Abstract
The energy consumption of buildings accounts for approximately 40% of total energy consumption. An accurate energy consumption analysis of buildings can not only promise significant energy savings but also help estimate the demand response potential more accurately, and consequently brings benefits to the upstream power grid. This paper proposes a novel physical-data fusion modeling (PFM) method for modeling smart buildings that can accurately assess energy consumption. First, a thermal process model of buildings and an electrical load model that focus on building heating, ventilation, and air conditioning (HVAC) systems are presented to analyze the thermal-electrical conversion process of energy consumption of buildings. Second, the PFM method is used to improve the accuracy of the energy consumption analysis model for buildings by modifying the parameters that are difficult to measure in the physical model (i.e., it effectively modifies the electrical load model based on the proposed PFM method). Finally, case studies involving a real-world dataset recorded in a high-tech park in Changzhou, China, demonstrate that the proposed method exhibits superior performance with respect to the traditional physical modeling (TPM) method and data-driven modeling (DDM) method in terms of the achieved accuracy.
WITH the continuous increase in urbanization and industrial restructuring, the energy consumption of buildings in urban cities has increased rapidly over the world [
With the advances in physical measurement tools and monitoring systems for buildings, the energy consumption can be measured more accurately [
Physical modeling methods can be further subdivided into simplified and precise physical models [
Precise modeling methods construct the models for thermal processes, fluids, and electrical equipment of buildings and then combine them to build complex physical process models. Therefore, a precise physical model is generally implemented using available commercial software such as eQUEST, PowerDOE, DeST, and FloVENT [
1) The time-varying characteristics of building information at multiple time scales are not properly considered in these programs [
2) The energy consumption analysis of buildings may require the use and coordination of multiple software programs, which are assigned different tasks according to their design features.
Reference [
DDM or statistical modeling methods are based on various statistical or machine learning methods to describe or predict the energy consumption of buildings through extensive real-time and historical measurement data. These methods do not rely on the accurate modeling of physical characteristics of buildings [
The results of DDM methods mostly depend on the quality of historical data. However, historical data have many problems such as poor data quality and low data density, which result in a loss of information. Consequently, the support from sophisticated algorithms is required [
Therefore, the main contribution of this study is to establish a detailed physical model for smart buildings and ensure that the energy consumption analysis is more precise by modifying the model through a PFM method. The energy consumption analysis model of buildings is based on the PFM method, which considers not only the interpretation ability of the physical mechanism but also the incidence relation of DDM methods. Physical methods can provide high-entropy information for DDM methods. In addition, physical methods can ensure that the parameters of physical model are more targeted and can prevent the modeling method from falling into a partial learning space. The critical factor is that an accurate analysis model for energy consumption of buildings based on the PFM method does not require extensive training data and can be run online. Finally, the PFM method has a high initial training accuracy rate, which means that this method is more scalable. Therefore, a detailed and accurate physical model needs to be constructed using DDM methods to compensate for the loss of rules derived from the simplification of physical processes.
The remainder of this paper is organized as follows. Section II presents the thermal process model that considers the structures and internal thermal-electrical conversion processes of buildings. Section III investigates a solution for improving the accuracy of the model, namely, a PFM method, which is used first to modify the key parameters in the physical model and then to determine the accuracy of the power load model while also providing a replacement strategy. The results of case studies are presented in Section IV, and conclusions are given in Section V.
The premise of establishing a precise energy consumption analysis model for buildings is to create a comprehensive and high-quality dataset. The dataset should include structural, environmental, electrical, and behavioral data of buildings, as shown in

