# Data Reconstruction of Wireless Sensor Network and Zonal Demand Control in a Large-Scale Indoor Space Considering Thermal Coupling

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. WSN Test-Bed and Data Analysis

_{2}concentration have been measured for nearly ten months. The vendor for the wireless temperature sensors is GreenOrbs. The communication protocol of the WSN is ZigBee with mesh topology, each wireless sensor node is powered by 2 alkaline batteries. The maintenance during the deployment is to replace the batteries when a low power warning signal is received. The measurement error for the wireless temperature sensor may reach to ±0.15 °C. To keep the accuracy of the CO

_{2}sensor, the CO

_{2}sensor is calibrated every 2 months. The sampling interval is set to 10 min for collecting the temperature data. The WSN was calibrated with another thermostat sensor and has an acceptable accuracy of the data measurement with an absolute error around 0.3 °C. The detailed information for wireless sensor node can be found in reference [17].

^{3}, which is a typical indoor large space building. The HVAC system used in this area is the most common Variable Air Volume (VAV) air conditioning system. The WSN test-bed consists of 20 wireless sensor nodes, a receiver device, and a desktop computer for storing and processing data. The 20 wireless sensor nodes were installed on 10 pillars, with two wireless sensor nodes installed on each pillar. Each wireless sensor node is 2 m above the ground and distinguished by a unique number. The layout of the WSN network-based monitoring platform is shown in Figure 1 as well. Since the space belongs to the inner area of the building and has a large area, the indoor space is divided into four subzones based on its functional, the air conditioning configuration and other factors: East, West, North and Middle. The East, West and North subzones are aisle areas and the Middle zone is a temporary study area. It is noted that the boundary between each subzone is defined as virtual boundary without any physical partitions.

#### Data Analysis

_{2}concentration data in July was selected as a typical summer month for analysis. Twenty sensors collected a total of 74,880 temperature data with an average of 3744 data collected by each node (both outlier and duplicated data were removed). The number of missing data was 639 with an average loss rate of 0.85%, see Table 1, of which No. 116 has the largest number of data loss (i.e., around 384 data missing, nearly 3 days of data loss), accounting for 10.26%, followed by node No. 129 with 131 lost data and node No. 123 with 63 lost data. Node No. 111 and 120 has data loss of 18 and 12 respectively, and the rest of the nodes have less than 5 data loss.

_{2}concentration profiles of node No. 113 from 2nd to 28th on July. It can be seen from Figure 2 that the daily corresponding temperature, humidity, and CO

_{2}concentration curves have clear peaks and valleys with time. The monitored maximum and minimum value of the temperature is 25.53 °C and 24.31 °C; the relative humidity ranges from 60% to 81%; the maximum concentration of CO

_{2}appeared at 17:00 on 17 July: 1055 ppm, and the minimum value occurred at 05:30 on 8 July: 414 ppm. The average temperature, humidity and CO

_{2}concentration is 24.78 °C, 68%, and 576 ppm in the time period of 08:00–20:00 (working time) in one month, respectively. The measured temperature by sensor node 113 generally meets the room set-point temperature 24.5 °C as well as CO

_{2}concentration is basically less than 1000 ppm.

_{2}concentration also show the phenomenon of uneven distribution in space and time.

## 3. Data Reconstruction

#### 3.1. Correlation Analysis of Sensor Nodes

_{1}and X

_{2}are two variables, ${\overline{X}}_{1}$ and ${\overline{X}}_{2}$ are the average values of X

_{1}and X

_{2}, respectively.

#### 3.2. Multiple Linear Regression Model (MLR) Based on Correlation Analysis

^{2}) and Mean Square Error (MSE) [33].

_{k}

_{1}, x

_{k}

_{2}, …, x

_{km}) can be obtained by the following equations [31,32].

_{0}, b

_{1}, …, b

_{m}are m + 1 regression coefficients to be solved, and the regression equation is obtained by solving the regression coefficient estimates by the least squares method.

_{1}, x

_{2}, …, x

_{m}. It mainly includes the significance of the regression equation and the significance test of the regression coefficients: the former is a test to determine whether there is linearity in the obtained regression equation, while the latter is a test to analyze the degree of influence of each independent variable on the dependent variable. The significance test allows analyzing the meaning of the regression equation and the contribution of the respective variables to the dependent variable. The steps of multiple linear regression using Statistical Product and Service Solutions (SPSS) software are given in Figure 5 [34,35].

