Critical Drop Height Prediction of Loquat Fruit Based on Some Engineering Properties with Machine Learning Approach

Abstract

The lowest height at which a product can fall without suffering severe harm is known as the “critical drop height” for agricultural products. It is a crucial factor to take into account for crops like loquats that are prone to bruising or damage upon impact. By establishing the minimum altitude at which the product can be dropped without experiencing substantial harm, suitable processing procedures may be established from harvest to the end consumer, thereby preserving product quality and worth. The critical drop height can be ascertained through swift, affordable, non-destructive, and non-traditional methods, rather than time-consuming and expensive laboratory trials. In the study, we aimed to estimate the critical drop height for loquat fruit using machine learning methods. Three different machine learning methods with different operating principles were applied. R², MAE, RMSE, and MAPE metrics were used to assess the models. There were no obvious differences in both the comparisons within the models, namely the training and test results and the mutual comparisons of the models. However, with a slight difference, the SVMs model performed better in the training data set, and the ETs model performed better in the test data set. Plots were drawn to visualize model performances, and the results obtained from the plots and metrics support each other.

1. Introduction

The loquat (Eriobotrya japonica Lindl.), native to China, is a fruit tree belonging to the Rosaceae family, and is also known as Japanese plum. China leads the world in loquat production, with about 89% of the crop produced worldwide, followed by India, Turkey, Italy, Spain, and Japan, according to the Food and Agriculture Organization [1,2]. Because of their distinct flavor and high nutritional content, loquats are regarded as extremely valuable fruits. They are a great source of dietary fiber, potassium, magnesium, and vitamins A, B, and C. The fruit also contains a lot of antioxidants, such as phenolic compounds and carotenoids, which have been related to a number of health advantages, including a lower chance of developing chronic illnesses like diabetes, cardiovascular disease, and cancer [3,4].

Considering that loquat is so important for human health, the systems used in the process from harvest to the consumer, including the harvest process should be designed to prevent fruit losses and increase work efficiency. The mechanical properties of loquat fruit are crucial in the design and manufacture of equipment, tools, and machinery to be used in the process from harvest to consumer (grading, sorting, cleaning, packing, handling, transport, and storage), in the optimization of existing equipment, in the assessment of fruit quality, and in the determination of susceptibility to mechanical damage that may occur during this process, leading to a profound reduction in commercial value [5,6]. For the optimization of the systems used in loquat processing, the mechanical properties such as rupture force, failure stress, deformation, Poisson’s ratio, deformation energy, toughness, hardness, and modulus of elasticity are important factors to consider. The critical drop height, also known as the minimum deformation height, is an important factor that is highly influential on the variation of these properties [7,8,9].

