Prediction of the maintenance performance cost in dwellings and building sites located in spain using multilayer perceptrons

PREDICTION OF THE MAINTENANCE PERFORMANCE COST IN REAL ESTATE ASSETS USING MULTILAYER PERCEPTRONS CONSTRUCTION TECHNOLOGY RESEARCH ARTICLE David Bienvenido-Huertas, David Marín, Daniel Sánchez-García, Pedro Fernández-Valderrama, Juan Moyano Buildings Publicaciones DYNA SL -- c) Mazarredo nº69 - 4º -- 48009-BILBAO (SPAIN) Tel +34 944 237 566 – www.revistadyna.com - email: [email protected] Pag. 1 / 14 PREDICTION OF THE MAINTENANCE PERFORMANCE COST IN DWELLINGS AND BUILDING SITES LOCATED IN SPAIN USING MULTILAYER PERCEPTRONS David Bienvenido-Huertas1, David Marín1, Daniel Sánchez-García2, Pedro Fernández-Valderrama1, Juan Moyano1 Universidad de Sevilla, 1Departamento de Expresión Gráfica e Ingeniería en la Edificación 2Departamento de Construcciones Arquitectónicas II Received: 3/Jan/2019 - Reviewed: 14/Feb/2019 - Accepted: 18/Feb/2019 - DOI: http://dx.doi.org/10.6036/9061 PREDICCIÓN DEL IMPORTE DE ACTUACIONES DE MANTENIMIENTO EN VIVIENDAS Y SOLARES UBICADOS EN ESPAÑA USANDO PERCEPTRONES MULTICAPA RESUMEN: La eficiente gestión de los activos inmobiliarios es una de las actividades con mayor demanda en el sector de la ingeniería de la edificación. La determinación y programación de los trabajos de mantenimiento resulta fundamental para que las entidades financieras establezcan el orden de inversión en función del importe presupuestado. Dado que es un proceso de trabajo lento, resulta necesario su optimización. En este trabajo se desarrollan dos perceptrones multicapa (PM) para la determinación del importe económico en los trabajos de mantenimiento en las dos tipologías de activos inmobiliarios de mayor interés para el sector de la edificación: solares y viviendas. En base al entrenamiento con 76 casos de estudio para solares y 317 para viviendas, se obtuvieron que las configuraciones de PM óptimas fueron las de 6 y 12 nodos, respectivamente, y se determinaron las variables de entrada que más influyen en su comportamiento. Además, los PM presentaron un comportamiento más óptimo con respecto a los de regresión lineal múltiple. Finalmente, se testearon los PM ante 15 casos de estudio nuevos para cada modelo, prediciendo los importes presupuestados para los trabajos de mantenmiento con una desviación inferior al 11% con respecto al valor real en la mayoría de ellos. Palabras clave: perceptrón multicapa, importe presupuestado, solar, vivienda, activo inmobiliario. ABSTRACT: The effective asset management of real estate is an area of great interest to the building engineering sector as a whole. The determination and programming of maintenance tasks is essential to allow finance entities to establish market order according to a given budget. The process works slowly, and some optimization is generally required. In this paper, two multilayer perceptrons (MLPs) are developed to determine the economic cost of maintenance works in the two types of real estate asset of more interest to building sector: building sites and dwellings. After training using 76 case studies for building sites and 317 for dwellings, the optimal MLP configurations are shown to have 6 and 12 nodes respectively, and the input variables that most influenced their behavior are also determined. Furthermore, the MLPs showed more optimal behavior than models using multiple linear regression. Finally, the MLPs were tested for 15 new case studies for each model, predicting the budgeted costs of the associated maintenance works with deviations of less than 11% compared with the actual value in most cases. Keywords: multilayer perceptron, budgeted cost, building site, dwelling, real estate asset. 1.