Efficiency in building energy use: Pattern discovery and crisis identification in hot-water consumption data

Contents lists available at ScienceDirect Energy & Buildings journal homepage: www.elsevier.com/locate/enbuild Efficiency in building energy use: Pattern discovery and crisis identification in hot-water consumption data Lina Morkunaite a,∗, Darius Pupeikisa, Nikolaos Tsalikidisb, Marius Ivaskeviciusa, Fallon Clare Manhangaa, Jurgita Cerneckienea, Paulius Spudysa, Paraskevas Koukaras b,c, Dimosthenis Ioannidisb, Agis Papadopoulos d, Paris Fokaidesa,e aFaculty of Civil Engineering and Architecture, Kaunas University of Technology, Kaunas, 51367, Lithuania bInformation Technologies Institute, Centre for Research & Technology, Thessaloniki, 57001, Greece cSchool of Science and Technology, International Hellenic University, Thessaloniki, 57001, Greece dProcess Equipment Design Laboratory, Department of Mechanical Engineering, Aristotle University, Thessaloniki, 54124, Greece eSchool of Engineering, Frederick University, Nicosia, 1036, Cyprus article i n f o Keywords: Predictive modelling Domestic hot water Control optimisation Severity level a b s t r a c t As global challenges such as climate change and pandemics increasingly disrupt urban systems, the need for efficient and resilient management of energy resources has become critical. The energy used to prepare domestic hot water (DHW) takes a large proportion of residential buildings’ total thermal energy demand. However, it is often overlooked in research due to its stochastic nature and high dependence on user behaviour. This study explores the identification of the crisis and its severity level in the DHW consumption data and the corresponding control actions necessary to mitigate its impact. To identify crisis severity, we utilised the mobility data of retail/recreation activities and transit stations, making the results generalisable for any crisis. In addition, we used power consumption for DHW preparation data from 10 residential apartment buildings located in Kaunas city to develop a machine learning-based hybrid ensembling stacking classifier (ESC) capable of predicting the crisis and its severity level. Finally, we applied principal component analysis (PCA) and k-means clustering to categorise DHW consumption hours throughout the day for each severity level. The results showed that the developed ESC classifier significantly outperforms (𝑅2= 0.99) the baseline LGBMC classifier (𝑅2= 0.92). Combining the classifier with extracted daily consumption patterns and clusters allows the optimisation of control actions on the supply, distribution, and demand side of the DHW system. 1. Introduction With increasing global temperatures, the need to optimise energy use and reduce carbon emissions from energy generation has become critical [1]. Ensuring energy is used efficiently, produced and delivered precisely when and where it is needed is one of the key aspects of tackling climate change [2]. Given that producing certain types of energy for end users is often an inert process, it is necessary to anticipate the energy demand in advance. For example, building heating energy consumption can be predicted using its strong correlation with weather patterns [3]. In contrast, domestic hot water (DHW) demand is a highly stochastic process [4], which is strongly dependent on user behaviour, making it a compelling area for further research. In addition, fluctuations in hot water consumption can reveal changes in factors such as population density and occupancy, which, in turn, may signal changes in urban use patterns [5]. The share of thermal energy used to prepare domestic hot ∗Corresponding author. E-mail address: [email protected] (L. Morkunaite). water accounts for a significant portion of the thermal energy consumed by households. According to the Lithuanian Data Agency, between 2009 and 2018 this share increased from 10.4 % to 18.6 % of the total thermal energy [6]. DHW systems are vulnerable to various crises triggered by different factors, such as natural disasters, pandemics, or economic downturns. For example, during the COVID-19 pandemic, many people had to switch to home offices, leading to significant changes in domestic water use [7]. However, to apply targeted control actions, it is important to identify the crisis and determine its severity level. In some cases, it might be beneficial to adjust control measures aiming for comfort or economic benefits; in others, it might even be necessary to prioritise certain areas over others to maintain service levels [8]. Identifying the change in energy consumption patterns is also economically significant for consumers, as the energy market is not fixed [9] and can offer more favourable rates during certain periods. To make https://doi.org/10.1016/j.enbuild.2025.115579 Received 14 November 2024; Received in revised form 23 February 2025; Accepted 6 March 2025 Energy & Buildings 336 (2025) 115579 Available online 10 March 2025 0378-7788/© 2025 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ). Morkunaite et al. use of that, the DHW control systems should be adjusted to account for current consumption patterns in relation to the energy price. For example, by combining energy demand forecasts with energy storage solutions [10], a more sustainable consumption model can be achieved. Similarly, hot water production, supported by mature technologies, can integrate energy storage with renewable energy sources [11]. To improve the accuracy of hot water demand forecasts under crisis conditions, it is essential to identify factors that signal potential changes in DHW usage. In previous studies, the number of daily cases of COVID19 was used as a factor [12]. However, such input data highly limit the applicability of the study to a specific pandemic event. In contrast, factors such as variation in mobility within urban areas allow the identification of various crises that result in urban mobility change. Reduced mobility flows suggest that more people are spending time at home, which in turn increases the hot water demand for activities like household chores, cooking, and personal hygiene. Under normal conditions, these fluctuations can be observed across different times of the year (e.g., school versus non-school periods) and different days of the week (e.g., weekdays versus weekends). A notable example occurred during the COVID-19 pandemic, when significant shifts in mobility were observed over a relatively short period [12]. Therefore, data from the COVID-19 pandemic period can serve as input in training forecasting models to identify different modes of DHW system operation. Given the importance of accurately predicting and adapting to DHW consumption patterns, multiple stakeholders are affected by these variations. Understanding how changes in hot water usage influence different sectors underscores the need for comprehensive analysis and datadriven decision-making. The following points highlight the key stakeholders affected by the fluctuations in DHW demand. •Energy and water utilities providers: Accurate DHW consumption patterns are essential to optimise water distribution and energy supply planning. Sudden usage changes, such as those caused by lockdowns, can affect demand forecasting and operational efficiency. •Policy makers: Understanding variations in DHW usage helps inform policies related to energy efficiency, water conservation, and crisis response planning. This is particularly relevant for regions transitioning to renewable energy sources. •Building engineers and facility managers: Detailed insights into DHW demand fluctuations enable better system optimisation, predictive control, and efficient scheduling to reduce energy waste and improve system performance. •Real estate developers: Data on DHW consumption trends can inform sustainable building design, ensuring that infrastructure adapts to both normal conditions and crisis scenarios. •Manufacturers of DHW systems: Insights from consumption pattern changes can guide the development of more adaptive, energyefficient DHW systems, improving their responsiveness to varying demand levels. •The research community and energy planners: Integration of demand patterns in energy planning, particularly for renewable-based DHW systems, is crucial to optimise resource allocation and ensure grid stability. In regions where solar thermal or heat pump systems are predominant, understanding peak demand shifts is critical for energy storage and distribution strategies. In this study, we employ Community Mobility Reports [13] data collected by Google on retail/recreation and transit stations to categorise the crisis severity levels. Further, we develop a hybrid ensembling stacking classifier (ESC) that can predict the crisis and its severity level based on DHW consumption data collected from 10 residential apartment buildings located in Kaunas, Lithuania. Finally, we perform PCA using the mean and STD values of hourly DHW consumption for each severity level and cluster them using the k-means algorithm. The proposed method combines predictive modelling and consumption patterns extraction to enable targeted control actions in distinct parts of the DHW system, aiming for more resilient and efficient systems. The main novelty of this work can be attributed to the following points. First, it addresses an often overlooked aspect of DHW consumption by focussing on crisis identification and predicting the severity of these events, which is typically challenging due to the unpredictable nature of user behaviour. Secondly, it incorporates mobility data from retail, recreation, and transit stations, allowing the model to become adaptable to various crises and making it applicable to broader contexts beyond just energy management. Third, the study introduces a new classification approach (a hybrid ensembling stacking classifier (ESC)) that performs significantly better than standard models, achieving high levels of accuracy in crisis and its severity level prediction. Fourth, using techniques such as PCA and k-means clustering enables categorisation of energy usage patterns, allowing targeted control actions for DHW systems supply, distribution and demand side management. This article is structured as follows. Section 2 presents the previous work done on the power consumption for DHW preparation forecasting and identification of changes in daily consumption patterns during crisis conditions. Section 3 introduces the case study building and data used in this research. Section 4 provides all the information required to reproduce the results presented in this article, including the methods for crisis and severity levels forecasting, daily DHW consumption petterns identification, and consumption hours clustering. Section 5 explores the results obtained from the analysis and discuss their application for DHW control enhancement. Section 6 concludes the work and Section 7 offers recommendations for areas of future research. 2. State of the art The COVID-19 pandemic impacted several industries, and the energy sector was no exception. The study of crisis severity in DHW consumption mirrors broader pandemic-driven research, including the prediction of healthcare needs [14] or the public sentiment of COVID-19 [15], highlighting the importance of data-driven approaches in addressing global health challenges. In most European countries, a state of emergency was declared in March 2020 and lasted several months thereafter, with a stricter period of lockdown observed from mid-March 2020 through April 2020 [16–18]. One of the most notable effects was the transition to working from home, which decreased industrial energy consumption but increased residential/domestic consumption in some countries [19]. Several researchers took to analysing the effect of the pandemic on energy demand within European countries [20,21] and other nations such as Canada [16,19], Brazil [22], the USA [23], among others [19,24]. Rayash et al. [16], for example, performed a comprehensive analysis of the hourly energy demand for the province of Ontario, Canada, for April pre-COVID (2019) and during COVID (2020) with the assumption that the heating energy data are equivalent to the electrical load. The results proved that the pandemic impacted electricity demand, with a total decrease of 14 % and a further reduction in demand over the weekend, reaching 15–25 %. In addition, the researchers found that the electricity demand during 2019 increased throughout the week but decreased over the weekend, while in 2020, the peak would be reached by midweek and decline throughout the rest of the week [16]. Similarly, Rouleu et al. [25] analysed the impact of the COVID-19 pandemic on energy consumption, not only considering electricity, but also taking into account hot water and space heating. The case study was conducted on a 40-unit apartment building in Quebec City, which relies on a district heating hot water loop that provides heat to the building