Analysing energy poverty in warm climate zones in Spain through artificial intelligence

Depósito de investigación de la Universidad de Sevilla https://idus.us.es/ Esta es la versión aceptada del artículo publicado en: This is an accepted manuscript of a paper published in: Journal of Building Engineering (2023): 23/10/2024 DOI: https://doi.org/10.1016/j.jobe.2023.106116 Copyright: © 2023 Elsevier Ltd. All rights reserved El acceso a la versión publicada del artículo puede requerir la suscripción de la revista. Access to the published version may require subscription. “This is an Accepted Manuscript of an article published by Elsevier in [Journal of Building Engineering ] on [2023], available at: https://doi.org/10.1016/j.jobe.2023.106116 ” 1 Title: Analysing energy poverty in warm climate zones in Spain through artificial intelligence Authors: David Bienvenido-Huertas1, Daniel Sánchez-García*2, David Marín-García3, Carlos Rubio-Bellido4 1Department of Building Construction, University of Granada. Granada, Spain 2Department of Electrical Engineering, University Carlos III of Madrid, Madrid, Spain 3Department of Graphical Expression and Building Engineering, University of Seville. Seville, Spain 4Department of Building Construction II, University of Seville. Seville, Spain Abstract: Using automated tools to detect energy poverty (EP) is a developing field. Artificial intelligence and data mining could be used to provide solutions to reduce EP cases. As for Spain, there is no study addressing this characterization that could be significant in warmer zones of the country (i.e., the most exposed zones to climate change). Simulated energy consumption s based on the public income indicator of multiple effects (IPREM in Spanish). In addition, the high share of energy expenditure in income (2M) was used to assess EP. A total of 36,230,400 cases were simulated to train and test 312 prediction models, 104 by each algorithm. The algorithms were multilayer perceptron (MLP), random forest (RF), and M5P. The results showed that these three algorithms were appropriate, with tree-type models obtaining better estimates. For greater effectiveness, prediction models should also be used for the income threshold considered in their development. The results also showed the utility of artificial intelligence in the prediction of EP work. In addition, prediction tools could be used to estimate mon Keywords: Energy poverty, artificial intelligence, warm climate zones, 2M, artificial neural network, tree models 1. Introduction Most built environment has poor performance [1,2] because many buildings were built before adopting the first building energy regulations and ineffective regulations were implemented [3]. Consequently, the built environment leads to high energy consumption and high greenhouse gas emissions [4,5], thus raising environmental and social problems, such as energy poverty (EP). EP could be considered a recent social problem. Some decades ago, family units could face their energy expenditure. However, constant economic crises and the rise of fossil fuel prices are increasing EP cases. EP is a broad concept, so it is detected in both developing and developed countries. Nevertheless, there are differences according to the country development [6]: the main problems in developing country are energy access [7,8] and systems available [9,10], whereas the difficulty to face energy expenditures is the main problem in developed countries [9,11]. Nonetheless, energy access could also be something of a challenge in developed countries (e.g., family units that do not pay bills and suffer from energy supply cuts [12]). Several studies have shown the significance of EP in Spain. The first study was conducted by Tirado Herrero [13], who determined the EP increase in Spain, particularly in dwellings where unemployed people lived. One-third of unemployed households in Spain spent more than 10% of their income in the energy bill. Likewise, households in EP increased by 142% in less than a lustrum. In a subsequent study, Tirado Herrero [14] detected that 11% of Spanish families could not keep their dwellings under appropriate thermal comfort conditions. Likewise, Sánchez-Guevara Sánchez et al. [15] reported that 24% of the family units in the region of Madrid were in EP situation. Afterwards, Sánchez-Guevara Sánchez et al. [16] reported the existence of a gender gap in the EP cases of the region. Plans and policies have therefore been developed to reduce EP in the country, such as programmes on built environment decarbonisation. The reason could be the current problems related to this aspect (e.g., greater mortality based on suffering inappropriate conditions in indoor spaces [17,18]) and long-term consequences if these situations continue (e.g., descendants that currently live in households in EP situation are very likely to be in the same situation when they are adults [19,20]). Since 2019, the National Strategy against Energy Poverty 2019-2024 exists in Spain. This strategy aims to reduce family units in EP situation by 50% by 2025 in the country [21]. To do this, the 4 indicators of the European Energy Poverty Advisory Hub are analysed, so EP could be assessed from various perspectives [22]. Most performance measures to analysis EP are based on two variables: energy cost and incomes. The former prioritizes performances to reduce the consumption of the HVAC systems of water warming systems. This consumption is very significant compared to the remaining household energy consumption [23,24]. At this point, most performance measures are based on energy renovation [25,26] and social aids, such as the electrical social bond [27]. However, each family unit should be assessed and analysed in detail to adopt these measures. The effort could be laudable because there are many family units in EP situation. To meet the goals set up by the national strategy, automatic tools should be used to assess their situation. Artificial intelligence and data mining approaches could be an opportunity to estimate it automatically. These techniques have been successfully used to generate prediction models in various energy variables related to building [28,29]. However, there are few studies in the state of the art that have assessed the possibility 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 2 of using artificial intelligence to assess EP [30]: (i) Pino-Mejias et al. [31] and Bienvenido-Huertas et al. [32] assessed the possibility of characterizing the fuel poverty potential risk index in households located in several climate zones in Chile. Artificial neural networks were developed to assess the optimal housing allocation of Chilean families to reduce their EP situation; (ii) Rajic et al. [33] used an endocrine nonlinear autoregressive exogenous (NARX) neural network to predict electricity and heat consumption in EP assessments in Serbia. Socioeconomic variables available in the Statistical Institute of the