- INTRODUCTION The outbreak of the financial crisis (following the bankruptcy of the Lehman Brothers in September 2008) was accompanied by significant changes in the economies of international markets [1], reflected in part in the particular characteristics in each country [2]. In Spain, one of the main factors was the failure of the real estate market due to rapid urban development between 1990 and 2006, together with speculation on the ultimate price of individual dwellings, with annual increases of up to 18% [3], although there are other possible causes, such as the buying and selling policy developed by the national government [4], or the tendency of Spanish citizens to purchase properties, to the detriment of rental values [5]. Consequently, finance entities played an important role during the peak of the real estate boom by PREDICTION OF THE MAINTENANCE PERFORMANCE COST IN REAL ESTATE ASSETS USING MULTILAYER PERCEPTRONS CONSTRUCTION TECHNOLOGY RESEARCH ARTICLE David Bienvenido-Huertas, David Marín, Daniel Sánchez-García, Pedro Fernández-Valderrama, Juan Moyano Buildings Publicaciones DYNA SL -- c) Mazarredo nº69 - 4º -- 48009-BILBAO (SPAIN) Tel +34 944 237 566 – www.revistadyna.com - email: [email protected] Pag. 2 / 14 financing, on the one hand, most of the land purchases, and on the other hand, much of the construction work carried out by property developers along with the purchasing of homes by citizens. This tendency was different between the autonomous regions of the country. In some of them, such as Andalusia, the building sector grew in importance in its productive process [6]. However, since the beginning of the crisis, the vast amount of activity generated by these entities has increased the number of mortgage defaults and foreclosures due to a lack of liquidity, both of commercial entities and individuals [7,8]. In this regard, there were more than 600 000 foreclosures in Spain [9] between 2008 and 2015. One of the key consequences was an increase in the number of real estate assets owned by banking institutions. Among the wide variety of types of asset are [10]: (i) a seemingly endless run of housing developments, (ii) dwellings, both singlefamily homes and flats, (iii) business premises, and (iv) building sites. The great variety of asset typologies makes their management something of a challenge. Nowadays, financial institutions are the most important real estate businesses [10]. In recent years, banking institutions have created specialist companies in real estate asset management, causing nationalized savings account managers to move their assets to the Management Company for Assets Arising from Bank Reorganisation (SAREB) in Spain [3,11], although some external investor groups have in fact acquired most of the existing stock [12]. The aim of these companies is to maximize the value of these assets by acquiring commercial advantage by means of their market placement [13,14], thereby reducing the risk associated with the assets as well as increasing the creditworthiness of the financial entities [15]. In effect, these companies provide the banks with warranties for adequate economic recovery, meaning that asset management is now one of the main activities in the real estate sector. However, for adequate management guaranteeing effective exploitation and promotion in the market, both human and time resources are needed. These resources are used to determine the state of the asset, as well as to establish the activities required to guarantee the adequacy of the conditions for habitability, although the process can in fact take a long time. Technical personnel from specialist companies must visit each asset, inspect its pathologies and record any imperfections, and issue a detailed report on the economic valuation of any maintenance works. One of the most significant aspects of this process is the economic valuation of the maintenance works required, which normally takes a considerable time and influences decision-making by the financial entity on the suitability of the process as a whole. Moreover, the huge variety of asset typologies (e.g. dwellings, building sites, commercial properties, garages, offices, or industrial units) can make their management quite challenging. Thus, techniques that speed up this working process could allow the technicians to work more effectively as well as affording the more rapid exploitation of the existing real estate stock. In this regard, the use of artificial intelligence has been widely applied in various industries as a system for optimizing the work order and reducing working