# Artificial Neural Network Based Apple Yield Prediction Using Morphological Characters

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Study Area and Data Description

#### 2.2. Development of Artificial Neural Network Model

_{t}is the output of the neural network model (yield per plant), n is number of hidden nodes, m is the number of input nodes, f is the net input of the activation function, ${\beta}_{ij}$ {i = 1, 2, …, m; j = 0, 1, …, n} are the weights from input to hidden nodes, ${\alpha}_{j}\{j=0,1,\dots ,n\}$ are the vectors of the weights from the hidden to output nodes, and ${\alpha}_{0}$ and ${\beta}_{0j}$ are the weights of arcs leading from bias terms. Activation function is a differentiable function that is used for smoothing the result of the cross product of the covariates or neurons and the weights. In the artificial neural networks, the activation function of a node defines the output of that node given an input or set of inputs.

#### 2.3. Development of Multiple Linear Regression Model

#### 2.4. Model Performance Measures

^{2}) [34]. The functional formula of these measures were used as follows

## 3. Results

#### 3.1. Selection of Input Variables

#### 3.2. ANN Model Development

^{2}, were considered for the evaluation of the model’s performance. The performance of different activation functions was also tested. It has been observed that logistic activation outperformed among the others due to its ability to capture nonlinear variation in the dataset. Ahmadi et al. [39], Hagan et al. [40], and Mansouri et al. [17] also reported the ability of nonlinear functions to cover nonlinear patterns in a dataset. The different number of hidden layers with a different number of nodes were fitted to obtain the best topology for the neural network model (Table 3). The results indicated that the ANN model with two hidden layers (5-5), i.e., 7-5-5-1 architecture provide best result. This ANN model (7-5-5-1) had the lowest RMSE, MAD, and MAPE values with the highest model accuracy in both the training and testing stages. The schematic diagram of the ANN structure (7-5-5-1) is presented in Figure 1.

#### 3.3. MLR Model Development

^{2}value (70.69%) in Figure 5a. The scatter plot indicated that the MLR model did not cover all of the data points and most of the data points deviated from the regression line. Further boxplots (Figure 5b) of the measured and predicted apple yield in the testing stage of MLR indicate the inefficiency of the MLR model to predict apple yield.

## 4. Discussion

#### 4.1. Comparison of Fitted Models

^{2}. The results are presented in Table 4. It has been observed that the selected ANN model outperformed with an 18.60% increase in R

^{2}and a reduction of 67.31%, 41.33%, and 21.80% in RMSE, MAD, and MAPE compared with the MLR model.

#### 4.2. Sensitivity Analysis

^{2}and highest RMSE (79.47), MAD (79.44), and MAPE (23.07). Therefore, FD can be considered as an influential factor to predict apple yield. In addition to these characteristics, FDI and FI also had a significant effect on predicting apple yield.

## 5. Conclusions

^{2}. The logistic activation function was found to outperform all other activation functions. This ANN model (7-5-5-1) had the lowest RMSE, MAD, and MAPE values with the highest model accuracy in both the training and testing stages. Furthermore, the results show a close association between the predicted and actual yield of apple. As MLR models are predominantly used in crop yield prediction, the MLR model was also used for the study and it was observed that the selected ANN model outperformed the MLR model with an 18.60% increase in R

