# UAV-Based Hyperspectral and Ensemble Machine Learning for Predicting Yield in Winter Wheat

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{2}between 0.62 and 0.73. The accuracy of the proposed ensemble learner model was higher than that of each base learner model; moreover, the R

^{2}(0.78) for the yield prediction model based on Boruta’s preferred characteristics was the highest at the grain-filling stage.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Design and Data Collection

^{2}. Thirty varieties of winter wheat were selected for this experiment, and each irrigation treatment was replicated twice in a group of 30 wheat varieties to ensure the objectivity of the experiment. For production fields, pesticide and fertilizer management was performed according to local management practices. At maturity (3 June 2020), winter wheat yields were collected using a plot combine.

#### 2.2. Acquisition and Processing of Hyperspectral Data

^{2}reference panels that differed in brightness (95% white, 40% grey, and 5% black) were placed within the study area for postprocessing and measured with the spectrometer. In this study, 12 ground control points (GCPs) were evenly distributed across the field as precise georeferenced positions, and their centimeter-level positioning accuracy was obtained through the differential global positioning systems.

#### 2.3. Acquisition of Spectral Indices

#### 2.4. Feature Selection Methods

_{xy}) may be calculated using the following equation:

#### 2.5. Decision-Level Fusion Model for Ensemble Learning

#### 2.5.1. Regression Methods

^{2}and high regression coefficients, and is widely used in co-linear problems and research with a large amount of data. The LRR algorithm was used in this study to construct yield estimation models.

#### 2.5.2. Cross-Validation and Parameter Optimization

#### 2.6. Statistical Analysis

^{2}), root mean square error (RMSE), ratio of performance to interquartile distance (RPIQ), and ratio of performance to deviation (RPD). The criteria for evaluating models are yield estimation models with higher accuracy, and an RPD of >1.5 is usually considered to indicate a reliable prediction. The formulae for the four evaluation methods are as follows:

## 3. Results

#### 3.1. Descriptive Statistics

^{−1}, and the mean yields differed for the three irrigation treatments. The yield statistics for the test plots under each irrigation treatment and all of the plots are shown in Table 3. In general, the treatments with higher irrigation levels were associated with higher yields. IT1 had the highest average yield of 7.97 t·ha

^{−1}, followed by IT2 at 6.73 t·ha

^{−1}, and IT3 at 4.94 t·ha

^{−1}. The data ranges, quantile statistics, standard deviations (SD), and coefficients of variation (CV) for the yield datasets for all of the plots and the three experimental treatments showed significant yield differences between the treatments and well separated datasets.

^{2}of each spectral index in the grain-filling stage was mostly greater than that in the flowering stage. The RVSI index performed best at both stages, with R

^{2}values of 0.48 at the flowering stage, and 0.49 at the grain-filling stage. The poorest performing index was CI in the flowering stage, with an R

^{2}of 0.08, and the index with the poorest performance in the grain-filling stage was TCARI/OSAVI, with an R

^{2}of 0.1.

#### 3.2. Feature Importance Ranking

#### 3.3. Comparison and Performance of Feature Selection Methods and Model Accuracy

^{2}of the four models constructed for the two growth stages showed that the LRR model had the lowest accuracy, with R

^{2}ranging from 0.48 to 0.54 at the flowering stage and 0.48 to 0.63 at the grain-filling stage, and after the input features were stable, the R

^{2}values were 0.54 and 0.59, respectively. The R

^{2}of the GP model ranged from 0.12 to 0.72 for the flowering stage, and 0.55–0.81 for the grain-filling stage. The RF model had the highest accuracy, with R

^{2}ranging from 0.76 to 0.94 at the flowering stage and 0.86–0.95 at the grain-filling stage, and when the input features were stabilized, the R

^{2}values were 0.93 and 0.95, respectively.

^{2}= 0.63, RMSE = 1.03 t·ha

^{−1}, RPIQ = 2.40, RPD = 1.60), and the validation set accuracy of the SVM model constructed using the Boruta method with the preferred features at the grain-filling stage was the highest (R

^{2}= 0.73, RMSE = 0.87 t·ha

^{−1}, RPIQ = 2.74, RPD = 1.90). Among the constructed DLF models, the best accuracy of the models constructed using the Boruta and PCC methods with the preferred features at the flowering stage achieved an R

^{2}of 0.66, and the highest accuracy of the models constructed using the Boruta method with the preferred features was at the grain-filling stage (R

^{2}= 0.78, RMSE = 0.79 t·ha

^{−1}, RPIQ = 2.99, RPD = 2.08). Overall, all of the methods gave an R

^{2}of 0.56 or higher, indicating the effectiveness of these models in estimating the winter wheat yield. The DLF models outperformed all of the individual models. The R

^{2}values for the DLF models constructed using the preferred features were ≥0.65 for the flowering stage, and 0.63 for the DLF models constructed using all features. At the grain-filling stage, the R

^{2}values were ≥0.77 for the DLF models constructed using the preferred features, and 0.75 for the DLF models constructed using all of the features at the grain-filling stage. The accuracy of all of the feature selection methods was improved in this study relative to the full feature model, and the RFE method improved the most at the flowering stage. The R

^{2}values of the SVM, GP, LRR, RF, and DLF models improved by 0.04, 0.03, 0.04, 0.03, and 0.02, reaching 0.63, 0.59, 0.62, 0.60, and 0.65, respectively, at the flowering stage. The Boruta method improved the most at the grain-filling stage. The R

^{2}values for the five models increased by 0.05, 0.05, 0.06, 0.03, and 0.03, reaching 0.73, 0.72, 0.66, 0.68, 0.78, respectively. In addition, the accuracy of the models was higher at the grain-filling stage compared to the flowering stage.

