## 1. Thermal Systems in Buildings

In building science, the improvement of energy efficiency has been regarded, beyond the purpose of saving costs for the building operation and maintenance, as a major factor that is closely related to the industrial workability and productivity. Therefore, no matter how efficient the building’s energy use is, it ignores the environmental requirements of the interior space. However, excluding the comfort of actual users will be an approach that undermines the sustainability of the building. However, not long ago, just improving the efficiency of energy use was quite a difficult problem for energy distribution systems that have become exponentially more complex as buildings have developed larger and more systematic. Unlike past systems reflecting limited test variables, many current diversified thermal control systems have pursued an efficient energy use by use of utilization of various control strategies to determine optimized rules. They have examined modern statistical models and advanced metering methods, and the various patterns were analyzed and compared each other. In the Heating, Ventilation, and Air Conditioning (HVAC) system, refined numerical information in its inner structure was utilized in reflecting the adjustment of various parameters, functions, and coefficients. Amongst this, the Proportional Integral Derivative (PID) model was frequently utilized to improve the control rules for generators, exchangers, and distributors, especially, in the field of rule-based thermal control systems [

1,

2,

3].

The control effectiveness of the approaches facilitating advanced hardware was remarkably improved with useful mathematical and statistical tools dealing with complex problems such as the Fuzzy Inference System (FIS) and Artificial Neural Network (ANN). The FIS linguistic model can interpret some complex problems requiring deterministic numbers to solve. One distinct characteristic of the FIS is to utilize linguistic deterministic rules to define ambiguous situations which have some hardships to approach with clear numbers by traditional rule-based controls. With the PID model, fuzzy-based diagrammatic node topology was examined to define better control strategies in building thermal system operation. Several structures finding effective nodes were examined to adjust existing control rules for fuel injection in boilers, building systems, and energy distribution networks [

4,

5]. Through the use of the combination method of the fuzzy-based deterministic and conventional methods, several diversified tuning rules were examined to optimize control signals in thermal systems in buildings. Its membership functions derived from existing and simulated data have facilitated to solve ambiguous situations and helped to determine delicate numbers by reducing unpredicted errors [

6,

7]. In developing genetic algorithms for the analysis of regression models, the adjustment or modification of control signals by use of multicriteria approaches in the FIS has effectively calibrated real signals at the several cases of actual buildings’ HVAC systems [

7,

8,

9]. The ANN model can help many researchers to solve complex calculation problems utilizing several polynomials which make them hard to handle by conventional approaches. Especially, when analyzing the effects of convection, radiation, ventilation, and infiltration between envelopes, the ANN models for various types of buildings have successfully provided precise regression models to find hidden interactions between several architectural elements [

10,

11]. Regarding various operational strategies in combustion and circulation of fuel depending on the types of energy systems in buildings, the ANN algorithm has been preferred to generate signals for sensitive controls of valves or dampers. The models based on the ANN were compared to traditional systems, and tested by means of combining theoretical rules responding to characterized conditions derived from various factors in actual buildings [

12,

13]. As effective components of dampers and resistance coils, they were examined to build auxiliary systems complementing main HVAC systems with newly analyzing multivariate regression models derived from situational and seasonal operation results. Connecting various building geometries and climate conditions, some systematic assumptions reflecting unpredictable occupant behaviors were investigated to define improved control or network strategies in combining the FIS and the ANN algorithms [

14,

15].

As the building thermal system aims to keep the indoor heat environment in association with user demands, many studies have been conducted on enhancing indoor thermal comfort as well as improving the efficiency in energy consumption. In order to effectively conclude the building performance of thermal comfort, survey-based and questionnaire-based studies were frequently utilized with subjective indicators based on various user’s responses and building’s characteristics [

16,

17]. In comparison with the qualitative approaches, objective and quantitative methods such as the Predicted Mean Vote (PMV) and the Predicted Percentage of Dissatisfied (PPD) have been preferred to effectively conclude the performance of thermal comfort in buildings as numerical indices. In order to assess more precise thermal sensation votes, the FIS and the ANN algorithms have been adopted in the PMV models to complement the interactions between initial configurations and adaptive processes. For the improved models to adjust conventional control rules, changes in occupant characteristics such as metabolic rates and clothing insulation in theoretical assumptions can be used to respond to changes in thermal situations associated with mechanical supply systems for cooling and heating air [

18,

19]. In addition to occupant related thermal factors, several conventional approaches reflecting spatial geometries, types of building envelopes, and motorized ventilation systems were developed to appropriately react extreme weather conditions. Meanwhile, comprehensive thermal comfort indices were gradually developed to approach specific requirements in respond to strengthened guidelines and regulations for local characteristics [

20,

21]. In many cases of modified approaches to effectively define meaningful interactions in the human factors, their inner structures of thermal systems and architectural components were investigated to compare mechanical functions with data-driven regression results for more reliable network-based models. Modified algorithms derived from experimental and presimulated data, in order to define several functions for several distinct situations, were examined to complement existing mechanical rules for energy supply and regression models for the PMV [

22,

23,

24]. For more precise models in combining methods, cosimulation applications based on programming language were utilized to deal with the communication between thermal calculation and programming modules were to conduct their real-time correction reflecting analyses of predicted and resulted values in calculating thermal demands. Additionally, a calibration of virtual models by energy conservation measures was utilized to complement physical gaps between actual and simulated architectural elements such as walls, doors, windows, electrical equipment, and heating and cooling systems. Recent studies dealing with network structures concluded the results that successfully explained hidden interactions between architectural components and mechanical thermal factors by means of multidimensioned matrixes adopting several experimental regression models [

25,

26].