^{2}and a reduction of 67.31%, 41.33%, and 21.80% in RMSE, MAD, and MAPE. All of the computations have been carried out by writing suitable codes in R software available with the authors.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- FAO. FAOSTAT. Food and Agriculture Organization of the United Nations. 2020. Available online: https://www.fao.org/faostat/en/#home (accessed on 20 May 2022).
- Lezzoni, A.; Pritts, M.P. Application of principal component analysis to horticultural research. Hortic. Sci.
**1991**, 26, 334–338. [Google Scholar] [CrossRef][Green Version] - Guimarães, B.V.C.; Donato, S.L.R.; Aspiazú, I.; Azevedo, A.M. Yield prediction of ‘Prata Anã’ and ‘BRS Platina’ banana plants by artificial neural. Pesq. Agropec. Trop. Goiânia
**2021**, 51, 1–11. [Google Scholar] [CrossRef] - Guimarães, B.V.C.; Donato, S.L.R.; Azevedo, A.M.; Aspiazú, I.; Silva Junior, A.A. Prediction of “Gigante” cactus pear yield by morphological characters and artificial neural networks. Rev. Bras. De Eng. Agrícola E Ambient.
**2018**, 22, 315–319. [Google Scholar] [CrossRef] - Khazaei, J.F.; Shahbazi; Massah, J. Evaluation and modeling of physical and physiological damage to wheat seeds under successive impact loadings: Mathematical and neural networks modeling. Crop Sci.
**2008**, 48, 1532–1544. [Google Scholar] [CrossRef] - Gutiérrez, P.A.; López-Granados, F.; Peña-Barragán, J.M.; Jurado-Expósito, M.; Hervás-Martínez, C. Logistic regression product-unit neural networks for mapping Ridolfia segetum infestations in sunflower crop using multitemporal remote sensed data. Comput. Electron. Agric.
**2008**, 64, 293–306. [Google Scholar] [CrossRef] - Huang, Y.; Lan, Y.; Thomson, S.J.; Fang, A.; Hoffmann, W.C.; Lacey, R.E. Development of soft computing and applications in agricultural and biological engineering. Comput. Electron. Agric.
**2010**, 71, 107–127. [Google Scholar] [CrossRef][Green Version] - Kravchenko, A.N.; Bullock, D.G. Correlation of corn and soybean grain yield with topography and soil properties. Agron. J.
**2000**, 92, 75–83. [Google Scholar] [CrossRef] - Park, S.J.; Hwang, C.S.; Vlek, P.L.G. Comparison of adaptive techniques to predict crop yield response under varying soil and land management conditions. Agric. Syst.
**2005**, 85, 59–81. [Google Scholar] [CrossRef] - Kitchen, N.R.; Drummond, S.T.; Lund, E.D.; Sudduth, K.A.; Buchleiter, G.W. Soil electrical conductivity and topography related to yield for three contrasting soil-crop systems. Agron. J.
**2003**, 95, 483–495. [Google Scholar] [CrossRef] - Miao, Y.; Mulla, D.J.; Robert, P.C. Identifying important factors influencing corn yield and grain quality variability using artificial neural networks. Precis. Agric.
**2006**, 7, 117–135. [Google Scholar] [CrossRef] - Schultz, A.; Wieland, R.; Lutze, G. Neural networks in agroecological modeling-stylish application or helpful tool? Comput. Electron. Agric.
**2000**, 29, 73–97. [Google Scholar] [CrossRef] - Fortin, J.G.; Anctil, F.; Parent, L.É.; Bolinder, M.A. A neural network experiment on the site-specific simulation of potato tuber growth in Eastern Canada. Comput. Electron. Agric.
**2010**, 73, 126–132. [Google Scholar] [CrossRef] - Jiang, P.; Thelen, K.D. Effect of soil and topographic properties on crop yield in a north-central corn-soybean cropping system. Agron. J.
**2004**, 96, 252–258. [Google Scholar] [CrossRef] - Das, P. Study on Machine Learning Techniques Based Hybrid Model for Forecasting in Agriculture. Ph.D. Thesis, PG-school IARI, New Delhi, India, 2019. [Google Scholar]
- Abdipour, M.; Younessi-Hmazekhanlu, M.; Ramazani, M.Y.H.; Omidi, A.H. Artificial neural networks and multiple linear regression as potential methods for modeling seed yield of safflower (Carthamus tinctorius L.). Ind. Crops Prod.
**2019**, 27, 185–194. [Google Scholar] [CrossRef] - Mansouri, A.; Fadavi, A.; Mortazavian, S.M.M. An artificial intelligence approach for modeling volume and fresh weight of callus–A case study of cumin (Cuminum cyminum L.). J. Theor. Biol.
**2016**, 397, 199–205. [Google Scholar] [CrossRef] - Hydrology. ASCE task committee on application of artificial neural networks in artificial neural networks in hydrology, I: Preliminary concepts. Hydrol. Eng.
**2020**, 5, 115–123. [Google Scholar] [CrossRef] - Treder, W. Relationship between yield, crop density coefficient and average fruit weight of ‘gala’ apple. J. Fruit Ornam. Plant Res.
