# Neural Network Model for Greenhouse Microclimate Predictions

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

_{2}), have an important contribution to the system.

_{2}concentration, and illumination. From this model, coefficients of determination greater than 0.9 were obtained, and more specifically their values for temperature and relative humidity were equal to 0.925 and 0.937, respectively. Moreover, Salah & Fourati [23] combined an Elman network with a deep multilayer FF neural network for the greenhouse control. The first network for the simulation of the direct dynamics of the internal processes was used, whereas the second one was for the inverse dynamics. Finally, Taki, et al. [24] compared three different models for the estimation of three different temperatures inside the greenhouse, the air temperature, the soil temperature, and the plants’ temperatures. After comparing a radial basis function (RBF) model, an MLP, and a support vector machine (SVM) model, it was found that the first one presented the best results.

_{in}) and relative humidity (RH

_{in}) inside the greenhouse, based on outside temperature (T

_{out}) and relative humidity RH

_{out}), wind speed (WS), solar irradiance (SR), as well as internal temperature and relative humidity up to half an hour before. After extensive research in the literature in recent years, no similar study has been found. The goal is for the model to show as low a maximum error as possible between the predicted and observed data so that it can respond adequately to a decision support system (DSS).

## 2. Materials and Methods

#### 2.1. Greenhouse

_{g}) is equal to 204.8 m

^{2}, the total volume (V) is 798.72 m

^{3}, and the surface of the cover (A

_{c}) is 461.44 m

^{2}. It is a high-tech greenhouse constructed of high-quality materials. Its frame is made up of steel pieces with different cross-sections. These glass panes in particular can withstand chemicals, high wind speeds, and pollution.

^{2}) was used. Within this section, in the center of the width of the unit and the positions corresponding to ¼ and ¾ of the length of the greenhouse, two ad hoc data acquisition systems have been installed. These systems are equipped with sensors that can record the inside temperature and relative humidity, the solar irradiance transmitted through the cover, and the photosynthetically active radiation (PAR). In addition to the sensors inside the greenhouse, an automatic weather station (AWS) has been placed outside the greenhouse facing the east side of it. The station can record environmental conditions, such as temperature, relative humidity, wind speed, solar radiation, sky temperature, IR radiation, and rainfall. The recorded data from the inside and outside of the greenhouse is stored in a data logger installed on the station and taken remotely. The sensors inside and outside the greenhouse are presented in Table 1.

#### 2.2. Data and Methodology

_{s}) is equal to 10 min. Data from 28 February 2022 9:20 to 3 March 2022 10:00 were missing. Therefore, the total amount of data is equal to 8594 samples. As independent input variables, data of the external environmental parameters were used, i.e., the outside temperature (T

_{out}), the outside relative humidity (RH

_{out}), the wind speed (WS), and the solar irradiance (SR). In addition to the parameters describing the external conditions, for the estimation of the temperature (T

_{in}) and relative humidity (RH

_{in}) inside the greenhouse at time t

_{0}equal to 0, as input variables were also used for the internal temperature and relative humidity with a time delay of one (t = t

_{0}− t

_{s}), two (t = t

_{0}− 2t

_{s}) and three (t = t

_{0}− 3t

_{s}) timesteps. The internal temperature and relative humidity were calculated as the average value of the two individual stations installed inside the greenhouse, which allows a more reliable view of the indoor conditions. The relationships between input and output variables are described by:

_{0}) are presented. On the right-hand side of these equations, the independent variables of the model are presented, based on what function f will give the predictions for the dependent variables. More specifically, the variables presented in Equations (1) and (2) are:

- –
- T
_{in}(t_{0}): the indoor temperature at time t_{0}[°C] - –
- RH
_{in}(t_{0}): the indoor relative humidity at time t_{0}[%] - –
- T
_{out}(t_{0}): the indoor temperature at time t_{0}[°C] - –
- RH
_{out}(t_{0}): the indoor relative humidity at time t_{0}[%] - –
- WS (t
_{0}): the wind speed at time t_{0}[m·s^{−1}] - –
- SR (t
_{0}): the solar irradiance at time t_{0}[W·m^{−2}] - –
- T
_{in}(t_{0}− t_{s}): the indoor temperature with a time delay of one timestep (t_{s}) [°C] - –
- RH
_{in}(t_{0}− t_{s}): the indoor relative humidity with a time delay of one timestep (t_{s}) [%] - –
- T
_{in}(t_{0}− 2 × t_{s}): the indoor temperature with a time delay of two timesteps (2 × t_{s}) [°C] - –
- RH
_{in}(t_{0}− 2 × t_{s}): the indoor relative humidity with a time delay of two timesteps (2 × t_{s}) [%] - –
- T
_{in}(t_{0}− 3 × t_{s}): the indoor temperature with a time delay of three timesteps (3 × t_{s}) [°C] - –
- RH
_{in}(t_{0}− 3 × t_{s}): the indoor relative humidity with a time delay of three timesteps (3 × t_{s}) [%] - –
- t
_{0}: the time equal to 0 - –
- t
_{s}: the timestep equal to 10 min

^{2}. Inside the greenhouse, the temperature ranges between 3.2 °C and 50.7 °C, whereas relative humidity shows a minimum of 5.7% and a maximum of 89.3%.

_{max}and r

_{min}are equal to 0.99 and 0.01, respectively. Min/max normalization was chosen because it is the fastest, easiest, and the most flexible normalization method, and with the addition of the parameters r

_{max}and r

_{min}, the normalization range can be easily changed depending on the needs of each activation function, setting the corresponding maximum and minimum limit of the range on them.