#### 3.4. Yield Distribution

^{−1}. Based on the observed results, the IT1 treatment had the highest yield of 5 to 9 t·ha

^{−1}, followed by the IT2 and IT3 treatments; this is consistent with the yield distribution predicted by the DLF model and demonstrates the feasibility of using a model to estimate yield.

## 4. Discussion

_{[553,682]}. The RVSI index, which consists of three bands including the red-edge band, performed well in assessing wheat rust symptoms and constructing rice physiological trait models [83], and was in the top five in the different methodological feature rankings in this study. This could be because it provided more spectral information and was more sensitive to the yield of the different feature selection methods at the different growth stages. The DWSI-4 index, originally a variant of the plant disease-water stress index constructed using simple and normalized ratios, also had good stability and performance in crop disease prediction [84]. The ND

_{[553,682]}index can be used to estimate the chlorophyll content and can minimize the effect of shading and leaf area index size [85,86]. Our study showed that these three spectral indices can be used for yield estimation. MCARI/MTVI2 and TCARI/OSAVI are integrated indices. In previous studies, their performance was better than the individual MCARI, MTVI2, and OSAVI indices, because the integrated indices had richer band information and effectively eliminate the background effects. [87,88]. The Boruta method was second to the RFE method for winter wheat at the flowering stage and performed best at the grain-filling stage, probably due to the difference in the performance between the two methods in the different environments. The Boruta method is a fully correlated feature selection method that aims to select features that are truly correlated with the dependent variable and can be used for prediction, rather than model-specific selection, and can help us to understand the characteristics of the dependent variable more comprehensively and make better and more effective feature selections [24,89]. The RFE method takes into account the correlation between the features, continuously builds models to find the best features, has good generalization ability, and is a suitable method for small sample data sets [90]. The PCC method, which performed the worst in this study, is very commonly used in sensitivity feature selection in the crop science community. It does not require any model training, but does not objectively represent correlations when the correlations between the variables are complex. There is also a risk of multicollinearity between features [91,92]. In this study, the accuracy of the model construction, based on the preferred features under feature selection, was better than that of the model under the full feature condition, which was consistent with the findings of Hsu et al. 2011 [93] and validated the effectiveness and generalizability of the feature selection method.

^{2}than the ordinary regression models but can generate a value on covariance problems [95]. The GP models use the full sample for prediction, and as the dimensionality of the data rises, the effectiveness decreases [96]. The SVM models did not perform well in the training set but had the highest accuracy in the validation. SVM is a machine learning method based on the inner product kernel function. The wrong choice of kernel hyperparameters may cause a decrease in the accuracy of the model training set estimation. However, the high accuracy of the SVM model validation set was due to its better robustness, suitability for small sample data regression, and the lack of sensitivity to kernel functions with the ability to avoid dimensional catastrophe problems. [97,98]. We also found that the accuracy of yield estimation models constructed using the four independent machine learning algorithms, SVM, GP, LRR, and RF, at the two developmental stages of winter wheat also differed greatly. Based on the model validation set, the accuracy of each model at the grain-filling stage was higher than that at the flowering stage under the different feature selections. This was due to the dry matter stored in the wheat seeds through carbon assimilation in the winter wheat during grain filling, indicating that this stage contains more spectral information that can be used to predict yield. In addition, the spectral information collected from the winter wheat was increased in order to provide a more comprehensive and accurate reflection of the yield of the winter wheat [2,99].

^{2}values of >0.65 at the flowering stage and >0.77 at the grain-filling stage. Overall, the DLF model gave more satisfactory and better results than the individual models. This was the same conclusion reached in a previous study [33] where the DLF model was able to minimize the individual model bias and improve the accuracy of the inverse model. Taken together, the above description suggests that adequacy and diversity are two important principles in the selection of base models in the decision-level fusion process [100]. This requires that the different base learners should all have a good predictive performance and be able to minimize inter-model dependencies and act as complementary information [101,102]. This prerequisite requirement is justified by the fact that the DLF methods fuse the prediction results of different independent machine learners so that the final fusion results are all influenced by each base model [103]. Furthermore, fusion of models with similar high performance will yield limited prediction results [104]. Based on the requirements of DLF and the limitation problem, this study used the SVM, GP, LRR, and RF machine learning algorithms with completely different training mechanisms to construct the yield estimation models and improved the model performance through parameter optimization, and the experimental results provided further evidence of the effectiveness of the underlying models.