Fig. 1 Dataset collection system of building.
In addition, with a large amount of heterogeneous data, it is necessary to consider multiple time-scale characteristics and perform data preprocessing.
The structural data of buildings mainly include measurement parameters such as area and floor height, structural parameters such as orientation and shape, material parameters such as roof materials, wall materials, and vent types, and empirical parameters such as heat transfer coefficients and specific heat capacities. Because most of this information is static data, the data processing is not necessary. However, problems of inaccurate measurement data and empirical parameters often arise and affect the accuracy of physical model. Therefore, a PFM method needs to be employed to solve these problems.
Correspondingly, the environmental information, electrical data, and behavioral data are dynamic parameters. These datasets can be collected by monitoring equipment such as circuit breakers and smart plugs, intelligent sensors, and environmental monitoring devices installed both inside and outside the building. The environmental data are categorized into external and internal environmental data. These data mainly include temperature, humidity, light intensity, and climate data, etc. The acquisition of these data can also be divided into fixed-period collection and trigger-mode collection. The trigger-mode collection means that some data such as CO2 concentration do not change considerably over a short period. We only needs to wait until a significant change is detected before collecting the data. Electrical data include the voltage, current, frequency, active power, reactive power, and accumulated electrical energy collected by each electrical device and each power node, EER, and coefficient of performance (COP), personal computer (PC) load, photovoltaic (PV), etc. Based on different types of electrical equipment, the collection period can be set to be seconds, minutes, or hours. Finally, the behavioral data include status data and operational logs of electrical equipment, doors, windows, and other vents as well as personnel data for each area, running scenarios, and others. Most of these data are collected in trigger mode.
To establish a refined physical model of a building, it is necessary to perform a detailed model of several internal areas such as rooms and aisles in the entire building. In this manner, the effects of the external environment and internal areas of the building can be fully considered. Simultaneously, this can also improve the accuracy of the thermal process and energy consumption analysis. Therefore, this study constructs two matrices to describe the structural relationships and corresponding parameters of each internal area of a building. The first is the structural association matrix of the building, which is given as:
(1) |
where is the internal structural association matrix of the building; is the property of the area, which includes rooms, open areas, corridors, etc; denotes whether one or more enclosure structures exist between the and areas of the building; denotes whether one or more vent structures exist between the and areas of the building; and n is the number of areas in the building.
Next, the structural parameter matrix of the building is given as (2), which provides detailed information about the internal areas.
(2) |
where is the structural parameter matrix of the building; contains the volume of the area inside the building; and are the parameter matrices of the enclosure structures and vents between the and areas, respectively, as given in (3) and (4).
(3) |
(4) |
where the superscripts and are the numbers of envelope structures and vents between the and areas of the building, respectively; , , , and are the acreage, heat transfer coefficient, material type, and orientation of the envelope structures between the and areas of the building, respectively; and , , , and are the acreage, heat transfer coefficient, material type, and orientation of the vents between the and areas of the building, respectively.
A dynamic thermal process model of a building needs to be established based on the structural model of building. Taking a single area inside the building as an example, the dynamic thermal process of a single area refers to the heat transfer process of internal and external disturbances, as shown in

Fig. 2 Dynamic thermal process model for a building.
To obtain a refined thermal process model for each area in a building, it is important to solve the partial differential equations for heat transfer of the enclosure structure in each area. In addition, the connectivity between regions needs to be considered. The model of dynamic thermal process for a single area is given as:
(5) |
where is the temperature of the area inside the building at time ; is the change of temperature in the area inside the building at time ; is the specific heat capacity of air in the area; is the air density in the area; is the heat transferred by the external disturbance heat process in the area at time ; and is the heat transferred by the internal disturbance heat process in the area at time .
Based on (5) and
(6) |
(7) |
(8) |
(9) |
where , , and are the heat transferred from the external area to the area through the enclosure structure, vent, and solar radiation at time , respectively, and is calculated by measuring the intensity of light [
The heat transferred by the internal disturbance heat process in buildings mainly includes heat transfer from HVAC, lights, personnel, and other equipment, as shown in (10).
(10) |
where , , , and are the heat transferred from the HVAC, lights, personnel [
To analyze the energy consumption of buildings, a thermal-electrical conversion model of buildings is established. First, the total power calculation model for a building is given as:
(11) |
(12) |
where , , , and are the electric power of HVAC, lights, other equipment, and PV generation in the area at time ; , , and are the thermal-electric conversion coefficient functions for HVAC, lights, and other equipment, respectively; , , and are the thermal-electric conversion coefficients of HVAC, lights, and other equipment in the area, respectively; , , and are the operating states of the HVAC, lights, and other equipment in the area, respectively; and is the thermal-electric conversion efficiency.
(13) |
(14) |
where is the operating mode of HVAC (refrigeration, heating, air supply); is the operating switch status (on/off) of HVAC; is the wind speed of HVAC; and , , and are the EER corresponding to HVAC, lights, and other equipment, respectively, which indicates the inherent energy efficiency of equipment. Under the specific circumstances, the EERs of different devices are differently defined. The calculation methods for the energy consumption and power of other electrical loads (e.g., lights, water boilers, PCs) in buildings are similar, and the formulas are shown as:
(15) |
(16) |
where is the period required to calculate the energy consumption; and , , , and are the energy consumptions of HVAC, lights, other equipment, and PV generation in the area during time period , respectively.
The basis of the PFM method is the fusion mode. The physical analysis method can provide high-entropy information, which helps improve the efficiency of the data model analysis. In other words, the input features contain the target features to be predicted, which can narrow the search space and reduce the computational complexity when solving the parameters of data model through the optimization process. However, the PFM method can be used to construct a better data model with high-entropy input features, achieving the goal of building a data model. This also ensures that the model parameter optimization is more targeted. To avoid falling into local optimization, the PFM method improves the rationality of the data model. This approach can compensate for the loss of physical discipline rules in physical analysis methods due to the model simplification.
This study proposes two PFM correction methods. One (method 1) modifies the key parameters in the physical model through the DDM method; the other (method 2) replaces the submodels in the PFM method through the model modification. The process flow of method 1 is shown in