_{i}presents the normalized value of the X

_{i}; X

_{max}and X

_{min}present the maximum and the minimum value of the variable X, respectively; and the parameters r

_{max}and r

_{min}obtain the values of the desired normalization range limits. This range was chosen due to the use of the logistic sigmoid activation function in the hidden layer of the neural network. The logistic sigmoid activation function is characterized by Equation (4) and receives values in a range of 0 to 1, as shown in Figure 7; however, it was chosen to use narrower boundaries due to the existence of possible discontinuities at the range limits. At the end of the process, the values were denormalized to complete the comparison between predictions and observations.

^{2}) (Equations (4)–(6)), as well as the maximum error were calculated. The maximum error is a very important value for a decision support system, which will activate the various system management devices based on the results of the model.

#### 2.3. Neural Network Model

_{0}. As for the intermediate layers, the addition of a single hidden layer was chosen because according to Kolmogorov’s theorem, in an MLP neural network one hidden layer with a suitable number of nodes can give reliable results for any process [2,26].

## 3. Results and Discussion

^{2}, and the maximum error, it was found that the best structure of the neural network is 10-7-2, which gave the most reliable results for the testing period. The model structure extracted from MATLAB is presented in Figure 9, whereas the values of the aforementioned indices are presented in Table 3, both for temperature and relative humidity. According to the specific structure of the neural network, the following graphs of comparison were made between the observed and predicted values of the two variables.

^{−5}. This value was obtained through the normalized input and output variables and presents the best performance of the model.

^{2}, for both temperature and relative humidity, proved to be very good, presenting values very close to 1. Finally, the maximum error is not a widespread data comparison value; however, for the needs of this work, it was a very useful parameter, with its value being quite small [29].

## 4. Conclusions

^{2}were calculated to equal 0.218 K, 0.271 K, and 0.999 for temperature, and to 0.339%, 0.481%, and 0.999 for relative humidity. The above values, both for the maximum error and for the rest of the statistics, prove that the specific model can satisfactorily meet the requirements of a decision support system.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 11.**Comparison between indoor temperature predictions and observations for the testing period and 10-7-2 NN structure.

**Figure 12.**Errors between indoor temperature predictions and observations for the testing period and 10-7-2 NN structure.

**Figure 13.**Comparison between indoor relative humidity predictions and observations for the testing period and 10-7-2 NN structure.

**Figure 14.**Errors between indoor relative humidity and observations for the testing period and 10-7-2 NN structure.

Recorded Parameter | Sensor | Manufacturer |
---|---|---|

Automatic Weather Station | ||

Datalogger | CR1000 | Campbell Scientific |

Temperature (T_{out}) | MP101A-T7-WAW at 3 m | Rotronic |

Relative Humidity (RH_{out}) | MP101A-T7-WAW at 3 m | Rotronic |

Wind Speed (WS) | A100K at 6 m | Scienter |

Solar Radiation (SR_{out}) | CMP3 at 5 m | Kipp & Zonen |

Rainfall (R) | 52203 | Campbell Scientific |

Sky Temperature (T_{sky}) | CGR3 at 5 m | Kipp & Zonen |

IR Radiation (IR_{rad}) | CGR3 at 5 m | Kipp & Zonen |

Greenhouse | ||

Temperature (T_{in,1} & T_{in,2}) | MP101A-T7-WAW | Rotronic |

Relative Humidity (RH_{in,1} & RH_{in,2}) | MP101A-T7-WAW | Rotronic |

Solar Radiation (SR_{in,1} & SR_{in,2}) | CMP3 | Kipp & Zonen |

Photosynthetically Active Radiation (PAR_{1} & PAR_{2}) | ParLite | Kipp & Zonen |

Name | MATLAB Coding |
---|---|

Training Algorithm | |

Levenberg–Marquardt backpropagation | “trainlm” |

Bayesian Regularization backpropagation | “trainbr” |

BFGS Quasi Newton backpropagation | “trainbfg” |

Activation Function | |

Logistic Sigmoid | “logsig” |

Hyperbolic Tangent Sigmoid | “tansig” |

Radial Basis | “radbas” |

Positive Linear | “poslin” |

**Table 3.**Statistical indicators of comparison between observed and predicted values of internal temperature and relative humidity.

Statistical Indicators | Temperature | Relative Humidity |
---|---|---|

MAE | 0.218 K | 0.339% |

RMSE | 0.271 K | 0.481% |

R^{2} | 0.999 | 0.999 |

MAX ERROR | 0.877 K | 2.838% |

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**MDPI and ACS Style**

Petrakis, T.; Kavga, A.; Thomopoulos, V.; Argiriou, A.A.
Neural Network Model for Greenhouse Microclimate Predictions. *Agriculture* **2022**, *12*, 780.
https://doi.org/10.3390/agriculture12060780

**AMA Style**

Petrakis T, Kavga A, Thomopoulos V, Argiriou AA.
Neural Network Model for Greenhouse Microclimate Predictions. *Agriculture*. 2022; 12(6):780.
https://doi.org/10.3390/agriculture12060780

**Chicago/Turabian Style**

Petrakis, Theodoros, Angeliki Kavga, Vasileios Thomopoulos, and Athanassios A. Argiriou.
2022. "Neural Network Model for Greenhouse Microclimate Predictions" *Agriculture* 12, no. 6: 780.
https://doi.org/10.3390/agriculture12060780