Evaluation of the Use of Machine Learning to Predict Selected Mechanical Properties of Red Currant Fruit ( Ribes rubrum L.) Ozonized during Storage

: The study examined selected biometric and mechanical properties of fruits of three varieties of red currant ( Ribes rubrum L.) from organic cultivation. The inﬂuence of the harvest date of red currant fruits, their storage time, and the use of ozone at a concentration of 10 ppm for 15 and 30 min on the water content, volume, and density, as well as the destructive force and the apparent modulus of elasticity, were determined. Fruits harvested at harvest maturity were characterized by a much larger volume and lower water content compared to fruits harvested seven days earlier. The ozonation process, regardless of the harvest date, resulted in a reduction in volume, density, and humidity. After 15 days of storage, the fruits of the tested varieties showed a decrease in the average water content from 86.15% to 83.79%. The tests showed a decrease in the destructive force and the apparent modulus of elasticity, the average value of which for fresh fruit was 76.98 ± 21.0 kPa, and after 15 days of storage, it decreased to 56.34 ± 15.96 kPa. The relationships between fruit-related parameters, harvesting, and storage conditions and fruit strength characteristics were modeled with the use of neural networks and support vector machines. These relationships are complex and nonlinear, and therefore, machine learning is usually more relevant than the traditional methods of modeling. For evaluation of the performance of the models, statistical parameters such as the coefﬁcient of correlation (R), root-mean-squared error (RMSE), and generalization ability coefﬁcient (GA) were used. The best models for the prediction of an apparent modulus of elasticity were developed with the use of ANNs. These models can be used in practice because the correlation between expected and predicted values was in the range 0.78–0.82, RMSE was in the range 13.38–14.71, and generalization ability was excellent. A signiﬁcantly lower accuracy was achieved for models with a destructive force as the output parameter (R ≤ 0.6).


Introduction
Berry fruit production is often linked to the improvement of plant biological traits adapted to the environmental conditions, processing technology, and user requirements.The introduction of new varieties into production and the assessment of resistance to damage during the harvesting, transport, and storage processes contribute to reducing losses and improving the quality of the raw material, leading to a reduction in costs incurred and environmental losses [1].Due to the need to reduce harvesting costs (e.g., by reducing the labor input) and to increase harvesting speed and efficiency, redcurrant fruit, like blackcurrant, gooseberries, and chokeberries, is most often harvested by machines using whole-row and half-row harvesters [2,3].One of the major disadvantages of this harvesting method is the greater mechanical damage (including abrasions, cuts, punctures, tion with mass, using the four equations, namely, linear, quadratic, power, and S-curve.For most models, the authors obtained a high concordance between experimental and predicted data (R 2 higher than 0.8).Similar techniques were used by Barbhuiya et al. [28] to develop predictive models of the Indian Coffee Plum mass based on physical characteristics of the fruit.The most appropriate mass models were created with the use of quadratic and power equations and with length, thickness, and volume as the predictors.The regression mass models were also reported by Vivek et al. [29].The authors employed linear, quadratic, S-curve, and power models to predict the mass of Sohiong fruit based on various physical properties.The highest accuracy was observed for quadratic models.The findings of the authors can be useful for the development of an automatic sorting system for the grading of Sohiong fruit based on the fruit mass.Moradi et al. [30] proposed a dimensionless model to predict the terminal velocity of the cucumbers.The model was of high accuracy with an R 2 of 0.9.Li et al. [31] presented the four-parameter sigmoidal model of the relationship between the internal damage volume of tomato fruit and its percentage deformation.This model can be used in practice for the optimization of postharvest classification of fruits.The finite element modelling is another popular method used to predict the mechanical responses in fruit upon loading [32][33][34].
Soft berries, which include currants, are very sensitive to mechanical damage during storage and processing.Therefore, the prediction and recognition of fruit damage depending on biometric characteristics and storage conditions is crucial for the loss minimization.Machine learning (ML) is relevant for developing accurate prediction or classification models.In our previous study [8], a multiple linear regression was compared with machine learning methods to estimate mechanical properties of large cranberry (Vaccinium macrocarpon Aiton) fruit.The accuracy of the regression models was significantly lower than that of models based on neural networks and support vector machines.In the study by Ropelewska [35], various machine learning methods combined with image analysis were used to develop an accurate tool for assessing the quality of red currant (Ribes rubrum L.) related to mechanical properties of fruit under different storage conditions.The author reported very high accuracy of models up to 100%.The prediction model of mechanical properties of blueberry (Vaccinium corymbosum) was presented by Hu et al. [36].They employed the least squares support vector machines to estimate texture profile and puncture parameters based on hyperspectral data.Huang et al. [37] employed four machine learning algorithms and multi-sensing technology to predict the freshness of blueberry fruit.The ML models outperformed the traditional Arrhenius equation method.
The aim of the research was to use machine learning modeling to demonstrate the relationships between biometric and mechanical parameters of ozonated and non-ozonated red currant fruit grown organically, and the harvest date and storage conditions.Such models allow for predicting the quality parameters of fruit and, consequently, appropriately design the harvesting and storage process to optimize product quality.