country were used; and (iii) Wang et al. [34] assessed the severe energy poverty index in India by using socioeconomic and geographic input variables. The model allowed the EP in the country to be accurately estimated. There is therefore a knowledge gap on the possibilities of using artificial intelligence to estimate EP. No study in Spain has addressed this possibility of characterization, which could be significant in the warm climate zones of the country. Studies that analyse EP and its performance measures in these regions are also lacking. The limited effectiveness of traditional building energy improvement measures in these regions [35] and the greater severity expected in the future due to climate change [36] could be something of a challenge to reduce EP situations. Bienvenido-Huertas et al. [37,38] reported that EP conditions in the future could be worse in these regions if current technical and socio-economic conditions are maintained. This study therefore suggests the possibility of characterizing EP in warm climate zones of the south of Spain. To do this, 36,230,400 case studies have been simulated and used to train and test 312 prediction models (104 by each algorithm). As a result, the possibilities to estimate models with the climate and characteristics of Spain have been determined, as well as the most useful methodology. 2. Methodology 2.1. Dataset generation A wide dataset with all the possibilities in the built environment of the south of Spain was generated to develop the prediction models. Buildings with good and poor performance were therefore included. A representative building with the typical geometries in the social housing of the south of Spain was selected. A social housing was selected in order to point out the actual problem of EP. The building has 51 social dwellings with 2 or 3 bedrooms and distributed in 4 floors. 0 and 90 m². The building was modelled and simulated in EnergyPlus. The model was validated through the criteria included in the ASHRAE Guideline 14 [39] in previous studies [37,40]. Moreover, the building was parametrized for simulation (Fig. 1). To do this, the dwellings on ground, middle and top floor were selected. As for the middle floor, dwellings on the second floor were used as previous studies did not detect differences in the energy consumption values among the dwellings on the first and second floor [37]. The geometric and orientation conditions of 37 dwellings of the case study were therefore considered. Each dwelling was parametrized. Parametrization consisted of using the building geometry and combining it by varying the variables of envelope, HVAC systems, and operational pattern. As for the envelope, the U-value varied between 0.1 and 2.0 W/(m²K), with an interval of 0.1 W/(m²K). This configuration allowed highly effective designs (i.e., low thermal transmittance values) and typical configurations of the envelope of the built environment of the region (i.e., high thermal transmittance values) to be included. It is worth stressing that these variations in the U-value did not change useful surface area. As for windows, 3 typologies with different thermal properties were considered (Table 1). As for HVAC systems, dwellings were thought to have heat pump, one of the most common typologies in the warm zones of the south of Spain. For parametrization, 17 heat pump models obtained by varying the energy efficiency ratio (EER) and the coefficient of performance (COP) were considered (Table 2). 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 3 Fig. 1. Workflow of the dataset simulation. Table 1. Windows included in the parametrization. Type of window U-value [W/(m²K)] Solar factor Window 01 5.7 0.85 Window 02 3.1 0.75 Window 03 2.5 0.67 Table 2. HVAC systems included in the parametrization. Type of HVAC systems EER COP HVAC 01 2.1 2.3 HVAC 02 2.2 2.4 HVAC 03 2.3 2.5 HVAC 04 2.4 2.6 HVAC 05 2.5 2.7 HVAC 06 2.6 2.8 HVAC 07 2.7 2.9 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 4 HVAC 08 2.8 3.0 HVAC 09 2.9 3.1 HVAC 10 3.0 3.2 HVAC 11 3.1 3.3 HVAC 12 3.2 3.4 HVAC 13 3.3 3.5 HVAC 14 3.4 3.6 HVAC 15 3.5 3.7 HVAC 16 3.6 3.8 HVAC 17 3.7 3.9 both fixed and adaptive setpoint temperatures was considered. A static operational pattern means that the setpoint temperature is independent of the outdoor temperature, and there are usually variations between cold and hot periods. As for the adaptive operational pattern, the setpoint temperature daily varies according to the oscillations of the average outdoor temperature. Setpoint temperatures were based on EN 16798-1:2019 [41], which is the standard on adaptive thermal comfort developed for Europe. The model included in this standard is an evolution of EN 15251:2007 [42] on the basis of the smart controls and thermal comfort (SCATs) project [43]. Both static and adaptive setpoints were taken from EN 16798-1:2019. Table 3 includes the values related to the operational pattern. Each combination of envelope, HVAC systems and operational pattern was simulated by EnergyPlus. To do this, the profile of internal loads for residential buildings included in the Spanish regulation was used [44]. This profile is based on the load variations between weekdays and weekends (Table 4). As for the climate file, climate data of the climate zone B4 of the Spanish regulation were used as it corresponds to the severest warm climates (Table 5). Table 3. Operational patterns considered in the parametrization. Mode Catego ry Acrony m Cooling setpoint temperature (°C) Heating setpoint temperature (°C) Static mode 1 Sta-C1 25.5 21 2 Sta-C2 26 20 3 Sta-C3 27 18 Adaptive model 1 Ada-C1 24.1 30.7 19.1 25.7 2 Ada-C2 25.1 31.7 18.1 24.7 3 Ada-C3 26.1 32.7 17.1 23.7 :Running mean outdoor temperature. Table 4. Load distribution in the simulations performed by EnergyPlus. Loads Load (W/m²) 0:00 6:59 7:00 14:59 15:00 17:59 18:00 18:59 19:00 22:59 23:00 23:59 Sensible load (W/m²) Weekdays 2.15 0.54 1.08 1.08 1.08 2.15 Weekend 2.15 2.15 2.15 2.15 2.15 2.15 Latent load (W/m²) Weekdays 1.36 0.34 0.68 0.68 0.68 1.36 Weekend 1.36 1.36 1.36 1.36 1.36 1.36 Lighting (W/m²) Weekdays and weekend 0.44 1.32 1.32 2.20 4.40 2.20 Equipment (W/m²) Weekdays and weekend 0.44 1.32 1.32 2.20 4.40 2.20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 5 Table 5. Average values of temperature and relative humidity in the analysed city. Month Dry bulb temperature [ºC] Dew point temperature [ºC] Relative humidity [%] January 10 5 69 February 11 3 59 March 13 4 55 Aprilç 14 5 53 May 18 8 52 June 22 8 43 July 26 9 37 August 26 10 38 September 23 10 45 October 18 10 57 November 13 7 65 December 11 5 68 A total of 8 different family units were considered in each combination. Differences were based on the income level. The public income indicator of multiple effects (IPREM in Spanish) was used to determine their income level. This is an index used in Spain to give economic aids and discounts. It is used to analyse family units and has