# Monitoring Indicators for Comprehensive Growth of Summer Maize Based on UAV Remote Sensing

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## Abstract

**:**

_{CV}and CGMI

_{CR}for summer maize were constructed by the coefficient of variation method and the CRITIC weighting method. After that, the CGMI

_{CV}and CGMI

_{CR}prediction models were established by the partial least-squares (PLSR) and sparrow search optimization kernel extremum learning machine (SSA-KELM) using eight typical vegetation indices selected. Finally, a comparative analysis was performed using ground-truthing data, and the results show: (1) For CGMI

_{CV}, the R

^{2}and RMSE of the model built by SSA-KELM are 0.865 and 0.040, respectively. Compared to the model built by PLSR, R

^{2}increased by 4.5%, while RMSE decreased by 0.3%. For CGMI

_{CR}, the R

^{2}and RMSE of the model built by SSA-KELM are 0.885 and 0.056, respectively. Compared to the other model, R

^{2}increased by 4.6%, and RMSE decreased by 2.8%. (2) Compared to the models by single indicator, among the models constructed based on PLSR, the CGMI

_{CR}model had the highest R

^{2}. In the models constructed based on SSA-KELM, the R

^{2}of models by the CGMI

_{CR}and CGMI

_{CV}were larger than that of the models by SPAD (R

^{2}= 0.837), while smaller than that of the models by LAI (R

^{2}= 0.906) and models by VH (R

^{2}= 0.902). In summary, the comprehensive growth monitoring indicators prediction model established in this paper is effective and can provide technical support for maize growth monitoring.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Overview of the Experimental Area

^{−2}, the row spacing is 0.6 m, and the plant spacing is 0.2 m. Its management methods, such as irrigation, fertilization, pest, and weed control, were the same as those of local conventional farmland.

#### 2.2. UAV Data Acquisition and Preprocessing

#### 2.3. Field Data Acquisition

- (1)
- Measurement of Relative Chlorophyll Content

- (2)
- Determination of Leaf Area Index

^{−2}), $n$ is the total number of leaves (pieces) of the $j$th plant, and $m$ is the number of plants measured.

- (3)
- Maize Height Measurement

#### 2.4. Comprehensive Growth Indicator Construction

_{CR}.

- (1)
- Data Normalization

- (2)
- Calculation of Indicator Volatility

- (3)
- Calculation of Conflicting Indicators

- (4)
- Calculation of the Information Content of the Indicator

- (5)
- Calculation of Objective Weights for Indicators

- (6)
- Comprehensive Growth Monitoring Indicator CGMI
_{CR}

_{CR}was constructed. The expression of CGMI

_{CR}is as follows:

#### 2.5. Selection of Vegetation Indices

#### 2.6. Model Construction

#### 2.7. Experimental Comparison Methods

#### 2.7.1. Coefficient of Variation Method

_{CV}was established.

- (1)
- The data normalization process is the same as the CRITIC weight method;
- (2)
- Calculation of the coefficient of variation.

- (3)
- Calculation of Indicator Weights

- (4)
- Comprehensive Growth Monitoring Indicator CGMI
_{CV}

_{CV}was constructed, and the expression of CGMI

_{CV}is as follows:

#### 2.7.2. Partial Least-Squares Regression (PLSR) Method

#### 2.8. Model Evaluation Methodology

^{2}), root mean square error (RMSE), and mean relative error (MRE) were used to judge the prediction effect of the model, and the specific formulas are shown below. R

^{2}indicates the degree of fit between the predicted value and the measured value, and RMSE reflects the degree of deviation between the predicted value and the measured value. The more R

^{2}tends to be close to 1, the smaller RMSE is, indicating that the model predicts better. MRE is used to describe the error between the model prediction result and the actual value to evaluate the model stability. The smaller the MRE is, the more stable the model is.

## 3. Results and Discussion

#### 3.1. Correlation Analysis of Different Vegetation Indices with Combined Growth Indicators and Single Growth Indicators

_{CV}, CGMI

_{CR}, and the individual growth indicators that make up the composite growth monitoring indicators with the eight vegetation indices in turn. The correlations are shown in Table 2.

_{CV}and CGMI

_{CR}and the vegetation index was generally lower than that of the VH indicators due to the simultaneous consideration of the three single growth indicators and the assignment of weights to each of them, with the lower correlation between the SPAD indicators and the vegetation index. For the composite growth monitoring indicator CGMI

_{CV}, the vegetation indices GOSAVI, VIopt, NDVI, GNDVI, CCCI, and CGMI

_{CV}were significantly correlated at the 0.01 level, whereas GRVI, GDVI, RVI, and CGMI

_{CV}were significantly correlated at the 0.05 level, and the correlation coefficients r were all greater than 0.5. For the comprehensive growth monitoring indicator CGMI

_{CR}, the correlation coefficients between the eight selected vegetation indices and CGMI

_{CR}were all greater than 0.6, which is a strong correlation, and all of them were significantly correlated at the 0.01 level.