Characteristics of the Research Material
The research material consisted of the fruits of the red currant cultivars 'Holenderska Czerwona', 'Luna', and 'Losan'.The fruits were grown on an organic farm in Łopuszka Wielka (49 • 56 12 N 22 • 23 35 E, Podkarpackie Voivodeship, Poland).From each variety, 6 kg of fruit was harvested by hand on two dates: in the first decade of July 2022, i.e., seven days before harvest maturity (P), and in the second decade of July 2022, i.e., at harvest maturity (O).The decision on the harvesting date was based on the producer's experience, taking into account the color of the fruit and the strength of bonding to the stalk.
The fruits, both ozonized and non-ozonized, were stored in a cold room (temperature 3 • C, average air humidity 81%).On days 1, 8, and 15 of storage, measurements were taken.

Ozonation Process
Red currant fruits immediately after harvest were randomly divided into three portions of 2 kg each.The first part was a control sample (non-ozonized), and the other two batches were ozonated with gaseous ozone in a plastic container with dimensions L × W × H-0.6 × 0.4 × 0.4 m.The conditions of the ozonation process were as follows: ozone concentration-10 ppm; ozonation time-15 and 30 min; flow rate-40 g O 3 •h −1 ; and temperature-20 • C. As an ozone generator, the KORONA A40 Standard generator (Korona Scientific and Implementation Laboratory, Piotrków Trybunalski, Poland) was used.The 106 M UV Ozone Solution detector (Ozone Solution, Hull, MA, USA) was used to control the gas concentration.

Determination of the Morphological and Physical Characteristics of Red Currant Fruit
The sample size was 15 pieces of fruit for each variant.For each piece of fruit, the measurement of the diameter d and the weight was conducted with the accuracy of 0.01 mm and 0.001 g, respectively.The density of fruit was determined as a ratio of weight to the volume of a sphere of diameter d.
The drying method for determining the water content of fruit was in accordance with PN-90/A-75101-03:1990 [38].The drying process was conducted at 105 • C with the use of a laboratory weighing machine (Radwag, Radom, Poland).

Determination of the Mechanical Properties of Red Currant Fruit
In a compression test between two horizontal planes using a Brookfield CT3-1000 Texture Analyser (AMETEK Brookfield, Middleboro, MA, USA) with TexturePro CT v. 1.2 software, the destructive force F D (N), absolute strain λ, and destructive energy E D were measured.The specimen preload was 0.05 N, and the compression velocity was 0.2 mm•s −1 .The value of the apparent modulus of elasticity E C (MPa), was calculated from the equation [8,12] where d is diameter of the fruit (mm), λ is the fruit deformation in the load direction (mm), and E D is destructive energy (mJ).

Statistical Analysis
The results obtained were subjected to statistical analysis using the Statistica v.13.3.environment (TIBCO Software Inc., Tulsa, OK, USA).Analysis of variance (ANOVA) and LSD significance tests were performed at a significance level of α = 0.05.

