Experimental Modelling of Sunflower Seed Moisture Content During Controlled Drying Using Machine Learning Methods
Abstract
1. Introduction
2. Materials and Methods
2.1. Laboratory Analysis
2.2. Drying Process
2.3. Data Processing
2.4. Data Cleaning and Encoding
2.5. Evaluation of Existing Machine Learning Models
2.6. Performance of Evaluated Machine Learning Models
3. Results
4. Discussion
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
| ANN | Artificial neural networks |
| ANOVA | Analysis of variance |
| BTR | Boosted tree regression |
| C | Carbon |
| DM | Drying method |
| F | Fat content |
| GCV | Generalized cross validation |
| H | Hydrogen |
| HSD | Honestly significant difference |
| LM | Linear model |
| MAE | Mean average error |
| MAPE | Mean absolute percentage error |
| MARS | Multivariate Adaptive Regression Splines |
| MC | Moisture content |
| N | Nitrogen |
| OLS | Ordinary least squares |
| P | Protein content |
| RBF | Radial basis function |
| RFR | Random forest regression |
| RMSE | Root mean squared error |
| R2 | Coefficient of determination |
| S | Sulfur |
| SD | Standard deviation |
| Smp. | Sample |
| T | Temperature |
| t | Time |
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| Laboratory Analysis | Protocol/Reference |
|---|---|
| Elemental analysis (determination of C, H, N, S and O) | ISO 16948:2015 [20] ISO 15178:2000 [21] |
| Determination of protein content | Kjeldahl Method [22] |
| Determination of fat content | ISO 659:2009 [23] |
| Moisture content determination | ISO 665:2020 [24] |
| Input Values | Output Value | ||||
|---|---|---|---|---|---|
| No. | Drying Method | Sample | Temperature (°C) | Time (Minutes) | MC (%) |
| 1 | 1 | 1 | 50 | 15 | 16.82 |
| 2 | 1 | 1 | 50 | 30 | 15.59 |
| … | |||||
| 21 | 1 | 2 | 60 | 15 | 14.87 |
| 22 | 1 | 2 | 60 | 30 | 13.91 |
| 23 | 1 | 2 | 60 | 45 | 11.16 |
| 24 | 1 | 2 | 60 | 60 | 11.12 |
| 25 | 1 | 2 | 70 | 15 | 13.68 |
| 26 | 1 | 2 | 70 | 30 | 12.87 |
| … | |||||
| 86 | 2 | 3 | 60 | 30 | 12.40 |
| 87 | 2 | 3 | 60 | 45 | 9.96 |
| 88 | 2 | 3 | 60 | 60 | 9.70 |
| 89 | 2 | 3 | 70 | 15 | 13.79 |
| … | |||||
| 120 | 3 | 2 | 60 | 60 | 8.09 |
| 121 | 3 | 2 | 70 | 15 | 10.36 |
| 122 | 3 | 2 | 70 | 30 | 9.66 |
| … | |||||
| 141 | 3 | 3 | 80 | 15 | 11.73 |
| 142 | 3 | 3 | 80 | 30 | 9.76 |
| 143 | 3 | 3 | 80 | 45 | 8.98 |
| 144 | 3 | 3 | 80 | 60 | 7.23 |
| Abb. | Model Settings | Equation | Explanation | Ref. |
|---|---|---|---|---|
| ANN | – learning cycles: 100,000 – data split: 70/15/15 – hidden neurons: 10 – learning rate: 0.01 | X denotes a vector of input variables. W1 is the weight matrix between the input and hidden layers. B1 is the bias of the hidden layer. f2 is the activation function of the hidden layer. W2 is the weight matrix between the hidden and output layers. B2 is the bias of the output layer. f1 is the output activation function. Y is the output value of the model. | [29] | |
| RFR | – number of trees: 500 – feature subset size: p/3 – bootstrap: enabled – node size: 5 | Y is the final prediction of the model. K is the total number of regression trees in the ensemble, hk(x) is the output of the kth regression tree for the given input. The final value is obtained by averaging all individual predictions. | [30] | |
