Office34Second floorNorth32.59
Office35Second floorNorth31.5
Office36Second floorNorth28.56
Office37Third floorSouth-West Corner38.68
Office38Third floorWest19.15
Office39Third floorWest19.15
Office40Third floorWest22.78
Office41Third floorWest22.78
Office42Third floorWest27.04
Office43Third floorWest27.04
Office44Third floorWest34.22
Office45Third floorNorth-West corner34.22
Office46Third floorNorth32.59
Office47Third floorNorth31.5
Office48Third floorNorth28.56
Office49Fourth floorSouth-West Corner38.68
Office50Fourth floorWest19.15
Office51Fourth floorWest19.15
Office52Fourth floorWest22.78
Office53Fourth floorWest22.78
Office54Fourth floorWest27.04
Office55Fourth floorWest27.04
Office56Fourth floorWest34.22
Office57Fourth floorNorth-West corner34.22
Office58Fourth floorNorth32.59
Office59Fourth floorNorth31.5
Office60Fourth floorNorth28.56
Office61Fifth floorSouth-West Corner38.68
Office62Fifth floorWest19.15
Office63Fifth floorWest19.15
Office64Fifth floorWest22.78
Office65Fifth floorWest22.78
Office66Fifth floorWest27.04
Office67Fifth floorWest27.04
Office68Fifth floorWest34.22
Office69Fifth floorNorth-West corner34.22
Office70Fifth floorNorth32.59
Office71Fifth floorNorth31.5
Office72Fifth floorNorth28.56
Office73Sixth floorSouth-West Corner38.68
Office74Sixth floorWest19.15
Office75Sixth floorWest19.15
Office76Sixth floorWest22.78
Office77Sixth floorWest22.78
Office78Sixth floorWest27.04
Office79Sixth floorWest27.04
Office80Sixth floorWest34.22
Office81Sixth floorNorth-West corner34.22
Office82Sixth floorNorth32.59
Office83Sixth floorNorth31.5
Office84Sixth floorNorth28.56

Appendix B. Chi-Square Test Results and Dynamic Trajectories (DTs)

Table A2. Chi-square test results for spring clusters.
Table A2. Chi-square test results for spring clusters.
VariableCategoryClustersTest Results
Cluster 1Cluster 2 x 2 p
Floor levelGround floor12055.5190.000 ***
First floor57
Second floor012
Third floor012
Fourth floor012
Fifth floor012
Sixth floor39
Floor area
m 2
Orientation North 8135.6110.060
*** p < 0.01.
Table A3. Chi-square test results for summer clusters.
Table A3. Chi-square test results for summer clusters.
Variable Category ClustersTest Results
Cluster 1Cluster 2 x 2 p
Floor levelGround floor120840.000 ***
First floor012
Second floor012
Third floor012
Fourth floor012
Fifth floor012
Sixth floor012
Floor area
m 2
Orientation North 3180.0001
*** p< 0.01.
Table A4. Chi-square test results for autumn clusters.
Table A4. Chi-square test results for autumn clusters.
Variable Category ClustersTest Results
Cluster 1Cluster 2 x 2 p
Floor levelGround floor01215.5150.017 **
First floor93
Second floor66
Third floor48
Fourth floor48
Fifth floor57
Sixth floor66
Floor area
m 2
19.1541038.9360.000 ***
Orientation North 8136.5220.038 **
*** p < 0.01, ** p < 0.05.
Table A5. Chi-square test results for winter clusters.
Table A5. Chi-square test results for winter clusters.
Variable Category ClustersTest Results
Cluster 1Cluster 2 x 2 p
Floor levelGround floor01252.8710.000 ***
First floor111
Second floor120
Third floor120
Fourth floor84
Fifth floor66
Sixth floor111
Floor area
m 2
Orientation North 1383.0390.219
*** p < 0.01.
Table A6. Chi-square test results for clusters of all seasons.
Table A6. Chi-square test results for clusters of all seasons.
Variable Category ClustersTest Results
Cluster 1Cluster 2 x 2 p
Floor levelGround floor12066.7060.000 ***
First floor48
Second floor012
Third floor012
Fourth floor012
Fifth floor012
Sixth floor012
Floor area
m 2
Orientation North 3180.6180.734
*** p < 0.01.
Table A7. List of offices in the eight DTs.
Table A7. List of offices in the eight DTs.
DT 1DT 2DT 3DT 4DT 5DT 6DT 7DT 8
Office3Office23 Office18Office74Office17Office60
Office4Office24 Office19Office79Office27Office63
Office5 Office25Office80Office28Office64
Office6 Office26Office82Office29Office65
Office7 Office31 Office30Office66
Office8 Office32 Office35Office72
Office9 Office33 Office36Office75
Office10 Office34 Office38Office76
Office11 Office37 Office39Office77
Office12 Office44 Office40Office78
Office45 Office41
Office46 Office42
Office49 Office43
Office56 Office47
Office58 Office48
Office61 Office50
Office62 Office51
Office68 Office54
Office70 Office55
Office73 Office59