Machine Learning Methods
Artificial neural networks (ANNs) are computational tools inspired by biological nervous systems.The Multilayer Perceptron (MLP) is one of the most popular architectures of ANNs used to solve regression problems.MLP consists of units arranged in layers.Layers are composed of nodes or artificial neurons.Nodes are units in the input layer that pass the input signals to the following layers.In MLP, there are one or more hidden layers and an output layer producing output signals of MLP.Hidden and output layers consist of artificial neurons-computational units connected to each other by weighted links.The output signal of neurons is calculated based on a weighted sum of input signals transformed by a transfer function (linear or nonlinear).A Radial Basis Function neural network (RBF) is a three-layer network composed of input, hidden, and output layers.The nodes in the input layer propagate input variables to the hidden layer.The neurons in the hidden layer are radial basis function units with Gaussian kernels.The output layer is a summation layer producing a weighted sum of output signals of neurons from the hidden layer.The practical use of ANNs for the modelling of complex and nonlinear relationships is a three-step process.The first step is to determine the structure of the ANN-the number of hidden layers, the number of units in each layer, and the type of neurons.The next step is the training of the ANN with the use of a supervised training method and based on the input and target matrix derived from the experimental datasets.During the training process, connection weights in the ANN are adjusted to minimize the error of the model (the difference between output values expected and calculated by the ANN).Sometimes, the training dataset is divided into two sets-for regular training and for validation-to help in fine-tuning of the model hyperparameters.The third step is the testing of the model.The training process is usually finished when the error of the model is lower than assumed.However, an undesirable phenomenon called overfitting may occur.Overfitting means that the model is perfectly adjusted to the training examples but has no generalization abilities.During the third step, the model is validated with the use of data not included in the training set (test data set).A small error during the testing process means that the model can be used in real-world applications.
Support Vector Machines (SVMs) were presented by Vapnik [39], originally for classification and then extended to regression problems [40].The SVM regression approach directly defines the kernel as a function of the input feature vector.As a kernel, the linear, polynomial, RBF, or sigmoid function can be employed.SVM minimizes the regularized error function: where C is the inverse regularization parameter, E ∈ is an ∈-insensitive error function (where ∈ can be interpreted as the required accuracy of the approximation), y n is the output and t n is the target for the n-th element of training data set, w is the weights vector, and N is the number of training vectors.For this research, Statistica v. 13 software (TIBCO Software Inc., Tulsa, OK, USA) was used as the machine learning environment.When ANNs were used for the development of regression models, 2000 structures with various number of neurons in hidden layer (from 10 to 50), and random initial values of connection weights were trained to find the optimal model.In the case of MLP models, various activation functions of neurons (linear, sigmoid, hyperbolic tangent, or exponential) were used.The experimental data set consisted of 810 vectors, 270 vectors each for the control, fruit ozonated for 15 min and 30 min.For the training process of ANNs, the data set was divided randomly into training, validation, and test sets at the 70:15:15 ratio.When SVM models were developed, the Gaussian RBF kernel function was utilized, according to Equation (3): where γ is a kernel parameter.
The parameters C, ∈, and γ were tuned via a grid search.For parameters C and ∈, the 10-fold cross-validation method was employed (C was tuned in the range of 1-15 with a step of 1, ∈ was adjusted in the range of 0.1-0.5 with a step of 0.1).The γ parameter of the Gaussian RBF kernel function was tuned in the range of 0.1-0.2 with a step of 0.01.The data set was divided randomly into training and test sets in an 80:20 ratio.The ten-fold cross-validation method was used.

Sensitivity Analysis
MLP is commonly called the black-box model because it provides little explanatory insight into relationships between input and output variables.However, there are some methods of sensitivity analysis which allow us to explore the relative importance of independent input variables.Previous studies have proposed a number of sensitivity analysis methods, such as the partial derivatives method (the partial derivatives of the output variables according to the input variables are calculated), the Weights method based on values of connection weights in the model, or the method based on indexes proposed by Yeh and Cheng [41].
This research used sensitivity analysis as implemented in the Statistica v.13 environment.In this method, the mean value of each input variable is calculated based on the training data set in order to replace a certain variable.Then, the percentage impact of independent input variables on output values is determined based on the quotient of two errors: the network error with an input replaced by its mean and the network error with the original inputs.