| BTR | – number of trees: 1000 – learning rate: 0.05 – tree depth: 3 – subsample: 0.7 | f(x) is the final prediction of the model. f0(x) is the initial baseline estimate. M is the number of iterations or trees. J is the number of terminal regions in each tree. cmj is the contribution of the jth region in the mth tree. Rmj is the corresponding region of the input variable space. The indicator function shows whether the input belongs to that region. | [31] | |
| SVR | – kernel: RBF – C: 10 – epsilon: 0.1 – gamma: 1/p | f(x) is the output regression function. W is the weight vector. WT is the transposed weight vector. φ(X) is the mapping of the input variables into the feature space. b is the free term of the model. X is the input vector. | [32] | |
| LM | – method: OLS – predictor scaling: yes – validation: 10-fold – significance level: 0.05 | y is the dependent variable, x1 is the independent variable, w1 is the regression coefficient, and b is the constant term. | [33] | |
| MARS | – max basis functions: 30 – interaction degree: 2 – pruning: GCV – knot penalty: default | y is the dependent variable. f(x) is the estimated nonlinear function composed of the basis functions. x is the predictor vector. e is the residual error of the model. | [34] |
| Model | Test No. | Learning Rate | Max Iter | Hidden Neurons | Trees | Tree Depth | Node Size | C | Epsilon | Max Basis Functions | Interaction Degree |
|---|---|---|---|---|---|---|---|---|---|---|---|
| ANN | Test 1 | 0.001 | 50,000 | 5 | – | ||||||
| Test 2 | 0.01 | 100,000 | 10 | ||||||||
| Test 3 | 0.01 | 100,000 | 15 | ||||||||
| Test 4 | 0.05 | 150,000 | 10 | ||||||||
| Test 5 | 0.01 | 100,000 | 20 | ||||||||
| Selected | 0.01 | 100,000 | 10 | ||||||||
| RFR | Test 1 | – | 100 | – | 3 | – | |||||
| Test 2 | 300 | 5 | |||||||||
| Test 3 | 500 | 5 | |||||||||
| Test 4 | 300 | 10 | |||||||||
| Test 5 | 500 | 10 | |||||||||
| Selected | – | – | 500 | 5 | |||||||
| BTR | Test 1 | 0.01 | 500 | 2 | – | ||||||
| Test 2 | 0.05 | 800 | 3 | ||||||||
| Test 3 | 0.05 | 1000 | 3 | ||||||||
| Test 4 | 0.10 | 800 | 3 | ||||||||
| Test 5 | 0.05 | 1000 | 4 | ||||||||
| Selected | 0.05 | 1000 | 3 | ||||||||
| SVR | Test 1 | – | 1 | 0.01 | – | ||||||
| Test 2 | 5 | 0.1 | |||||||||
| Test 3 | 10 | 0.1 | |||||||||
| Test 4 | 10 | 0.2 | |||||||||
| Test 5 | 20 | 0.1 | |||||||||
| Selected | 10 | 0.1 | |||||||||
| MARS | Test 1 | – | 20 | 1 | |||||||
| Test 2 | 30 | 1 | |||||||||
| Test 3 | 30 | 2 | |||||||||
| Test 4 | 40 | 2 | |||||||||
| Test 5 | 40 | 3 | |||||||||
| Selected | 30 | 2 | |||||||||
| Model | Hyperparameter | Search Range | Selected Value |
|---|---|---|---|
| ANN | Hidden neurons | [5, 10, 15, 20] | 10 |
| Learning rate | [0.001, 0.01, 0.05] | 0.01 | |
| Max iterations | [50,000, 100,000, 150,000] | 100,000 | |
| RFR | Number of trees | [100, 300, 500] | 500 |
| Node size (min samples leaf) | [3, 5, 10] | 5 | |
| BTR | Number of trees | [500, 800, 1000] | 1000 |
| Learning rate | [0.01, 0.05, 0.10] | 0.05 | |
| Tree depth | [2, 3, 4] | 3 | |
| SVR | C | [1, 5, 10, 20] | 10 |
| Epsilon | [0.01, 0.1, 0.2] | 0.1 | |
| MARS | Max basis functions | [20, 30, 40] | 30 |
| Interaction degree | [1, 2, 3] | 2 | |
| Linear model | Method | OLS | OLS |
| Predictor scaling | [No, Yes] | Yes | |
| Validation | [5-fold, 10-fold] | 10-fold | |
| Significance level | [0.01, 0.05] | 0.05 |
