# Combining Recurrent Neural Network and Sigmoid Growth Models for Short-Term Temperature Forecasting and Tomato Growth Prediction in a Plastic Greenhouse

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## Abstract

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^{2}, MAPE, and RMSE values were 0.962, 3.216%, and 1.196 °C, respectively. Subsequently, the outputs of the temperature forecasting model were used to calculate growing degree days (GDDs), and the predicted GDDs were used as an input variable for the sigmoid growth models to simulate the leaf area index, fresh fruit weight, and aboveground dry matter of tomatoes. The R

^{2}values of the growth model for the three growth traits were all higher than 0.80. Moreover, the fitted values and the parameter estimates of the growth models were similar, irrespective of whether the observed GDD (calculated using the actual observed data) or the predicted GDD (calculated using the temperature forecasting model output) was used. These results indicated that the proposed temperature forecasting model could accurately predict the temperature changes inside a greenhouse and could subsequently be used for the growth prediction of greenhouse tomatoes.

## 1. Introduction

## 2. Materials and Methods

_{2}concentration (ppm), wind speed (m ${\mathrm{s}}^{-1}$), and wind direction (0–360°) were utilized as the input variables to forecast the internal greenhouse temperature for the following 30 min. As climate data are treated as the time series, the LSTM, GRU, and BILSTM were used to establish the temperature forecasting model. Furthermore, the forecasting models established in Greenhouse #1 were used to predict the internal temperature of Greenhouse #2. Finally, the forecasting temperature was applied to calculate GDD and fit a nonlinear growth model to simulate tomato growth in Greenhouse #2. The conceptual diagram of the greenhouse production framework is displayed in Figure 1.

#### 2.1. Greenhouse #1 Specification and Measurements

^{−2}.

_{2}sensor (GMP343; Vaisala Inc., Vantaa, Finland). The climate data of Greenhouse #1 were collected from 6 November 2019 to 8 December 2021. All of the climate data were collected every 10 min by the data logger (CR300; Campbell Scientific Inc., Logan, UT, USA).

#### 2.2. Greenhouse #2 Specification, Measurements, and Tomato Growth Data Collection

^{−2}. The growth data were collected from 12 October 2021 to 17 January 2022. Five plants were randomly chosen each week to measure the growth parameters, including LAI (cm

^{2}cm

^{−2}), fresh fruit weight (g plant

^{−1}), and aboveground dry matter (g plant

^{−1}). The plant was separated into three parts: stem, leaves, and fruits. The total leaf area was measured using a leaf area meter (LI-3000a; LI-COR Biosciences, Lincoln, NE, USA). The fresh fruit weight was measured using an electronic balance (resolution: ±0.01 g). After measuring the leaf area and fresh fruit weight, plants were dried in an oven at 80 °C for approximately three days until the weight no longer changed, and then, the aboveground dry matter was measured using an electronic balance (resolution: ±0.01 g).

#### 2.3. RNN Architectures for the Temperature Forecasting Model

#### 2.3.1. Long Short-Term Memory (LSTM)

#### 2.3.2. Gated Recurrent Unit (GRU)

#### 2.3.3. Bi-Directional LSTM (BILSTM)

#### 2.3.4. Climate Data Preprocessing and Model Hyperparameter Settings

^{−4}, and the momentum of the neural network models was 0.99. In addition, this study chose a 90%–5%–5% split to allow the models to learn changing patterns well, but this extreme split could bring the risk of overfitting. Therefore, L2 regularization, dropout rate, and patience value were considered to prevent overfitting. L2 regularization is a commonly used technique to prevent overfitting by penalizing the model for having a large weight, which helps the model to prevent from fitting the noise in the training data [32]. Moreover, overfitting can be reduced by using dropout procedure [33], and the conventional dropout rate is 0.2 or 0.3. In this study, a higher dropout rate (0.4) was assigned to strengthen the effect. Finally, a patience value of 5 was set so that if there was no improvement in the validation error after 5 epochs, the model training process was stopped.