Despite the improvement of mechanical thermal models associated with advanced statistical tools have been performed, there is a necessity of the investigation of sensitive control models for supply heating and cooling energy into a single space scale which can be closely related to users’ workability and productivity. In addition, considering how to sustainably maintain the users’ thermal comfort, it is also necessary to examine control methods for the change of seasons when cooling and heating can be required at the same time. In this study, an adaptive controller-equipped, network-based model dealing with simultaneous controls of supply air mass and its temperature is proposed with comparative assessments by using thermal comfort indices and heat transfer. The proposed approaches are examined through the comparison of simple and fuzzy-based deterministic models in the Discussion, and both sides of the strengths and weaknesses are addressed to complement the proposed model by follow-up studies in the Conclusions.

## 2. Methodology

#### 2.1. Overall Framework

This study aims to analyze the effectiveness of the ANN model with an adaptive controller to respond to the change of thermal demands through the deterministic methods of supply air conditions in a day of a mid-spring season. The inner structure of the combined model finds optimized points between the thermal energy transfer and the human comfort sensation vote, and sends refined signals to a room space. In order to understand the model’s work, a flow of the process is described as below:

- (1)
A thermal transfer model calculates the heating and cooling energy transfer based on the characteristics of a small commercial office, occupant, and outdoor temperature conditions.

- (2)
After the determination of the thermal energy transfer, the optimized supply air conditions go to the building space model to define thermal comfort levels by the PMV index at each one-minute time interval.

- (3)
Based on the result, when the PMV level is over or under the setting range (−0.5 < x < 0.5), an equipped adaptive model changes T_{set} by ±0.5 for cooling or heating.

- (4)
If the PMV level is still over or under the setting range (x < −0.5 or 0.5 < x), an adaptive model additionally adds values for T_{set}.

- (5)
If the PMV level is still over or under the setting values, the adaptive model repeats the previous process. If not in any point, it stops the adaptive process and bypass the signals.

As it was generally known that the flow rate of air was linear-proportional, rather than that of water, it was assumed that the percentage of the damper opening was the same as the air amount into the space. In addition, it was assumed that the heat loss through the envelope occurred through the only conduction of walls, window, and roof, and the heat gain was from the HVAC model only. For the effective simulation process, the spatial variations of air pressure, velocity, and infiltration in the space, envelope, and duct systems were not considered.

Figure 1 and

Table 1 display a conceptual framework for the deterministic processes and initial configurations for building geometries. Except for some assumptions, such as external work rate (0), relative humidity (50%), and air speed (0.1 m/s), the institutional standards and online-based template were utilized for specific parameters and values for recommended

T_{room},

MET, and

clo. The building thermal system was simulated by using separate heating and cooling systems in a single duct. As comparison models, a conventional thermostat and a fuzzy-based deterministic model were built. The proposed model was structured by use of the ANN algorithm with an adaptive controller which consisted of a dual switch for heating and cooling, and adjusted

T_{set} according to the result of the PMV in the feedback process.

#### 2.2. Heat Transfer Model

From the thermodynamic first law, the energy transfer by heat loss and gain through the building envelopes is given by [

27]:

where

${Q}_{loss}$ is heat loss through the building envelopes,

${Q}_{gain}$ is heat gain from the heater or cooler,

U is internal energy, and

t is time.

From the heat conduction transfer through the building envelopes, the heat loss of the building space,

${Q}_{loss}$, is given by:

where

${h}_{out}$ and

${h}_{in}$ are heat transfer coefficients,

$k$ is transmission coefficient,

$A$ is area,

$D$ is depth of envelope.

From the enthalpy and the mass flow rate, assuming that there is no work in the system, heat gain transfer of the building space,

${Q}_{gain}$, is given by [

27]:

The rate of internal energy is given by:

From the processes, time derivative of

T_{room} is rewritten by:

#### 2.3. PMV and PPD Models

Mathematically, indoor thermal comfort is measured by the PMV, and, from the PMV model developed by F.O. Fanger, the Predicted Percentage of Dissatisfied (PPD) is developed [

28,

29].

where

M is metabolic rate, and

L is thermal load.