nothing to do with the minimum guaranteed interprofessional wages. The IPREM basis for the year 2019 was used. IPREM was used as referential value to determine various income levels by applying factors between 0.5 and 4 times the IPREM, with intervals of 0.5 (Table 6). As a result, a dataset of 36,230,400 instances was obtained by combining technical aspects of the building (envelope and HVAC systems), operational patterns, and incomes. Table 6. Combinations of incomes according to the IPREM. Abbreviations IPREM 0.5 0.5 3,759.80 IPREM 1.0 1.0 7,519.59 IPREM 1.5 1.5 11,279.39 IPREM 2.0 2.0 15,039.18 IPREM 2.5 2.5 18,798.98 IPREM 3.0 3.0 22,558.77 IPREM 3.5 3.5 26,318.57 IPREM 4.0 4.0 30,078.36 EP was assessed in each instance by using the high share of energy expenditure in income (2M). This is an indicator analysed in the National Strategy against Energy Poverty 2019-2024 and used by other entities, such as the European Energy Poverty Advisory Hub. Moreover, 2M establishes that households that spend in energy consumption more than 2 times the average national energy expenditure are in EP situation [45]. This indicator has been widely used to characterize EP [46,47] because EP could be quantified and thresholds could be adapted to the characteristics of each region. To do this, the energy poverty ratio (EPR) should be obtained. The EPR is a relationship between household energy cost and income level (Eq. (1)). It is worth stressing that households were considered to not assume thermal discomfort. Other situations related to EP, such as hidden EP [48], were therefore not considered. Likewise, the threshold value of 10% was used according to Sánchez- Guevara Sánchez et al. [22]. (1) where This analysis was performed for each of the 36,203,400 instances of the dataset. The process to determine household energy cost was as follows: unlike the energy consumption of each instance, which was obtained through EnergyPlus, energy cost (EC) was obtained by using energy consumption data and by applying the rate of the voluntary price for the small consumer (PVPC in Spanish). This is a regulated market rate implemented in Spain in 2014 [49]. PVPC is used by studies on EP in Spain as it is related to both low income family units and access to social aids [50,51]. EC of the household is obtained (2) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 6 Where ET is the energy term, PT is the power term, ElT is the electricity tax, EMR is the rent of measurement equipment, and VAT is the added value tax. ET is the price related to each kWh consumed. The price daily varies throughout the year according to market oscillations and is obtained by applying the schedule rate to the schedule energy consumption of the dwelling (Eq. (3)). The kWh prices of the year 2019 were used (Fig. 2). PT is the fixed price that users should pay to have contracted power. It is obtained by multiplying the contracted power by both the number of bill days (ND) and the price of the access to the contracted power (grid access (0.104229 power of 4.6 kW was considered (Eq. (4)). ElT is a concept obtained by applying 5.1127% to the ET and PT price (Eq. (5)), whereas EMR is a fixed price of the rent of measurement equipment. Finally, VAT is a percentage of 21% applied to the sum of ET, PT, ElT, and EMR (Eq. (6)). (3) (4) (5) (6) Fig. 2. Price values of the ET of the PVPC in the year 2019. 2.2. Prediction model development After the analysis, a dataset with 36,203,400 instances (4,528,800 instances by each family income typology) and their EPR values was obtained. Some input variables were selected from this dataset, and the EPR was used as output variable. A total of 3 algorithms were used to generate models. The next subsection describes the algorithms and the procedure to train and test models. 2.2.1. Algorithms A total of 3 algorithms were used (Fig. 3): multilayer perceptron (MLP), random forest (RF), and M5P. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 7 Fig. 3. Scheme of MLP, RF, and M5P. MLP is a mathematical model based on the human brain structure. Its goal is to solve regression and classification problems [52 54]. It is widely used because of its universal approximation capacity [55 57]. Its architecture consists in 3 or more layers made up of neurons or nodes (Fig. 3). One of the layers is the input layer, where the input variables of the system are included. The output layer is constituted by the output layer of the system, whereas the intermediate layers (also known as hidden layers) process the input information through synaptic weights and activation, transfer, and propagation functions. It has been widely used as prediction tool in building energy analyses [58,59] and is the most used algorithm in studies on energy poverty [30]. In this study, MLPs were trained through backpropagation [60 62] using the Broyden- Fletcher-Goldfarb-Shanno [63] algorithm (which belongs to quasi-Newton methods). Like other studies [31], one hidden layer was only considered as its performance is better than that of more complex architectures [64]. Likewise, sigmoidal functions were used. RF is an evolution of the classification and regression tree (CART) models. CART creates the relationships among variables in tree models, and RF generates a set of CART models. RF therefore creates a forest of CART models (Fig. 3). The accurately (tree leaf). Its limitations could be addressed through RF models to reduce the variance and the bias [65,66] because a learning combined model is generated: its performance is better than that of an individual model [67]. Likewise, many data could be used with RF without affecting the atypical values of the dataset [68]. This algorithm is therefore widely used to estimate building energy variables [69 71]. The number of CART models affects performance [72], so the models developed in this study oscillated the number of trees from 50 to 100 to obtain the optimal configuration. M5P is also an evolution of CART [73,74], but it is different in that leaves have multiple linear regression (MLR). The algo the effective use of huge dataset and its robustness because of the lack of values in the instances of the dataset analysed [75,76]. Consequently, this algorithm has been successfully used in studies on characterizing energy variables [77,78]. 