and uses natural ventilation during the hot months. The authors found that the peak hot water consumption was reached at 7 PM in the control period. In contrast, in the COVID period, the peak was reached in the afternoon hours with an increase 103 %, indicating that the lockdown period during the pandemic influenced the hot water consumption pattern [25]. Researchers in Qatar [24] used machine learning techniques to compare the actual usage of electricity and the simulated usage of electricity, then used these data to predict energy consumption in the years 2021 Energy & Buildings 336 (2025) 115579 2 Morkunaite et al. and 2022. The pandemic was found to have a negative effect on electricity consumption in the residential sector in that it increased during the pandemic due to the stay-at-home policy. Electricity is free for Qatari citizens and the application of charges to it could decrease the demand for energy in domestic areas and curb the effects of crises on the energy sector. By analysing the effects of a crisis such as the COVID-19 pandemic, researchers and policy makers can predict, similarly to the work of Abulibdeh et al. [24], energy consumption patterns and better prepare for future disruptions. Nepal et al. [26] analysed building electricity data using the K-means approach; instead of randomly selected centroids, the researchers chose initial centroids based on the hourly distribution of electricity data for one year. The percentile method was used to select the initial centroids, where the cumulative density was divided into (𝑘+ 2) equally separated percentiles (k being the number of clusters). The results showed that the patterns among the six buildings analysed were similar, with an increase during the day and a decrease in electricity consumption at night. The author determined the accuracy of the proposed method by applying the methodology on four different real-world data sets and found that the technique resulted in much higher accuracy than the randomly selected centroid for K-means clustering. To understand the full impact of the crisis, it is necessary to investigate all aspects of energy consumption. DHW usage is often overlooked due to its stochastic nature and high dependency on user behaviour [25]. However, neglecting this aspect can lead to inaccurate energy management strategies. 2.1. Power consumption for domestic hot water preparation daily patterns prediction Several factors, including geographic location, outdoor conditions, indoor conditions, number of occupants, and occupant behaviour, influence DHW use. In other cases, these factors can extend to cultural behaviour or socioeconomic behaviour [27–29]. Moreover, as described in the literature, advanced forecasting methods can provide useful insights for improving the management of DHW systems, aiding in the prediction of crisis severity and enhancing the allocation of energy resources in residential settings [30–32]. In residential buildings, DHW accounts for 14–25 % of total energy consumption [4,12,28,33]. Typically, daily DHW patterns have two peaks in the morning and evening [28], which are largely contributed by the fact that occupants either go to school or work in the morning and then return around the evening to continue domestic activities such as showering and cooking. In the design process, most of these peaks are often estimated values. Empirical models are a common method for estimating DHW demands, where, as an example, standards like EN 12831-3 provide equations based on per capita water consumption and system efficiency factors [28] to determine the demand. Indicators of the DHW system in the design stage, such as peak power and thermal energy demand, can be determined using relevant standards [34]. However, dynamic simulations should be used more as they offer more details by incorporating several elements, aside from the theory-based calculations as shown by Rashad et al. [35] through the use of TRNSYS for analysing energy demand. Understanding peak power consumption from DHW usage is important in predicting the impact of crises conditions on daily patterns. However, owing to the various factors influencing peak power demand, the DHW systems are often not designed to meet the requirements of such fluctuating needs, which usually leads to inefficiencies, increased operational costs or system failures, especially in multiple occupancy buildings such as apartments. As discussed in the review by Fuentes et al. [28], most DHW systems are designed based on standards and not real data, and as such, many systems are often oversized or undersized. Several modelling tools [36] are used in designing DHW systems with consideration of occupancy and usage patterns through representative days; however, this approach doesn’t take into account the dynamic nature of water consumption. Amanowicz [37] highlights the need to be attentive to peak power selection, which, as the author describes, affects cost, size and efficiency of DHW systems. The author used three different methods to analyse peak power consumption and found that the method with the highest confidence of results is the Sander’s method which uses hot water volume flowing from the water device, temperature of water and time use to determine energy requirements. Rubina et al. [38] emphasized the importance of understanding peak water flow rates in the design of DHW systems, which also influences factors like pipe design. The authors used a new empirical calculation of the water flow estimation and compared actual water flows with the new design water flow values and found that the method resulted in a reduction in energy demands for water heating, as well as a reduction in pipe size, which ultimately reduces the cost of manufacturing. User behaviour plays an important role in power consumption of DHW, and generally, this criteria is not considered fully in the design of the systems and as such would affect the prediction of hot water usage in crisis or non-crisis conditions. Hansen et al. [39] conducted an interesting study to determine how occupation, age, income, and other can affect the peak power usage of a building. It was found that households with white-collar workers had higher morning peaks, whereas pensioners’ homes had lower and later peaks. Households with ages 41–50 years had higher morning peaks with 4.5 kWh in the 7th hour, whereas age groups 18–40 years and 51–60 years had a lower power consumption with 4 kWh in the 7th hour as well. High-income households