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Disclaimer

## Appendix A

**Table A1.**The coefficients of determination for the 60 spectral indices under simple linear regression.

Full Form | Spectral Index or Ratio | R^{2} | |
---|---|---|---|

Flowering | Grain Filling | ||

Curvative index | CI | 0.08 | 0.33 |

Chlorophyll index red-edge | CIre | 0.21 | 0.40 |

Datt1 | 0.30 | 0.31 | |

Datt4 | 0.14 | 0.41 | |

Datt6 | 0.05 | 0.29 | |

Double difference index | DDI | 0.24 | 0.26 |

Double peak index | DPI | 0.14 | 0.30 |

Gitelson2 | $0.21$ | 0.45 | |

Green normalized difference vegetation index | GNDVI | $0.21$ | 0.40 |

Leaf chlorophyll index | LCI | $0.20$ | 0.42 |

Modified chlorophyll absorption ratio index | MCARI | $0.17$ | 0.41 |

MCARI3 | $0.22$ | 0.43 | |

Modified normalized difference | MND_{[680,800]} | $0.26$ | 0.45 |

Modified normalized difference | MND_{[705,750]} | $0.20$ | 0.43 |

Modified simple ratio | mSR | $0.22$ | 0.32 |

Modified simple ratio 2 | mSR2 | $0.23$ | 0.41 |

MERIS terrestrial chlorophyll index | MTCI | $0.13$ | 0.31 |

Modified triangular vegetation index 1 | MTVI1 | $0.43$ | 0.40 |

Modified triangular vegetation index 2 | MTVI2 | $0.36$ | 0.47 |

Normalized difference 550/531 | ND_{[531,550]} | $0.13$ | 0.28 |

Normalized difference 682/553 | ND_{[553,682]} | 0.41 | 0.48 |

Normalized difference chlorophyll | NDchl | 0.23 | 0.36 |

New double difference index | DDn | 0.45 | 0.39 |

Normalized difference red-edge | NDRE | $0.18$ | 0.36 |

Normalized difference vegetation index | NDVI_{[650,750]} | $0.32$ | 0.47 |

NDVI_{[550,750]} | $0.23$ | 0.42 | |

NDVI_{[710,750]} | $0.22$ | 0.43 | |

Normalized pigment chlorophyll index | NPCI | $0.17$ | 0.35 |

Normalized difference pigment index | NPQI | 0.13 | 0.31 |

Optimized soil-adjusted vegetation index | OSAVI | 0.31 | 0.48 |

Plant biochemical index | PBI | 0.20 | 0.37 |

Plant pigment ratio | PPR | 0.09 | 0.25 |

Physiological reflectance index | PRI | 0.40 | 0.48 |

Pigment-specific normalized difference | PSNDb1 | 0.31 | 0.46 |

PSNDc1 | 0.28 | 0.44 | |

PSNDc2 | $0.26$ | 0.43 | |

Plant senescence reflectance index | PSRI | $0.24$ | 0.31 |

Pigment-pecific simple ratio | PSSRc1 | $0.26$ | 0.39 |

PSSRc2 | $0.24$ | 0.38 | |

Photosynthetic vigor ratio | PVR | $0.40$ | 0.48 |

Plant water index | PWI | $0.15$ | 0.28 |

Renormalized difference vegetation index | RDVI | $0.43$ | 0.44 |

RDVI2 | $0.42$ | 0.44 | |

Reflectance at the inflexion point | Rre | $0.35$ | 0.14 |

Red-edge stress vegetation index | RVSI | $0.48$ | 0.49 |

Soil-adjusted vegetation index | SAVI | $0.31$ | 0.47 |

Structure intensive pigment index | SIPI | $0.44$ | 0.35 |

Spectral polygon vegetation index | SPVI | $0.44$ | 0.40 |

Simple ratio | SR_{[430,680]} | $0.17$ | 0.34 |

SR_{[440,740]} | $0.31$ | 0.46 | |

SR_{[550,672]} | $0.02$ | 0.25 | |

SR_{[550,750]} | $0.01$ | 0.05 | |

Disease-water stress index 4 | DSWI-4 | $0.43$ | 0.47 |

Simple ratio pigment index | SRPI | $0.17$ | 0.34 |

Transformed chlorophyll absorption ratio | TCARI | $0.01$ | 0.34 |

Triangular chlorophyll index | TCI | $0.08$ | 0.40 |

Triangular vegetation index | TVI | $0.43$ | 0.42 |

Water band index | WBI | $0.30$ | 0.31 |

Combined MCARI/MTVI2 | MCARI/MTVI2 | $0.13$ | 0.39 |

Combined TCARI/OSAVI | TCARI/OSAVI | $0.03$ | 0.10 |

**Table A2.**Ranking of all 60 features for the three feature selection methods at the flowering and grain-filling stages of winter wheat.