times [16]. From the various existing algorithms, artificial neural networks (ANNs) is a technique that has shown high reliability and viability [17]. ANNs, which have been the focus of much of the research in this area over the last few years along with expert systems, are computational algorithms that imitate the behavior of brain neurons with the aim of building adaptive information-processing systems, which can be used to predict an efficient response [18]. Their main characteristics are their learning, adaptation and generalization ability, allowing us to estimate unknown situations with respect to a set of training data. In the building engineering sector, ANN has been applied more and more over the last few years through different methods, such as: (i) estimation of the economic value of business premises [19]. The estimations carried out by ANNs obtained an increase of 10% in the correlation between the actual and the estimated values with respect to the traditional hedonic modelling approaches; (ii) prediction of costs during the project phase. In the study by Lesniak and Juszczyk [20], the authors analysed the feasibility of using ANNs to estimate the site overhead costs in the early stages of a project. The estimations of the model obtained a coefficient of determination of 84.13%; (iii) Hola and Schabowicz [21] used ANNs to estimate the execution time cost of earthworks. The model works by using input variables of the machines to be used so that the best machined is selected; (iv) Luo et al. [22] developed an ANN to optimize the selection process of suppliers. The selection model had advantages with respect to other models, such as cluster models; and (v) cost valuation of maintenance of construction equipment [23] to ease the resource planning and the decision-makings. However, there is no research on the feasibility of using ANNs to optimize the performance of real estate assets, or predicting the associated economic cost. PREDICTION OF THE MAINTENANCE PERFORMANCE COST IN REAL ESTATE ASSETS USING MULTILAYER PERCEPTRONS CONSTRUCTION TECHNOLOGY RESEARCH ARTICLE David Bienvenido-Huertas, David Marín, Daniel Sánchez-García, Pedro Fernández-Valderrama, Juan Moyano Buildings Publicaciones DYNA SL -- c) Mazarredo nº69 - 4º -- 48009-BILBAO (SPAIN) Tel +34 944 237 566 – www.revistadyna.com - email: [email protected] Pag. 3 / 14 1.1.- AIM OF THE PAPER This paper aims to develop prediction models using ANN, which could allow us to estimate the cost associated with the maintenance performance of real estate assets, the results of which could be useful for establishing a priority ranking when instigated by finance entities. The suggested ANN models are therefore focused on the results, with the objective of minimizing the management time of the maintenance activities of real estate assets and of determining precisely the cost of the units of work to be carried out. Because most existing real estate assets are building sites and dwellings, two different models are suggested for each. In total, 393 case studies were compiled (76 building sites and 317 dwellings) for the training and the testing of the suggested models to determine the most adequate configuration. Furthermore, the results were compared with multiple linear regression models, given that these models are a technique widely used in other types of economic prediction, such as the sale price of real estate assets [24]. 2.- METHODOLOGY 2.1.- CHARACTERISTICS OF THE ARTIFICIAL NEURAL NETWORKS DEVELOPED In this study, the multilayer perceptron (MLP) is used as the architecture of an ANN. This specific class of ANN is characterized by dividing its structure into three or more layers: (i) an input layer, which obtains the information from the different variables; (ii) one or several hidden layers, which extract the information required; and (iii) an output layer, which indicates the value estimated by the MLP. In each layer, there are several nodes connected to those of the following layer by means of weighted connections with synaptic weights. The value estimated by the output layer is thus given by the following expression: 𝑧𝑘=𝜎(∑𝑤𝑘𝑗 (2)𝜎(∑𝑤𝑗𝑖(1)𝑥𝑖 