exhibited higher consumption in the morning and evening peaks, whereas lowerincome groups presented much flatter peaks. These results indicate that peak power consumption is affected by occupants and their behaviour, and as such, it should also be considered in design and management of utilities. Cao et al. [33] predicted hot water demand using seven occupants’ hot water usage behaviour by collecting shower data. The researchers trained the data using the Support Vector Machine (SVM), a data mining technology, to analyse the showering habits of the occupants. They found that it was possible to predict the hot water usage and implement a hot water supply strategy. However, this predictive model achieved a root mean square error (RSME) of 77.63 when the shower habits of the occupants were analysed individually versus the RSME value of 58.65 when the data were aggregated, which led the researchers to conclude that a separate analysis provided better accuracy. The researchers also note that the different choice of evaluation criteria is the main reason for this difference. To form more accurate predictive models of DHW consumption, it is necessary to perform an extensive data review when analysing larger data sets to remove any outliers. Sonnekalb et al. [40] used neural networks and Gaussian processes to evaluate data sets to learn and predict human behaviour concerning DHW to adapt heating times to reduce energy consumption. The initial data for the hot water preparation were presented in minutes; therefore, data pre-processing was necessary to convert the data into hourly intervals and add other specific features. Incomplete data sets were eliminated and the results showed that it would be possible to reduce the window of hot water preparation, thus reducing the energy consumption of hot water preparation by up to 33–85 %. Maltais et al. [4,41] used model predictive control (MPC) relying on data provided by neural networks that were trained from real data for the energy management of DHW for single-family residential units. It was found that the long-term predictions from machine learning models can show higher inaccuracies compared to the theoretical approach [4]. However, these models can still be used to predict DHW demand, and if used together with a storage tank, where the MPC is inaccurate, a supply would still be present to meet the demand. The author also suggested that prediction inaccuracies are reduced by increasing the time interval to 2h. Clustering is not limited to analysing building electricity data, as mentioned earlier. Ritchie et al. [42] used clustering and statistical analysis to model DHW usage. The researchers created clusters and sub-clusters of time, volume, and flow rates, and the generated model Energy & Buildings 336 (2025) 115579 3 Morkunaite et al. determined the probability of occurrence of these clusters over the specific distribution. The model showed high accuracy compared to the measured data. With that in mind, the authors proposed that the model could be used for energy management strategies as the energy drawn from the grid can be predicted. DHW forecasting models can potentially optimise system control, leading to energy savings and economic benefits. However, developing robust models that can account for the stochastic nature of user behaviour and disruptive events remains a challenge. Therefore, training these models to recognise and respond to crises is crucial. 2.2. Changes in daily patterns during crisis conditions A national or global crisis can occur at any moment. Recessions, pandemics, or natural disasters are all examples of crises. Policymakers and governments can learn from crises such as the COVID-19 pandemic and better prepare by creating forecasting and prevention strategies in various disciplines to mitigate future disasters [43]. Generally, energy consumption during the COVID-19 pandemic saw a change in daily patterns. The prepandemic conditions had a peak energy consumption in the morning hours of the weekday and significantly lower values on weekends; however, during the pandemic, no typical morning peaks were observed, and the energy consumption was lower [17]. Zhang et al. [20] simulated the impact of the COVID-19 pandemic on energy demand in a building matrix in Sweden using the UMI tool. The buildings were divided according to their archetype, where occupancy and DHW, among other parameters, were considered. The researchers showed that the average system energy demand, which includes heating, cooling, and domestic water, decreases in a range of 7.1 % to 12.0%. It was also concluded that increasing confinement constraints increase the DHW energy demand in residential buildings; however, less heating is required due to greater internal heat gains [20]. Kim et al. [12] analysed real data from an apartment complex in South Korea to determine changes in DHW demand during the pandemic. Unlike most European countries, the state of emergency in Korea was issued on 20 January (2020), almost two months before it was issued in Europe. Data were collected at hourly intervals and included DHW accumulated energy, flow rate, supply temperature, outdoor temperature, and city water temperature. The analysis identified a significant increase in DHW demand after the pandemic, which is due to changes in the daily consumption patterns of the occupants as a result of the stay-at-home policy, similar to what was identified by Rouleu et al. [25]. Abu-Bakar et al. [44] used clustering to determine the impact of the COVID-19 pandemic on water consumption patterns in England. The patterns were divided into four clusters: the evening peak, the late morning, the early morning, and multiple peaks, which were identified using the “elbow” method. The researchers found that there was an increase in water demand in each of the clusters during the lockdown period defined as January to May 2020. Using K-means clustering from May 2019 to October 2020 (considering workdays, weekends, and holidays), Dziminska et al. [45] revealed that the patterns obtained for three different buildings were similar, differing only in volume of water consumption in a given hour. A change in the morning and evening peak is observed, with a shift of about two hours later in the morning hours and about two hours earlier during the night. There is also increased usage during the afternoon. 