Ranking | Flowering Features | Grain-Filling Features | ||||
---|---|---|---|---|---|---|

RFE | Boruta | PCC | RFE | Boruta | PCC | |

1 | RVSI | Gitelson2 | RVSI | DSWI-4 | Gitelson2 | RVSI |

2 | RDVI | RVSI | DDn | ND_{[553,682]} | RVSI | ND_{[553,682]} |

3 | WBI | NDchl | SPVI | MTVI2 | NDchl | PVR |

4 | NDVI_{[650,750]} | ND_{[553,682]} | SIPI | RVSI | ND_{[553,682]} | OSAVI |

5 | PRI | OSAVI | MTVI1 | Gitelson2 | OSAVI | PRI |

6 | PWI | CIre | RDVI | PVR | CIre | NDVI_{[650,750]} |

7 | DSWI-4 | NDVI_{[710,750]} | DSWI-4 | CI | NDVI_{[710,750]} | MTVI2 |

8 | SR_{[440,740]} | DPI | TVI | OSAVI | DPI | DSWI-4 |

9 | SAVI | MSR2 | RDVI2 | NDchl | MSR2 | SAVI |

10 | TCI | MTCI | ND_{[553,682]} | Datt1 | MTCI | SR_{[440,740]} |

11 | MTVI1 | DSWI-4 | PRI | SR_{[450,550]} | DSWI-4 | PSNDb1 |

12 | OSAVI | MND_{[705,750]} | PVR | PPR | MND_{[705,750]} | MND_{[680,800]} |

13 | Datt4 | MTVI2 | MTVI2 | CIre | MTVI2 | Gitelson2 |

14 | MSR | PVR | Rre | PRI | PVR | RDVI2 |

15 | DDn | NDVI_{[650,750]} | NDVI_{[650,750]} | NPQI | NDVI_{[650,750]} | RDVI |

16 | RDVI2 | SAVI | SR_{[440,740]} | SR_{[450,690]} | SAVI | PSNDc1 |

17 | MCARI | PRI | PSNDb1 | Rre | PRI | MND_{[705,750]} |

18 | ND_{[553,682]} | Datt6 | OSAVI | MSR2 | Datt6 | PSNDc2 |

19 | PSNDb1 | SR_{[440,740]} | SAVI | TCARI/OSAVI | SR_{[440,740]} | NDVI_{[710,750]} |

20 | SIPI | DDI | WBI | DDI | DDI | MCARI3 |

21 | Rre | PSNDb1 | PSNDc1 | MCARI | PSNDb1 | NDVI_{[550,750]} |

22 | TVI | LCI | PSNDc2 | PSRI | LCI | LCI |

23 | Gitelson2 | MND_{[680,800]} | MND_{[680,800]} | LCI | MND_{[680,800]} | TVI |