#### 3.2. Construction and Testing of the CGMI Model for Comprehensive Growth Monitoring Indicators

#### 3.2.1. Construction and Testing of the CGMI_{CV} Monitoring Model

_{CV}and CGMI

_{CR}. The effect of the prediction model of CGMI

_{CV}built based on PLSR and SSA-KELM is shown in Table 3, and the linear fitting comparison between its predicted and measured values is shown in Figure 4.

^{2}of the training set was 0.820, the RMSE was 0.043, the validation set decreased by 0.004, the RMSE increased by 0.005 from the prediction set R

^{2}, and the prediction effect decreased slightly. For the SSA-KELM model, the training set has an R

^{2}of 0.865 and an RMSE of 0.040, and the validation set has an increase of 0.006 and an increase of 0.005 in the RMSE over the prediction set, with a small increase in accuracy but an increased in prediction error. Overall, the SSA-KELM model increased the R

^{2}of the training set by 0.045 and decreased the RMSE by 0.003 compared to the PLSR model, while the validation set increased the R

^{2}by 0.055 and decreased the RMSE by 0.003. The prediction of both the training set and validation set of the SSA-KELM model is better than that of the PLSR model.

#### 3.2.2. Construction and Testing of the CGMI_{CR} Monitoring Model

_{CR}prediction model based on PLSR and SSA-KELM are shown in Table 4, and the linear fit comparison of its predicted and measured values is shown in Figure 5.

^{2}over the training set, with essentially the same prediction effect. For the SSA-KELM model, the R

^{2}of the training set was 0.885, the RMSE was 0.056, and the validation set had an increase of 0.004 in R

^{2}and an increase of 0.002 in RMSE compared to the training set, with a decreased in the fitting effect but a smaller overall difference. In summary, the model built by SSA-KELM increased R

^{2}by 0.046 and decreased RMSE by 0.028 for the training set and increased R

^{2}by 0.049 and decreased RMSE by 0.026 for the validation set compared to the PLSR model. The prediction effect of both training and validation sets of the SSA-KELM model is better than the PLSR model.

_{CV}and CGMI

_{CR}, the prediction effect of the CGMI

_{CR}model is better than that of the CGMI

_{CV}model because of the CRITIC weighting method, compared with the coefficient of variation method, not only takes into account the fluctuation of each evaluation index, but also involves the conflict between different indexes, and it can more realistically reflect the crop’s growth situation.

#### 3.3. Stability Analysis of the Comprehensive Growth Monitoring Indicator Model

_{CV}and CGMI

_{CR}regression models, constructed using PLSR and SSA-KELM methodologies, respectively, underwent rigorous testing in 100 random runs. The average mean relative error (MRE) across the 100 prediction results were calculated. The results are shown in Figure 6.

_{CV}models constructed by different algorithms varies less, and the fluctuation range of the average relative error of the PLSR-CGMI

_{CV}model is from 8.2% to 24.0%, with a median of 17.4% and a mean of 17.3%. The fluctuation range of the average relative error of the SSA-KELM-CGMI

_{CV}model is from 6.5% to 22.1%, with a median of 12.7% and a mean of 12.9%. The overall average relative error is smaller than PLSR-CGMI

_{CV}, which indicates that the SSA-KELM-CGMI

_{CV}model is more stable.

_{CR}model’s average relative error fluctuates from 6.8% to 20.0%, with a median of 12.8% and a mean of 13.0%. The SSA-KELM-CGMI

_{CR}model’s average relative error fluctuates from 2.7% to 11.9%, which is reduced compared to that of PLSR-CGMI

_{CR}, with a median of 7.2% and a mean of 7.1%, which likewise indicates the greater stability of modeling using SSA-KELM.

#### 3.4. Discussions

#### 3.4.1. Comparative Analysis of the Predictive Effects of Different Growth Indicators

^{2}of the SSA-KELM model is greater than that of the PLSR model. Among all the models constructed using a single growth indicator, the SSA-KELM-LAI model had the best prediction effect, with an R

^{2}of 0.906, which is 8.5% higher than that of PLSR-LAI. The R

^{2}of the SSA-KELM-VH model is 0.902, which is 6.8% higher than that predicted by PLSR-VH. The accuracy of the SSA-KELM-SPAD model is low, and the R

^{2}is 0837, which is 10.5% higher than that predicted by PLSR-VH. Among all the models constructed using the comprehensive growth monitoring indicators, the CGMI

_{CR}monitoring model was better than the CGMI

_{CV}monitoring model, with SSA-KELM-CGMI

_{CR}achieving the best monitoring effect (R

^{2}= 0.885). The reason is that when constructing the comprehensive growth monitoring indicators, the CRITIC weighting method, compared with the coefficient of variation method, not only takes into account the influence of the volatility of the evaluation indicators on the weights but also involves the conflicting nature between different indicators. Therefore, the weights of LAI and VH are appropriately reduced, and the weight of SPAD is increased, which improved the prediction effect of the constructed CGMI

_{CR}model compared with that of CGMI

_{CV}. However, the sensitivity of SPAD to multispectral information is relatively weak in this stage, and increasing the weights of SPAD also weakened the monitoring ability of CGMI

_{CR}.