Fig. 3 Process flow of method 1.
The PFM method for energy consumption analysis of smart buildings requires the configuration of model parameters. The parameters include the static parameters that are input when the model is built and the dynamic parameters obtained in real-time collection when the model is running. In this paper, the parameters of thermal-electrical conversion model for a smart building that need to be modified mainly include the heat exchange coefficient and EER. Therefore, the final PFM can be obtained by guiding and correcting a simple physical model using the measurement data. The methodology for correcting the key parameters in the physical model through a DDM method is given as:
(17) |
(18) |
where and are the functions of physical model and DDM methods, respectively; is the function of PFM method, which uses the same algorithm as ; is the input dataset of the model at time ; and are the output datasets of the model at time ; is the parameter vector in the model; is the parameter vector after DDM correction; and and are the random errors. In this study, may include the parameters such as the heat exchange coefficient and EER.

Fig. 4 Process flow of method 2.
(19) |
(20) |
where is the function set of the modified PFM, which is obtained after replacing the submodels with DDM. The replacement method and selection mechanism of submodels in PFM are later analyzed in detail in conjunction with the building.
Based on the PFM method, this study divides the process for energy consumption analysis of the building into two steps. The first step involves modifying the key parameters in the precise physical model through DDM method. The second step involves modifying some of the submodels in the entire energy consumption analysis model and then building a model selection mechanism to improve the accuracy of PFM. The overall process is shown in

Fig. 5 PFM process for energy consumption analysis of building.
In Section II, a precise physical model of the building is established. Next, the key parameter modification in a physical model using DDM method is discussed. The parameters to be modified include the heat transfer coefficient of enclosure structures and vents and the conversion efficiency of HVAC. These parameters are difficult to be measured or calculated. For example, the heat transfer coefficient can be affected by the wall material, shape, aging degree, and other factors.
In this paper, a long short-term memory (LSTM) algorithm is used to modify the key parameters. LSTM has been a popular machine learning algorithm in recent years [
As a recurrent neural network, the input, output, and error calculation forms of LSTM are explained in this study. The input of the DDM method is a matrix. The horizontal axis represents the characteristic quantity of sample datasets that includes electrical, environmental, and behavioral information as well as key parameters that must be modified. The vertical axis represents the time-sequenced values. In the case studies, each sample dataset is selected for one day, with an interval period of 5 min. The output of LSTM is divided into two data parts: thermal process data of various areas in the building including the external and internal heat exchange at various time, and power and status information of different power loads in the building. The error is generated between the output of each loop and the target measurement. The error is also calculated backwards, affecting every gate in the output back to the input stage until this value is filtered out.
The second process involves modifying the submodels. In the process of energy consumption analysis of an entire building, problems may occur in which the physical modeling of some links is inaccurate or the parameters are difficult to modify. Therefore, this study proposes a model modification mechanism. Other modeling methods can be used to replace some of the modeling aspects in the energy analysis, such as thermal process links, HVAC modeling, or other electrical load modeling, as shown in
The HVAC model is selected as a submodel for discussion. This study presents two typical HVAC algorithms and provides a simple introduction. First, the modification and selection mechanism in this study are discussed through these two typical models. Second, two models, i.e., the traditional physical modeling (TPM) and DDM are used for comparison purposes in the case studies to evaluate the effects of the PFM proposed in this paper.
In [
(21) |
(22) |
where is the cost of HVAC considering the users’ comfort [
In [
(23) |
where and are the indoor and outdoor temperatures of the building, respectively; , , and are the conversion coefficients, and their specific meanings and values are described in [
In [
It should be noted that the role of the data-driven module in PFM is to modify the key parameters and to select submodels. However, the DDM mentioned above is an option in the optional model list for the HVAC submodel. Furthermore, an accuracy evaluation method needs to be established to improve the model correction and selection mechanism. This paper chooses the conventional average relative error to measure the accuracy of the algorithm fitting. The algorithm also calculates the average relative error from the two perspectives of area temperature and total electricity consumption of the building.
In this case study, a high-tech park with multiple types of buildings in Changzhou, China, is selected as an example. The park covers an area of approximately 4 k
In this study, a typical office building in the park is selected, which is an L-shaped structure with four floors and a total area of approximately 11000
Both environmental energy monitoring system and BEMS are installed in the building. Environmental monitoring outside the building mainly relies on a miniature weather station installed on the roof. The weather station monitors the environmental information, including temperature, humidity, light intensity, carbon dioxide concentration, PM2.5, wind speed, and rainfall. The monitoring period is 5 min. Similarly, the environmental monitoring inside the building is realized using numerous environmental monitoring sensors throughout the building. The BEMS measures the amount of distributed PV power generation and the power consumption of various internal areas. The electricity consumption in the internal areas inside the building is mainly composed of the electricity consumption of HVAC, lights, office computers, and other equipment. The collection period of the electrical quantity is also 5 min. Simultaneously, the building is equipped with a variety of smart sensing devices to monitor the opening and closing statuses of doors, windows, and the equipment, and the flow of people throughout the building. Most of these information collection cycles are triggered. The buildings selected in this study have a year-and-a-half’s worth of sample data.
Typical days in summer and winter are selected as the calculation periods. Based on the two aspects of regional temperature and energy consumption of the building, the accuracies of the PFM, TPM, and DDM methods are compared. First, a refined physical model is established for the building selected in the calculation example to analyze the energy consumption. The LSTM algorithm is then used to modify the key parameters in the refined physical model to obtain the temperature and electric power of each area in the building. The partial load model in the PFM is replaced with a TPM method to obtain the TPM-based calculation results. The partial load model in the PFM is replaced with a DDM, and the DDM-based calculation results are obtained. Finally, the results obtained by PFM and other two methods on a typical day in summer are compared, as shown in