24 | Datt1 | NDRE | PSSRc1 | Datt4 | NDRE | MSR2 |

25 | NDchl | PSSRc1 | DDI | MCARI/MTVI2 | PSSRc1 | Datt4 |

26 | TCARI | PSNDc1 | PSSRc2 | MTCI | PSNDc1 | MCARI |

27 | MCARI3 | NDVI_{[550,750]} | PSRI | PSNDc2 | NDVI_{[550,750]} | CIre |

28 | MCARI/MTVI2 | NPQI | NDVI_{[550,750]} | WBI | NPQI | TCI |

29 | PSNDc2 | MCARI3 | MSR2 | DPI | MCARI3 | GNDVI |

30 | Datt6 | CI | NDVI_{[710,750]} | PWI | CI | MTVI1 |

31 | SR_{[450,550]} | ND_{[531,550]} | MSR | MTVI1 | ND_{[531,550]} | SPVI |

32 | ND_{[531,550]} | MCARI | GNDVI | PSNDb1 | MCARI | DDn |

33 | PSNDc1 | MCARI/MTVI2 | CIre | MSR | MCARI/MTVI2 | MCARI/MTVI2 |

34 | CI | TCARI/OSAVI | PBI | MND_{[705,750]} | TCARI/OSAVI | PSSRc1 |

35 | SPVI | PBI | MND_{[705,750]} | TCI | PBI | PSSRc2 |

36 | NDRE | PSNDc2 | LCI | MCARI3 | PSNDc2 | PBI |

37 | TCARI/OSAVI | PSSRc2 | NDRE | NDVI_{[650,750]} | PSSRc2 | NDRE |

38 | PVR | PSRI | NPCI | PSNDc1 | PSRI | NPCI |

39 | MTVI2 | Datt1 | SR_{[430,680]} | SR_{[440,740]} | Datt1 | SIPI |

40 | PPR | SRPI | SRPI | Datt6 | SRPI | TCARI |

41 | DDI | RDVI2 | MCARI | TCARI | RDVI2 | SR_{[430,680]} |

42 | NPQI | GNDVI | PWI | SR_{[430,680]} | GNDVI | SRPI |

43 | MND_{[680,800]} | RDVI | Datt4 | NDVI_{[710,750]} | RDVI | CI |

44 | PSSRc1 | NPCI | ND_{[531,550]} | NDVI_{[550,750]} | NPCI | MSR |

45 | PSRI | TVI | MTCI | ND_{[531,550]} | TVI | WBI |

46 | PSSRc2 | SR_{[450,550]} | MCARI/MTVI2 | PSSRc2 | SR_{[450,550]} | MTCI |

47 | MTCI | SR_{[430,680]} | TCI | SIPI | SR_{[430,680]} | PSRI |

48 | SR_{[450,690]} | PPR | Datt1 | NDRE | PPR | DPI |

49 | MND_{[705,750]} | DDn | Datt6 | SAVI | DDn | Datt6 |

50 | GNDVI | MSR | DPI | NPCI | MSR | ND_{[531,550]} |

51 | CIre | TCI | NPQI | PSSRc1 | TCI | PWI |

52 | LCI | SR_{[450,690]} | NDchl | RDVI2 | SR_{[450,690]} | DDI |

53 | NPCI | PWI | TCARI/OSAVI | SRPI | PWI | PPR |

54 | NDVI_{[550,750]} | Datt4 | PPR | SPVI | Datt4 | SR_{[450,550]} |

55 | SR_{[430,680]} | SIPI | SR_{[450,550]} | DDn | SIPI | NDchl |

56 | DPI | MTVI1 | MCARI3 | GNDVI | MTVI1 | Rre |

57 | SRPI | SPVI | SR_{[450,690]} | TVI | SPVI | TCARI/OSAVI |

58 | PBI | WBI | Gitelson2 | PBI | WBI | SR_{[450,690]} |

59 | MSR2 | TCARI | TCARI | MND_{[680,800]} | TCARI | NPQI |

60 | NDVI_{[710,750]} | Rre | CI | RDVI | Rre | Datt1 |

**Figure A1.**Scatter plots of observed versus predicted yields for the five models constructed from the three different feature selection methods. In the figure labels (

**a1**–

**f5**), the letters (

**a**,

**b**,

**c**) indicate the RFE, Boruta, and PCC feature selection methods used at the flowering stage, respectively; (

**d**,

**e**,

**f**) indicate the RFE, Boruta, and PCC feature selection methods used at the grain-filling stage, respectively; the numbers

**1**–

**5**indicate the SVM, GP, LRR, RF, and DLF models.

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**Figure 1.**Meteorological conditions during the wheat growth period from November to May: (

**a**) total monthly rainfall, (

**b**) average monthly temperature, (

**c**) average monthly humidity, and (

**d**) average monthly sunshine hours.

**Figure 2.**Distribution of test sites and test plots. IT1: high irrigation; IT2: moderate irrigation; IT3: low irrigation.

**Figure 3.**Workflow of a DLF (decision-level fusion) model for grain yield prediction; the model included SVM (support vector machine), GP (Gaussian process), LRR (linear ridge regression), and RF (random forest). The “e” is the model prediction.

**Figure 5.**The relationships between model training accuracy and number of features. (

**a1**,

**a2**), SVM model at the flowering and grain-filling stages, respectively; (

**b1**,

**b2**), GP model at flowering and grain-filling stages, respectively; (

**c1**,

**c2**) LRR model at flowering and grain-filling stages, respectively; (

**d1**,

**d2**) RF model at flowering and grain-filling stages, respectively.

**Figure 6.**Yield distribution chart for the three irrigation treatments. The color scale from blue to red indicates the increasing grain yield from 4 to 10 t ha

^{−1}.

**Table 1.**Summary of irrigation volumes for the three treatments at six stages of growth for winter wheat.

Growth Itage | High Irrigation (mm) | Moderate Irrigation (mm) | Low Irrigation (mm) |
---|---|---|---|

Tillering | 35 | 35 | 35 |

Overwintering | 35 | 35 | 35 |

Greening | 35 | 25 | 20 |

Jointing | 50 | 35 | 20 |

Heading | 50 | 35 | 20 |

Grain filling | 35 | 25 | 15 |

Total | 240 | 190 | 145 |

Full Form | Spectral Index or Ratio | Formula | Application | Reference |
---|---|---|---|---|

Curvative index | CI | $\mathrm{R}675\times \mathrm{R}690/\mathrm{R}{683}^{2}$. | Chlorophyll | [40] |

Chlorophyll index red-edge | CIre | $\mathrm{R}750/\mathrm{R}710-1$ | Vegetation, chlorophyll | [41] |

Datt1 | $\left(\mathrm{R}850-\mathrm{R}710\right)/\left(\mathrm{R}850-\mathrm{R}680\right)$ | Vegetation, chlorophyll | [42] | |

Datt4 | $\mathrm{R}672/\left(\mathrm{R}550\times \mathrm{R}708\right)$ | |||

Datt6 | $\mathrm{R}860/\left(\mathrm{R}550\times \mathrm{R}708\right)$ | |||

Double difference index | DDI | $\left(\mathrm{R}749-\mathrm{R}720\right)-\left(\mathrm{R}701-\mathrm{R}672\right)$ | Vegetation | [43] |

Double peak index | DPI | $\left(\mathrm{R}688+\mathrm{R}710\right)/\mathrm{R}{697}^{2}$ | Vegetation, chlorophyll | [44] |

Gitelson2 | $\left(\mathrm{R}750-\mathrm{R}800\right)/\left(\mathrm{R}695-\mathrm{R}740\right)-1$ | Chlorophyll | ||

Green normalized difference vegetation index | GNDVI | $\left(\mathrm{R}750-\mathrm{R}550\right)/\left(\mathrm{R}750+\mathrm{R}550\right)$ | Vegetation, chlorophyll | [45] |