2.2.2. Training and testing approach Individual models were developed for each output variable. The output variable was the EPR. The difference among each model was that a prediction model was therefore developed for 1 out of the 8 income thresholds considered in this study, so datasets with 4,528,800 instances were used (Fig. 4). The EPR could be annually and monthly assessed, so the EPR estimates were obtained in each analysis period. Thus, each combination of the EPR with incomes was obtained in 13 different periods (1 annually and 12 monthly). A total of 312 prediction models (104 by each algorithm) was developed (Fig. 3). Table 7 includes the input variables. These variables could be easily determined by energy managers, thus grouping the characteristics related to geometry, envelope, and HVAC systems. Datasets were randomly divided into two sets (Fig. 4): 75% corresponded to the training dataset, and 25% to the testing dataset. A 10-fold cross validation was conducted to reduce the bias and the variance of the models [79]. All training datasets were randomly divided into 10 subsets. For each fold, 9 subsets were used for training, and the remaining for testing. Model performance was obtained by the average value of the 10 folds. Three statistical parameters were used to assess model performance: (i) the determination coefficient ( ) (Eq. (7)), the mean absolute error ( ) (Eq. (8)), and the root mean square error ( ) (Eq. (9)). These are statistical relationships between the actual value ( ), the predicted value ( ), and the number of instances of the dataset ( ). These parameters allow model performance to be correctly defined [80]. They are quality indicators of the model when and are as low as possible, and when has a value greater than 0.95 [31,81]. (7) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 8 (8) (9) Table 7. Input and output variables. Input variables Output variables Façade surface ( FS ) Ground surface (GS) Roof surface (RS) Window surface (WS) Compactness (C) Orientation (Or) Façade U-value (FU) Roof U-value (CU) Ground U-value (GU) Window (WU) Operational model (Op) Behaviour category (Cat) COP EER EPR (IPREM 0.5) EPR (IPREM 1.0) EPR (IPREM 1.5) EPR (IPREM 2.0) EPR (IPREM 2.5) EPR (IPREM 3.0) EPR (IPREM 3.5) EPR (IPREM 4.0) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 15 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 16 Fig. 6. Box plots with the error of the estimates made in the testing dataset by each model. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 17 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 18 Fig. 7. MAE obtained in the EPR estimates made by the models with other income levels. 3.3. EP cases considering 2M threshold Although income thresholds close to that of the model could obtain valid estimates (particularly with high income thresholds), the most ad final goal was to estimate the EPR to know whether the family units were in EP situation, so the percentage of EP cases was compared by using the threshold of 2M for Spain. Estimates were obtained by the models in their period-incomes combination. Fig. 8 shows the percentage of EP cases with both actual data and MLP, RF, and M5P estimates. The percentages of EP cases were similar among the various data cohorts. As for the income thresholds of 0.5 and 1.0, 100% of the cases were in EP situation with actual data as all instances had an EPR greater than 10%. Moreover, most models and combinations made the same estimates, except 0.5% of MLP instances in the annual period that were wrongly classified outside the EP situation. The percentages of EP cases varied in the remaining income thresholds. All these variations obtained a lower percentage of cases in EP situation. The greater variations in the percentage of EP cases were detected in MLP estimates: (i) in IPREM 1.5, deviations with MLP were between 0.6 and 23.5%, whereas they oscillated between 0.1 and 12.4% with treetype models; (ii) in IPREM 2.0, the percentage variation with MLP was up to 18.1%, whereas it was 3.6% with RF, and 9.2% with M5P; and (iii) for income values between 2.5 and 4.0 times the IPREM, the deviation with MLP was up to 9.9%, although the differences in these cases were not so stressed with tree-type models. MLP therefore estimated a lower percentage of IPREM. These family units could easily vary their EP situation (because their incomes are close to the minimum guaranteed interprofessional wages), so the variation with MLP could limit its use. Although the error distributions in the estimates were satisfactory (Fig. 6), the variations in the percentage of cases would limit the use of the MLPs compared to tree-type models, which obtained a lower variation in the percentage of EP cases. The relationship in the error of the estimates with the months with greater energy demand should also be stressed. As Fig. 6 shows, the months with greater energy demand obtained greater errors in estimates. This aspect was also shown in the percentage deviation of EP cases with MLP estimates. The greater concentration of cases wrongly classified was therefore obtained in the months with greater demand. However, there could also be significant variations in the months with lower energy demand. Nonetheless, the results obtained by the tree-type models were satisfactory to estimate EP cases. This could be conducted without performing an energy analysis in detail, thus optimizing energy managers and estimate the EPR accurately in family units that live in the south of Spain. In addition, prediction tools could be used to estimate the EP situation of the family units. These results are in line with those obtained by studies conducted in other countries, such as Chile [31,32] or Serbia [33]. However, the actual scope of the effectiveness of these techniques to predict EP is unknown because studies on this issue are lacking. The greater effectiveness of tree-type models compared to MLP has been reported by other studies on characterizing energy variables, such as the thermal properties of the envelope [82] or solar thermal energy systems [83], although using them as a tool to characterize EP is a gap that should be addressed. In this sense, most studies in the state of the art have used MLP or decision trees [30], whereas algorithms such as RF or M5P have not been used. Their great effectiveness recommends their use to estimate EP compared to other algorithms, such as MLP. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 19 Fig. 8. Heatmap with the percentage of case studies in EP situation. 4. Limitations of the study These results are limited. Firstly, EP estimate is only based on the 2M indicator. Various EP scenarios, such as hidden EP [84], are not considered, as well as other assessment indicators, such as the index of vulnerable homes [85] or the multidimensional energy poverty index [86]. The assessment analysis of other indicators should be addressed in further studies to know the limitations related to the use of prediction models. Secondly, data were obtained from a parametric analysis with simulated data. The energy analysis methodology is validated and widely used in works on the energy assessment of the built environment. However, using actual data could vary the estimates obtained by the models. This aspect could solve the lack of detailed datasets to develop models in many regions, a limitation reported in several studies [30,87,88]. Thirdly, these results are adapted to the warm climate characteristics of the south of Spain. Climate has not been considered. The analysis focused on warm zones of the south of Spain because there are no studies that assess the possibilities of estimating EP in warm climate zones. Although significant variations in the remaining climate zones in Spain are not expected due to the results obtained in other countries [32], this aspect should be addressed in further studies. 