#### 3.4.2. Stability Analysis of Predictive Models for Different Growth Indicators

_{CV}and CGMI

_{CR}models is smaller than that of the SPAD model, mainly because the error fluctuation range of the LAI indicator is large, which leads to the larger error fluctuation range of CGMI

_{CV}and CGMI

_{CR}. The stability of the CGMI

_{CV}and CGMI

_{CR}models was greater than that of the LAI and VH models because a single growth indicator has limitations and can only simply reflect a certain physiological information of the crop, which is essentially a ‘point’ of data and cannot uniformly reflect the overall characteristics of the crop. Zhai LT et al. [41] inverted the nitrogen content, chlorophyll content, and water content of winter wheat based on the PLSR model, the R

^{2}of single index inversion was 0.72, 0.31, 0.61, respectively, and the R

^{2}of comprehensive index inversion was 0.75. The results showed that the inversion effect of the comprehensive index model was better than that of a single index, and the results of this study were similar to the present study. In summary, compared with the single growth indicator, the comprehensive growth monitoring indicator has a better prediction effect. Compared with the comprehensive growth monitoring indicator CGMI

_{CV}and CGMI

_{CR}, the error fluctuation range, median error and mean value of the error of the CGMI

_{CR}model are smaller than those of the CGMI

_{CV}model, which indicates that the comprehensive growth monitoring indicator CGMI

_{CR}has better stability.

## 4. Conclusions

- (1)
- The comprehensive growth monitoring indicators CGMI
_{CV}and CGMI_{CR}constructed using the coefficient of variation method and the CRITIC weighting method were both positively correlated with the vegetation index. The correlation coefficients between CGMI_{CR}and the vegetation index were both greater than the correlation coefficients between CGMI_{CV}and CGMI_{CR}. - (2)
- A comprehensive growth monitoring indicator model based on SSA-KELM was established. For CGMI
_{CV}, the model R^{2}was 0.871, and the RMSE was 0.045; for CGMI_{CR}, the model R^{2}was 0.889, and the RMSE was 0.058, which shows that the model built by SSA-KELM-CGMI_{CR}is more stable and more effective. - (3)
- Based on the CGMI
_{CV}and CGMI_{CR}monitoring models built by PLSR, the monitoring effect of the PLSR-CGMI_{CV}model is lower than that of the PLSR-CGMI_{CR}model, and both of them are lower than that of the model constructed by SSA-KELM. In summary, the model constructed based on SSA-KELM has a better monitoring effect.

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Geographical location of China’s first tractor company limited intelligent agriculture demonstration farm.

**Figure 2.**ROI regional distribution map [20].

**Figure 4.**Relationship between predicted and measured values of the CGMI

_{CV}models based on PLSR and SSA-KELM: (

**a**) PLSR-CGMI

_{CV}predictive model; (

**b**) SSA-KELM-CGMI

_{CV}predictive model.

**Figure 5.**Relationship between predicted and measured values of the CGMI

_{CR}models based on PLSR and SSA-KELM: (

**a**) PLSR-CGMI

_{CR}predictive model; (

**b**) SSA-KELM-CGMI

_{CR}predictive model.

**Figure 6.**Predictive effects of CGMI models constructed based on PLSR and SSA-KELM: (

**a**) prediction effects of CGMI

_{CV}models; (

**b**) prediction effects of CGMI

_{CR}models.

**Table 1.**Vegetation indices and its calculation formula [20].

Vegetation Indices | Equation | References |
---|---|---|

GOSAVI | $\left(1+0.16\right)\times \left(\mathrm{N}\mathrm{I}\mathrm{R}-\mathrm{R}\mathrm{E}\right)/\left(\mathrm{N}\mathrm{I}\mathrm{R}+\mathrm{R}\mathrm{E}+0.16\right)$ | Marin D B et al. [28] |

GDVI | $\mathrm{N}\mathrm{I}\mathrm{R}-\mathrm{G}$ | Zhou X F et al. [29] |

RVI | $\mathrm{N}\mathrm{I}\mathrm{R}/\mathrm{R}$ | Jiang J et al. [30] |

GNDVI | $\left(\mathrm{N}\mathrm{I}\mathrm{R}-\mathrm{G}\right)/\left(\mathrm{N}\mathrm{I}\mathrm{R}+\mathrm{G}\right)$ | Jiang J et al. [30] |