𝑑 𝑖=0 ) 𝑀 𝑗=1 +𝑤10 (2)𝑦0) (1) Where 𝑧𝑘 is the output of the final layer, 𝜎 is the activation function, 𝑤𝑘𝑗 (2) are the weights of the output layer, 𝑤𝑗𝑖(1) are the weights of the hidden layer, 𝑥𝑖 are the values of the input layer, 𝑤10 (2) and 𝑦0 are the weight and the input value of the bias neuron of the hidden layer respectively. The adjustment of synaptic weights is achieved by MLP training, which consists of applying a learning algorithm to a training dataset. In the present case, the MLP was trained by means of back propagation [25–27], using the Broyden- Fletcher-Goldfarb-Shanno algorithm ( BFGS) [28], which belongs to the set of Quasi-Newton methods. The training was undertaken using 10-fold cross validation. For each of the MLP layers, a sigmoidal activation function was used (Eq. (2)). Other parameters that configured the MLP were the learning rate and the momentum, with values of 0.3 and 0.2, respectively. 𝜎(𝑥)=1 1+𝑒−𝑥 (2) Where x is the weighted sum of the inputs to the neuron. For this study, we only considered a single architecture of MLP with a hidden layer. The number of neurons in the hidden layer and the training time varied in the design phase until the most adequate MLP model was determined according to the aim of this study. The most appropriate number of neurons, as obtained for the hidden layer, is discussed in Section 3 of this paper. To obtain the best model, the following three statistical parameters were used: (i) the linear correlation coefficient (R2) (see Eq. (3)); (ii) the mean absolute error (MAE) (see Eq. (4)); and (iii) the root mean square error (𝑅𝑀𝑆𝐸) (see Eq. (5)). As a quality indicator, it was established that R2 should have a value greater PREDICTION OF THE MAINTENANCE PERFORMANCE COST IN REAL ESTATE ASSETS USING MULTILAYER PERCEPTRONS CONSTRUCTION TECHNOLOGY RESEARCH ARTICLE David Bienvenido-Huertas, David Marín, Daniel Sánchez-García, Pedro Fernández-Valderrama, Juan Moyano Buildings Publicaciones DYNA SL -- c) Mazarredo nº69 - 4º -- 48009-BILBAO (SPAIN) Tel +34 944 237 566 – www.revistadyna.com - email: [email protected] Pag. 4 / 14 than 0.95 and that both MAE and RMSE should be as low as possible. The determination of the number of nodes in the hidden layer to achieve an optimal yield is also discussed in Section 3. 𝑅2=100∙(1−∑ (𝑥𝑖−𝑦𝑖)2 𝑛 𝑖=1 ∑ (𝑥𝑖−𝑥)2 𝑛 𝑖=1 ) [%] (3) 𝑀𝐴𝐸=∑ |𝑥𝑖−𝑦𝑖| 𝑛 𝑖=1 𝑛 (4) 𝑅𝑀𝑆𝐸=(∑ (𝑥𝑖−𝑦𝑖)2 𝑛 𝑖=1 𝑛)1/2 (5) Where 𝑥𝑖 is the actual value of the 𝑖-th instance, 𝑦𝑖 is the value estimated by the ANN of the 𝑖-th instance, 𝑥 is the average of the actual values, and n is the number of instances in the dataset. 2.2.- MODELS SUGGESTED For each MLP, the main factors that influenced the economic valuation of the maintenance tasks were considered. These factors constituted the input variables from the two models developed: one for building sites (MLP-BS) and another for dwellings (MLP-D) (see Fig. 1). The input variables were selected according to the criteria used by the main companies of real estate asset management to analyse the maintenance works to be carried out. The output response was the budgeted cost of the associated maintenance works. Fig. 1. Structure of the MLPs suggested: (a) building sites, (b) dwellings. PREDICTION OF THE MAINTENANCE PERFORMANCE COST IN REAL ESTATE ASSETS USING MULTILAYER PERCEPTRONS CONSTRUCTION TECHNOLOGY RESEARCH ARTICLE David Bienvenido-Huertas, David Marín, Daniel Sánchez-García, Pedro Fernández-Valderrama, Juan Moyano Buildings Publicaciones DYNA SL -- c) Mazarredo nº69 - 4º -- 48009-BILBAO (SPAIN) Tel +34 944 237 566 – www.revistadyna.com - email: [email protected] Pag. 5 / 14 It is important to stress that the discrete values generally used in these tasks to define the input variables were normalized on a scale from 0 to 1. This normalization both made the training process of the MLP easier and hastened the process of field data acquisition by establishing a value on a scale. Values were established according to the level of severity, and the extremes of the distribution of the values corresponded to when the asset was in good condition and when the maintenance was urgent. In the case of building sites, factors