**2008**, 16, 53–63. [Google Scholar] - Gholipoor, M.; Rohani, A.; Torani, S. Optimization of traits to increasing barley grain yield using an artificial neural network. Int. J. Plant Prod.
**2013**, 7, 1–17. [Google Scholar] - Tiwari, M.K.; Chatterjee, C. Uncertainty assessment and ensemble flood forecasting using bootstrap based artificial neural networks (BANNs). J. Hydrol.
**2010**, 382, 20–33. [Google Scholar] [CrossRef] - Tripathy, M. Power transformer differential protection using neural network principal component analysis and radial basis function neural network. Simul. Model. Pract. Theory
**2010**, 18, 600–611. [Google Scholar] [CrossRef] - Abdipour, M.; Ramazani, S.H.R.; Younessi-Hmazekhanlu, M.; Niazian, M. Modeling oil content of sesame (Sesamum indicum L.) using artificial neural network and multiple linear regression approaches. J. Am. Oil Chem. Soc.
**2018**, 95, 283–297. [Google Scholar] [CrossRef] - May, R.; Dandy, G.; Maier, H. Review of input variable selection methods for artificial neural networks. Artificial Neural Networks—Methodological Advances and Biomedical Applications. InTech
**2011**, 10, 16004. [Google Scholar] [CrossRef][Green Version] - Elhami, B.; Khanali, M.; Akram, A. Combined application of Artificial Neural Networks and life cycle assessment in lentil farming in Iran. Inform. Process. Agric.
**2017**, 4, 18–32. [Google Scholar] [CrossRef][Green Version] - Samarasinghe, S. Neural Networks for Applied Sciences and Engineering: From Fundamentals to Complex Pattern Recognition; CRC Press: Boca Raton, FL, USA, 2016. [Google Scholar]
- Hoskins, J.C.; Himmelblau, D.M. Artificial neural network models of knowledge representation in chemical engineering. Comput. Chem. Eng.
**1988**, 12, 881–890. [Google Scholar] [CrossRef] - Sheela, K.G.; Deepa, S.N. Review on methods to fix number of hidden neurons in neural networks. Math. Probl. Eng.
**2013**, 2013, 425740. [Google Scholar] [CrossRef][Green Version] - Tufail, M.; Ormsbee, L.; Teegavarapu, R. Artificial intelligence-based inductive models for prediction and classification of fecal coliform in surface waters. J. Environ. Eng.
**2008**, 134, 789–799. [Google Scholar] [CrossRef] - Haykin, S. Neural Networks: A Comprehensive Foundation; Prentice Hall: Ontario, CA, USA, 1999. [Google Scholar]
- Buyukozturk, S. Sosyal Bilimler Icin very Analizi el Kitabi; Pegem Yayincihk: Ankara, Turkey, 2002. [Google Scholar]
- Tabachnick, B.G.; Fidell, S.L. Using Multivariate Statistics; Harper Collins College Publishers: New York, NY, USA, 1996. [Google Scholar]
- Unver, O.; Gamgam, H. Uygulamah Istatistik Yontemleri; Siyasal Kitabevi: Ankara, Turkey, 1999. [Google Scholar]
- Das, P.; Paul, A.K.; Paul, R.K. Non-linear mixed effect models for estimation of growth parameters in Goats. J. Indian Soc. Agric. Stat.
**2016**, 70, 205–210. [Google Scholar] - Emamgholizadeh, S.; Parsaeian, M.; Baradaran, M. Seed yield prediction of sesame using artificial neural network. Eur. J. Agron.
**2015**, 68, 89–96. [Google Scholar] [CrossRef] - Forshey, C.G.; Elfving, D.C. Fruit numbers, fruit size and yield relationship in ‘McIntosh’ apple. J. Am. Soc. Hortic.
**1977**, 24, 399–402. [Google Scholar] [CrossRef] - Treder, W.; Mike, A. Relationship between yield, crop density and average fruit weight in ‘lobo’ apple trees under various planting systems and irrigation treatments. Horttech
**2001**, 11, 248–254. [Google Scholar] [CrossRef][Green Version] - Westwood, M.N.; Roberts, A.N. The relationship between trunk cross-sectional area and weight of apple trees. J. Am. Soc. Hortic.
**1970**, 95, 28–30. [Google Scholar] [CrossRef] - Ahmadi, S.H.; Sepaskhah, A.R.; Andersen, M.N.; Plauborg, F.; Jensen, C.R.; Hansen, S. Modeling root length density of field grown potatoes under different irrigation strategies and soil textures using artificial neural networks. Field Crops Res.
**2014**, 162, 99–107. [Google Scholar] [CrossRef] - Hagan, M.T.; Demuth, H.B.; Beale, M. Neural Network Design; PWS Publishing, Co.: Boston, MA, USA, 1997. [Google Scholar]
- Balas, C.F.; Koc, M.L.; Tur, R. Artificial neural network based on principal component analysis, fuzzy systems and fuzzy neural networks for preliminary design of rubble mound breakwaters. Appl. Ocean Res.
**2010**, 32, 425–433. [Google Scholar] [CrossRef] - Singh, T.N.; Kanchan, R.; Verma, A.K.; Singh, S. An intelligent approach for prediction of triaxial properties using unconfined uniaxial strength. Miner. Eng.
**2003**, 5, 12–16. [Google Scholar]