_{2}concentration data were determined as follows:

_{120,T}represents temperature data of node 120, X

_{125,T}, X

_{114,T}, and X

_{129,T}represent temperature of nodes 125, 114, and 129, respectively; Y

_{120,H}represents humidity data of node 120, X

_{125,H}, X

_{114,H}and X

_{129,H}represent humidity of nodes 125, 114, and 129; Y

_{120,CO2}represents CO

_{2}of node 120, X

_{125,CO2}, X

_{114,CO2}, and X

_{129,CO2}represent CO

_{2}of nodes 125, 114, and 129, respectively.

#### 3.3. Support Vector Regression Model

_{i}(j), y(j), i = 1, 2, …, M, j = 1, 2, …, N), x

_{i}(j) is the jth sample of the ith variable, y(j) is the corresponding output value, N is the sample capacity. The basic idea of SVR is to map the sample X to a high-dimensional feature space (as shown in Figure 6a) by a nonlinear mapping function φ(x), and to perform linear regression analysis in this feature space, and then construct the optimal decision function y(x) in Equation (7). The output of SVR is a linear combination of intermediate nodes, each of which corresponds to a support vector, and its structure is shown in Figure 6b.

^{2}/2 and the training model complexity. The kernel function is used to achieve a high-dimensional mapping feature space for the data, and the Lagrange equation is further introduced to solve Equation (8) to obtain the SVR output model results,

_{j}, x) is the kernel function and α is the Lagrange multiplier.

#### 3.4. Back Propagation (BP) Neural Network Model

_{i}(j), y(j), i = 1, 2, …, M, j = 1, 2, …, N), where the input layer contains m nodes, the implicit layer contains n nodes, and the output layer has one node. W

_{ih}(i = 1, 2, …, m; h = 1, 2, …, p) is the weight between the i

_{th}neuron in the input layer to the h

_{th}neuron in the hidden layer, and W

_{ho}(h = 1, 2, …, p; o = 1) is the weight from the h

_{th}neuron in the hidden layer to the o

_{th}neuron in the output layer, and θ

_{h}(h = 1, 2, …, p) is the threshold of the h

_{th}neuron in the hidden layer, σ

_{1}is the threshold of the output layer, X

_{i}(i = 1, 2, …, m) is the I neuron of the input layer of the BP neural network, Y

_{1}is the neuron of the output layer of the BP neural network, Y

_{k}is the expected output of the BP neural network, and e is the error between the expected output and the actual output of the BP neural network [42,43].

_{th}neuron in the hidden layer is α

_{h}, the input received by the neuron in the output layer is β, see Equations (10) and (11), and b

_{h}is the output of the h

_{th}neuron in the hidden layer. It is assumed that the Sigmoid function is used in both the hidden layer and the output layer.

_{k}, y

_{k}), the output of the output layer is noted by $\widehat{y}$, then the mean square error E

_{k}of the BP neural network on (x

_{k}, y

_{k});

#### 3.5. Reconstructed Data Analysis

_{2}concentration fitting curve was the worst. It indicates that the three algorithms have good accuracy in reconstructing temperature, humidity, and CO

_{2}concentration data.

^{2}and Mean Square Error are selected and their formulas are given in Equations (14) and (15), where M is the total number of samples, and y

^{(i)}, $\widehat{y}$

^{(i)}, $\overline{y}$ are the ith measured data, the ith reconstructed data, and the average value of the samples, respectively. The closer the R

^{2}is to 1 and the Mean Square Error is to 0, the better the model reconstruction is. It should be emphasized that since temperature, humidity, and CO

_{2}concentration have different units and magnitudes. Therefore, in the procedure of data preprocessing, the three data are normalized so that they are all distributed between 0 and 1. As an example to analyze the accuracy of the three algorithms in reconstructing temperature data, Figure 10 gives the specific performance of the three algorithms in reconstructing temperature data in the training and test sets. It can be seen that the performance of each model on the training and test sets is very close to each other, with no overfitting phenomenon. The R

^{2}based on the SVR model reconstruction is 0.9915, the MSE based on the MLR model reconstruction is 0.0044, and the R

^{2}and MSE based on the BP neural network model reconstruction are 0.9808 and 0.0126, and their performance is the worst in comparison with other methods. The results demonstrate that the accuracy of reconstructing temperature data based on SVR model and MLR model is higher than that based on BP neural network model. It has different performance in reconstructing temperature, humidity and CO

_{2}with exactly same algorithm, Figure 10c shows the accuracy of reconstructing the data based on BP algorithm is humidity, temperature, and CO

_{2}concentration in order. The accuracy of reconstructing the same data based on different algorithms also varies. Figure 10d reveals the highest accuracy of reconstructing temperature data is MLR algorithm, followed by SVR and BP algorithm. Accuracy is not the only index to measure the superiority of the algorithm. From the perspectives of program complexity, computing speed and difficulty in obtaining input conditions, MLR is the most suitable one of the three methods.