Fig. 6 Results of comparison between PFM and other two methods on a typical day in summer. (a) Comparison of regional temperature. (b) Comparison of regional energy consumption.
It can be observed from

Fig. 7 Box plot of accuracy comparison between PFM and other two methods on a typical day in summer.
We then consider an example of a typical day in winter. Three differences from the calculation examples on a typical day in summer are observed. First, the working hours of employees in winter are shorter than those in summer; therefore, it is necessary to fully consider the behavioral parameters of employees in the building. Second, the working mode of HVAC changes from cooling to heating; therefore, the operating status of HVAC varies, which makes HVAC have different electrical characteristics. The third point is that in summer, the main function of HVAC is cooling, but the solar radiation increases the temperature, which is the opposite of air conditioning. However, in winter, the main function of HVAC is heating, which is similar to solar radiation. The results of comparison between the PFM and other two methods on a typical day in winter are shown in

Fig. 8 Results of comparison between PFM and other two methods on a typical day in winter. (a) Comparison of regional temperature. (b) Comparison of regional energy consumption.
It can be concluded that the temperature and power values obtained based on the PFM method are more in line with the actual values, and thus the accuracy rate is higher than that of the TPM and DDM methods.

Fig. 9 Box plot of accuracy comparison between PFM and other two methods on a typical day in winter.
Finally, we present the accuracy comparison of the PFM and other two methods in the training process, as shown in

Fig. 10 Accuracy comparison between PFM and other two methods in training process.
The PFM method has a higher training accuracy and a higher starting point for training accuracy. This is because the PFM method is based on an accurate physical model and thus has a high training accuracy from the beginning. The final training accuracy of TPM method is low at only 70% to 80%. However, due to the inherent characteristics of the physical model, the TPM methods could also have a certain initial training accuracy. Because the DDM method is completely based on data, the initial training accuracy is 0, but the DDM method shows a good learning effect and thus the final accuracy is basically the same as that of the PFM method. However, because of its dependence on sample data, the DDM method could not achieve high training accuracy when the amount of training data is relatively small. As shown by the dotted blue line, when the training accuracy of PFM method reaches 90%, the accuracies of the TPM and DDM methods are less than 70% and 80%, respectively.
An office building in a high-tech park is used as an example to construct a precision physical model of the building. A PFM method is proposed to correct the accuracy of the model through the parameter and model correction. The relevant conclusions are as follows.
1) Existing studies on the architectures for energy consumption analysis have given little attention to precise physical models. This paper constructs a refined physical model for energy consumption analysis of buildings. This model describes in detail the structural matrix and the thermal and thermal-electric conversion processes of a building through physical modeling. In particular, the interaction between the interior areas of the building and behavioral information is considered in the form of a structural matrix.
2) This paper proposes a method for analyzing energy consumption of building through the PFM method. The accuracy of the energy consumption analysis could be improved by modifying the parameters and model. The interactive mechanism of energy conversion in buildings could be retained through a physical model, and the accuracy of the energy consumption analysis could be improved by the DDM method.
3) The energy consumption analysis based on the PFM method proposed in this study can obtain higher accuracy (over 90%) when the sample data volume is relatively small. The problem that the DDM method for building energy consumption analysis of buildings requires a large amount of sample data is solved.
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