5. Conclusions The National Strategy against Energy Poverty in Spain aims to reduce EP cases in the country by the year 2025. This strategy is based on analysing and using some indicators, including the disproportionate expenditure indicator (2M). To do this, family situations should be assessed, and technical (energy consumption) variables are combined in the analysis. Given both the high consumption of resources and the time required for assessments, this study assessed the possibility of using prediction tools based on artificial intelligence. The analysis focused on the warm climate zones in Spain due to the differences in their energy consumption compared to cold regions. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 20 The results showed that the use of algorithms (MLP, RF, and M5P) estimated EP rations appropriately. This could be done by approaching individual models of the prediction models by developing certain models for the combinations of income thresholds and analysis periods. The EP situation of family units could therefore be obtained monthly. For a greater effectiveness of the models, the results have shown that the models should be used only for the income threshold considered in their development. If they are used with income thresholds not considered in their training, there could be significant errors in the estimates. Nonetheless, they could be used with other income thresholds if the difference of income thresholds is small. The 3 algorithms obtained appropriate results, but there were better estimates in the tree-type models used in the study. In this sense, MLPs obtained greater deviations in the percentage of cases in EP situation compared to the actual data. This aspect was less stressed in the tree-type models, which obtained a percentage of cases in EP situation close to the actual values. Nonetheless, all prediction models obtained percentages of cases in EP situation slightly lower than the actual values. The potential of using these prediction techniques becomes important if the great effort required to assess family units in EP situation is considered. In quantified data from the National Strategy against Energy Poverty, 8.1 million people have a disproportionate expenditure of their incomes. These data were given at the beginning of the plan in 2019, so results could today be greater due to both the effects of the Covid-19 pandemic and the strong inflation. It is therefore imperative to have means to optimize processes to assess the EP of family units. Further studies should address the limitations of this methodology. Moreover, models that characterize hidden EP situations should be developed, as well as other EP indicators. 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The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Title: Analysing energy poverty assessment in warm climate zones in Spain through artificial intelligence Authors: David Bienvenido-Huertas1, Daniel Sánchez-García*2, David Marín-García3, Carlos Rubio-Bellido4 1Department of Building Construction, University of Granada. Granada, Spain 2Department of Electrical Engineering, University Carlos III of Madrid, Madrid, Spain 3Department of Graphical Expression and Building Engineering, University of Seville. Seville, Spain 4Department of Building Construction II, University of Seville. Seville, Spain 6 (2) Where ET is the energy term, PT is the power term, ElT is the electricity tax, EMR is the rent of measurement equipment, and VAT is the added value tax. ET is the price related to each kWh consumed. The price daily varies throughout the year according to market oscillations and is obtained by applying the schedule rate to the schedule energy consumption of the dwelling (Eq. (3)). The kWh prices of the year 2019 were used (Fig. 2). PT is the fixed price that users should pay to have contracted power. It is obtained by multiplying the contracted power by both the number of bill days (ND) and the price of the access to the contracted power power of 4.6 kW was considered (Eq. (4)). ElT is a concept obtained by applying 5.1127% to the ET and PT price (Eq. (5)), whereas EMR is a fixed price of the rent of measurement equipment. Finally, VAT is a percentage of 21% applied to the sum of ET, PT, ElT, and EMR (Eq. (6)). (3) (4) (5) (6) Fig. 2. Price values of the ET of the PVPC in the year 2019. 2.2. Prediction model development After the analysis, a dataset with 36,203,400 instances (4,528,800 instances by each family income typology) and their EPR values was obtained. Some input variables were selected from this dataset, and the EPR was used as output variable. A total of 3 algorithms were used to generate models. The next subsection describes the algorithms and the procedure to train and test models. 2.2.1. Algorithms A total of 3 algorithms were used (Fig. 3): multilayer perceptron (MLP), random forest (RF), and M5P. 7 Fig. 3. Scheme of MLP, RF, and M5P. MLP is a mathematical model based on the human brain structure. Its goal is to solve regression and classification problems [52 54]. It is widely used because of its universal approximation capacity [55 57]. Its architecture consists in 3 or more layers made up of neurons or nodes (Fig. 3). One of the layers is the input layer, where the input variables of the system are included. The output layer is constituted by the output layer of the system, whereas the intermediate layers (also known as hidden layers) process the input information through synaptic weights and activation, transfer, and propagation functions. It has been widely used as prediction tool in building energy analyses [58,59] and is the most used algorithm in studies on energy poverty [30]. In this study, MLPs were trained through backpropagation [60 62] using the Broyden- Fletcher-Goldfarb-Shanno [63] algorithm (which belongs to quasi-Newton methods). Like other studies [31], one hidden layer was only considered as its performance is better than that of more complex architectures [64]. Likewise, sigmoidal functions were used. RF is an evolution of the classification and regression tree (CART) models. CART creates the relationships among variables in tree models, and RF generates a set of CART models. RF therefore creates a forest of CART models (Fig. 3). The accurately (tree leaf). Its limitations could be addressed through RF models to reduce the variance and the bias [65,66] because a learning combined model is generated: its performance is better than that of an individual model [67]. Likewise, many data could be used with RF without affecting the atypical values of the dataset [68]. This algorithm is therefore widely used to estimate building energy variables [69 71]. The number of CART models affects performance [72], so the models developed in this study oscillated the number of trees from 50 to 100 to obtain the optimal configuration. M5P is also an evolution of CART [73,74], but it is different in that leaves have multiple linear regression (MLR). The the effective use of huge dataset and its robustness because of the lack of values in the instances of the dataset analysed [75,76]. Consequently, this algorithm has been successfully used in studies on characterizing energy variables [77,78]. 