# Modeling the Dynamic Response of Plant Growth to Root Zone Temperature in Hydroponic Chili Pepper Plant Using Neural Networks

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Plant Materials

^{−1}.

#### 2.2. Experimental Design

^{−2}s

^{−1}PPFD (photosynthetic photon flux density) as measured at the base of the growth chamber using a T&D TR-74i illuminance ultraviolet (UV) recorder (T&D Corporation, Matsumoto, Japan), day/night temperature 25/20 ± 1°C, relative humidity 55/70 ± 5%, and nutrient solution 2.3 ± 0.2 dS m

^{−1}. Meanwhile, the dissolved oxygen level of the nutrient solution was maintained with the application of an air bubble generator.

#### 2.3. Measurement of Plant Growth

#### 2.4. System Identification Method

#### 2.4.1. Data Preprocessing

^{®}Signal Processing Toolbox™ R2019a (MathWorks

^{®}Inc., Natick, MA, USA).

#### 2.4.2. Dynamic Neural Networks for System Identification

#### 2.4.3. Model Validation and Model Structure Selection

#### 2.4.4. Model Performance

## 3. Results

#### 3.1. The Response of Plant Growth to Root Zone Temperature (RZT) for Identification

#### 3.2. Determination of the Model Structure

^{2}reaching the best value when the time-delay order and number of neurons in the hidden layer were 2 and 10, respectively. Therefore, the foregoing suggests that the neural network structure with time-delay order dt = 2 and number of neurons in the hidden layer h = 10 is useful for identification.

#### 3.3. Identification Results

^{2}values of 0.49 g and 0.99, respectively, it was found that the estimated response closely correlated with the observed response.

#### 3.4. Estimation of the Characteristics of Plant Response

#### 3.5. Estimation of the Relationship between RZT and the Growth Rate of Plant Weight

## 4. Discussion and Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Root zone temperature control system and plant growth measuring system using a load cell sensor.

**Figure 2.**Block diagram of the single input–single output (SISO) system for system identification, and non-linear autoregressive with exogenous input (NARX) network structure with three layers, one input time series of the root zone temperature $T\left(k\right)$, one hidden layer (h), one output time series of the growth rate of plant weight $WR\left(k\right)$, and a time-delay ($dt)$ neural network for identifying a dynamic model.

**Figure 4.**Sample preprocessing of observation data from sensor 14: (

**a**) the original data were cleaned of unreliable records using the Hampel Identifier and reconstructed using the moving average method; (

**b**) the cleaned data were then resampled on a daily basis and smoothed using the Savitzky–Golay filter.

**Figure 5.**Typical daily change in plant weight (

**a**), the growth rate in plant weight (

**b**), and the RZT (

**c**) in hydroponic pepper cultivation.

**Figure 6.**The relationship between the time-delay order (dt), the number of neurons in the hidden layer (h), and model performances: (

**a**) root-mean-squared error (RMSE) and (

**b**) R

^{2}.

**Figure 7.**Comparison of the estimated response calculated by the developed neural network model and the observed growth rate of plant weight.

**Figure 8.**Estimated step response of the growth rate of plant weight to stepped RZT input, obtained via simulation.

**Figure 9.**The estimated static relationship between the growth rate of plant weight and RZT, obtained via simulation.

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**MDPI and ACS Style**

Aji, G.K.; Hatou, K.; Morimoto, T.
Modeling the Dynamic Response of Plant Growth to Root Zone Temperature in Hydroponic Chili Pepper Plant Using Neural Networks. *Agriculture* **2020**, *10*, 234.
https://doi.org/10.3390/agriculture10060234

**AMA Style**

Aji GK, Hatou K, Morimoto T.
Modeling the Dynamic Response of Plant Growth to Root Zone Temperature in Hydroponic Chili Pepper Plant Using Neural Networks. *Agriculture*. 2020; 10(6):234.
https://doi.org/10.3390/agriculture10060234

**Chicago/Turabian Style**

Aji, Galih Kusuma, Kenji Hatou, and Tetsuo Morimoto.
2020. "Modeling the Dynamic Response of Plant Growth to Root Zone Temperature in Hydroponic Chili Pepper Plant Using Neural Networks" *Agriculture* 10, no. 6: 234.
https://doi.org/10.3390/agriculture10060234