2.3. Identified challenges in managing DHW consumption under crisis conditions The state-of-the-art review revealed that recent research has addressed changes in energy consumption patterns, including crises such as the COVID-19 pandemic, which significantly altered daily routines and subsequently affected residential energy use. Studies have demonstrated how mobility restrictions during lockdowns influenced DHW demand and other utilities, noting shifts in peak consumption times and increased residential demand due to stay-at-home policies. In particular, researchers have used machine learning techniques to predict energy consumption and categorise usage patterns, integrating data from both environmental factors and user behaviour. However, several gaps remain unaddressed: •DHW demand analysis under crisis conditions. While various studies have explored general energy consumption during the pandemic, few have focused specifically on DHW demand [16,24,26]. DHW consumption is highly variable and user dependent, making it challenging to manage, especially in crisis conditions [25]. More research is needed to identify the change in DHW consumption daily patterns during crisis and segregate them based on the severity level. •Model generalisability to various crises. Existing studies often rely on specific data related to pandemics, such as COVID-19 case counts, limiting their applicability to similar crises [12]. This reduces the generalisability of the prediction models to other crisis scenarios. There is a need for models that can leverage broader indicators, such as urban mobility data. •Control optimisation based on crisis severity level. Current models focus on forecasting energy demand [30–32], but further discussion on targeted control actions based on the results is lacking. Effective crisis management in energy systems should include dynamic control strategies that respond to predicted changes in demand, particularly considering the intermittent nature of renewable energy sources [35]. 3. Case study introduction 3.1. Case study buildings Ten residential apartment buildings in Kaunas (Lithuania) were selected as a case study (Fig. 1). The urban block has clear boundaries of intensive streets and natural elements. It contains multi-flat housing built from the 1960s to the late 1980s, accommodating diverse social groups. Several multi-flat residential buildings have been modernised by increasing the thermal resistance of the building envelope and applying autonomous room temperature control. The basic description of building service systems is as follows. •Heating system. Buildings are heated by thermal energy supplied through a centralised district heating (DH) network operated by the city’s thermal energy provider. The DH network in Kaunas city covers all the major populated areas. For all buildings, the thermal energy supply for heating is regulated according to the outdoor temperature by a sensor. •Water system. The cold water supply and sewerage systems follow the same principle, i.e. district (centralised) supply and disposal by the city’s water services provider. Hot water is prepared within the Fig. 1. Arrangement of selected multi-flat residential buildings. Energy & Buildings 336 (2025) 115579 4 Morkunaite et al. Table 1 Characteristics of selected multi-flat residential buildings. Building no. Useful area (m2) Number of apartments Average apartment area (m2) Number of taps Number of occupants 92 1042 32 32.6 64 32 90 1524 32 47.6 64 44 89 891 18 49.5 36 26 88 1511 32 47.2 64 44 87 812 18 45.1 36 23 86 1416 32 44.3 64 41 82 1517 32 47.4 64 44 80 1530 32 47.8 64 44 79 1423 87 16.4 87 87 75 1400 86 16.3 86 86 building’s heating unit, heated through a dedicated heat exchanger, and distributed throughout the building’s hot water network for consumption. Since the buildings contain many flats, location and distance between the pipelines are significant factors. To address this, recirculation loops are installed in the system. These parallel and additional pipelines, along with the recirculation pump and other necessary equipment, continuously circulate hot water through the system to ensure a timely hot water supply at the most inconvenient (furthest) point (tap) from the heat exchanger. Hot water is prepared using the same thermal energy sourced from the DH system at the building’s heating distribution plant. All buildings are equipped with instantaneous domestic hot water heat exchangers, without storage tanks. The principal schemes of the system are defined by the energy provider [46]. The useful (heated) area of the buildings varies from 812m2 to 1795m2, which corresponds to between 18 and 87 apartments with corridors and basement spaces. The number of occupants ranges from 23 to 87 and the number of taps for food processing and hygiene activities ranges from 26 to 87 (Table 1). The information provided is based on data from the State Enterprise Centre of Registers information system [47]. 3.2. Building data description Data on energy consumption for hot water preparation and maintenance have been collected from separate smart metres, which are installed in the heat distribution plants of buildings and measure the thermal energy consumption at 1-h intervals. In addition, smart metres measure the temperature of the inlet and outlet heat agents and the flow rate. The data collection period for pilot case buildings ranges from 2 to 10 years between 2011-10-01 and 2021-09-30. The whole set consists of 480,580 entries (timestamps) of thermal energy for hot water measured in kWh. Data were retrieved from smart metres in the CSV (Comma Separated Values) data format. Subsequently, it had to be treated accordingly by filtering, cleaning, aggregating, and interpolating. To ensure data comparability for objective evaluation and analysis, normalisation was applied based on the most significant influencing factor: the number of occupants. By dividing the energy consumption for hot water preparation by the number of occupants (Table 1), a derived unit of kWh∕occupant is obtained, eliminating the influence of building size. Fig. 2 shows the normalised daily thermal energy consumption for DHW preparation. The data collected from all buildings and used for this analysis span from 01/01/2018 to 30/09/2021. The vertical red transparent bars mark the lockdown periods: the first from 16/03/2020 to 16/06/2020, and the second from 7/11/2020 to 30/06/2021. The green vertical bars indicate the corresponding periods prior to the lockdowns. The blue curve represents the total daily energy consumption, while the orange curve shows the average monthly daily