Many studies have been conducted by researchers to determine various properties (chemical, pomological, physiological, color, and breeding) of the loquat. In these studies, only the firmness value has been measured for the mechanical properties of the fruit. As can be seen from the literature review, there is almost no comprehensive study on the determination of mechanical properties of loquat fruit. Hadjipieri et al. (2020) [10] investigated the effect of genotype and harvest time on the qualitative characteristics of the fruit. Ding et al. (2006) [11] conducted a study on the physiological response of loquat fruit to different storage conditions. Cai et al. (2006) [12] determined the effect of short-term low temperatures on damage and fruit quality on loquat fruit. Wang et al. (2016) [13] conducted research on the effect of four different packaging materials of different thicknesses on post-harvest fruit quality. Ding et al. (1998) [14] reported the effect of storage temperatures on the physiology and quality of loquat fruit. Abbasi et al. (2013) [15] examined the effects of films of different packaging materials and thicknesses on loquat fruit quality. Pareek et al. (2014) [16] studied the determination of post-harvest physiology and technology of loquat fruit. Lloha et al. (2023) [17] determined the physical and biochemical profile of loquat (Eriobotrya japonica Lindl.) harvested in Albania. Ullah et al. (2018) [18] analyzed the effects of different drying methods on some physical and chemical properties of Loquat fruits. Shahi-Gharahlar et al. (2009) [19] developed the most suitable model for predicting loquat fruit mass and volume according to their geometric characteristics. Gentile et al. (2016) [20] conducted studies on the determination of pomological, sensory, and nutritional properties of nine types of loquat fruits grown in the Mediterranean region. Ding et al. (2002) [21] determined the effect of modified atmosphere packaging on the chemical properties of loquat fruit. Barchi et al. (2002) [22] studied the vibrations transmitted to the fruits during transportation of loquat (Eriobotrya japonica Lindl.). Ercişli et al. (2012) [23] investigated some physicochemical properties, bioactive content, and antioxidant capacities of seven loquat varieties. In addition to these studies, Xu et al. (2021) [24] examined the relationships between drop height, mass, impact material, and damage factors through pressure-sensitive film tests. They found that each factor was positively correlated with the degree of damage to the loquat and that the critical fall height for loquat was 0.4 m. Cañete et al. (2015) [25] determined the susceptibility to mechanical damage and fruit quality of ‘Algerian’ loquat fruits collected at four different ripening stages to recommend the best ripening stage for harvest. Various studies and trials have also been conducted on the effect of fruit drop height on the mechanical properties of fruit in many agricultural crops such as avocado [26], loquat [24], olive [27], kiwifruit [28], tomato [29], sweet cherry [30], apple [31], litchi [32], pomegranate [33], blueberry [34], and pear [35].

When we look at all the studies, whether it is physical properties, pomological properties, chemical properties, or mechanical properties, all of these properties are determined as a result of a long, tiring, costly process that requires a lot of labor and involves a destructive series of analyses that are prone to human errors. In the modern world, where labor, energy, economy, and time are all crucial factors, non-experimental methods can be utilized in place of experiments to accurately and error-freely determine these essential parameters without human errors. Additionally, this method helps in quickly transforming massive data sets made up of various types of information gathered from numerous sources into meaningful information.

Machine learning (ML) is one of the most widely used non-traditional methods for identifying the stated properties of plant products. Estimation with ML methods has become the most extensively used method recently, and has proven to be incredibly efficient, fast, and accurate in problem-solving in the past few years [36,37]. ML, a subfield of artificial intelligence, is defined as a technique that uses data from the past and inferences to make predictions. Numerous research articles have shown that ML approaches can effectively solve regression problems. The models exhibit low RMSE and MAPE values, as well as high R² values when evaluated using the same criteria as regression models. In recent years, there has been a noticeable increase in the amount of research conducted on this topic, and the application of ML techniques in many areas of agricultural production, quality, chemical content, physical and color properties, maturity estimation, and proper product selection and classification has become more widespread [38,39].

Many studies have reported using ML techniques to determine various properties (chemical, pomological, physiological, color, classification, and defect) of loquat fruit. Huang et al. (2021) [40] used multiple linear regression (MLR) and artificial neural networks (ANN) to evaluate the ability of models to predict SSC, TAC, and SSC/TAC in loquat fruits based on mineral elements in the fruits. Munera et al. (2021) [41] used hyperspectral imaging in combination with two ML algorithms, RF and XGBoost, to discriminate pixels of common defects such as purple spots, russeting, bruising, and flesh browning of loquat cv. ‘Algerie’. Han et al. (2022) [42] conducted a study on the determination of storage time of slightly rotten loquat fruits using hyperspectral imaging and ML methods. Meng et al. (2024) [43] studied the rapid detection of MC and freshness of loquat fruits using fiber optic spectroscopy technology and ML methods. Li et al. (2022) [44] studied the classification of shell defects in loquat fruit with an ML algorithm and hyperspectral imaging technology. Feng et al. (2023) [45] studied the non-destructive quality assessment and maturity classification of loquats based on hyperspectral imaging and machine learning algorithms. However, to our knowledge, no study has been conducted in the literature on the prediction of mechanical properties of loquat using ML methods.