considered when carrying out the economic valuation of performances are as follows: (i) status of the perimeter fence index; (ii) status of existing vegetation index; (iii) level of health index; and (iv) surface area. These factors constituted the input variables (see Fig. 1). Table 1 (a) describes each variable and the associated values. Table 1. Input variables: (a) input variables in the MLP-BS model, and (b) input variables in the MLP-D model. PREDICTION OF THE MAINTENANCE PERFORMANCE COST IN REAL ESTATE ASSETS USING MULTILAYER PERCEPTRONS CONSTRUCTION TECHNOLOGY RESEARCH ARTICLE David Bienvenido-Huertas, David Marín, Daniel Sánchez-García, Pedro Fernández-Valderrama, Juan Moyano Buildings Publicaciones DYNA SL -- c) Mazarredo nº69 - 4º -- 48009-BILBAO (SPAIN) Tel +34 944 237 566 – www.revistadyna.com - email: [email protected] Pag. 6 / 14 For dwellings, the main factors considered when determining the state of the real estate asset as well as the maintenance needed are as follows: (i) index of the state of the walls; (ii) index of the state of the floors; (iii) index of moisture pathologies; (iv) index of the state of the interior finishing work; (v) index of the state of the exterior finishing work; (vi) index of the state of the water installation; (vii) index of the state of the electrical installation; (viii) index of the state of the domestic heating water (DHW) system; (ix) index of the existence of waste; and (x) index of the level of cleanliness. These indexes are included as input variables to the MLP-D model (see Fig. 1). As with the building site variables, each of the variables is described more fully in Table 1 (b). Works related to the management and removal of material to a waste plant are included in the associated values. Unlike the model for building sites, the surface area of the dwelling is not considered because all the analysed dwellings have surface areas between 60 and 90 m2. The output values predicted by the model determine the cost associated with the maintenance works. In each of the case studies included in the training dataset, the cost associated with the maintenance was determined. For that purpose, a budgeting model of the construction work units was used [29]. In this model, the maintenance to be carried out is divided into a number of work units, and a cost is obtained related to the maintenance, by applying a measure or quantity to an assigned price (Eq. (6)) [29]. The total cost of the maintenance work is obtained from the sum of the direct costs, which are in turn obtained from the sum of the cost of all units (Eq. (7)) [29], and of the indirect costs (Eq. (8)) [29]. Prices were obtained using the database called “Precio Centro de la Construcción en España” [30]. 𝑈𝑖=𝑀∙ 𝑃 [€] (6) 𝐷𝐶=∑𝑈𝑖 [€] 𝑛 𝑖=1 (7) 𝐵𝐶=𝐷𝐶+𝐼𝐶 [€] (8) Where 𝑀 and 𝑃 are the measure and price of the work unit 𝑈𝑖, DC is the amount of direct costs, BC is the budgeted cost of maintenance and IC is the amount of indirect costs. Direct costs are expenses directly attributable to construction work units, and indirect costs are items such as indirect labor, auxiliary means, or technical and administrative personnel. Because the exact determination of indirect costs is complex due to the large number of factors that usually affect these, common practice is to use a percentage of the total of the direct costs (Eq. (9)) [29]. %𝐼𝐶=𝐼𝐶 𝐷𝐶∙100 [%] (9) Where %𝐼𝐶 is the percentage of indirect costs related to the work. For this study, a survey of 12 previous cases was undertaken, with the aim of determining the percentage of indirect costs that is usually assigned to this kind of maintenance (see Table 2). The results show that the use of a figure of 3% is adequate to assess the maintenance of building sites, and 20% can be used for maintenance of dwellings. These percentages were used to determine the BC for the dataset obtained. PREDICTION OF THE MAINTENANCE PERFORMANCE COST IN REAL ESTATE ASSETS USING MULTILAYER PERCEPTRONS CONSTRUCTION TECHNOLOGY RESEARCH ARTICLE David Bienvenido-Huertas, David Marín, Daniel Sánchez-García, Pedro Fernández-Valderrama, Juan Moyano Buildings Publicaciones DYNA SL -- c) Mazarredo nº69 - 4º -- 48009-BILBAO (SPAIN) Tel +34 944 237 566 – www.revistadyna.com - email: [email protected] Pag. 7 / 14 Table 2. Percentage of indirect costs for several maintenance works for real estate assets. 