**Figure 4.**(

**a**) Scatter plot of the measured and predicted yield of apple in the testing stage of ANN; (

**b**) boxplot of measured and predicted apple yield in the testing stage of ANN. Green dots denote the observations and root mean square error (RMSE), mean absolute deviation (MAD), mean absolute percentage error (MAPE), and coefficient of determination (R

^{2}) are the performance measures.

**Figure 5.**(

**a**) Measured and predicted apple yield in testing stage of MLR; (

**b**) boxplot of the measured and predicted apple yield in the testing stage of MLR. Blue dots denote the observations.

**Figure 7.**Sensitivity analysis of input variables on apple yield in ANN model. A: The best ANN model without CD; B: The best ANN model without FI; C: The best ANN model without FDI; D: The best ANN model without FD; E: The best ANN model without plant girth; F: The best ANN model without canopy spread; G: The best ANN model without plant height; H: The best ANN model (with plant height, canopy spread, plant girth, FD, FDI, FI, and CD as the input).

Characters | Range | Mean | Std. Deviation |
---|---|---|---|

Plant height (m) | 3.05–11.89 | 7.22 | 2.21 |

Canopy spread (m) | 1.32–9.48 | 5.57 | 2.03 |

Plant girth (cm) | 0.15–0.91 | 0.61 | 0.18 |

Flower density | 1.00–10.82 | 3.54 | 1.99 |

Flower density index | 0.10–1.08 | 0.35 | 0.18 |

Flowering intensity | 0.35–0.50 | 0.41 | 0.03 |

Fruit set | 0.15–0.57 | 0.31 | 0.08 |

Crop density | 0.30–4.40 | 1.09 | 0.66 |

Length diameter ratio | 6.84–10.28 | 8.22 | 0.68 |

Characters | PH | CS | PG | FD | FDI | FI | FS | CD | LDR | EV | CV |
---|---|---|---|---|---|---|---|---|---|---|---|