energy consumption, highlighting a clear seasonal trend. The increase in energy consumption during the heating season can be attributed to the lower temperature of cold water, as more thermal energy is required to reach the hot water set-point temperature, i.e. 55◦C. In addition, occupant consumption habits and the recirculating hot water loop contribute to higher energy demand during the heating season due to a slight decrease in indoor temperature. During the heating season, the indoor temperature tends to be lower than during the nonheating season period, which increases the heat loss to the environment from the circulating hot water loop pipes and thus the energy demand, even though the hot water loop is used continuously. Comparing the same periods before and during lockdown, the plot does not indicate significant differences in energy consumption. However, there are recurring outliers with values of 0 or significantly lower values during the warm season. This is likely due to the annual maintenance of the building’s heating and hot water systems when they are temporarily shut down. 3.3. Mobility data description In response to the COVID-19 pandemic, Google developed Community Mobility Reports [13] to provide public health officials with aggregated anonymised mobility data for informed critical decision making. These reports tracked movement trends across various geographic regions and categories, including retail and recreation, groceries and pharmacies, parks, transit stations, workplaces, and residential areas. In this study, data specific to Kaunas city were extracted and analysed, with a focus on changes in mobility patterns in response to COVID19 related policies. Changes were examined in two key categories: retail and recreation activities (including places such as restaurants, cafes, shopping centres, theme parks, museums, libraries, and movie theatres) and transit station activities (encompassing public transport hubs such as bus stations). The categories of retail recreation and transit stations were chosen due to their significant impact on urban mobility and public behaviour during the COVID-19 pandemic. Retail and recreation activities serve as key indicators of economic activity and social interaction, reflecting changes in consumer behaviour and adherence to public health measures such as lockdowns or social distancing guidelines. Meanwhile, transit station activities provide critical insights into public transport usage, which is directly correlated with mobility patterns, access to essential services, and the broader functioning of the urban economy. By concentrating on these two categories, the study aimed to capture the most influential aspects of daily life in Kaunas affected by COVID-19 related policies. The data, provided in the form of time series, span from February 2020 to December 2021. Mobility data, including the categories of retail / recreational and transit stations from Google mobility reports, clearly indicates the start of both lockdown periods in Kaunas, Lithuania, during the COVID-19 pandemic (Fig. 3). The percentage change from baseline, depicted in the graph, highlights the sharp declines in mobility corresponding to the onset of the first and second lockdown periods. These lockdown periods are reflected in the different severity levels of restrictions, represented by colour-coded bands ranging from baseline (normal activity) to severity 5 (the most stringent restrictions). The data show that mobility decreased significantly at the beginning of the pandemic, especially Energy & Buildings 336 (2025) 115579 5 Morkunaite et al. Fig. 2. Normalised daily thermal energy consumption for domestic hot water preparation. Fig. 3. Mobility changes in retail/recreation activities and transit stations in relation to crisis severity levels. during the strictest lockdown phases, before gradually recovering in line with the easing of restrictions. However, mobility levels remained below baseline throughout the study period, indicating a prolonged impact of the pandemic on public activity, particularly in transit and recreational spaces. The extraction of the Severity levels are further detailed in the Methodology section. 4. Methodology The overall research approach is illustrated in Fig. 4. It consists of three main parts: data collection and preparation, crisis and severity forecasting, and pattern extraction and clustering. The first part involves data from two main sources: 10 case study buildings in Kaunas (Lithuania) and Google Community Mobility Reports [13]. In this phase, the building data undergo the usual data cleaning, normalisation, and preprocessing steps. Crisis severity levels are extracted from the datasets on retail/leisure activity and transit stations collected in the Google Community Reports. Finally, the pre-processed data are merged into a single dataset that includes additional temporal features. In the next phase, the ESC classifier is used to forecast the crisis and its severity level. The forecasting model is further cross-validated to ensure its reliability and accuracy.Further, daily DHW consumption patterns are extracted for each of the crisis severity levels. Additionally, PCA and k-means clustering are used to define the clusters of daily consumption hours. The results of forecasting, pattern extraction and clustering acts as an input for DHW systems control optimisation. Each part of the methodology is further detailed in this chapter. 4.1. Data collection and preparation 4.1.1. Calculation of hot water consumption The collected raw data pertain the amount of thermal energy used for hot water preparation. However, to determine the distinct hot water consumption patterns, the DHW consumption data are needed. The main factor determining the amount of thermal energy is the temperature of the cold water to be heated, which varies throughout the year due to the changing temperature of the outdoor air. However, the cold water temperature variation is significantly influenced by the thermal inertia Energy & Buildings 336 (2025) 115579 6 Morkunaite et al. Fig. 4. Research approach. of the ground (soil), as the supply pipelines are laid at a depth of at least 1,8m underground to prevent freezing during the coldest periods of winter. The average depth of the pipelines in Kaunas varies between 2 and 2.5m. Kaunas (central Lithuania) is in the cold-temperature zone, with moderately warm summers and cold winters. The city of Kaunas has an average long-term outdoor temperature of around 7–8 ◦C. The average outdoor temperature in July is around 17◦C, and in winter around −5◦C. Lithuania has relatively hot summers, daytime highs above +35◦C, and cold winters, with nighttime lows below −30 ◦C. Therefore, the amount of hot water consumed 𝑉ℎ𝑤, 𝑚3 knowing the thermal energy consumed 𝑄ℎ𝑤, 𝐽 was calculated using Eq. (1). 