#### 2.3.5. Evaluation Metrics of Temperature Forecasting Model

^{2}), mean absolute percentage error (MAPE), and root mean square error (RMSE) [34]. The corresponding equations are as follows:

^{2}was between 0 and 1 inclusive, which was an indicator to evaluate the linear relationship between the predicted and the observed values. RMSE was used to measure the deviation between the predicted value and the observed value, with a value from 0 to infinity. MAPE was applied to quantify and evaluate the accuracy of the predicted value.

#### 2.4. Sigmoid Model for Predicting Greenhouse Tomato Growth

#### 2.5. Data Analysis Software

## 3. Results and Discussion

#### 3.1. Performance Evaluation of Temperature Forecasting Model

^{2}, MAPE, and RMSE, respectively. When the MAPE value is less than 10%, it indicates an accurate prediction. R

^{2}was closer to 1, and RMSE was closer to 0, suggesting a more accurate predicted result. Figure 6 shows the R

^{2}tendencies for the LSTM, GRU, and BILSTM models with different numbers of hidden layers and hidden units when forecasting the 30-min-ahead temperature inside Greenhouse #2. The following characteristics were observed: (1) the best accuracy in each model with the number of hidden units was not very low or high, (2) the accuracy was not always better for the three-layer-type models than that for the single-layer-type or two-layer-type models, and (3) the accuracy of the GRU had a large degree of variability.

^{2}values and lower MAPE and RMSE values among the nine models. With an accurate temperature forecast model, growers can make early decisions based on the forecast results to control the temperature in the greenhouse within a suitable range. Previous research has demonstrated that ANNs have significant advantages in their flexibility to adapt to nonlinear and non-physical data—this characteristic provides ANNs with considerable potential for application to the environmental control of greenhouses [38]. ANNs on greenhouse microclimate prediction, such as multilayer perceptron [7,39], radial basis function [40], and RNN based on LSTM, GRU, or BILSTM [18,19,21], have exhibited satisfactory performances on temperature prediction. Considering the performance of each model, the LSTM2 with 190 hidden units was chosen as the best temperature forecasting model and had an R

^{2}of 0.962, MAPE of 3.2%, and RMSE of 1.2 °C (Table 2); its forecasting results were subsequently used to calculate the predicted GDD.

#### 3.2. Comparison of Daily Mean Temperature and GDD between Predicted and Observed Values

^{2}was 0.981 (Figure 8). These results show that the LSTM2 model is accurate in predicting internal temperature and has no tendency of overestimation or underestimation, even when applied to a greenhouse that was not used in the modeling.

^{2}and higher MAPE and RMSE) were compared to demonstrate the benefits of accurate temperature forecasting models. The GDD values were calculated using the observed and predicted mean temperatures from the two temperature forecasting models. Figure 9 shows the observed and predicted GDD values for the 94-day investigation period. For the last day of investigation, the predicted GDD calculated using the results of the LSTM2 model was 16.28 °C higher than the observed GDD. However, the predicted GDD calculated using the BILSTM2 model results was 65.47 °C higher than the observed GDD. The comparison results indicated that if the temperature forecasting model had a better performance, the value of the predicted GDD would be closer to the actual value. As the prediction error of the forecasting model increased over time, the difference between the predicted and the observed GDD values increased. When the crop growth days were longer, the gap between the actual and the predicted values would be wider. Therefore, an accurate temperature forecasting model would be beneficial for monitoring the changes in the microclimate conditions inside the greenhouse.

#### 3.3. Sigmoid Growth Model for Greenhouse Tomato Production

^{2}values ranging between 0.80 and 0.91. This indicated that the predicted temperature results obtained from the temperature forecasting model were highly effective in fitting the growth models and accurately predicting various important traits of tomatoes. As a common crop growth index, LAI is closely related to photosynthesis, evapotranspiration, dry matter accumulation, and the aboveground productivity of crops. The general method of measuring LAI is mainly through destructive sampling or by using canopy analyzers and spectral telemetry. These methods are time-consuming or have high instrument costs [45]. Therefore, the establishment of the LAI model is helpful to track the growth status of crops. High yield is one of the most important objects of greenhouse cultivation. With the yield prediction model, relevant information can be obtained before crop harvesting, which can be used as the base for subsequent harvesting, storage, and other planning.