2.2.2. Training and testing approach Individual models were developed for each output variable. The output variable was the EPR. The difference among each model was that a prediction model was therefore developed for 1 out of the 8 income thresholds considered in this study, so datasets with 4,528,800 instances were used (Fig. 4). The EPR could be annually and monthly assessed, so the EPR estimates were obtained in each analysis period. Thus, each combination of the EPR with incomes was obtained in 13 different periods (1 annually and 12 monthly). A total of 312 prediction models (104 by each algorithm) was developed (Fig. 3). Table 6 7 includes the input variables. These variables could be easily determined by energy managers, thus grouping the characteristics related to geometry, envelope, and HVAC systems. Datasets were randomly divided into two sets (Fig. 34): 75% corresponded to the training dataset, and 25% to the testing dataset. A 10-fold cross validation was conducted to reduce the bias and the variance of the models [79]. All training datasets were randomly divided into 10 subsets. For each fold, 9 subsets were used for training, and the remaining for testing. Model performance was obtained by the average value of the 10 folds. Three statistical parameters were used to assess model performance: (i) the determination coefficient ( ) (Eq. (7)), the mean absolute error ( ) (Eq. (8)), and the root mean square error ( ) (Eq. (9)). These are statistical relationships between the actual value ( ), the predicted value ( ), and the number of instances of the dataset ( ). These parameters allow model performance to be correctly defined [80]. They are quality indicators of the model when and are as low as possible, and when has a value greater than 0.95 [31,81]. (7) 8 (8) (9) Table 67. Input and output variables. Input variables Output variables Façade surface (FS) Ground surface (GS) Roof surface (RS) Window surface (WS) Compactness (C) Orientation (Or) Façade U-value (FU) Roof U-value (CU) Ground U-value (GU) Window (WU) Operational model (Op) Behaviour category (Cat) COP EER EPR (IPREM 0.5) EPR (IPREM 1.0) EPR (IPREM 1.5) EPR (IPREM 2.0) EPR (IPREM 2.5) EPR (IPREM 3.0) EPR (IPREM 3.5) EPR (IPREM 4.0) 9 Fig. 4. Workflow of the training and testing process of the models. 3. Results and discussion 3.1 EPR characterization The first step to analyse the possibility of characterizing the EPR was assessing the statistical parameters used in the study. The performances obtained in the training were assessed (Table 78). As mentioned in the Methodology section, the approach consisted of developing individual models for each combination of income level, period, and algorithm. The performances obtained in the training were satisfactory: oscillated between 87.5 and 100%, whereas MAE and RMSE obtained values of 0.516 and 0.642, respectively. After analysing the values related to the statistical parameters in the training, they were assessed in the testing (Table 89). Results were satisfactory. was greater than 90% in all combinations, whereas the error parameters obtained satisfactory values for the range of EPR values. In this sense, MAE values oscillated between 0 and 0.529, and RMSE values oscillated between 0.001 and 0.658. Performances obtained fewer average errors in the EPR assessments of lowhigh-income family units. The average errors obtained with family units of the IPREM 4.0 were lower than those obtained with family units of the IPREM 0.5. This aspect was detected with the 3 algorithms. The greater variability of the expected results with the EPR in low-income family units could therefore imply greater errors than in family units with greater incomes. Likewise, Formatted: Normal 10 performances varied according to the analysis period considered. Performances were satisfactory in the periods where the greatest EPR values were obtained (annual period and the months with greater climate severity). However, performances slightly decreased in low demand months: decreases in between 1.3 and 8.3% with MLP, between 1 and 4.4% with RF, and between 1.1 and 9.9% with M5P. As for the differences among the 3 algorithms, performances were similar for both the and error parameters: (i) MLP obtained values between 91 and 100%, MAE between 0 and 0.503, and RMSE between 0.004 and 0.605; (ii) RF obtained values between 95.1 and 100%, MAE between 0 and 0.243, and RMSE between 0.001 and 0.357; and (iii) M5P obtained values between 89.8 and 99.9%, MAE between 0 and 0.52, and RMSE between 0.002 and 0.658. Nevertheless, the performances obtained by the tree-type models were related to lower error values than in the case of the MLPs: MAE decreases reached 0.38 with RF and 0.355 with M5P, whereas RMSE decreases reached 0.382 and 0.359 with RF and M5P, respectively. Table 78. values and error parameters obtained in the training. Period IPREM MLP RF M5P [%] MAE RMSE [%] MAE RMSE [%] MAE RMSE Full 0.5 99.9 0.280 0.338 100.0 0.052 0.124 99.9 0.188 0.293 1.0 99.5 0.290 0.355 100.0 0.024 0.080 99.8 0.100 0.196 1.5 99.1 0.274 0.341 100.0 0.015 0.063 99.7 0.065 0.155 2.0 98.9 0.239 0.293 99.9 0.011 0.054 99.6 0.048 0.132 2.5 98.8 0.132 0.212 99.9 0.009 0.048 99.6 0.038 0.117 3.0 98.6 0.096 0.180 99.9 0.008 0.045 99.5 0.034 0.111 3.5 98.3 0.096 0.171 99.9 0.007 0.042 99.4 0.030 0.104 4.0 98.4 0.064 0.138 99.9 0.005 0.037 99.3 0.023 0.091 Jan. 0.5 99.9 0.287 0.348 100.0 0.095 0.173 99.9 0.334 0.446 1.0 99.7 0.347 0.425 100.0 0.045 0.115 99.8 0.191 0.289 1.5 99.4 0.264 0.313 100.0 0.029 0.093 99.7 0.136 0.233 2.0 99.0 0.375 0.456 99.9 0.022 0.080 99.6 0.106 0.201 2.5 98.6 0.264 0.323 99.9 0.018 0.072 99.5 0.086 0.180 3.0 98.2 0.220 0.283 99.9 0.015 0.065 99.4 0.071 0.163 3.5 97.9 0.192 0.262 99.9 0.012 0.059 99.3 0.060 0.149 4.0 97.5 0.321 0.418 99.9 0.012 0.058 99.1 0.057 0.145 Feb. 0.5 99.8 0.336 0.413 100.0 0.058 0.135 99.8 0.224 0.324 1.0 99.5 0.262 0.310 99.9 0.028 0.094 99.7 0.127 0.223 1.5 98.6 0.249 0.307 99.9 0.019 0.076 99.5 0.088 0.182 2.0 98.0 0.209 0.271 99.9 0.015 0.067 99.3 0.069 0.159 2.5 97.3 0.341 0.389 99.9 0.011 0.059 99.2 0.054 0.140 3.0 97.1 0.154 0.231 99.8 0.010 0.054 99.1 0.047 0.131 3.5 97.0 0.126 0.193 99.2 0.020 0.098 98.8 0.039 0.119 4.0 97.5 0.116 0.188 99.8 0.065 0.044 98.9 0.031 0.107 Mar. 0.5 99.2 0.309 0.376 99.9 0.025 0.090 99.7 0.113 0.208 1.0 97.8 0.233 0.296 99.9 0.012 0.062 99.4 0.059 0.146 1.5 97.0 0.168 0.253 99.8 0.009 0.052 99.2 0.041 0.119 