I Introduction
The residential and commercial building sector is known to use around 40% of the total enduse energy and, hence, is considered to be the largest energyconsuming sector in the world [1]. Approximately half of this energy is used for heating, cooling, ventilation, and air conditioning (HVAC), and this usage is increasing % per year in developed countries [2]. This trend is similar to the rest of the world. Therefore, finding solutions to reduce energy use and/or increase energy efficiency in the building sectors, particularly for smart buildings in the smart city environment, is of crucial importance.
The majority of building thermal controls are based on modelbased approaches. In modelbased control designs, the controller is designed based on the mathematical model of the plant, assuming that the model represents the actual plant. However, model uncertainties and modeling errors always exist in the modeling process. One of the efficient modelbased techniques in building thermal control is model predictive control (MPC) [3]. Just like other modelbased strategies, MPC requires an accurate model (mathematical model) to predict the process inputs/outputs and obtain the control signal [46]. The performance of MPC is directly relevant to the accuracy of the model, and it diminishes by the model inaccuracy. In the context of building management, it is difficult to accurately identify the building’s thermal models, due to vast differences in construction materials and architectures, timevarying thermal dynamics, huge load of complex data processing, high cost of accurate modeling, and difficulties in modeling the residents’ behavior and occupancy.
Learningbased modeling is known to be efficient in accurate modeling of multizone buildings with nonlinearities, uncertainties, timevarying characteristics, the vast number of variables and components, nonuniform zone temperatures, and zonal couplings [7]. A machine learning algorithm can utilize the building’s historical datasets to improve the modeling or control framework over time by learning the model uncertainties and reallife conditions [8]. Machine learning algorithms can address the complex data such as occupant behavior and varying operating costs in a building management system, without requiring a detailed model and explicit programming [9].
By integrating learningbased algorithms with modelbased controls, one can utilize both advantages of learning and modelingbased designs. On the one hand, modelbased design assists the learningbased design in learning explorations with maximum learning rate. On the other hand, occupants’ behaviors, and various cyber physical interactions can be handled by the learners and fed into the modelbased management structure. The use of learningbased algorithms in building modeling and control have been studied in the literature [10][12]. In [10], an ANN model is used to decrease the temperature overshoot and undershoots in the HVACs, which result in the reduction of energy consumption. Authors in [11] and [12] employed feedforward ANN to build a predictive thermal model to determine the ON/OFF time for the HVAC. None of the mentioned works considered the occupancy profile in the learning process. Moreover, none of them incorporated a modelbased control framework with the learningbased algorithm to get the most advantage of both designs.
In this paper, a learningbased modeling strategy is incorporated with a modelbased predictive control algorithm to manage a multizone building’s thermal property. An ANN is utilized to predict the occupancy profile; then this data is fed into the modelbased control (MPC). The datasets of ANN are generated by simulating an actual building in Energy Plus software, considering the indoor temperature, time of day, weather data, energy consumption data, and setpoint temperatures. Through the MPC algorithm, the optimum setpoints are generated as the control inputs at each step to conserve energy and improve the comfort level. In contrast to the previous works, this work utilized both modelbased and learningbased modeling in the MPC algorithm to enhance robustness and stability of the modelbased control framework as well as improving the controlled system performance through learning from historical datasets.
The rest of the paper is organized as follows. Section II describes the building model and its components. Section III and IV explain the learningbased and modelbased modeling techniques, respectively. The next section introduces the proposed learningbased MPC approach. The simulation results and simulation assumptions are presented in section VI. Finally, section VII provides conclusions and discusses future research.
Ii System Definition
A twostory office building with four zones and one HVAC system per zone is considered in this work. Each zone thermostat is dual setpoint. Fig. 1 shows the fourzone building CAD model. The floor area is with the orientation to the north. Windows include shadings, overhangs, and fins. Several materials are used in various layers of the walls (exterior and interior), window frames, door, roof, ceiling, and interzone walls. Table I contains the building materials’ specifications.
4 inch dense face brick  2 inch insulation  4 inch concrete block  3/4 inch plaster board  1/8 inch hardwood  8 inch concrete block  acoustic tile  1/2 inch stone  3/8 inch membrane  
Roughness  Rough  Very rough  Medium rough  Smooth  Medium smooth  Rough  Medium smooth  Rough  Rough 
Thickness  
Conductivity  
Density  
Specific heat  
Thermal absorptance  
solar absorptance  
Visible absorptance 
Iii Occupancy Predictions
This section explains the learningbased approach to predict the occupancy impact on the indoor temperature. Occupancy information is important in energyefficient building climate control since it can impact the temperature, environmental conditions, energy usage, and comfort constraints [2]. The goal of this work is to predict the occupancy information in the longterm through the ANN and investigate its influence on the building energy consumption and residents’ comfort. The selected ANN model is a Nonlinear Autoregressive netwoRk with eXogenous inputs (NARX). In the NARX model, at least three layers of nodes (input, output, and hidden layer) are used to approximate the outputs in (1).
(1) 
, , , and denote the inputs, outputs, input delays, and output delays of the ANN, respectively.
is the mapping function. There are generally two architectures of NARX neural networks; i.e., seriesparallel architecture and parallel architecture. The seriesparallel configuration provides better prediction performance in training the model than the parallel configuration. The better performance is because the input of the feedforward network is more accurate, and the static backpropagation can be used for training. Since in our work the actual output is available during the training of the network (from Energy Plus data), we have chosen the seriesparallel architecture to train the network. The seriesparallel NARX network is represented in Fig.
2.The reason we used the NARX neural network for the occupancy predictions is that the occupancy profile is a time series, and one of the primary applications of NARX is predicting the time series models [13]. Moreover, since the occupancy produces heating, it is highly nonlinear, and NARX model is very beneficial for nonlinear models of this type. After training the network, it is validated. To evaluate the stopping criterion and the expected performance of the predicted data, the test data is used. Therefore, three datasets are used; training, validation, and test. Mean square error (MSE) and the regression value, representing the square error and the correlation between the output and the target values are utilized to validate the training performance. Thus, the NARX neural network algorithm is as follows:

Define the input and output datasets.

Define three sets of training, validation, and testing data.

Choose a network architecture and a training algorithm by trial and error method.

Train the network, and evaluate its performance.

If the network performance is satisfactory, the problem is solved, otherwise, change the network size, retrain, or use larger datasets.
The ANN specifications of this work are described in section VI.
Iv Indoor Temperature Predictions
This section explains the modelbased approach to predict the indoor temperature. Considering the thermal convection and conduction equations, the mathematical model of the indoor temperature is represented as (2) [14], [15].
(2)  
where and are the estimated indoor temperature and the outdoor temperature, respectively. is the time step, and is the heating power. and are the parameters to be identified. is the estimated occupancy at time . In the learningbased simulation, the estimated value of occupancy is fed into the modelbased predictor. In the conventional MPC; i.e., without learning, the occupancy profile is chosen constant at its average value ().
The parameters of the thermal model (2) are identified through the recursive least square (RLS) identification algorithm using the Energy Plus input/output data. To evaluate the identification algorithm performance, the root mean square (RMS) criterion is used. The RLS algorithm is represented in brief as follows.
(3)  
where , , , and are the gain, forgetting factor, observations and estimated parameter, respectively. represents the error between the measurements and identification outputs.
V LearningBased Model Predictive Control
Having the weather and occupancy forecasts, the model predictive control (MPC) comes into play. MPC is a modern control technique that has been applied in many areas due to its ability to handle constrained control problems [3]. At each time instant, an optimal control problem is solved to obtain the optimal control action over the time horizon. Using MPC in the building temperature control, a plan for the HVAC system control is generated based on the predicted weather conditions and occupancy profiles over the time horizon. The first control action that minimizes the energy consumption and satisfies the comfort is applied to the building’s HVACs, then the control algorithm is repeated with the feedback information of building states and outputs at the next time instant. Fig. 3 represents the proposed learningbased model predictive control approach.
MPC cost function is defined as (4), such that it penalizes the deviations from the comfort level and optimum energy consumption.
(4) 
where and are the weighting factors associated with the states and inputs, respectively. is the time horizon, and is the comfort setpoint temperature. Therefore, the MPC problem is to minimize (4) subject to the performance constraints (5), robustness constraints (6), and limit constraints ((7)). It is worth mentioning that equation (5) incorporates the learning while (6) is solely based on modelbased design.
(5)  
(6)  
(7)  
MPC algorithm is as follows:

Define the system states and inputs at the current time, and their estimations up to the time horizon.

Solve the optimization problem (cost function) to get the optimum inputs at time .

At time , solve the optimization to get the input signal over the horizon.

Apply the first control input, , and go to the second step.
Vi Simulation Results
In this section, all the simulation assumptions and results from the proposed learningbased MPC and the conventional MPC (without learning) are illustrated. The simulations are performed for one year, with 6 time steps per hour. To provide the ANN dataset, Energy Plus simulations on the building model of Fig. 1 were completed from the 1st of July to 31st of December. The simulation assumptions are as follows.

The desired temperature of all zones are between 20 C and 25 C.

The control variables are the HVAC setpoints.

The maximum and minimum supply air temperatures are 50 C and 13 C, respectively.

The maximum drybulb temperature for winter and summer days in Chicago Ohare location are considered 16.6 C and 31.6 C, respectively.

The weather data at Chicago Ohare location is used.

The number of people per zonal area is 0.1.

The ANN input layer includes the environmental measures; the time of day, date, weather data, and the historical occupancy data.

The input and output delays of NARX model are both chosen 2.

One output layer and 10 hidden layers are chosen.

The LevenbegrgMarquardt backpropagation training algorithm is chosen.
The NARX neural network implemented in MATLAB is presented in Fig. 4. Fig. 5 compares the network’s response with the actual vacancy profile, and shows the error values between the occupancy predictions and its actual profile throughout one month (To get a clear image, these plots are presented for onemonth period). The maximum error value at each time is ; i.e., the target occupancy profile is welltracked. Fig. 6 presents the regression and performance plots of the training, validation, and testing datasets. The regression values are all close to and the MSE error is ; i.e., the training performance is satisfactory.
Parameters  Conventional MPC  Learningbased MPC  Change 

Average cooling power  396.28 W  235.55 W  40.56% 
Average heating power  2.43 KW  2.02 KW  16.73% 
Fig. 7 shows the results of indoor temperature model identification throughout onemonth simulation. From Fig. 7, the identification error does not exceed 0.05; i.e., the identified outputs (indoor temperature) are very close to the actual indoor temperature values. Figs. 8 and 9 show the results of the proposed learningbased MPC and conventional MPC approaches on the building throughout oneyear simulation. Comparing the power rate graphs and Table II values using the two approaches, the proposed method decreased the cooling and heating power consumption by and , respectively. Furthermore, the deviations from the comfort level in the conventional approach is extremely higher compared to the proposed method. The zone temperature using the conventional MPC even violates the minimum comfort level.
Vii Conclusions
In this paper, a learningbased MPC strategy is introduced to control the thermal property of a fourzone office building. Predicting the building parameters is a crucial and challenging part of MPC since the building’s thermal model is nonlinear, associated with uncertainties, and strongly coupled. Thus, ANN is incorporated with the model based control approach to address the mentioned issues. The occupancy profile predictions are generated through ANN, and then this data is fed into the modelbased controller. Energy Plus software is used in this work to simulate a building with real materials and components, and to test the proposed approach on it. Results from the proposed learningbased approach showed significantly better performance, in maintaining the residents’ comfort and minimizing energy usage ( energy savings), compared to the conventional MPC. For future work, implementing learningbased control to consider the impact of occupants behavior, such as window opening, or the energy storage devices in the building management system will be considered.
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