Criteria of Accuracy Assessment of Models
For quantifying the performance of the regression models, two error measures were used, namely, the coefficient of correlation (R) and root-mean-squared error (RMSE), and calculated as follows: where Y pred denotes the target value estimated by the model, Y pred is the mean of estimated target, Y meas is the actual target value (experimental), and Y meas is the mean of experimental target.
The closer to 1 that the R value is and the lower the RMSE error is, the better the model is.For the assessment of the quality of models, the classification proposed by Her and Wong [42] was employed: an R value lower than 0.40 is interpreted as a weak correlation, an R value in the range of 0.40-0.69means moderate correlation, and an R value higher than 0.70 is considered as a strong correlation.The models with a strong correlation between the target and predicted values for test data set were considered as useful for real-life applications.
A value of the coefficient of correlation close to 1 and a low value of RMSE are not trustworthy enough for the assessment of the model accuracy.Therefore, Yoon et al. [43] an additional metric-the generalization ability (GA) calculated according to the following equation: where RMSE test is the RMSE error for the test data set and RMSE train is the RMSE error for the training data set.
Based on the rules developed by El Bilali et al. [44], the generalization ability of the models created in this research was evaluated.A model with GA = 1 was classified as perfect, and a model with GA higher than 0.75 was classified as excellent.

Results
The detailed values obtained for the morphological characteristics, moisture content, and mechanical parameters of the fruits of the three redcurrant cultivars for the applied harvest dates, ozonation times, and storage times are presented in Table 1.Fruits of the studied cultivars differed in morphological characteristics regardless of the harvesting date.The largest volume was characterized by the fruit of the 'Holenderska Czerwona' cultivar and the smallest by the 'Luna' cultivar.Analyzing the results of this parameter, it should be emphasized that the currant fruit volume significantly decreased after 7 days of storage for the fruit harvested seven days before harvest maturity and not ozonized ('Holenderska Czerwona' and 'Losan' cultivars) and the fruit ozonized for 15 and 30 min ('Losan').The density of the fruit of the 'Luna' cultivar was the highest, while the density of fruit of the 'Losan' and 'Luna' cultivars collected at harvest maturity decreased significantly during storage.The greatest decrease in red currant fruit moisture content was recorded for the 'Holenderska Czerwona' currant cultivar at harvest maturity and ozonized at a dose of 10 ppm, regardless of the ozonation time.The mean values of fruit moisture content were, respectively, as follows: fruit not ozonated, 84.2% ± 1.73%; ozonated for 15 min, 83.4% ± 1.24%; and ozonated for 30 min, 83.0% ± 1.59%.
Analyzing the plane diagrams for fruit harvested before harvest maturity (Figure 1), there was a decrease in the destructive power of the currant fruit with an increasing storage time and shorter ozonation time.With regard to the modulus of elasticity of the currant fruit (Figure 2), a decrease in the value of this mechanical parameter was found with an increasing storage time for fruit harvested at harvest maturity, while for fruit harvested seven days before harvest maturity, the highest value of the modulus was recorded after seven days of storage.In the case of the staple puncture of highbush blueberry fruit, ozone treatments had no significant effect on the stiffness, breaking force, or mechanical work required to break the epidermis of highbush blueberry fruit [20].

Machine Learning Models
Before modeling, it is important to verify that the input parameters selected based on expert knowledge of the object under study are not highly correlated with each other.In the case of correlated parameters, only one of them should be retained to avoid redundancy of input information.It is also necessary to check the correlation between input and output parameters because machine learning methods are particularly useful for modeling multidimensional nonlinear relationships.Table 2 shows the Pearson linear correlation coefficients between all parameters under study.The linear correlations between input parameters of models are weak.Therefore, all features related to fruit properties and storage conditions can be used in the modeling process.The correlations between destructive force or apparent modulus of elasticity and other features under study are also weak-the highest is R = −0.55 between fruit volume and E C .
The two approaches to the development of machine learning models were applied in this research.The first one is based on all parameters measured-the seven input parameters (harvest date, cultivar, ozone exposure time, duration of storage, volume of fruit, fruit density, and moisture content) and one output feature: the modulus of elasticity or destructive force.In the second approach, it is assumed that the ozone exposure time is of a fixed value (0 min-control; 15 min; and 30 min).For each value of ozone treatment time, the separate models were developed with six input features: harvest date, cultivar, duration of storage, volume of fruit, fruit density, and moisture content.The ozonation process is an additional treatment during storage and can influence the physicochemical parameters of fruit.The two approaches proposed in this research allow us to compare the accuracy of models including or not the impact of ozonation time.Each relationship under study was modeled with the use of three machine learning methods: the multilayer perceptron, radial basis function neural network, and support vector machine.