Leaf chlorophyll index | LCI | $\left(\left|\mathrm{R}850|-|\mathrm{R}710\right|\right)/\left(\left|\mathrm{R}850|+|\mathrm{R}680\right|\right)$ | Vegetation, chlorophyll | [46] |

Modified chlorophyll absorption ratio index | MCARI | $\left[\left(\mathrm{R}700-\mathrm{R}670\right)-0.2\left(\mathrm{R}700-\mathrm{R}550\right)\right]\left(\mathrm{R}700/\mathrm{R}670\right)$ | Vegetation, chlorophyll | [47] |

MCARI3 | $[\left(\mathrm{R}750-\mathrm{R}710\right)-0.2(\mathrm{R}750-$$\mathrm{R}550\left)\right](\mathrm{R}750/\mathrm{R}715)$ | |||

Modified normalized difference | MND_{[680,800]} | $\left(\mathrm{R}800-\mathrm{R}680\right)/\left(\mathrm{R}800+\mathrm{R}680-2\times \mathrm{R}445\right)$ | Pigments | [48] |

Modified normalized difference | MND_{[705,750]} | $\left(\mathrm{R}750-\mathrm{R}705\right)/\left(\mathrm{R}750+\mathrm{R}705-2\times \mathrm{R}445\right)$ | ||

Modified simple ratio | mSR | $\left(\mathrm{R}800-\mathrm{R}445\right)/\left(\mathrm{R}680-\mathrm{R}445\right)$ | Vegetation | [43] |

Modified simple ratio 2 | mSR2 | $\left(\mathrm{R}750/\mathrm{R}705-1\right)/\left(\sqrt{\mathrm{R}750/\mathrm{R}705+1}\right)$ | [44] | |

MERIS terrestrial chlorophyll index | MTCI | $\left(\mathrm{R}754-\mathrm{R}709\right)/\left(\mathrm{R}709-\mathrm{R}681\right)$ | Vegetation, chlorophyll | [49] |

Modified triangular vegetation index 1 | MTVI1 | $1.2\left[1.2\left(\mathrm{R}800-\mathrm{R}550\right)-2.5\left(\mathrm{R}670-\mathrm{R}550\right)\right]$ | Vegetation | [50] |

Modified triangular vegetation index 2 | MTVI2 | $\left(1.5\frac{1.2\left(\mathrm{R}800-\mathrm{R}550\right)-2.5\left(\mathrm{R}670-\mathrm{R}550\right)}{\sqrt{\left(2\times \mathrm{R}800+{1}^{2}\right)-(6\times \mathrm{R}800-5\sqrt{\mathrm{R}670)}-0.5}}\right)$ | ||

Normalized difference 550/531 | ND_{[531,550]} | $(\mathrm{R}550-\mathrm{R}531)/(\mathrm{R}550+\mathrm{R}531)$ | Vegetation, chlorophyll | [44] |

Normalized difference 682/553 | ND_{[553,682]} | (R682 − R553)/(R682 + R553) | ||

Normalized difference chlorophyll | NDchl | (R925 − R710)/(R925 + R710) | [51] | |

New double difference index | DDn | $2\times \left(\mathrm{R}710-\mathrm{R}760-\mathrm{R}760\right)$ | Chlorophyll | |

Normalized difference red-edge | NDRE | $\left(\mathrm{R}790-\mathrm{R}720\right)/\left(\mathrm{R}790+\mathrm{R}720\right)$ | Vegetation | [52] |

Normalized difference vegetation index | NDVI_{[650,750]} | $\left(\mathrm{R}750-\mathrm{R}650\right)/\left(\mathrm{R}750+\mathrm{R}650\right)$ | Vegetation, vitality | [53] |

NDVI_{[550,750]} | $\left(\mathrm{R}750-\mathrm{R}550\right)/\left(\mathrm{R}750+\mathrm{R}550\right)$ | |||

NDVI_{[710,750]} | $\left(\mathrm{R}750-\mathrm{R}710\right)/\left(\mathrm{R}750+\mathrm{R}710\right)$ | |||

Normalized pigment chlorophyll index | NPCI | $(\mathrm{R}680-\mathrm{R}430)/(\mathrm{R}680+\mathrm{R}430)$ | Vegetation, chlorophyll | [54] |

Normalized difference pigment index | NPQI | (R415 − R435)/(R415 + R435) | Vegetation, chlorophyll | [55] |

Optimized soil-adjusted vegetation index | OSAVI | $\left(1+0.16\right)\left(\mathrm{R}800-\mathrm{R}670\right)\left(\mathrm{R}800+\mathrm{R}670+0.16\right)$ | Vegetation | [56] |

Plant biochemical index | PBI | $\mathrm{R}810/\mathrm{R}560$ | Vegetation | [57] |

Plant pigment ratio | PPR | $\left(\mathrm{R}550-\mathrm{R}450\right)/\left(\mathrm{R}550+\mathrm{R}450\right)$ | Vegetation | [58] |

Physiological reflectance index | PRI | $\left(\mathrm{R}550-\mathrm{R}530\right)/\left(\mathrm{R}550+\mathrm{R}530\right)$ | Vegetation | [59] |