𝑉hw =𝑄hw 𝐶𝑣⋅(𝜃hw −𝜃cw)(1) where: –𝐶𝑣 is the volumetric heat capacity of the water. The standard value is 4,160,000 J∕(m3◦C). –𝜃ℎ𝑤 is the standardised hot water temperature (◦C). A temperature of 55 ◦C should be maintained, considering the Building Regulations’ requirements. –𝜃𝑐𝑤 is the supplied cold water temperature (◦C), which varies between 4◦C and 16◦C over the year. The cold water temperature in the network throughout the year is determined based on the average daily outdoor temperature. To take into account the thermal inertia of the soil, i.e. the variation in outdoor temperature, which is normally most significant over 24h, a moving average method was adopted. The relationship between the cold water temperature and the moving average outdoor temperature is based on the cold water temperature measurements declared by the provider, where a lower limit of −4◦C water temperature corresponds to an outdoor temperature of −20◦C and an upper boundary of −16◦C corresponds to +25 ◦C. The cold water and outdoor air temperature measurements were used to apply a linear regression method and derive the Eq. (2). 𝜃𝑐𝑤 =𝜃𝑜𝑢𝑡 ⋅0.2667 + 9.3333 (2) where: –𝜃𝑜𝑢𝑡 is the 24-h moving average of daily outdoor temperature, ◦C. Table 2 Lockdown severity characterization based on mobility changes (Kaunas). Labels Description Baseline Percentage change equal or greater than 0 Severity1 Percentage change between −1 % and −20 % Severity2 Percentage change between −20 % and −40 % Severity3 Percentage change between −40 % and −60 % Severity4 Percentage change between −60 % and −80 % Severity5 Percentage change between −80 % and −100 % Fig. 5 shows the variation of the cold water temperature in the supply networks according to the fluctuation of the outdoor air temperature. The results are plotted for the period, starting from 2016 to the end of September 2021. 4.1.2. Characterisation of severity based on local mobility patterns Google mobility data include percentage changes measured against a baseline that represents typical mobility levels before the COVID-19 pandemic. Using predefined thresholds, a characterisation scheme was implemented for these deviations to illustrate the varying levels of departure from baseline mobility patterns (Table 2): •If the mobility change for retail/recreation and transit stations was the same, this value was assigned to the subsequent label. •If the mobility change differed, only the mobility change value for retail/recreation was used as the subsequent label. The Google mobility data begins in February 2020, while the water usage volume data begins in February 2019. Hence, all data points for 2019 were labelled with the “Baseline” label to distinguish the pre-COVID-19 period when mobility patterns were unaffected by lockdowns. This characterisation determines the severity of COVID-19 lockdowns and the general restrictions imposed on local residents. The “Baseline” label represents normal conditions, i.e. indicating the preCOVID level of mobility. In contrast, severity levels (Severity 1 through Severity 5) denote increasing levels of restricted mobility correlating with the intensity of lockdown measures and other restrictions in the urban area of Kaunas. Although mobility changes are recorded daily, the characterisations were applied to represent conditions for all subsequent hours of each day. Fig. 6 shows an aggregated view of the hourly counts of COVID-19 quarantine severity levels impacting mobility data for each month from January 2020 to May 2021. It is highlighted that there is a clear rise in hours characterised as more severe in terms of the lockdown effect, particularly in April 2020 and December 2020, where the most instances of Severity 5 are recorded, which is in line with the historical timeline of the austerity of the lockdown measures. 4.1.3. Combined dataset and feature extraction Following the characterisation scheme for each timestamp described in Section 4.1.2, the resulting hourly labels were merged with the hourly domestic water volume intake data. Consequently, the combined data set spans from February 6, 2019, to September 29, 2021, for each building. The domestic water volume intake data for each of the ten buildings (as described in Section 4.1.1) were sequentially combined into a single dataset. Using the characterisation scheme outlined in Section 4.1.2 for each timestamp, the resulting hourly labels were merged concurrently with the corresponding water intake data. For the analysed dataset, time was incorporated as a feature by splitting the timestamp into categorical values to create additional temporal features. In addition to standard temporal features, such as the hour of the day, day of the week, and month, specific features were synthesised based on the unique characteristics of our dataset, reflecting the location of the case study. Lithuanian holiday data for 2019 to 2021 were included using the ‘holiday’ Python library. An additional feature Energy & Buildings 336 (2025) 115579 7 Morkunaite et al. Fig. 5. Relationship between outdoor air temperature and cold water temperature in supply networks. Fig. 6. Quarantine severity characteristic instances (hourly count). Table 3 Predictive modelling: features description. Feature Labelling lockdSeverity Baseline: 0, Severity1: 1,…Severity5: 5 W_vol Water intake for each building (m3) Quarter 1 to 4 Month 1 to 12 DayofMonth 1 to 31 Weekday 0 to 6 Hour 0 to 23 IsWknd_Holiday 0, 1 (IsWknd_Holiday) was created to identify whether a given date falls on a Saturday or Sunday and coincides with any Lithuanian holiday. An outlier detection strategy was applied to the water volume data, identifying values above the 99.99th percentile for each of the ten buildings and replacing them with the maximum value corresponding to this percentile. The final data set for the ESC forecast was divided into training and test sets, with 80% training and 20 % for testing [48]. 