This work will significantly fill the gap in the literature by conducting a comprehensive survey on the mechanical properties of the loquat and using machine learning to predict these properties. This study aims to comprehensively determine the mechanical properties of the loquat fruit and identify the critical drop height based on these properties using ML algorithms. For this purpose, three different ML methods with different operating principles were selected. These methods are Artificial Neural Networks, Support Vector Machines, and Extra Trees.

2. Materials and Methods

An Algar cultivar of loquat fruits, sourced from the local market and cultivated in Alicante, Valencia region, Spain, was used for the research (Figure 1). In the harvest season of 2024, a total of 240 fruits with a mean moisture content of 89.63% were carefully selected at the commercial ripeness stage and transported to the laboratory using refrigerated polyethylene bags to minimize dehydration during transport. All experiments were carried out in the laboratory of the Department of Rural and Agri-Food Engineering at the Universitat Politècnica de València.

The diameters (mm), lengths (mm), and sphericity (%) of loquat fruit samples, as well as the final diameters and final lengths of the fruit after compression used in the Poisson’s ratio calculation, were determined using the GreenVision image system and X-AnyLabelling image processing software based on Python 3.12.4 (Figure 2).

The weight of the loquat fruit (W, g) was determined using a digital balance with a sensitivity of 0.01 g (Mettler Toledo AL104 electronic balance, Im Langacher 44, Horticulturae 2023, 9, 1286, 5 of 118606, Greifensee, Switzerland). The liquid displacement method was used to calculate the volume of the fruit (V, cm³) [5,46].

Using a universal stress–strain machine (Ibertest, Madrid, Spain, model IBTH 2730, www.ibertest.es, accessed on 11 July 2024) running at a steady speed of 30 mm min⁻¹, the rupture force and deformation values of the loquat fruit were determined. The experiments were carried out from three different points on the fruit using an 8 mm probe, with three repetitions for each fruit (Figure 3).

The energy absorbed by the fruit (E, mJ) during loading until rupture was determined by calculating the area under the load deformation curve using the following formula [5,47]. Furthermore, stress values (σ, N mm⁻²) were computed using the following formula [48,49]:

$$\mathrm{E}=1/2(F \mathsf{\Delta }D),$$

(1)

$$\mathsf{\sigma }=\raisebox{1ex}{$\mathrm{F}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{A}$}\right.,$$

(2)

where ΔD is the deformation at rupture in millimeters (mm), F is the rupture force in newtons (N), and A is the section’s area in square millimeters (mm²).

The elastic modulus E (N mm⁻²) of the test loquat fruit was determined using the Boussinesq formula [50].

$$\mathrm{E}=\raisebox{1ex}{$\mathrm{F}(1-{\mathsf{\lambda }}^2)$}\!\left/ \!\raisebox{-1ex}{$\mathrm{d}\mathsf{\Delta }\mathrm{D}\mathrm{R}$}\right.,$$

(3)

where ΔD is the deformation at rupture in diameter (mm), d is the diameter of the cylindrical probe (8 mm), R is the radius of curvature of the loquat fruit (mm), F is the rupture force (N), and λ is Poisson’s ratio.

To find Poisson’s ratio, firstly determined the initial diameter D and initial length L of the loquat fruit using the X-AnyLabelling image processing program. Next, compress the loquat fruit body until it is deformed, and determine the final diameter D_o and final length (L_o) of the fruit. Finally, calculate Poisson’s ratio using the following equations (Figure 4) [51,52].

$${\mathsf{\epsilon }}_{\mathrm{x}}=\raisebox{1ex}{$\mathsf{\Delta }\mathrm{D}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{D}$}\right.=\raisebox{1ex}{$(\mathrm{D}-{\mathrm{D}}_{\mathrm{o}})$}\!\left/ \!\raisebox{-1ex}{$\mathrm{D}$}\right.,$$