Pigment-specific normalized difference | PSNDb1 | $\left(\mathrm{R}800-\mathrm{R}650\right)/\left(\mathrm{R}800+\mathrm{R}650\right)$ | Vegetation, chlorophyll | [60] |

PSNDc1 | $\left(\mathrm{R}800-\mathrm{R}500\right)/\left(\mathrm{R}800+\mathrm{R}500\right)$ | |||

PSNDc2 | $\left(\mathrm{R}800-\mathrm{R}470\right)/\left(\mathrm{R}800+\mathrm{R}470\right)$ | |||

Plant senescence reflectance index | PSRI | $\left(\mathrm{R}678-\mathrm{R}500\right)/\mathrm{R}750$ | Vegetation | [61] |

Pigment-specific simple ratio | PSSRc1 | $\mathrm{R}800/\mathrm{R}500$ | Vegetation, chlorophyll | [62] |

PSSRc2 | $\mathrm{R}800/\mathrm{R}470$ | |||

Photosynthetic vigor ratio | PVR | $\left(\mathrm{R}550-\mathrm{R}650\right)/\left(\mathrm{R}550+\mathrm{R}650\right)$ | Vegetation | [53] |

Plant water index | PWI | $\mathrm{R}970/\mathrm{R}900$ | Vegetation, water stress | [63] |

Renormalized difference vegetation index | RDVI | $\left(\mathrm{R}800-\mathrm{R}670\right)/(\sqrt{\mathrm{R}800+\mathrm{R}670)}$ | Vegetation | [64] |

RDVI2 | $\left(\mathrm{R}833-\mathrm{R}658\right)/\left(\sqrt{\mathrm{R}833+\mathrm{R}658}\right)$ | |||

Reflectance at the inflexion point | Rre | $\left(\left|\mathrm{R}670|+|\mathrm{R}780\right|\right)/2$ | Vegetation | [51] |

Red-edge stress vegetation index | RVSI | $\left(\left(\mathrm{R}718+\mathrm{R}748\right)/2\right)-\mathrm{R}733$. | Vegetation | [65] |

Soil-adjusted vegetation index | SAVI | $1.16\left(\left(\mathrm{R}800-\mathrm{R}670\right)/\left(\mathrm{R}800+\mathrm{R}670+0.16\right)\right)$ | Vegetation | [66] |

Structure intensive pigment index | SIPI | $\left(\mathrm{R}800-\mathrm{R}445\right)/\left(\mathrm{R}800-\mathrm{R}680\right)$. | Pigments | [46] |

Spectral polygon vegetation index | SPVI | $0.4\left(3.7\left(\mathrm{R}800-\mathrm{R}670\right)-1.2\left|\mathrm{R}530-\mathrm{R}670\right|\right)$ | Vegetation | [44] |

Simple ratio | SR_{[430,680]} | $\mathrm{R}430/\mathrm{R}680$ | Vegetation | [67] |

SR_{[440,740]} | $\mathrm{R}440/\mathrm{R}740$ | [44] | ||

SR_{[550,672]} | $\mathrm{R}550/\mathrm{R}672$ | |||

SR_{[550,750]} | $\mathrm{R}550/\mathrm{R}750$ | |||

Disease-water stress index 4 | DSWI-4 | $\mathrm{R}550/\mathrm{R}680$ | Vegetation, water stress | [68] |

Simple ratio pigment index | SRPI | $\mathrm{R}430/\mathrm{R}680$ | Vegetation, chlorophyll | [69] |

Transformed chlorophyll absorption ratio | TCARI | $3\left(\left(\mathrm{R}700-\mathrm{R}670\right)-0.2\left(\mathrm{R}700-\mathrm{R}550\right)\left(\mathrm{R}700/\mathrm{R}670\right)\right)$ | Vegetation, chlorophyll | [45] |

Triangular chlorophyll index | TCI | $1.2\left(\mathrm{R}700-\mathrm{R}550\right)-1.5\left(\mathrm{R}670-\mathrm{R}550\right)\times \sqrt{\mathrm{R}700/\mathrm{R}670}$ | Vegetation, chlorophyll | [45] |

Triangular vegetation index | TVI | $0.5\left(120\left(\mathrm{R}750-\mathrm{R}550\right)-200\left(\mathrm{R}670-\mathrm{R}550\right)\right)$ | Vegetation | [69] |

Water band index | WBI | $\mathrm{R}970/\mathrm{R}902$ | Vegetation, water stress | [70] |

Combined MCARI/MTVI2 | MCARI/MTVI2 | $\mathrm{MCARI}/\mathrm{MTVI}2$ | Vegetation, chlorophyll | [45] |

Combined TCARI/OSAVI | TCARI/OSAVI | $\mathrm{TCARI}/\mathrm{OSAVI}$ | Vegetation, chlorophyll | [56] |

**Table 3.**Descriptive statistics for the data sets from all test plots and the test plots from the three different irrigation treatments (t·ha

^{−1}).