2.3.- DATA COLLECTION To develop the ANN, a robust dataset, which can be used for training and validating the system, is required. For this purpose, 393 different case studies were compiled (76 from building sites and 317 from dwellings), all located in the province of Seville (see Fig. 2). These case studies were selected because of their different characteristics, with the aim of obtaining a greater heterogeneity in the dataset. For instance, dwellings with different ages and state of conservation were selected, and building sites were included in the dataset after assessing the surface and state of maintenance. In each case, the input variables were analysed, the required maintenance was determined, and an economic valuation of these works was obtained. Fig. 2. Case studies: (a) photograph of one of the analysed building sites, and (b) photographs of several aspects analysed inside a dwelling. Despite the case studies are from Seville, the results obtained in this research can be extrapolated to other regions of Spain by calculating the costs with the “Precio Centro de la Construcción en España” database. If it is necessary to use another database as a reference point, the budgeted costs of the training dataset should be recalculated. Regarding the variety of possible typologies of building sites, building sites were included with some generic conditions in fulfilment of the following requirements: (i) no elements of environmental pollution hazard needing specialist treatment; (ii) no constructive elements at risk of collapse; (iii) no archaeological remains; and (iv) no works in progress, machinery, or earthworks in progress or recently completed. For the training and validation of the MLPs, 61 case studies were used for building sites and 302 for dwellings. These case studies were radomly selected. The remaining case studies were used for testing the models generated as well as for looking at their behavior in new real estate assets not included in the training process. PREDICTION OF THE MAINTENANCE PERFORMANCE COST IN REAL ESTATE ASSETS USING MULTILAYER PERCEPTRONS CONSTRUCTION TECHNOLOGY RESEARCH ARTICLE David Bienvenido-Huertas, David Marín, Daniel Sánchez-García, Pedro Fernández-Valderrama, Juan Moyano Buildings Publicaciones DYNA SL -- c) Mazarredo nº69 - 4º -- 48009-BILBAO (SPAIN) Tel +34 944 237 566 – www.revistadyna.com - email: [email protected] Pag. 8 / 14 3.- RESULTS AND DISCUSSION As mentioned above, the validity of the MLPs was determined using the statistical parameters R2, MAE and RMSE. Table 3 indicates the results obtained for both MLPs, according to the number of neurons in the hidden layer for a training time of 500 (the most optimal parameters were obtained using this training time). In all the configurations, R2 shows high values, with 97.40% being the lowest value obtained for the configuration of 4 nodes of MLP-D, and 98% or more for most of the architectures suggested. However, great variations occurred in the parameters MAE and RMSE, which were useful to determine the optimal architecture of both MLPs suggested. In this sense, the optimal configuration for MLP-BS was the one with 6 nodes, because it had a MAE of 270.05 and a RMSE of 357.18, with deviations regarding the next nearest value of 6.46% and 4.97%, respectively. On the other hand, the best configuration for MLP-D was the one with 12 neurons with values of MAE and RMSE of 170.97 and 290.14, with deviations of 2.22% and 7.04%, respectively. Table 3. Results obtained in the training phase: (a) behavior of the MLP-BS models for a training time of 500, (b) behavior of the MLP-D models for a training time of 500, and (c) influence of the input variables on quality indicators. These configurations produced acceptable behavior, although it was essential to determine the importance of the input variables used in both models. To gauge the impact of the input variables considered in the network behavior, the influence