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Figure 1. The system framework of clustering-based indoor temperature profiling.
Figure 1. The system framework of clustering-based indoor temperature profiling.
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Figure 2. The seven-floor conceptual office modeled in DesignBuilder, (a) front elevation; (b) north-east elevation; (c) south elevation.
Figure 2. The seven-floor conceptual office modeled in DesignBuilder, (a) front elevation; (b) north-east elevation; (c) south elevation.
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Figure 3. Floor plan of the conceptual office, (a) floor plan of the ground floor, (b) floor plan of the non-ground floor.
Figure 3. Floor plan of the conceptual office, (a) floor plan of the ground floor, (b) floor plan of the non-ground floor.
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Figure 4. Average indoor temperature of different floors in different seasons. OT: outdoor temperature.
Figure 4. Average indoor temperature of different floors in different seasons. OT: outdoor temperature.
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Figure 5. Dynamic analysis to capture seasonal change.
Figure 5. Dynamic analysis to capture seasonal change.
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Figure 6. A comparison of CVIs of consensus-based clustering in different seasons and the whole year. The gray vertical dashed line indicates the optimal cluster number for each CVI.
Figure 6. A comparison of CVIs of consensus-based clustering in different seasons and the whole year. The gray vertical dashed line indicates the optimal cluster number for each CVI.
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Figure 7. The cluster centroids of clusters in different seasons and the whole year. OT: outdoor temperature.
Figure 7. The cluster centroids of clusters in different seasons and the whole year. OT: outdoor temperature.
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Table 1. Physical information for the simulated offices.
Table 1. Physical information for the simulated offices.
Physical InformationCategoryNumber of Offices on Each FloorNumber of Offices on Seven Floors% of Total Number of Offices in the Building
Orientation North 32125
Floor area (m 2 )19.1521416.7
Table 2. Hopkins statistical scores.
Table 2. Hopkins statistical scores.
Cluster Tendency (Hopkins Statistic)
Raw data0.960.950.960.91
Z-normalized data0.980.980.980.97
Table 4. Parameter settings for the consensus-based clustering.
Table 4. Parameter settings for the consensus-based clustering.
Clustering Algorithmkdistancecentroidwindow.size
Eucl. + K-means[2:10]Euclideanmean-
Eucl. + PAM[2:10]Euclideanpam-
DTW + DBA[2:10]dtwdba10
SBD + Shape extraction[2:10]sbdshape-
Table 5. Performance comparison of clustering algorithms with the optimal cluster number in four seasons and the whole year (all-seasons data).
Table 5. Performance comparison of clustering algorithms with the optimal cluster number in four seasons and the whole year (all-seasons data).
Spring CVIs (k = 2)
Clustering algorithmSilhouetteDBCH
Eucl. + K-means0.560.6483.42
Eucl. + PAM0.123.2623.26
DTW + DBA0.610.63116.25
SBD + Shape extraction0.311.8550.42
Summer CVIs (k = 2)
Clustering algorithmSilhouetteDBCH
Eucl. + K-means0.780.22134.24
Eucl. + PAM0.780.2179.52
DTW + DBA0.830.14169.73
SBD + Shape extraction0.640.33194.72
Autumn CVIs (k = 2)