## 4. TRNSYS Modeling and Control Simulation

#### 4.1. Description of Three Control Modes

- The traditional single-input-single-output (SISO) control: the use of only one temperature sensor to synchronously control the entire large space, the temperature sensor is usually located at the return air outlet, the airflow rate is delivered to the space evenly by the air terminals (e.g., square ceiling diffuser). This is the current temperature control mode for this large space. The baseline model or the benchmark model introduced here is for energy consumption comparison purpose.
- Zonal temperature control: The whole space is separated into four individual subzones, with each subzone can be independently controlled to its corresponding zonal set-point temperature (zonal set-point temperature may varies with different subzones for energy conservation).
- Zonal demand control: Based on the zonal temperature control, the following two aspects were considered: (i) The relationship between room set-point temperature and room load is shown in Figure 13. The temperature set-point changes with the load, when the load is on a small scale, the temperature set-point increases appropriately, when the load exceeds a certain value, for example 2 kW, the temperature set-point decreases accordingly; (ii) the airflow coupling between virtual boundaries are considered and calculated by CONTAM program.

#### 4.2. Simulation Results

## 5. Discussion and Conclusions

_{2}in a selected large indoor space with the purposes of improving the temperature control for energy saving as well as improving thermal comfort.

_{2}concentration was analyzed and summarized. Uneven distribution of temperature, humidity and CO

_{2}was observed, it is found the temperature in horizontal breathing level can be reached to 2.5 °C, which indicates the existence of local overcooling/overheating phenomenon in the large space for the current temperature control system, consequently, thermal comfort is not guaranteed.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 2.**Temperature, Humidity and CO

_{2}concentration profile in July (No. 113): (

**a**) Temperature profile; (

**b**) Humidity profile; (

**c**) CO

_{2}concentration profile.

**Figure 3.**Temperature curve within 4 subzones for a specific day (8th July): (

**a**) West subzone; (

**b**) East subzone; (

**c**) Middle subzone; (

**d**) North subzone.

**Figure 6.**Schematic map of SVR: (

**a**) a diagram of mapping optimal separating hyper plane; (

**b**) structure of kernel function.

**Figure 9.**Reconstruct data prediction results based on three models: (

**a**) Temperature; (

**b**) Humidity; (

**c**) CO

_{2}concentration.

**Figure 10.**Performance analysis of three models: (

**a**) Comparison of R

^{2}of the three algorithms in the training set; (

**b**) Comparison of MSE of the three algorithms in the training set; (

**c**) Comparison of R

^{2}of the three algorithms in the test set; (

**d**) Comparison of MSE of the three algorithms in the test set.

Sensor No. | 116 | 129 | 123 | 111 | 120 |
---|---|---|---|---|---|

Data loss | 384 | 131 | 63 | 18 | 12 |

Percentage (%) | 10.26 | 3.5 | 1.68 | 0.48 | 0.32 |

Control Strategies | SISO Control (Benchmark) | Zonal Temperature Control | Zonal Demand Control |
---|---|---|---|

Room set-point | 24.5 °C | 24.5 °C | 24.5–26.5 °C |

Fan energy consumption | 420.4 kWh | 370 kWh | 343.5 kWh |

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**MDPI and ACS Style**

Zhou, P.; Wang, S.; Jin, Z.; Huang, G.; Zhu, J.; Liu, X.
Data Reconstruction of Wireless Sensor Network and Zonal Demand Control in a Large-Scale Indoor Space Considering Thermal Coupling. *Buildings* **2022**, *12*, 15.
https://doi.org/10.3390/buildings12010015

**AMA Style**

Zhou P, Wang S, Jin Z, Huang G, Zhu J, Liu X.
Data Reconstruction of Wireless Sensor Network and Zonal Demand Control in a Large-Scale Indoor Space Considering Thermal Coupling. *Buildings*. 2022; 12(1):15.
https://doi.org/10.3390/buildings12010015

**Chicago/Turabian Style**

Zhou, Pei, Songjie Wang, Zhao Jin, Gongsheng Huang, Jian Zhu, and Xiaoping Liu.
2022. "Data Reconstruction of Wireless Sensor Network and Zonal Demand Control in a Large-Scale Indoor Space Considering Thermal Coupling" *Buildings* 12, no. 1: 15.
https://doi.org/10.3390/buildings12010015