Multilayer Perceptron
In Table 2, the structures and error metrics for the best models based on the seven input features are presented.The meaning of the model structure is as follows: the number of input parameters-the number of neurons in one hidden layer-the number of output parameters.In this research, the number of input parameters is determined by the approach (seven or six), and the number of neurons in hidden layer was adjusted experimentally.For all models, one output feature was defined (E C or F D ).
As presented in Table 3, the best models developed for both output features, the modulus of elasticity and destructive force, consist of eight neurons in the hidden layer.In the case of E C as the output value, the quality metrics for training, validation, and test data sets are similar to each other-the RMSE is low, and the R is high.The metrics calculated for the test data set are only slightly worse than those calculated for the training process.This indicates that the model is not overfitted.Additionally, the GA metric suggests an excellent generalization ability of the model.For F D as the output feature, based on the GA metric, the model can be classified as excellent, but the high values of RMSE error and the low correlation between the expected and predicted values for all data sets imply a low practical usefulness of the model.Neural models for the prediction of the modulus of elasticity depending on harvest date, cultivar, duration of storage, volume of fruit, fruit density, and moisture content have a high accuracy for the three ozone treatment procedures.When the fruit was ozonized for 15 or 30 min, the correlation between E C expected and predicted by the model exceeded 0.80 for the test data set.Slightly worse accuracy was achieved when the fruit was not treated with ozone (R = 0.77).All these models can be classified as excellent according to the GA metric.Significantly lower accuracy was achieved for models with F D as the output parameter.The best correspondence between the measured and predicted destructive force was observed in the case of ozone treatment for 30 min.However, the correlation coefficient was no greater than 0.6, which means that the practical value of the models is questionable.

RBF Neural Networks
In Table 5, the details of the best models developed with the use of RBF neural networks are presented.These models represent the relationships between harvest date, cultivar, ozone exposure time, duration of storage, volume of fruit, fruit density, and moisture content as input parameters and the modulus of elasticity or destructive force as the output feature.The number of neurons in the hidden layer in RBF neural models is significantly higher than in their MLP counterparts.In the model for E C prediction, the correlation between experimental and predicted values is similar for training, validation, and test data sets.This means that there is no overfitting phenomenon during the training process.The accuracy of the model (R = 0.75) can be considered as acceptable.The generalization ability of the model is excellent.When destructive force is the output parameter, the accuracy of the RBF models is low (R = 0.38), and this model is not useful for practical applications.
In Table 6, the best RBF models for the prediction of the modulus of elasticity or destructive force based on the harvest date, cultivar, duration of storage, volume of fruit, fruit density, and moisture content are described-separately for the control (no ozone treatment) and fruit ozonized for 15 and 30 min.
Among the models for the estimation of the modulus of elasticity, the most accurate was the model developed based on the data on no-ozonized fruit (R = 0.78).The accuracy of models based on the data on fruit exposed to ozone for 15 and 30 min was lower (R = 0.70 and R = 0.64, respectively).According to the generalization ability, these models are excellent.The precision of RBF models with destructive force as the predicted parameter is low for all three data sets.The highest correlation between the measured and predicted F D was observed for fruit ozonized for 15 min (R = 0.49).The quality of these models makes them not useful in real-world applications.The third machine learning method employed for modelling in this research is the support vector machine.The details of SVM regression models of relationships between the seven input features described in Section 3.1.and the modulus of elasticity or destructive force are presented in Table 7.The values of error metrics of the model for the prediction of the modulus of elasticity are very similar for training and test data sets.Therefore, the generalization ability of the model is very high.The accuracy of the model is acceptable, with a high correlation between expected and predicted values of E C for the test data set (R = 0.78).On the other hand, the quality of the model with destructive force as the output parameter is too low for practical applications (R = 0.28 for test data set).
Table 8 summarizes the best models obtained using the SVM method for the three data sets: non-ozonized fruit and fruit after ozone treatment for 15 and 30 min.The accuracy of models for E C prediction based on the six parameters (harvest date, cultivar, duration of storage, volume of fruit, fruit density, and moisture content) based on data sets for a specific ozone exposure time was lower than for the model trained with the use of all experimental data (Table 7).The highest accuracy was observed for the control data set and for fruit ozonized for 30 min (R = 0.76 for test data set).The quality of the model for fruit exposed to ozone for 15 min was lower (R = 0.65).The generalization ability of these three models was excellent.The accuracy of the models for F D prediction is far too low to make them useful in practice, as the correlation between expected and predicted values for the test data set does not exceed 0.43.
In Figures 3 and 4, the performance of the best models of the modulus of elasticity E C and destructive force F D for the test data set is depicted.