(4)

$${\mathsf{\epsilon }}_{\mathrm{z}}=\raisebox{1ex}{$\mathsf{\Delta }\mathrm{L}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{L}$}\right.=\raisebox{1ex}{$(\mathrm{L}-{\mathrm{L}}_{\mathrm{o}})$}\!\left/ \!\raisebox{-1ex}{$\mathrm{L}$}\right.,$$

(5)

$$\mathsf{\lambda }=\raisebox{1ex}{${\mathsf{\epsilon }}_{\mathrm{x}}$}\!\left/ \!\raisebox{-1ex}{${\mathsf{\epsilon }}_{\mathrm{z}}$}\right.,$$

(6)

where λ is Poisson’s ratio, D is the initial diameter in mm, D_o is the final diameter in mm, L is the initial length in mm, L_o is the final length of the loquat fruit in mm, ε_x is the lateral strain, and ε_z is the longitudinal strain.

The ratio of the fruit’s volume (V, cm³) to its absorbed energy (E, mJ) up to the rupture point is known as toughness (P, mJ cm⁻³). The following formula was used to calculate it [2,53]:

$$P=\raisebox{1ex}{$E$}\!\left/ \!\raisebox{-1ex}{$V$}\right.,$$

(7)

Hardness (H, N/mm) was calculated as follows [54,55] by dividing the rupture force (F) by the deformation at rupture (ΔD):

$$H=\raisebox{1ex}{$F$}\!\left/ \!\raisebox{-1ex}{$\mathsf{\Delta }D$}\right.,$$

(8)

The following formula was used to calculate each loquat fruit radius of curvature (R, in mm) (Figure 5) [56]:

$$R=\raisebox{1ex}{${\left(AC\right)}^2$}\!\left/ \!\raisebox{-1ex}{$8\left(BD\right)$}\right.+\raisebox{1ex}{$\left(BD\right)$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$$

(9)

The following equation was used to determine the critical drop height for loquat fruit [48,57,58]:

$$\mathrm{h}=\raisebox{1ex}{${\left(1.5\right)}^5\mathsf{\sigma }\mathsf{\epsilon }{\mathrm{R}}^3$}\!\left/ \!\raisebox{-1ex}{$\mathrm{m}\mathrm{g}$}\right.$$

(10)

where h is critical drop height (in mm), σ is average stress (in N mm⁻²), ε is the elongation (in %), R is radius of curvature (in mm), m is the mass (in kg), and g is gravity (in m s⁻²).

According to Equation (10), the critical drop height (h) can be calculated using various parameters such as mean stress (σ), elongation (ε), radius of curvature (R), mass (m), and gravitational acceleration (g). The average stress and elongation values are not available in the data set used in the models where the critical drop height is estimated. In this study, the h value was tried to be estimated with the machine learning methods without the average stress and elongation values. The variables used in ML models are shown in Figure 6.

2.1. Artificial Neural Networks (ANNs)

ANNs are systems designed to imitate the biological organization of neurons in the nervous systems of living things. These systems are groups of connected neurons that receive, process, and transmit external signals to another neuron or to the external environment [59]. Neurons, or processing units as they are also known, consist of the following six parts: input signals, weights, summing function, transfer function (activation), bias, and output [60]. Neurons can receive one or more input signals. They weigh these signals and then process them with the help of an activation or transfer function to produce an output [61]. In the training of ANNs, many examples are given to the network, the results of which contain known input and output data. Thus, the weights between neurons are adjusted so that the network produces the most accurate result from the given inputs. In short, training in ANN is adjusting the weights to minimize the difference between the actual results and the predicted results [62].

2.2. Support Vector Machines (SVMs)

SVMs, developed by Vapnik, is one of the supervised learning methods based on statistical learning theory [63]. Originally developed to solve classification problems, SVMs were later extended to solve regression problems [64]. In classification problems, SVM looks for the maximum margin to separate two classes with an optimal hyperplane [65], while in regression problems, it is formulated as an optimization problem that minimizes the error and looks for the narrowest tube centered around the surface that contains the most of the training samples [66].