2.0 96.1 0.148 0.212 99.8 0.006 0.044 99.0 0.031 0.104 2.5 97.3 0.058 0.145 99.8 0.006 0.042 98.8 0.027 0.097 3.0 96.7 0.051 0.133 99.0 0.011 0.072 98.4 0.023 0.094 3.5 95.0 0.042 0.127 99.7 0.003 0.032 98.2 0.016 0.076 4.0 96.0 0.126 0.173 99.2 0.008 0.063 98.9 0.016 0.075 Apr. 0.5 94.5 0.268 0.334 99.7 0.013 0.071 98.9 0.046 0.133 1.0 93.0 0.052 0.118 99.5 0.003 0.032 97.8 0.011 0.065 1.5 94.9 0.064 0.161 99.5 0.006 0.049 98.5 0.021 0.088 2.0 93.7 0.092 0.167 99.4 0.007 0.051 97.9 0.024 0.096 2.5 93.4 0.011 0.079 99.4 0.002 0.024 97.5 0.007 0.049 3.0 91.1 0.044 0.121 99.4 0.003 0.030 97.7 0.010 0.061 3.5 95.4 0.000 0.004 98.6 0.000 0.001 87.5 0.000 0.002 4.0 93.6 0.008 0.056 99.2 0.001 0.020 96.9 0.004 0.040 May 0.5 99.6 0.351 0.423 100.0 0.028 0.093 99.9 0.105 0.207 1.0 98.9 0.262 0.350 99.8 0.028 0.115 99.7 0.056 0.151 1.5 98.3 0.298 0.347 99.7 0.020 0.101 99.5 0.040 0.127 2.0 95.8 0.387 0.473 99.9 0.007 0.048 99.5 0.030 0.104 2.5 98.3 0.132 0.186 99.9 0.005 0.038 99.5 0.022 0.089 3.0 98.1 0.082 0.165 99.5 0.012 0.078 99.3 0.023 0.091 3.5 98.1 0.022 0.092 99.9 0.002 0.026 99.1 0.011 0.063 4.0 98.2 0.048 0.125 99.6 0.007 0.056 99.2 0.014 0.074 Jun. 0.5 99.9 0.299 0.370 100.0 0.078 0.163 99.9 0.251 0.379 1.0 99.7 0.253 0.311 99.0 0.060 0.174 99.9 0.106 0.208 1.5 99.5 0.230 0.289 99.9 0.040 0.140 99.8 0.077 0.177 2.0 99.2 0.319 0.384 100.0 0.014 0.066 99.8 0.055 0.140 2.5 98.9 0.187 0.257 99.9 0.011 0.060 99.7 0.046 0.128 3.0 98.5 0.199 0.264 99.8 0.021 0.103 99.6 0.042 0.127 11 3.5 98.5 0.123 0.206 99.9 0.006 0.043 99.7 0.028 0.098 4.0 98.3 0.231 0.281 99.9 0.007 0.048 99.6 0.031 0.103 Jul. 0.5 100.0 0.503 0.605 100.0 0.179 0.265 99.9 0.507 0.632 1.0 99.9 0.295 0.356 100.0 0.058 0.143 99.9 0.180 0.294 1.5 99.8 0.294 0.362 99.9 0.069 0.189 99.9 0.123 0.225 2.0 99.6 0.252 0.305 100.0 0.024 0.090 99.9 0.093 0.189 2.5 99.5 0.271 0.328 100.0 0.020 0.081 99.8 0.074 0.166 3.0 99.3 0.226 0.283 99.8 0.033 0.129 99.8 0.062 0.151 3.5 99.2 0.227 0.318 99.8 0.027 0.116 99.7 0.054 0.146 4.0 99.1 0.243 0.302 99.8 0.026 0.114 99.7 0.047 0.131 Aug. 0.5 100.0 0.384 0.475 100.0 0.181 0.263 99.9 0.516 0.642 1.0 99.9 0.259 0.318 100.0 0.056 0.134 99.9 0.188 0.300 1.5 99.8 0.267 0.322 100.0 0.032 0.100 99.9 0.126 0.227 2.0 99.6 0.321 0.397 100.0 0.023 0.085 99.9 0.096 0.191 2.5 99.5 0.322 0.382 100.0 0.018 0.074 99.8 0.076 0.167 3.0 99.3 0.249 0.323 100.0 0.015 0.067 99.8 0.064 0.152 3.5 99.3 0.236 0.283 100.0 0.012 0.060 99.8 0.053 0.138 4.0 99.0 0.172 0.252 100.0 0.011 0.057 99.7 0.047 0.129 Sep. 0.5 99.9 0.473 0.557 99.9 0.093 0.221 99.9 0.175 0.297 1.0 99.6 0.225 0.293 99.9 0.043 0.148 99.8 0.086 0.190 1.5 99.2 0.199 0.270 99.8 0.030 0.124 99.8 0.057 0.150 2.0 98.9 0.265 0.307 99.7 0.025 0.115 99.7 0.043 0.124 2.5 98.5 0.214 0.277 99.7 0.018 0.097 99.6 0.037 0.120 3.0 98.4 0.125 0.205 99.7 0.016 0.093 99.5 0.033 0.112 3.5 98.6 0.055 0.139 99.7 0.009 0.065 99.5 0.018 0.083 4.0 98.3 0.078 0.170 99.6 0.014 0.085 99.5 0.025 0.094 Oct. 0.5 98.8 0.246 0.322 99.8 0.034 0.136 99.7 0.052 0.145 1.0 98.5 0.094 0.164 99.6 0.013 0.082 99.5 0.021 0.090 1.5 97.9 0.094 0.171 99.4 0.015 0.091 99.4 0.022 0.089 2.0 97.8 0.064 0.147 99.8 0.005 0.041 99.3 0.017 0.077 2.5 98.7 0.022 0.080 99.6 0.003 0.045 99.6 0.005 0.042 3.0 99.3 0.009 0.058 99.8 0.002 0.034 99.8 0.003 0.033 3.5 98.2 0.004 0.042 96.5 0.002 0.030 95.3 0.003 0.035 4.0 97.2 0.211 0.249 99.8 0.003 0.031 99.4 0.007 0.051 Nov. 0.5 99.8 0.419 0.506 100.0 0.054 0.130 99.8 0.206 0.310 1.0 99.2 0.250 0.312 99.7 0.059 0.171 99.5 0.121 0.228 1.5 98.1 0.413 0.490 99.9 0.018 0.073 99.4 0.082 0.175 2.0 97.6 0.237 0.298 99.9 0.014 0.064 99.3 0.063 0.153 2.5 97.7 0.160 0.230 99.9 0.010 0.054 99.1 0.047 0.131 3.0 97.5 0.113 0.196 99.8 0.008 0.049 99.1 0.038 0.117 3.5 97.7 0.084 0.158 99.8 0.007 0.045 98.8 0.032 0.109 4.0 96.1 0.141 0.224 99.1 0.017 0.089 98.7 0.032 0.108 Dec. 0.5 99.9 0.354 0.446 100.0 0.115 0.192 99.9 0.407 0.526 1.0 99.8 0.278 0.335 100.0 0.053 0.124 99.8 0.217 0.317 1.5 99.6 0.264 0.312 99.8 0.084 0.200 99.7 0.157 0.254 2.0 99.2 0.422 0.507 99.9 0.026 0.086 99.6 0.122 0.218 2.5 98.7 0.287 0.349 99.9 0.021 0.077 99.5 0.100 0.198 3.0 98.4 0.257 0.315 99.9 0.017 0.069 99.4 0.084 0.178 3.5 97.9 0.248 0.300 99.6 0.035 0.128 99.4 0.071 0.163 4.0 97.9 0.191 0.260 99.9 0.013 0.061 99.3 0.065 0.155 Table 89. values and error parameters obtained in the testing. Period IPREM MLP RF M5P [%] MAE RMSE [%] MAE RMSE [%] MAE RMSE Full 0.5 99.9 0.280 0.338 99.9 0.112 0.230 99.9 0.200 0.312 1.0 99.5 0.290 0.355 99.9 0.055 0.157 99.8 0.107 0.211 1.5 99.1 0.274 0.341 99.8 0.036 0.125 99.7 0.070 0.167 2.0 98.9 0.239 0.293 99.8 0.027 0.107 99.6 0.051 0.143 2.5 98.8 0.133 0.213 99.7 0.021 0.096 99.5 0.041 0.127 3.0 98.6 0.096 0.180 99.6 0.019 0.092 99.4 0.037 0.120 3.5 98.3 0.096 0.171 99.6 0.016 0.084 99.2 0.032 0.113 4.0 98.4 0.064 0.138 99.5 0.013 0.075 99.2 0.025 0.098 Jan. 0.5 99.9 0.287 0.348 99.9 0.198 0.320 99.8 0.360 0.480 1.0 99.7 0.347 0.425 99.9 0.104 0.226 99.7 0.207 0.314 12 1.5 99.4 0.265 0.313 99.8 0.070 0.184 99.6 0.147 0.253 2.0 99.0 0.375 0.457 99.7 0.053 0.159 99.5 0.114 0.219 2.5 98.6 0.265 0.323 99.7 0.043 0.142 99.3 0.093 0.196 3.0 98.2 0.220 0.283 99.6 0.035 0.129 99.2 0.077 0.178 3.5 97.9 0.192 0.262 99.5 0.030 0.118 99.1 0.065 0.163 4.0 97.5 0.321 0.418 99.5 0.028 0.115 99.0 0.061 0.159 Feb. 0.5 99.8 0.336 0.412 99.9 0.130 0.257 99.8 0.243 0.351 1.0 99.3 0.262 0.310 97.7 0.066 0.181 99.6 0.137 0.243 1.5 98.6 0.249 0.307 99.7 0.044 0.148 99.4 0.095 0.198 2.0 98.0 0.209 0.272 99.5 0.035 0.131 99.2 0.075 0.175 2.5 97.3 0.341 0.389 99.5 0.027 0.115 99.0 0.058 0.153 3.0 97.1 0.154 0.231 99.4 0.024 0.107 98.9 0.050 0.143 3.5 96.9 0.126 0.193 99.2 0.020 0.098 98.5 0.042 0.130 4.0 97.6 0.116 0.188 99.3 0.015 0.086 98.7 0.034 0.117 Mar. 0.5 99.2 0.309 0.376 99.8 0.057 0.170 99.6 0.121 0.226 1.0 97.8 0.233 0.297 99.6 0.028 0.118 99.2 0.063 0.158 1.5 97.0 0.167 0.253 99.4 0.020 0.099 99.0 0.044 0.130 2.0 96.0 0.148 0.212 99.3 0.015 0.085 98.8 0.034 0.114 2.5 97.3 0.058 0.145 99.1 0.013 0.081 98.5 0.029 0.107 3.0 96.7 0.051 0.133 99.0 0.011 0.072 98.4 0.023 0.094 3.5 95.0 0.042 0.127 98.8 0.008 0.062 97.9 0.018 0.083 4.0 95.9 0.126 0.173 99.2 0.008 0.063 98.6 0.017 0.082 Apr. 0.5 94.5 0.267 0.333 98.9 0.029 0.128 98.7 0.049 0.144 1.0 92.9 0.052 0.118 98.1 0.007 0.059 97.4 0.012 0.071 1.5 94.9 0.064 0.161 98.5 0.013 0.088 98.2 0.022 0.096 2.0 93.7 0.092 0.167 98.0 0.015 0.093 97.5 0.026 0.104 2.5 93.3 0.011 0.080 97.9 0.004 0.045 97.0 0.007 0.053 3.0 91.0 0.044 0.121 98.0 0.006 0.057 97.2 0.011 0.067 3.5 95.6 0.000 0.004 95.1 0.000 0.001 89.8 0.000 0.002 4.0 93.5 0.009 0.056 97.5 0.002 0.036 96.3 0.005 0.043 May 0.5 99.6 0.351 0.423 99.9 0.059 0.171 99.8 0.113 0.223 1.0 98.9 0.263 0.350 99.8 0.028 0.115 99.7 0.056 0.151 1.5 98.3 0.298 0.347 99.7 0.020 0.101 99.5 0.040 0.127 2.0 95.8 0.387 0.472 99.6 0.017 0.090 99.4 0.032 0.113 2.5 98.3 0.132 0.186 99.6 0.012 0.074 99.4 0.024 0.097 3.0 98.1 0.083 0.165 99.5 0.012 0.078 99.2 0.025 0.099 3.5 98.1 