GRVI | $\mathrm{N}\mathrm{I}\mathrm{R}/\mathrm{G}$ | Motohka T et al. [31] |

VIopt | $\left(1+0.45\right)\times \left(2\mathrm{N}\mathrm{I}\mathrm{R}+1\right)/\left(\mathrm{R}+0.45\right)$ | Motohka T et al. [31] |

NDVI | $\left(\mathrm{N}\mathrm{I}\mathrm{R}-\mathrm{R}\right)/\left(\mathrm{N}\mathrm{I}\mathrm{R}+\mathrm{R}\right)$ | Deng L et al. [32,33] |

CCCI | $\left(\mathrm{N}\mathrm{I}\mathrm{R}-\mathrm{R}\mathrm{E}\right)/\left(\mathrm{N}\mathrm{I}\mathrm{R}+\mathrm{R}\mathrm{E}\right)$ | Shu M Y et al. [34] |

Vegetation Indices | LAI | SPAD | VH | CGMI_{CV} | CGMI_{CR} |
---|---|---|---|---|---|

GRVI | 0.630 ** | 0.540 * | 0.701 ** | 0.552 * | 0.656 ** |

GOSAVI | 0.652 ** | 0.567 ** | 0.704 ** | 0.575 ** | 0.674 ** |

VIopt | 0.648 ** | 0.564 ** | 0.707 ** | 0.573 ** | 0.673 ** |

NDVI | 0.776 ** | 0.590 * | 0.735 ** | 0.605 ** | 0.704 ** |

GDVI | 0.608 ** | 0.536 * | 0.654 ** | 0.528 * | 0.626 ** |

RVI | 0.589 ** | 0.517 * | 0.663 ** | 0.514 * | 0.616 ** |

GNDVI | 0.687 ** | 0.589 ** | 0.798 ** | 0.612 ** | 0.714 ** |

CCCI | 0.630 ** | 0.601 ** | 0.743 ** | 0.616 ** | 0.710 ** |

Algorithm Model | Training | Validate | ||
---|---|---|---|---|

R^{2} | RMSE | R^{2} | RMSE | |

PLSR | 0.820 | 0.043 | 0.816 | 0.048 |

SSA-KELM | 0.865 | 0.040 | 0.871 | 0.045 |

Algorithm Model | Training | Validate | ||
---|---|---|---|---|

R^{2} | RMSE | R^{2} | RMSE | |

PLSR | 0.839 | 0.084 | 0.840 | 0.084 |

SSA-KELM | 0.885 | 0.056 | 0.889 | 0.058 |

Growth Indicator | PLSR | SSA-KELM |
---|---|---|

LAI | 0.821 | 0.906 |

SPAD | 0.723 | 0.837 |

VH | 0.834 | 0.902 |

CGMI_{CV} | 0.820 | 0.865 |

CGMI_{CR} | 0.839 | 0.885 |

**Table 6.**Stability comparison of all growth indicator prediction models constructed based on SSA-KELM.

Growth Indicator | Error Fluctuation Range | Median Error | Mean Value of Error |
---|---|---|---|

CGMI_{CV} | 6.5~22.1% | 12.7% | 12.9% |

CGMI_{CR} | 2.7~11.9% | 7.2% | 7.1% |

LAI | 9.7~42.5% | 22% | 23.4% |

SPAD | 1.3~5.9% | 3.9% | 3.8% |

VH | 4.8~22.2% | 14.8% | 14.6% |

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## Share and Cite

**MDPI and ACS Style**

Ma, H.; Li, X.; Ji, J.; Cui, H.; Shi, Y.; Li, N.; Yang, C.
Monitoring Indicators for Comprehensive Growth of Summer Maize Based on UAV Remote Sensing. *Agronomy* **2023**, *13*, 2888.
https://doi.org/10.3390/agronomy13122888

**AMA Style**

Ma H, Li X, Ji J, Cui H, Shi Y, Li N, Yang C.
Monitoring Indicators for Comprehensive Growth of Summer Maize Based on UAV Remote Sensing. *Agronomy*. 2023; 13(12):2888.
https://doi.org/10.3390/agronomy13122888

**Chicago/Turabian Style**

Ma, Hao, Xue Li, Jiangtao Ji, Hongwei Cui, Yi Shi, Nana Li, and Ce Yang.
2023. "Monitoring Indicators for Comprehensive Growth of Summer Maize Based on UAV Remote Sensing" *Agronomy* 13, no. 12: 2888.
https://doi.org/10.3390/agronomy13122888