2.3. Extra Trees (ETs)

ETs is a tree-based ensemble model developed as an extension of the Random Forest (RF) method [67]. RF and ETs algorithms choose the features they use in each decision tree differently, and this is the main difference between them [68]. While the ET al algorithm chooses a random binary split value to split the nodes of the tree, it overcomes the problem of overfitting due to its high randomness and uses all data points to minimize deviation [69].

The workflow diagram of the study is shown in Figure 7. While the process of obtaining knowledge from data in databases is called data mining, data mining and machine learning are often used interchangeably in the literature. In fact, ML is just one step of this process. Obtaining a data set suitable for the purpose, preprocessing the data, selecting the most appropriate features to be used to predict the target variable, partitioning the data set, applying ML techniques, making evaluations according to appropriate metrics, visualization and interpretation stages are the main steps of the data mining process. The operations performed at all steps in the data mining process are important, but it is important to clearly state the operations performed at some steps. The steps and operations performed in the data mining process of this study are shown in Figure 8.

Although there are many criteria used to evaluate regression models, Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), Root Mean Square Error (RMSE), and Coefficient of Determination (R²) are the most preferred criteria. Information about the evaluation criteria, equation representations, and interpretations used in the study are shown in

Table 1. Evaluation criteria and their information.

Evaluation Criteria	Equation Representation	Best Case	Worst Case
MAE	$\frac{1}{m}{\displaystyle \sum _{i=1}^m}\left|e\right|$	0	∞
MAPE	$\frac{1}{m}{\displaystyle \sum _{i=1}^m}\left|\frac{Y_i-{\widehat{Y}}_i}{Y_i}\right|$	0	∞
RMSE	$\sqrt{\frac{1}{m}{\displaystyle \sum _{i=1}^m}{e}^2}$	0	∞
R2	$1-\frac{\sum _{i=1}^m{\left(Y_i-{\widehat{Y}}_i\right)}^2}{\sum _{i=1}^m{\left(Y_i-\overline{Y}\right)}^2}$	1	0

[70,71,72,73].

In Table 1, $e$ is error $(Y_i-{\widehat{Y}}_i)$, $Y_i$ is actual value of each h, ${\widehat{Y}}_i$ is predicted value of each h, and $\overline{Y}$ is average of $Y$ values.

3. Results and Discussion

Table 2. Descriptive statistics of the variables used in modeling.

	Mass (g)	Diameter (mm)	Length (mm)	Volume (cm3)	Sphericity (%)	Radius of Curvature (mm)	Compression Force (N)
min	55.19	38.51	44.16	34.66	71.63	22.24	51.32
max	88.08	49.68	64.28	77.78	89.30	25.78	87.51
mean	64.85	45.25	57.54	62.20	82.06	24.16	72.22
std. dev.	9.91	2.95	3.93	10.21	3.98	0.88	8.11
	Compression deformation (mm)	Poisson ratio	Elasticity of modulus (Nmm−2)	Absorbed energy (mJ)	Toughness (mJ cm−3)	Hardness (Nmm−1)	Critical Drop Height (cm)
min	11.99	0.21	0.14	629.70	5.45	3.15	12.20
max	19.13	0.60	2.10	1117.50	19.76	6.62	22.83
mean	15.44	0.34	0.37	873.38	9.27	4.76	17.82
std. dev.	2.07	0.10	0.35	110.82	2.71	0.86	3.33

shows the min, max, arithmetic mean, and standard deviation—that is, the descriptive statistics—of the loquat fruit used in the analysis and modeling.

Modeling was conducted using four different kernel functions in the SVM model, and suitable parameters for each kernel function were found using the tuning process. The kernel function that gives the best metric results is “Polynomial”. As a result of the tuning process, the parameters of the SVM model are C = 3.0, degree = 5, and epsilon = 0.05.