| Sample | MC (%) |
|---|---|
| Sumiko | 18.35 ± 0.06 c |
| Pioneer | 15.4 ± 0.18 a |
| Agromatic Lidea | 16.1 ± 0.10 b |
| Statistical significance | * |
| Variable | Range | Mean | SD | Mean ± SD | |
|---|---|---|---|---|---|
| Minimum | Maximum | ||||
| O (%) | 21.70 | 54.66 | 47.03 | 7.62 | 47.03 ± 7.62 |
| N (%) | 1.75 | 3.12 | 2.37 | 0.30 | 2.37 ± 0.3 |
| C (%) | 36.10 | 65.19 | 42.95 | 6.88 | 42.95 ± 6.88 |
| S (%) | 0.12 | 0.52 | 0.20 | 0.05 | 0.2 ± 0.05 |
| H (%) | 6.67 | 9.74 | 7.50 | 0.62 | 7.5 ± 0.62 |
| Proteins (%) | 9.26 | 16.51 | 12.56 | 1.62 | 12.56 ± 1.62 |
| Fat (%) | 38.71 | 51.22 | 47.12 | 2.85 | 47.12 ± 2.85 |
| Effect | O (%) | N (%) | C (%) | S (%) | H (%) | Proteins (%) | Fat (%) |
|---|---|---|---|---|---|---|---|
| DM | <0.001 | <0.001 | <0.001 | <0.001 | <0.001 | <0.001 | <0.001 |
| Smp. | <0.001 | <0.001 | <0.001 | 0.27 | 0.67 | <0.001 | <0.001 |
| T | <0.001 | <0.001 | <0.001 | <0.001 | <0.001 | <0.001 | <0.001 |
| t | <0.001 | <0.001 | <0.001 | 0.04 | 0.16 | <0.001 | <0.001 |
| DM × Smp. | <0.001 | <0.001 | <0.001 | 0.62 | 0.05 | <0.001 | <0.001 |
| DM × T | <0.001 | <0.001 | <0.001 | <0.001 | <0.001 | <0.001 | <0.001 |
| Smp. × T | <0.001 | <0.001 | 0.01 | 0.32 | 0.03 | <0.001 | <0.001 |
| DM × t | 0.01 | 0.02 | <0.001 | 0.36 | 0.17 | 0.02 | <0.001 |
| Smp. × t | 0.12 | 0.15 | 0.07 | 0.29 | 0.80 | 0.15 | <0.001 |
| T × t | <0.001 | 0.32 | <0.001 | 0.10 | 0.06 | 0.32 | <0.001 |
| DM × Smp. × T | <0.001 | <0.001 | <0.001 | 0.24 | <0.001 | <0.001 | <0.001 |
| DM × Smp. × t | 0.03 | 0.02 | 0.02 | 0.37 | 0.56 | 0.02 | <0.001 |
| DM × T × t | <0.001 | 0.11 | <0.001 | 0.15 | 0.08 | 0.11 | <0.001 |
| Smp. × T × t | 0.04 | 0.08 | 0.14 | 0.09 | 0.27 | 0.08 | <0.001 |
| DM × Smp. × T × t | 0.02 | <0.001 | 0.03 | 0.76 | 0.37 | <0.001 | <0.001 |
| Model | R2 | RMSE (%) | MAE (%) | MAPE (%) |
|---|---|---|---|---|
| ANN | 0.97 | 0.46 | 0.32 | 2.97 |
| RFR | 0.76 | 1.28 | 1.03 | 9.47 |
| BTR | 0.85 | 1.00 | 0.82 | 7.46 |
| SVR | 0.94 | 0.66 | 0.51 | 4.60 |
| Linear | 0.69 | 1.45 | 1.11 | 10.13 |
| MARS | 0.85 | 1.00 | 0.80 | 7.33 |
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Matin, A.; Brandić, I.; Špelić, K.; Tomić, I.; Pavlović, A.; Matin, B.; Krička, T.; Galić, A. Experimental Modelling of Sunflower Seed Moisture Content During Controlled Drying Using Machine Learning Methods. Agriculture 2026, 16, 695. https://doi.org/10.3390/agriculture16060695
Matin A, Brandić I, Špelić K, Tomić I, Pavlović A, Matin B, Krička T, Galić A. Experimental Modelling of Sunflower Seed Moisture Content During Controlled Drying Using Machine Learning Methods. Agriculture. 2026; 16(6):695. https://doi.org/10.3390/agriculture16060695
Chicago/Turabian StyleMatin, Ana, Ivan Brandić, Karlo Špelić, Ivana Tomić, Aleksandra Pavlović, Božidar Matin, Tajana Krička, and Ante Galić. 2026. "Experimental Modelling of Sunflower Seed Moisture Content During Controlled Drying Using Machine Learning Methods" Agriculture 16, no. 6: 695. https://doi.org/10.3390/agriculture16060695
APA StyleMatin, A., Brandić, I., Špelić, K., Tomić, I., Pavlović, A., Matin, B., Krička, T., & Galić, A. (2026). Experimental Modelling of Sunflower Seed Moisture Content During Controlled Drying Using Machine Learning Methods. Agriculture, 16(6), 695. https://doi.org/10.3390/agriculture16060695