0.022 0.092 99.4 0.006 0.050 98.9 0.012 0.069 4.0 98.2 0.048 0.125 99.6 0.007 0.056 99.2 0.014 0.074 Jun. 0.5 99.9 0.299 0.370 100.0 0.129 0.254 99.9 0.251 0.379 1.0 99.7 0.253 0.311 99.9 0.060 0.174 99.9 0.114 0.223 1.5 99.5 0.230 0.288 99.9 0.040 0.140 99.8 0.077 0.177 2.0 99.2 0.319 0.384 99.8 0.030 0.123 99.8 0.059 0.152 2.5 98.9 0.188 0.258 99.8 0.025 0.112 99.7 0.050 0.140 3.0 98.5 0.200 0.265 99.8 0.021 0.103 99.6 0.042 0.127 3.5 98.5 0.123 0.206 99.8 0.015 0.083 99.6 0.030 0.108 4.0 98.9 0.231 0.281 99.7 0.016 0.091 99.5 0.033 0.113 Jul. 0.5 100.0 0.503 0.605 100.0 0.243 0.357 99.9 0.519 0.648 1.0 99.9 0.295 0.356 99.9 0.105 0.235 99.9 0.191 0.311 1.5 99.8 0.294 0.363 99.9 0.069 0.189 99.9 0.131 0.241 2.0 99.6 0.253 0.305 99.9 0.051 0.162 99.8 0.100 0.204 2.5 99.5 0.371 0.328 99.9 0.042 0.146 99.8 0.079 0.180 3.0 99.3 0.226 0.283 99.8 0.033 0.129 99.8 0.067 0.164 3.5 99.2 0.227 0.319 99.8 0.027 0.116 99.7 0.054 0.146 4.0 99.1 0.243 0.302 99.8 0.026 0.114 99.7 0.050 0.141 Aug. 0.5 100.0 0.383 0.474 100.0 0.242 0.349 99.9 0.529 0.658 1.0 99.9 0.260 0.318 100.0 0.103 0.223 99.9 0.200 0.320 1.5 99.8 0.267 0.322 99.9 0.066 0.177 99.9 0.135 0.244 2.0 99.6 0.321 0.397 99.9 0.050 0.154 99.8 0.103 0.206 2.5 99.5 0.322 0.381 99.9 0.039 0.137 99.8 0.081 0.181 3.0 99.3 0.025 0.323 99.9 0.033 0.125 99.8 0.069 0.166 3.5 99.3 0.236 0.283 99.8 0.028 0.114 99.7 0.058 0.150 4.0 99.0 0.172 0.251 99.8 0.024 0.107 99.7 0.051 0.140 Sep. 0.5 99.9 0.473 0.557 99.9 0.093 0.221 99.9 0.175 0.297 1.0 99.6 0.225 0.293 99.9 0.043 0.148 99.8 0.086 0.190 1.5 99.2 0.199 0.270 99.8 0.030 0.124 99.8 0.057 0.150 2.0 98.9 0.265 0.307 99.7 0.025 0.115 99.7 0.046 0.134 2.5 98.5 0.213 0.276 99.7 0.018 0.097 99.6 0.037 0.120 3.0 98.4 0.125 0.205 99.7 0.016 0.093 99.5 0.033 0.112 3.5 98.6 0.054 0.139 99.7 0.009 0.065 99.5 0.018 0.083 4.0 98.3 0.078 0.170 99.6 0.014 0.085 99.4 0.027 0.103 13 Oct. 0.5 98.8 0.246 0.322 99.8 0.036 0.136 99.7 0.052 0.145 1.0 98.5 0.095 0.165 99.6 0.013 0.082 99.5 0.021 0.090 1.5 97.9 0.095 0.171 99.4 0.015 0.091 99.3 0.024 0.096 2.0 97.8 0.064 0.147 99.4 0.011 0.075 99.2 0.018 0.083 2.5 98.6 0.022 0.081 99.6 0.003 0.045 99.6 0.005 0.044 3.0 99.3 0.009 0.058 99.8 0.002 0.034 99.8 0.003 0.035 3.5 93.0 0.004 0.042 96.5 0.002 0.030 95.3 0.003 0.035 4.0 97.2 0.211 0.249 99.4 0.005 0.055 99.4 0.008 0.054 Nov. 0.5 99.8 0.419 0.506 99.9 0.120 0.248 99.8 0.222 0.335 1.0 99.2 0.250 0.312 99.7 0.059 0.171 99.5 0.121 0.228 1.5 98.1 0.413 0.490 99.6 0.042 0.143 99.3 0.088 0.190 2.0 97.6 0.237 0.298 99.5 0.032 0.124 99.2 0.068 0.166 2.5 97.7 0.160 0.230 99.4 0.024 0.107 99.0 0.050 0.143 3.0 97.5 0.113 0.196 99.4 0.019 0.096 98.9 0.041 0.128 3.5 97.7 0.084 0.158 99.2 0.016 0.089 98.5 0.035 0.119 4.0 96.1 0.141 0.223 99.1 0.017 0.089 98.5 0.034 0.117 Dec. 0.5 99.9 0.354 0.446 99.9 0.229 0.346 99.8 0.435 0.561 1.0 99.8 0.279 0.335 99.9 0.122 0.244 99.8 0.235 0.344 1.5 99.6 0.264 0.312 99.8 0.084 0.200 99.7 0.170 0.276 2.0 99.2 0.422 0.506 99.8 0.063 0.172 99.6 0.132 0.238 2.5 98.7 0.287 0.349 99.7 0.050 0.153 99.4 0.108 0.212 3.0 98.4 0.256 0.315 99.7 0.042 0.139 99.3 0.091 0.193 3.5 97.9 0.248 0.300 99.6 0.035 0.128 99.2 0.077 0.178 4.0 97.9 0.191 0.259 99.6 0.032 0.122 99.1 0.070 0.169 3.2. Actual and estimated EPR differences The analysis performed with statistical parameters in both training and testing therefore showed an appropriate performance to estimate the EPR. Nonetheless, the analysis should be extended in the testing to know the limitations of this methodology. To do this, the differences between the actual and estimated values in the distributions of the testing datasets were analysed. By way of an example, Fig. 5 includes the point clouds between the actual and estimated EPR values for family units with incomes of the IPREM 0.5. Estimates were accurate. However, there were differences between the actual and estimated values, an aspect that was significant in the assessments in the various months of the year. Fig. 6 shows the error distributions obtained in the models. Error distributions were different in each combination. Firstly, the income level influenced the oscillation of the error values, going from big errors in the models of the IPREM 0.5 to small error values in the models of IPREM 4.0. In this sense, error distributions obtained percentile values from 95% to 1.5% with IPREM 0.5, with atypical error values greater than 6%. As with both lower interquartile range and smaller atypical error values. The result is obtaining maximum error values greater than 6% with IPREM 0.5 and maximum error values slightly greater than 2% with IPREM 1.5. The error of estimates is closely related to the income level considered to generate the prediction models. The use of greater income levels reduced EPR values, an aspect shown in the error values obtained by the prediction models. The relationship between EPR values and the expected error level was also observed by comparing for a same income level the variations between the periods considered in the analysis (annually and monthly). The months related to lower energy demand (e.g., April) obtained the lowest error values of the distributions, with estimates adjusted to actual values, as Fig. 5 shows. However, the months with greater demand (e.g., July) obtained a greater error obtained in EPR estimates. The estimates obtained by the models are therefore less accurate in the months with greater demand. Nonetheless, it is worth stressing that these error values are satisfactory to estimate the EPR values accurately in family units. Except with low-income family units, the EPR values were in an appropriate range to make adjusted estimates of the EPR value of the family unit without performing an energy analysis in detail. This is possible by using models developed for the The estimates made by the models were therefore analysed by comparing the remaining income thresholds (e.g., estimates of the models of IPREM 0.5 were analysed by using the remaining income levels). Fig. 7 summarizes the MAE values obtained by these estimates. The MAE obtained was greater than that obtained in the estimates of the models of their income threshold, thus obtaining MAE values up to 37.9559%. The error values of the estimates therefore increased in each algorithm: MLP increased its MAE between 0.02 and 37.38%, RF between 0.05 and 37.29%, and M5P between 0.23 and 37.52%. Nonetheless, the estimates given by the models obtained lower errors in the income cohorts closer to those of the model used. The use of models designed with income thresholds close to that assessed could increase the average error between 0.02 and 21.65%, whereas the average error increased between 2.64 and 37.52% in further income thresholds. Formatted: Heading 2 14 15 Fig. 5. Point clouds between actual and estimated EPR values with the models developed for IPREM 0.5. 22 [22] C. Sánchez-Guevara Sánchez, A. Sanz Fernández, M. Núñez Peiró, G. 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