The Feedforward Artificial Neural Network was used in the ANN model. In the study where Relu was used as the activation function, the stochastic gradient descent method was used for weight optimization. There are 32 neurons in the first hidden layer and 256 neurons in the second hidden layer of the topology, which has two hidden layers. Since the target variable is single, there is one output neuron in the model. As a result of the tuning process, the other parameters of the ANN model are learning rate = ‘adaptive’, max_iter = 3000, and power = 0.4.

According to the tuning process for the ET model, the number of trees used in the solution forest is 300, the maximum tree depth is 11, and the number of features to be considered when searching for the best split is 3. The MAE criterion was used to measure the quality of the split that will occur in trees.

In each ML model, default parameters values were used without any changes in other settings other than the given parameter settings.

Table 3. Modeling results of ANN, SVM, and ET.

Method	Partition	Evaluation Metrics
		MAE	MAPE	RMSE	R2
ANN	Training	0.3012	0.0172	0.3845	0.9859
	Testing	0.3491	0.0207	0.4247	0.9844
SVM	Training	0.0720	0.0044	0.1107	0.9988
	Testing	0.3356	0.0200	0.4678	0.9811
ET	Training	0.1081	0.0062	0.1947	0.9964
	Testing	0.2194	0.0132	0.3248	0.9909

shows the modeling results of the ANN, SVM, and ET models. The training and test data set performances of the models established with the SVM, ANN, and ET methods to estimate the critical drop height are close to each other. While this is an indication that the trained models make consistent predictions, it can also be expressed as an indication that there is no overlearning problem in the models. The model established with the SVM method in the training data set is successful, and the model established with the ET method in the test data set is successful. The MAE, MAPE, RMSE, and R² values obtained from the model established with SVM in the training data set are 0.0720, 0.0044, 0.1107, and 0.9988, respectively. The MAE, MAPE, RMSE, and R² values obtained from the model established with ET in the test data set are 0.2194, 0.0132, 0.3248, and 0.9909, respectively.

Based on the test data set findings, the ET model predicts the critical drop height with an average error of 0.2194. A MAE value close to 0 means that the predicted variable is predicted with small errors. Accordingly, the critical drop height value can be expressed as “It is successfully estimated according to the MAE metric”. When we look at to the RMSE result, the ETs model estimates with a RMSE error of 0.3248. Just like the MAE metric, values close to 0 indicate that the predicted variable is predicted with high accuracy. According to this information and the RMSE result of the model, the critical drop height value can be expressed as “It is successfully predicted according to the RMSE metric”. The R² value being close to 1 indicates that the established regression models can make successful predictions. The R² of the ETs model is approximately 0.99. This indicates that the ETs model can be used to successfully predict the critical drop height value. The R² value can also be interpreted as the following: “in the ETs model the explained variation is approximately 99%”. As stated in Table 2, it is desirable for the MAPE metric to be close to 0. This can be expressed as the regression model predicting the target variable with a low average percentage error. The MAPE value is 0.0132, the target variable can be predicted with an error of approximately 1.3%.

MAE, MAPE, RMSE, and R² values are close to each other in all of the models in the training and test data set. While this shows that the performance of the models is quite good, it also indicates that some models are more successful with minor differences. It can be said that all models can be used to successfully predict the critical drop height.

The actual and predicted values of the machine learning models established to estimate the critical drop height of the loquat fruit in the training and test data set were compared. The scatter plots and the boxplots for the models training and testing partitions are displayed in Figure 9 and Figure 10. In the scatterplots (Figure 9), especially for SVM and ET models, it is seen that the distribution model of the measured and estimated critical drop height is very close to each other (almost the same). Scatter plots of the training part of SVM and ET models are very similar to each other. Because in the metric results shown in detail in Table 3, the values of the SVM and ET models are very close to each other. Plots that visualize these results support these numerical data. Similarly, the test data set results of the ET model are successful, and the success of these results is reflected in the plot.