#### 3.4. Limitations of Present Study and Suggestions for Future Works

^{2}of 0.962, MAPE of 3.2%, and RMSE of 1.2 °C, but the performance can be further improved by increasing the data collection period, or by grouping the data into different seasons to establish a model which is suitable for each season [34]. Although the proposed model has been evaluated using another different-sized plastic greenhouse, the model’s performance may be reduced when applied in different regions or climate conditions. Therefore, the generalizability of the proposed forecasting model needs to be tested in various conditions. Furthermore, to the best of our knowledge, the most suitable deep learning model for modeling time series data is the RNN and its derived models, so three types of RNN (i.e., LSTM, GRU, and BILSTM) were used to build a temperature forecasting model. However, for 30-min-ahead temperature forecasting, it is possible to achieve acceptable accuracy using simpler models; therefore, simpler models should be considered for building microclimate forecasting models to reduce training time and computing costs.

_{2}concentrations are also important microclimate factors related to crop production and environmental control in greenhouses [19,46,47]. Therefore, forecasting models for these microclimate factors could also be developed. Finally, this study only utilized GDD as the input to simulate tomato growth. In the future, different environmental data could be considered to improve the accuracy of growth simulations for a more comprehensive greenhouse production framework.

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 6.**R

^{2}for LSTM, GRU, and BILSTM models with the different numbers of hidden layers and hidden units: (

**a**) LSTM models, (

**b**) GRU models, and (

**c**) BILSTM models. The temperature data used for evaluation were collected from Greenhouse #2.

**Figure 7.**Comparison between the predicted and observed daily mean temperatures for Greenhouse #2. Data were collected from October 2021 to January 2022.

**Figure 8.**Scatter plot of LSTM2-predicted and observed internal daily mean temperatures for Greenhouse #2. The solid points (•) denote the predicted and observed daily mean temperatures. The solid line (—) represents the fitted regression line, and the dashed line (---) indicates the straight line with a slope of 1.

**Figure 9.**Growing degree days calculated using the observed daily mean temperature and predicted daily mean temperature for Greenhouse #2.

**Figure 10.**Scatter plots of the actual growth trait observations versus the observed growing degree days and the predicted growing degree days, respectively. The solid point (•) denotes the observed trait values and the growing degree days, and the blue curves represent the predicted value using the Logistic growth model. (

**a**) Leaf area index, (

**b**) fresh fruit weight, and (

**c**) dry matter fitted with the growing degree days calculated using the observed daily mean temperature. (

**d**) Leaf area index, (

**e**) fresh fruit weight, and (

**f**) dry matter fitted with the growing degree days calculated using the LSTM2-predicted daily mean temperature.

**Figure 11.**Scatter plots of the actual growth trait observations versus the observed growing degree days and the predicted growing degree days. The solid point (•) denotes the observed trait values and the growing degree days, and the blue curves represent the predicted value obtained using the Gompertz growth model. (

**a**) Leaf area index, (

**b**) fresh fruit weight, and (

**c**) dry matter fitted with the growing degree days calculated using the observed daily mean temperature. (

**d**) Leaf area index, (

**e**) fresh fruit weight, and (

**f**) dry matter fitted with the growing degree days calculated using the LSTM2-predicted daily mean temperature.

Model Name | Structure |
---|---|

LSTM1 | One-layer LSTM and one dense layer |

LSTM2 | Two-layer LSTM and one dense layer |

LSTM3 | Three-layer LSTM and one dense layer |

GRU1 | One-layer GRU and one dense layer |

GRU2 | Two-layer GRU and one dense layer |

GRU3 | Three-layer GRU and one dense layer |

BILSTM1 | One-layer BILSTM and one dense layer |

BILSTM2 | Two-layer BILSTM and one dense layer |

BILSTM3 | Three-layer BILSTM and one dense layer |

**Table 2.**Best performance and number of hidden units for nine temperature forecasting models. The temperature data used for evaluation were collected from Greenhouse #2.