Category | N | Mean | SD | Min | Q25 | Q50 | Q75 | Max | CV |
---|---|---|---|---|---|---|---|---|---|

All datasets | 180 | 6.55 | 1.59 | 3.13 | 5.27 | 6.65 | 7.71 | 9.71 | 24.33% |

IT1 dataset | 60 | 7.97 | 1.01 | 5.58 | 7.43 | 7.97 | 8.65 | 9.71 | 12.68% |

IT2 dataset | 60 | 6.73 | 1.02 | 4.28 | 6.08 | 6.75 | 7.55 | 8.75 | 15.16% |

IT3 dataset | 60 | 4.94 | 0.96 | 3.13 | 4.31 | 4.89 | 5.55 | 7.54 | 19.50% |

**Table 4.**Test accuracies of the support vector machine (SVM), Gaussian process (GP), linear ridge regression (LRR), random forest (RF), and decision layer fusion (DLF) models in predicting winter wheat yield.

Feature | Model | Flowering | Grain Filling | ||||||
---|---|---|---|---|---|---|---|---|---|

R^{2} | RMSE(t/ha) | RPIQ | RPD | R^{2} | RMSE(t/ha) | RPIQ | RPD | ||

Selected features (RFE) | SVM | 0.63 | 1.03 | 2.40 | 1.60 | 0.71 | 0.90 | 2.64 | 1.83 |

GP | 0.59 | 1.09 | 2.25 | 1.51 | 0.69 | 0.94 | 2.52 | 1.75 | |

LRR | 0.62 | 1.03 | 2.38 | 1.59 | 0.64 | 1.00 | 2.36 | 1.64 | |

RF | 0.60 | 1.05 | 2.35 | 1.57 | 0.67 | 0.94 | 2.51 | 1.74 | |

DLF | 0.65 | 0.99 | 2.47 | 1.65 | 0.77 | 0.81 | 2.94 | 2.04 | |

Selected features (Boruta) | SVM | 0.62 | 1.03 | 2.31 | 1.60 | 0.73 | 0.87 | 2.74 | 1.90 |

GP | 0.57 | 1.11 | 2.12 | 1.48 | 0.72 | 0.89 | 2.65 | 1.84 | |

LRR | 0.62 | 1.03 | 2.29 | 1.59 | 0.66 | 0.98 | 2.42 | 1.68 | |

RF | 0.58 | 1.07 | 2.21 | 1.54 | 0.68 | 0.94 | 2.53 | 1.76 | |

DLF | 0.66 | 0.98 | 2.40 | 1.67 | 0.78 | 0.79 | 2.99 | 2.08 | |

Selected features (PCC) | SVM | 0.62 | 1.03 | 2.29 | 1.61 | 0.67 | 0.94 | 2.52 | 1.74 |

GP | 0.58 | 1.11 | 2.12 | 1.49 | 0.68 | 0.96 | 2.49 | 1.71 | |

LRR | 0.62 | 1.03 | 2.28 | 1.60 | 0.63 | 1.03 | 2.32 | 1.60 | |

RF | 0.58 | 1.08 | 2.19 | 1.54 | 0.66 | 0.96 | 2.47 | 1.70 | |

DLF | 0.66 | 0.99 | 2.39 | 1.68 | 0.77 | 0.82 | 2.91 | 2.01 | |

Full features | SVM | 0.59 | 1.05 | 2.25 | 1.56 | 0.68 | 0.95 | 2.51 | 1.73 |

GP | 0.56 | 1.10 | 2.14 | 1.48 | 0.67 | 0.97 | 2.45 | 1.69 | |

LRR | 0.58 | 1.07 | 2.22 | 1.53 | 0.60 | 1.05 | 2.26 | 1.56 | |

RF | 0.57 | 1.08 | 2.20 | 1.52 | 0.65 | 0.97 | 2.44 | 1.68 | |

DLF | 0.63 | 1.00 | 2.36 | 1.63 | 0.75 | 0.84 | 2.84 | 1.96 |

Feature | t | p-Value |
---|---|---|

IT1 VS IT2 | 7.097 | 0.000 |

IT1 VS IT3 | 16.661 | 0.000 |

IT2 VS IT3 | 9.348 | 0.000 |

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## Share and Cite

**MDPI and ACS Style**

Li, Z.; Chen, Z.; Cheng, Q.; Duan, F.; Sui, R.; Huang, X.; Xu, H.
UAV-Based Hyperspectral and Ensemble Machine Learning for Predicting Yield in Winter Wheat. *Agronomy* **2022**, *12*, 202.
https://doi.org/10.3390/agronomy12010202

**AMA Style**

Li Z, Chen Z, Cheng Q, Duan F, Sui R, Huang X, Xu H.
UAV-Based Hyperspectral and Ensemble Machine Learning for Predicting Yield in Winter Wheat. *Agronomy*. 2022; 12(1):202.
https://doi.org/10.3390/agronomy12010202

**Chicago/Turabian Style**

Li, Zongpeng, Zhen Chen, Qian Cheng, Fuyi Duan, Ruixiu Sui, Xiuqiao Huang, and Honggang Xu.
2022. "UAV-Based Hyperspectral and Ensemble Machine Learning for Predicting Yield in Winter Wheat" *Agronomy* 12, no. 1: 202.
https://doi.org/10.3390/agronomy12010202