PC1 | −0.4223 | −0.4222 | −0.4178 | 0.3909 | 0.2924 | 0.1073 | 0.1183 | 0.4389 | 0.1108 | 3.07 | 34.15 |

PC2 | 0.3905 | 0.3051 | 0.3672 | 0.3810 | 0.4114 | 0.4333 | −0.0969 | 0.3284 | −0.011 | 2.01 | 56.53 |

**Table 3.**The performance of ANN models with different hidden layers in the training and testing set.

Hidden Layer | Best Topology | RMSE | MAD | MAPE | R^{2} | Accuracy (%) | Error Rate | |
---|---|---|---|---|---|---|---|---|

Training | 1 | 7-3-1 | 36.3360 | 25.7337 | 0.2306 | 0.8121 | 90.36 | 0.2422 |

2 | 7-5-5-1 | 24.8300 | 18.2607 | 0.1523 | 0.9430 | 98.72 | 0.0736 | |

3 | 7-3-3-3-1 | 31.0590 | 22.3937 | 0.2053 | 0.8629 | 93.59 | 0.1769 | |

4 | 7-3-3-3-3-1 | 27.4964 | 21.2744 | 0.2136 | 0.8924 | 92.23 | 0.1386 | |

5 | 7-5-5-1-5-5-1 | 24.9840 | 19.8195 | 0.1556 | 0.9116 | 93.10 | 0.1140 | |

6 | 7-3-3-3-3-5-5-1 | 34.8300 | 17.81 | 0.2426 | 0.9113 | 95.10 | 0.11438 | |

Testing | 1 | 7-3-1 | 63.2026 | 43.9649 | 0.3582 | 0.5622 | 93.01 | 0.2422 |

2 | 7-5-5-1 | 36.6078 | 28.1045 | 0.2151 | 0.8685 | 95.36 | 0.0736 | |

3 | 7-3-3-3-1 | 52.2906 | 38.2418 | 0.2974 | 0.7129 | 91.32 | 0.1769 | |

4 | 7-3-3-3-3-1 | 43.7711 | 28.2788 | 0.1900 | 0.7935 | 93.49 | 0.1386 | |

5 | 7-5-5-1-5-5-1 | 40.0703 | 28.2700 | 0.2111 | 0.8239 | 92.65 | 0.1140 | |

6 | 7-3-3-3-3-5-5-1 | 43.2684 | 32.92371 | 0.2360 | 0.8073 | 89.33 | 0.1144 |

Model | RMSE | MAD | MAPE | R^{2} |
---|---|---|---|---|

ANN | 36.6078 | 28.1045 | 0.2151 | 0.8685 |

MLR | 61.2501 | 39.7203 | 0.2620 | 0.7069 |

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**MDPI and ACS Style**

Bharti; Das, P.; Banerjee, R.; Ahmad, T.; Devi, S.; Verma, G. Artificial Neural Network Based Apple Yield Prediction Using Morphological Characters. *Horticulturae* **2023**, *9*, 436.
https://doi.org/10.3390/horticulturae9040436

**AMA Style**

Bharti, Das P, Banerjee R, Ahmad T, Devi S, Verma G. Artificial Neural Network Based Apple Yield Prediction Using Morphological Characters. *Horticulturae*. 2023; 9(4):436.
https://doi.org/10.3390/horticulturae9040436

**Chicago/Turabian Style**

Bharti, Pankaj Das, Rahul Banerjee, Tauqueer Ahmad, Sarita Devi, and Geeta Verma. 2023. "Artificial Neural Network Based Apple Yield Prediction Using Morphological Characters" *Horticulturae* 9, no. 4: 436.
https://doi.org/10.3390/horticulturae9040436