4.2. Crisis and severity forecasting 4.2.1. Predictive modelling of lockdown-type emergencies As indicated in the relevant literature, the COVID-19 lockdown and its consequences on daily routines directly affected residents’ energy and hot water consumption patterns. Therefore, it has become critical to identify such abrupt future emergencies so that utility providers can make immediate adjustments and preparations to ensure that no severe disruptions occur for tenants. In this study, a data-driven pattern recognition mechanism was developed to identify potential future irregularities in residential water demand under unforeseen circumstances resembling a lockdown event, such as the post-COVID-19 period. Using severity level labels, a machine learning-based classifier was created to predict whether such an emergency might be imminent and, if so, to estimate the expected severity of the situation. To achieve this, a hybrid ensemble stacking classifier (ESC) was implemented. This meta-ensemble learning model combines the strengths of multiple individual classifiers through a two-level stacking approach, enhancing predictive accuracy for irregular demand patterns. Energy & Buildings 336 (2025) 115579 8 Morkunaite et al. The first layer consists of two base classifiers: LGBMClassifier (LGBMC) and HistGradientBoostingClassifier (HGBC). The LGBMC classifier optimises the following objective function: 𝐿(𝜃) = 𝑛 ∑ 𝑖=1 𝑙(𝑦𝑖, 𝑓(𝑥𝑖;𝜃)) + Ω(𝑓)(3) where: –𝐿(𝜃) is the overall loss function. –𝑙 is the loss function. –𝑦𝑖 is the true label. –𝑓(𝑥𝑖;𝜃) is the predicted value. –Ω(𝑓) is the regularisation term to avoid overfitting. HistGradientBoostingClassifier uses the gradient boosting framework: 𝐹𝑚(𝑥) = 𝐹𝑚−1(𝑥) + 𝛾𝑚ℎ𝑚(𝑥)(4) where: –𝐹𝑚(𝑥) is the current model at iteration 𝑚. –𝐹𝑚−1(𝑥) is the previous model. –𝛾𝑚 is the learning rate. –ℎ𝑚(𝑥) is the base learner at iteration 𝑚. The second layer, the meta-learner, integrates the output from the base-level classifiers. The meta-learner chosen is XGBClassifier (XGBC). The XGBoost classifier can be formulated as follows: 𝐿(𝜃) = 𝑛 ∑ 𝑖=1 𝑙(𝑦𝑖, 𝑓(𝑥𝑖;𝜃)) + 𝐾 ∑ 𝑘=1 Ω(𝑓𝑘)(5) where: –𝐿(𝜃) is the overall loss function. –𝑙 is the loss function. –𝑦𝑖 is the true label. –𝑓(𝑥𝑖;𝜃) is the predicted value. –Ω(𝑓𝑘) is the regularisation term for the 𝑘th tree. The stacking process involves two layers: •First layer: 𝑦𝐿𝐺𝐵𝑀𝐶 =𝐿𝐺𝐵𝑀𝐶(𝑋)(6) 𝑦𝐻𝐺𝐵𝐶 =𝐻𝐺𝐵𝐶(𝑋)(7) •Second layer (meta learner). The meta-learner 𝑋𝐺𝐵𝐶 uses the predictions of the base classifiers as its input: 𝑦𝑚𝑒𝑡𝑎 =𝑋𝐺𝐵𝐶([ 𝑦𝐿𝐺𝐵𝑀𝐶 , 𝑦𝐻𝐺𝐵𝐶 ]) (8) 4.2.2. Cross-validation All models were used for one-step (i.e. 1 h) forecasting. Additionally, the ESC employs 5-fold cross-validation during the training of the metalearner (Eqs. (9) and (10)). The data were split into 5-equal folds in 5-fold CV and hence in each fold, 20 % of the data is available. One fold is left for testing, and the remaining four folds are used for training. The decision to use 5-fold cross-validation is commonly made because it achieves a good balance between computational efficiency and model evaluation reliability. It is less computationally expensive than higherfold cross-validation, especially when dealing with large data sets or complex models such as meta-learning. 𝐶𝑉𝐸𝑆𝐶 =1 𝐾 𝐾 ∑ 𝑘=1 𝑦(𝑘) 𝑚𝑒𝑡𝑎 (9) where: –𝐾 is the number of folds (in this case, 5). –𝑦(𝑘) 𝑚𝑒𝑡𝑎 is the prediction of the meta-learner on the 𝑘th fold. Table 4 ESC hyperparameters. Classifier Hyperparameters LGBMC reg_alpha=0.7, reg_lambda=0.7 learning_rate=0.07 HGBC max_leaf_nodes=30, learning_rate=0.07 XGBC max_depth=6, subsample=0.8 Combining the base classifiers and meta-learner in a two-level stacking framework can be expressed as: 𝑦 =𝑋𝐺𝐵𝐶([ 𝑦𝐿𝐺𝐵𝑀𝐶 , 𝑦𝐻𝐺𝐵𝐶 ]) (10) Here 𝑦 is the final prediction of the ESC model. The hyper parameters for each base classifier were carefully selected to balance bias and variance, aiming to reduce over-fitting. Specific values were determined using grid or random search methods along with selected trial and error compiles, ensuring optimal performance on the test sets (Table 4). 4.3. Pattern extraction and clustering For the five defined crises severity levels and the baseline (normal conditions), daily patterns for DHW consumption were extracted using the mean values for each hour of the day. The standard deviation (STD) was calculated to evaluate the possible high variation in the data. In addition, weekends and holidays were excluded, while daily patterns were extracted based on observations during data exploratory analysis. The data points corresponding to each severity level and the baseline were split into six data sets that were further used for clustering. Each data set included 24 rows representing values of hot water consumption for each hour of the day; however, the number of dimensions differed for each data set since not all months showed the six severity levels. The structure and months included in each data set are presented in Table 5. Principal component analysis (PCA) and the k-means method were used to cluster separate hours in a day of energy consumption for DHW preparation. The data set used included mean and STD values for all investigated buildings. Using the mean and STD allowed us to consider possible strong discrepancies between separate buildings’ hot-water consumption patterns. 5. Results and discussion 5.1. Predictive modelling results The performance metrics considered for the tested classifiers are Accuracy, Precision, Recall, and F1 Score (Table 6). Overall, the developed ESC exhibits very good performance, achieving high accuracy. The accuracy of the test data is aligned with the accuracy of the training data, indicating that the model is not overfitting and generalises very well to unseen data. The high precision, recall, and F1 scores in both datasets underscore the robustness of the model and its ability to classify positive instances correctly. Compared to a base classifier, the ESC significantly outperforms the LGBMC in all performance metrics. Although LGBMC and HGBC are gradient-boosting algorithms, they optimise differently and have different biases. Combining their outputs through a meta-learner like XGBC, a powerful boosting algorithm, allows the ESC to learn more complex patterns in the data. An overview of ESC performance is also illustrated in a confusion matrix (Fig. 7); it represents the results of a classification task, dividing test samples into four categories, depending on their true and predicted labels: true positives (TP), true negatives (TN), false positives (FP), false negatives (FN). The only misclassifications are limited to Label 0 (Baseline), while there are no misclassifications for any of the severity levels. 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