Sensitivity Analysis
The best neural models presented in Table 3 were used for the sensitivity analysis.In Figure 5, the percentage influence of a certain input variable on the modulus of elasticity and destructive force is illustrated.The highest impact on the modulus of elasticity is observed for the volume of fruit (33%).The second most influencing parameter is the fruit cultivar.Other parameters affect the modulus of elasticity at a similar level (8-12%).The fruit cultivar has the highest impact on the destructive force (17%).Other analyzed parameters influence F D at a level of around 14%.

Discussion
According to [20], ozone treatments significantly increased the weight loss of ozonated blueberries during storage compared to untreated fruit.At the same exposure time, the higher the ozone concentration, the higher the weight loss was.Several studies mention that higher ozone levels can lead to epidermal and epidermal tissue damage and oxidation of epidermal waxes due to the high oxidative power of ozone [45][46][47].Some studies conducted on 'Casselman' plums treated with gaseous ozone showed significant differences in waxes and scale thickness compared to the control fruit.They suggested that the effect of ozone in cuticles and waxes contributed to the observed weight loss [48].
The fruit of the 'Luna' cultivar had the highest resistance to mechanical damage and the highest modulus of elasticity.According to Panfilova et al. [3], for the optimal operation of the harvester, the crushing force of the red currant fruit must be greater than 2 N. Taking into account the obtained values of the destructive force of the fruits of the analyzed red currant cultivars, it can be concluded that they are suitable for mechanical harvesting.
Our results indicate that for fruit harvested before the harvest maturity stage, increasing the storage time and reducing the ozonation time resulted in a decrease in the destructive power.According to the authors of [20,22,49], changes in the mechanical properties of fruit during storage were similar for untreated and ozonated fruit.Thus, the changes in mechanical behavior can be attributed mainly to metabolic reactions of ripening and ageing, without a significant effect of ozone exposure.In the process of compressing red currant fruits, a decrease in the elastic modulus was found with an increasing storage time of fruits harvested at harvest ripeness, while for fruits harvested seven days before harvest maturity, the highest value of the modulus was recorded on the seventh day of storage.
In the case of the staple puncture of highbush blueberry fruit, ozone treatments had no significant effect on the stiffness, breaking force, and mechanical work required to break the epidermis of highbush blueberry fruit [20].
The models for the modulus of elasticity prediction developed in this research can be considered as useful for practical implementation.The best models were created using the MLP neural network, and only for non-ozonized fruit, the best technique was RBF.The correlation between expected and predicted values of E C for test data sets is high-the R value is in the range 0.78-0.82.Based on the error metrics presented in Tables 3-8 it can be concluded that no overfitting phenomenon occurred during the training process.The generalization ability of the models is excellent.The error metrics regarding models for destructive force prediction detailed in Tables 3-8 suggest the low quality of models.The correlation between measured and predicted values of F D for test data sets does not exceed 0.6.This suggests that F D is significantly influenced by additional parameters that are not considered in this research.Therefore, the potential usefulness of these models in real-life application is questionable.A subdivision of a data set into subsets according to ozone exposure time has no significant impact on the accuracy of the models.