Model | Number of Hidden Units | R^{2} | MAPE (%) | RMSE (°C) |
---|---|---|---|---|

LSTM1 | 170 | 0.961 | 3.429 | 1.210 |

LSTM2 | 190 | 0.962 | 3.216 | 1.196 |

LSTM3 | 190 | 0.958 | 3.403 | 1.254 |

GRU1 | 20 | 0.961 | 3.490 | 1.215 |

GRU2 | 60 | 0.964 | 3.279 | 1.157 |

GRU3 | 160 | 0.958 | 3.676 | 1.249 |

BILSTM1 | 180 | 0.960 | 3.383 | 1.227 |

BILSTM2 | 170 | 0.954 | 3.596 | 1.316 |

BILSTM3 | 110 | 0.958 | 3.382 | 1.259 |

**Table 3.**Parameters of the Logistic model estimated for three growth traits. The values in parentheses represent the percentage error between two sets of model parameter estimates.

Growth Trait | Temperature Data | ${\mathit{\beta}}_{1}$ | ${\mathit{\beta}}_{2}$ | ${\mathit{\beta}}_{3}$ |
---|---|---|---|---|

LAI | Observed GDDs | 1.5345 | 2.9658 | 0.0039 |

Predicted GDDs | 1.5229 | 2.9487 | 0.0038 | |

(0.76%) | (0.58%) | (2.56%) | ||

Fresh fruit weight | Observed GDDs | 1006.0000 | 13.0300 | 0.0148 |

Predicted GDDs | 1005.0000 | 12.9100 | 0.0145 | |

(0.10%) | (0.92%) | (2.03%) | ||

Dry matter | Observed GDDs | 134.7000 | 5.3270 | 0.0064 |

Predicted GDDs | 134.7000 | 5.2650 | 0.0062 | |

(0) | (1.16%) | (3.13%) |

**Table 4.**Parameters of the Gompertz model determined for three growth traits. The values in parentheses represent the percentage error between two sets of model parameter estimates.

Growth Trait | Temperature Data | ${\mathit{\beta}}_{1}$ | ${\mathit{\beta}}_{2}$ | ${\mathit{\beta}}_{3}$ |
---|---|---|---|---|

LAI | Observed GDDs | 1.9248 | 4.1142 | 0.0020 |

Predicted GDDs | 1.8968 | 4.0918 | 0.0020 | |

(1.45%) | (0.54%) | (0) | ||

Fresh fruit weight | Observed GDDs | 1039.0000 | 2814.0000 | 0.0095 |

Predicted GDDs | 1039.0000 | 2618.0000 | 0.0093 | |

(0) | (6.97%) | (2.11%) | ||

Dry matter | Observed GDDs | 164.2000 | 12.7900 | 0.0032 |

Predicted GDDs | 164.7000 | 12.3200 | 0.0031 | |

(0.30%) | (3.67%) | (3.13%) |

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## Share and Cite

**MDPI and ACS Style**

Lin, Y.-S.; Fang, S.-L.; Kang, L.; Chen, C.-C.; Yao, M.-H.; Kuo, B.-J.
Combining Recurrent Neural Network and Sigmoid Growth Models for Short-Term Temperature Forecasting and Tomato Growth Prediction in a Plastic Greenhouse. *Horticulturae* **2024**, *10*, 230.
https://doi.org/10.3390/horticulturae10030230

**AMA Style**

Lin Y-S, Fang S-L, Kang L, Chen C-C, Yao M-H, Kuo B-J.
Combining Recurrent Neural Network and Sigmoid Growth Models for Short-Term Temperature Forecasting and Tomato Growth Prediction in a Plastic Greenhouse. *Horticulturae*. 2024; 10(3):230.
https://doi.org/10.3390/horticulturae10030230

**Chicago/Turabian Style**

Lin, Yi-Shan, Shih-Lun Fang, Le Kang, Chu-Chung Chen, Min-Hwi Yao, and Bo-Jein Kuo.
2024. "Combining Recurrent Neural Network and Sigmoid Growth Models for Short-Term Temperature Forecasting and Tomato Growth Prediction in a Plastic Greenhouse" *Horticulturae* 10, no. 3: 230.
https://doi.org/10.3390/horticulturae10030230