Clustering algorithmSilhouetteDBCH
Eucl. + K-means0.450.9486.81
Eucl. + PAM0.431.2565.81
DTW + DBA0.660.4594.05
SBD + Shape extraction0.620.44135.20
Winter CVIs (k = 2)
Clustering algorithmSilhouetteDBCH
Eucl. + K-means0.420.9081.24
Eucl. + PAM0.371.3760.84
DTW + DBA0.510.93113.45
SBD + Shape extraction0.610.60135.32
All seasons CVIs (k = 2)
Clustering algorithmSilhouetteDBCH
Eucl. + K-means0.630.3778.07
Eucl. + PAM0.421.0779.70
DTW + DBA0.670.53131.82
SBD + Shape extraction0.410.80100.89
Table 6. Lists of the optimal clustering algorithms and their corresponding CVIs for four seasons and the whole year (all-seasons data).
Table 6. Lists of the optimal clustering algorithms and their corresponding CVIs for four seasons and the whole year (all-seasons data).
SeasonOptimal Clustering AlgorithmOptimal Cluster NumberCVIs
SpringDTW + DBA20.610.63116.25
SummerDTW + DBA20.830.14169.73
AutumnSBD + Shape extraction20.620.44135.20
WinterSBD + Shape extraction20.610.60135.32
All seasonsDTW + DBA20.670.53131.82
Table 7. Clusters profile summary for different seasons and the whole year (all seasons).
Table 7. Clusters profile summary for different seasons and the whole year (all seasons).
ClusterFloor LevelFloor AreaMean Temp.Max/Min Temp.Cluster Label
12.1529.6521.1426.66/16.11Low floor level;
medium office size;
lower indoor temperature.
24.5827.6725.1332.55/18.44Medium floor level;
medium office size;
higher indoor temperature.
11.0028.1423.1128.02/18.61Low floor level;
medium office size;
lower indoor temperature.
24.5028.1434.4142.61/26.89Medium floor level;
medium office size;
higher indoor temperature.
14.2431.8622.4228.57/16.74Medium floor level;
large office size;
higher indoor temperature.
23.8425.6221.9826.55/17.67Low–Medium floor level;
small office size;
lower indoor temperature.
13.7828.6015.2219.52/10.82Low–Medium floor level;
medium office size;
higher indoor temperature.
24.3227.4714.9718.50/11.44Medium floor level;
medium office size;
lower indoor temperature.
All seasons
11.2527.3420.6925.34/16.56low floor level;
medium office size;
lower indoor temperature.
24.6528.3324.3030.56/18.50Medium floor level;
medium office size;
higher indoor temperature.
Table 8. Category summary for the dynamic cluster trajectories over the year. DT: dynamic trajectory.
Table 8. Category summary for the dynamic cluster trajectories over the year. DT: dynamic trajectory.
Spring ClusterSummer ClusterAutumn ClusterWinter ClusterFloor LevelFloor AreaMean Temp.DT No.
11221 (low)28.14 (med.)19.581
2112 (low)31.72 (large)22.532
124.50 (med.)34.22 (large)22.793
227 (high)30.03 (med.)23.424
22114 (med.)32.11 (large)24.565
126.50 (high)30.24 (med.)24.146
213.88 (low–med.)24.87 (small)24.687
226.08 (high)23.85 (small)24.698
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Chen, H.; Dai, S.; Meng, F. Smart Building Thermal Management: A Data-Driven Approach Based on Dynamic and Consensus Clustering. Sustainability 2023, 15, 15489.

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Chen H, Dai S, Meng F. Smart Building Thermal Management: A Data-Driven Approach Based on Dynamic and Consensus Clustering. Sustainability. 2023; 15(21):15489.

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Chen, Hua, Shuang Dai, and Fanlin Meng. 2023. "Smart Building Thermal Management: A Data-Driven Approach Based on Dynamic and Consensus Clustering" Sustainability 15, no. 21: 15489.

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