Equation (6) and Equation (7) are used to detect thermal comfort level for buildings. Additionally, the PPD levels are defined by an exponential function of the PMV like below [

28,

29]:

#### 2.4. Three Different Controllers

As a comparison model, a thermostat controller works according to the setting value of T_{set}, 18 °C for heating and 25.5 °C for cooling. It automatically turns on and off within T_{set} = ± 1 °C, which is a dead-band as a default configuration frequently used in practice. For instance, if T_{room} reaches 26.5 °C, the thermostat sends an on-signal to the cooling system. On the contrary, if T_{room} reaches 24.5 °C, it sends an off-signal to the cooling system.

As an additional comparison model, the FIS algorithm is utilized and mainly investigate the effectiveness of real-time deterministic control by the decision numbers from multiple membership functions, which uses the temperature differences between

T_{set} and

T_{room}. A basic structure of two different membership functions is described by the differences between

T_{set} and

T_{room} (

E) and their time serial derivative of

E (Δ

E) [

30]:

Two output variables of the amount of air, from 0 (0%) to 1 (100%), and its temperature, from −10 °C to 10 °C, adopt multiple membership functions calculated from the two inputs,

E and Δ

E. The first layer consists of inputs 1 and 2, which delivers the values to the two membership functions for the mass and the temperature, then, each triangle membership function is chosen with maximum equal to 1 and minimum equal to 0 divided by 4 intervals like below.

As a proposed model to be analyzed, the ANN algorithm is utilized as a main structure, which consists of a large class of several structures. The approximation of the function is the multilayer perception built by 2 input layers, 10 hidden layers, and 1 output layer. After, the inputs

x_{1},…x_{k} into the network are multiplied by weights

w_{ki}, they are summed up with the constant bias term

θ_{i}. The result of

n_{i} is the input to the activation function

g [

31,

32]. Finally, the weights and thresholds are updated, this network runs with the gradient of errors as followings [

31,

32].

In the ANN structure, two inputs are E and ΔE from the thermostat signals like the FIS. Then one output layer is sent as a control signal for air mass and temperature. Training of the ANN algorithm is conducted to investigate an optimized regression model which can maintain T_{room} to within the setting range of the PMV value. As data for training the ANN algorithm, the thermostat and the fuzzy controlled energy consumption pattern of 3 different building types (commercial office, retail, restaurant) in 7 weather conditions in the US from the Energy Efficiency & Renewable Energy report of the US Department of Energy was used with the heat transfer formula used in the heat transfer model. For source-effective results, a scale conjugate gradient algorithm was adopted in the simulation configuration of maximum 1000 times iterations, and under 10 times epoch number to receive a satisfactory statistical validation. After these repetitions, the simulation results displayed statistical validated R^{2} values as 0.99438 for controlling heating or cooling supply air mass and as 0.99749 for controlling its temperature, respectively.

#### 2.5. Simulation Model

As indicated in

Figure 2, a simulation block diagram for this study utilized the energy transfer which occurred through the difference between

T_{room} and

T_{out}. The thermal system sends optimized signals for heating or cooling supply air with appropriate air mass and its temperature. From the analysis of

T_{room} and human factors, the PMV value at every 1 min was calculated and an adaptive comfort model adjusted

T_{set} for recalculation of the amount of cooling or heating supply air to mitigate thermal dissatisfaction.

As previously mentioned, the results of the PMV index can be higher than 0.5 or lower than −0.5, then, the adaptive model sends modified signals for −0.5 for cooling or 0.5 heating. This additional signal is connected to the thermal system to adjust T_{set} by 0.5 °C higher or lower. The simulation process is conducted in a way that mitigates the difference between setting values and actual values in the PMV, but the energy consumption during the process can be increased. One of the main purposes of this simulation study is to explore how much this energy use is increasing, and how much the PMV value is increasing due to this increase is correspondingly.

## 5. Conclusions

In this study, three distinct models were proposed to effectively maintain the room temperature within the setting range by controlling the conditions of heating and cooling supply air. During the process, an adaptive model complemented the network-based learning algorithm by the adjustment of output signals to reduce energy use within designated setting ranges for thermal comfort. In terms of the energy efficiency, the FIS and the ANN models resulted in a slight efficiency degradation which was caused as a result of precision control to improve indoor thermal comfort. As indicated in the results of thermal comfort by the PMV index, the ANN model showed an improved performance of more than 14% over the thermostat and the FIS models. Even though all of the effective elements and parameters in typical HVAC and comfort models were not considered in this simulation, theoretical advantages of combining network and adaptive algorithms were confirmed in terms of improving both aspects of energy consumption and thermal comfort.

As a result, a network and learning algorithm equipped with an adaptive controller properly worked to improve users’ comfort level and system’s energy use. This improvement implies the fact that the better thermal comfort levels can be remarkable in places where several types of building spaces systematically connected. Additionally, this improvement would be more significant where the place can be directly affected by the environmental comfort, so highly intensive workability and usability are required. With the improvement of the simulation framework and modification, a follow-up study with a lab-scaled model can be performed to examine the actual energy transfer and occupant responses by expanding thermal and architectural components.