To date, accurate models for predicting the mechanical properties of fruit have been developed using machine learning techniques.Cevher and Yıldırım [50] used ANNs to create neural models for estimation of rupture energy of pear fruit under conditions of loading position and storage duration.The authors compared neural models of various structures and trained using three different methods.The best models reported in that study had a high accuracy, with a coefficient of correlation R between expected and predicted values for the test data set exceeding 0.95.Vasighi-Shojae et al. [51] applied the ANN modeling technique to estimate the mechanical properties of Golden Delicious apples.They developed three independent neural models to estimate the firmness, elastic modulus, and stiffness of the apple based on data from ultrasonic measurements.The accuracy of the models was very high (R > 0.9).Abasi et al. [52] used the PLS regression technique to analyze the relationships between apple firmness and the spectral absorbance response of the fruit.They obtained a high agreement between expected and predicted values (R = 0.77).Neural networks were employed by Saiedirad and Mirsalehi [53] to predict the rupture force and rupture energy of cumin seeds.The input parameters selected for the models were moisture content, seed size, rate loading, and seed orientation.The agreement between experimental and predicted values for both models was high (R = 0.98 for rupture force and R = 0.97 for rupture energy).Hu et al. [36] used hyperspectral interactance imaging combined with machine learning to estimate mechanical parameters of blueberry (Vaccinium corymbosum) fruit.They reported a high accuracy of prediction assessed on the basis of the correlation between target and predicted values (R = 0.91 for cohesiveness, R = 0.84 for springiness, R = 0.86 for resilience, R = 0.65 for maximal force strain, R = 0.62 for final force, R = 0.77 for hardness, and R = 0.71 for maximal force).Huang et al. [37] compared the traditional method of fruit freshness prediction (Arrhenius equation based on temperature and quality parameters) with machine learning methods.They created the four ML models with the use of backpropagation (BP) ANN, RBF neural network, SVM, and extreme learning machine (ELM) to estimate the freshness of blueberry fruit based on multi-sensing data.The accuracy of the ML models was higher (90.87% (BP), 92.24% (RBF), 94.01%(SVM), and 91.31% (ELM)) in comparison to traditional modeling (85.10%).

Conclusions
The destructive force of redcurrant fruit harvested before harvesting maturity decreased with increasing storage time and with shorter ozonation time, whereas the dependence on ozonation time was reversed for fruit harvested at harvesting maturity.The value of the modulus of elasticity of currant fruit did not depend on the ozonation time

Figures 1 and 2 7 )Figure 1 .
Figures 1 and 2 show the analyzed mechanical parameters of the red currant fruit of the cultivars studied for the two harvest dates in relation to ozonation time and storage time.The relationships are in the form of a quadratic function described by the equation z = a + bx + cy+ dx 2 + exy + fy 2 (7)

Figure 2 .
Figure 2. Dependence of apparent modulus of elasticity E C on ozone treatment time O T and storage time S T for redcurrant fruit harvested seven days before harvest maturity P and at harvest maturity O.

Figure 5 .
Figure 5.The relative importance of input variables of MLP model on modulus of elasticity E C and destructive force F D .

Table 1 .
Morphological characteristics, moisture content, and mechanical properties of red currant fruit for cultivars, harvest date, storage time, and ozonation time.

Table 2 .
Correlation coefficients between explanatory and response variables.

Table 3 .
Structures and error metrics of the best MLP models.

Table 4 ,
the best MLP models of the relationships under study with established values of ozone exposure time are depicted.

Table 4 .
Structures and error metrics of the best MLP models.

Table 5 .
Structures and error metrics of the best RBF models.

Table 6 .
Structures and error metrics of the best RBF models.

Table 7 .
Error metrics of the best SVM models.

Table 8 .
Error metrics of the best SVM models.