Similarly, in both the training and testing phases, the actual and predicted critical drop height values of the boxplots (Figure 10) for all models have almost the same structure. Figure 11 shows the graphics obtained from the training and test data sets of the models. In these plots drawn using the predicted value and the actual value, the lines overlap almost completely in all models (both train and test).

In fact, this was an expected situation, because the performance of the models was clearly stated in the metrics shown in Table 3. On the other hand, as mentioned before, since some models achieve more successful results with small differences, it can be seen in Figure 10 that the graphics of these models are better by a very small difference. Although this situation is not clearly evident in the graphs drawn with the training data set results, it is evident in the graphs drawn for the test data set.

In recent years, ML techniques have been a frequently preferred method not only in education, health, engineering, economics, and sports sciences, but also in agriculture and agricultural sub-disciplines. Unlike traditional statistical methods, ML methods are primarily preferred in solving many classification and regression problems due to their better prediction abilities and tuning advantages. Huang et al. (2021) [40] used ANN and MLR methods to estimate SSC, TAC, and SSC/TAC in loquat fruit. According to the results obtained, ML methods achieved better results compared to traditional methods. While the ANN model achieved higher R² values compared to the MLR model in both the training and test data sets, it obtained lower RMSE and MAE values. Munera et al. (2021) [41] classified the loquat fruit using RF and XGBoost methods to distinguish common defects such as purple spots, reddening, bruising, and browning of the flesh. At the end of the study, high AUC and accuracy values were obtained, and the classification task of ML methods in loquat was successfully completed. Meng et al. (2024) [43] used ML methods to determine and classify the moisture content and freshness of loquat fruit.

In this study, the critical drop height value of loquat fruit was estimated using the ANN, SVM, and ET methods. The performances of the models were interpreted with the R², RMSE, MAE, and MAPE criteria used in the evaluation of the regression models, and the success performances of the models were compared. Both the metric results and the plots shown that the models were extremely successful. Guided by this information, it can be said that machine learning methods will successfully predict the critical drop height value. There are no obvious differences in both the comparisons within the models, namely the training and test results, and the mutual comparisons of the models. However, with a slight difference, the SVMs model performed better in the training data set and the ET model performed better in the test data set. Of course, the tuning processes detailed above had an impact on obtaining these results. With these tunings were intended to make the models perform better. These are clearly seen in both mathematical results and visual results. This is also an indication that the models do not have overlearning problems.

4. Conclusions

According to Equation (10), the critical drop height (h) can be calculated using various parameters such as mean stress (σ), elongation (ε), radius of curvature (R), mass (m), and gravitational acceleration (g). The average stress and elongation values are not available in the data set used in the models where the critical drop height is estimated. In this study, the h value was tried to be estimated with the machine learning methods without the average stress and elongation values. The critical drop height value of loquat fruit was estimated using three different machine learning methods with different operating principles. These methods were Artificial Neural Networks, Support Vector Machines, and Extra Trees. The models’ performances were calculated and interpreted with the R², RMSE, MAE, and MAPE criteria. In fact, although the results of the models were very close to each other, some models were more successful in the training and test data set, coming to the fore with a very small difference. The model established with the SVM method in the training data set was successful, and the model established with the ET method in the test data set was successful. MAE, MAPE, RMSE, and R² values obtained from the model established with SVM in the training data set were 0.0720, 0.0044, 0.1107, and 0.9988, respectively. The MAE, MAPE, RMSE, and R² values obtained from the model established with ET in the test data set were 0.2194, 0.0132, 0.3248, and 0.9909, respectively. Both metric results and plot representations show that the models obtained similar results and were very successful. In light of this obtained information, the critical drop height value of the loquat fruit was successfully estimated. The results of the established ML models show that the variables, whose details are given in Figure 5 and Table 2, can predict the critical drop height “h” value with small errors.