of removing each variable was assessed. This training and testing was carried out using the optimal configurations for each MLP (6 nodes for MLP-BS and 12 nodes for MLP-D), and all training runs ended at the same training time as that of the previous phase. To determine the impact of each variable, the variations in the statistical parameter RMSE, which reflects the modified network with respect to the original, were studied. In general terms, the different input variables had a considerable influence on the estimated values (see Table 3 (c)). For MLP-BS, variables with the greatest influence were the status of the perimeter fence index (Ibs,p) and the surface area (S). The first outcome PREDICTION OF THE MAINTENANCE PERFORMANCE COST IN REAL ESTATE ASSETS USING MULTILAYER PERCEPTRONS CONSTRUCTION TECHNOLOGY RESEARCH ARTICLE David Bienvenido-Huertas, David Marín, Daniel Sánchez-García, Pedro Fernández-Valderrama, Juan Moyano Buildings Publicaciones DYNA SL -- c) Mazarredo nº69 - 4º -- 48009-BILBAO (SPAIN) Tel +34 944 237 566 – www.revistadyna.com - email: [email protected] Pag. 9 / 14 relates to the high cost associated with work to adapt the safeguarding perimeter of the building site, thus it is necessary to remove the existing fence in bad conditions, to manage the waste, and to install the new fence; the surface area also decisively influences the associated direct costs of the three indexes of MLP-BS (Ibs,p, Ibs,v and Ibs,h). From the four variables considered, the level of health index (Ibs,h) was the one with the lowest impact on the behavior of the model, with a deviation of 9.78%, because the work units for this variable were of low value in most of the building sites analysed. For MLP-D, the variable with the highest influence was the index of the state of the electrical installation (Id,ei), with a deviation of RMSE of 205.84% with respect to that obtained in the model without modifications. This was due to the high cost associated with the maintenance of the electrical installation. Other significant variables were the index of moisture pathologies (Id,m) and the index of the state of the walls (Id,wl), with percentage deviations of RMSE of 159.56% and 97.83%, respectively. The variable with the lowest influence on the network behavior was the index of cleanliness (Id,c) due to the low cost associated with the maintenance included in this index. With the aim of determining the efficiency of the results obtained through the optimal architecture of MLP-BS and MLP-D, the same training dataset was used in order to predict the economic valuation of maintenance works by means of multiple linear regression (MLR) (Eq. (10)), given its widespread use as an analysis technique in other fields of economic estimation, such as the price valuation of real estate asset acquisition [24]. In Eq. (10) 𝑌 is the dependent variable, 𝛽0 is the independent term, 𝛽𝑖 are the partial regression coefficients, 𝑥𝑖 are the predictor variables, and 𝜀 is the error. The predictor variables were those used in the MLPs suggested, and the dependent variable was the budgeted cost for maintenance performances (BC). 𝑌=𝛽0+∑(𝛽𝑖𝑥𝑖) 𝑛 𝑖=1 +𝜀 (10) The results indicate that the quality indicators associated with MLPs were better than those of MLR (see Fig. 3). This superior behavior was due to the capacity of MLPs for detecting nonlinear relationships between the variables. In Fig. 3 it is notable how the cloud points for the estimated and predicted values showed a higher correlation in MLP than in MLR, with lower associated errors in each value. In this sense, the values for R2 were higher in MLP than in MLR, and both MAE and RMSE had lower values. For the building sites, R2 of the MLP showed a better adjustment than for MLR, being 5.38% higher, whereas MAE and RMSE were 54.65% and 55.35% lower, respectively. For dwellings, the R2 values of the two systems were very similar, with MLP being slightly higher (98.32%) than MLR (97.34%), although the parameters of the error were more optimal in MLP, because MLR increased MAE by 28.99% and RMSE by 25.77%. Thus, the MLPs showed better behavior than MLR for both types of real estate assets.