Abstract
The utilization of Açaí residues holds significant economic and environmental importance in Brazil. The drying technique is an alternative for preserving Açaí kernel from fresh fruit processing. This study employed diffusive, empirical, and Artificial Neural Network (ANN) models to simulate the convective drying of ground Açaí kernel, with air temperature and air velocity ranging from 80 to 120 °C and 0.5 and 0.9 m/s, respectively. To assess the robustness of the models, a validation step using experimental conditions distinct from those used in the training dataset was carried out. The impact of cross-validation on the generalization capacity of the ANN-based models was investigated. Furthermore, input importance techniques were employed to gain insights into the functioning of the ANN models. The diffusivity coefficient exhibited values between 9.22 × 10−10 and 2.26 × 10−9 m2/s. The Page was the best empirical model (R2 = 0.9918). For the ANN-based models, five pairs of input–output variables were considered and produced models with comparable or superior performance compared to the diffusive and empirical models. The best ANN model achieved an R2 > 0.9999. The cross-validation technique only enhanced the generalization capacity of ANN-based models that used delayed variables in the input instead of the drying time. Additionally, the feature importance analysis revealed that the best ANN model effectively captured the essential drying aspects: air temperature and velocity effects, the falling rate period, and higher drying rates at the beginning of the experiments.
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Abbreviations
- ANN:
-
Artificial neural network
- ANOVA:
-
Analysis of variance
- MC:
-
Moisture content
- SHAP:
-
Shapley additive explanations
- \(a,b,{b}_{1},{b}_{2},{b}_{3},{k}_{o},n\) :
-
Empirical coefficients
- \({B}^{\langle 1\rangle }\) :
-
Bias of the hidden layer
- \({B}^{\langle 2\rangle }\) :
-
Bias of the output layer
- \({D}_{\mathrm{eff}}\) :
-
Effective moisture diffusivity (\({\mathrm{m}}^{2}/\mathrm{s})\)
- \({D}_{o}\) :
-
Pre-exponential factor (\({\mathrm{m}}^{2}/\mathrm{s}\))
- \({E}_{a}\) :
-
Activation energy (kJ/mol)
- \({f}_{\langle 1\rangle }(\bullet )\) :
-
Activation function in the hidden layer
- \({f}_{\langle 2\rangle }(\bullet )\) :
-
Activation function in the output layer
- \(L\) :
-
Thickness of the sample (\(\mathrm{m}\))
- \(m(t)\) :
-
Mass of the material at a specific time t (kg)
- \({m}_{d}\) :
-
Mass of the dry solids (kg)
- \({M}_{\mathrm{eq}}\) :
-
Equilibrium moisture content (\({\mathrm{kg}}_{\mathrm{water}}/{\mathrm{kg}}_{\mathrm{dry matter}})\)
- \({M}_{o}\) :
-
Initial moisture content (\({\mathrm{kg}}_{\mathrm{water}}/{\mathrm{kg}}_{\mathrm{dry matter}})\)
- \({M}_{t}\) :
-
Moisture content at specific time t (\({\mathrm{kg}}_{\mathrm{water}}/{\mathrm{kg}}_{\mathrm{dry matter}}\))
- \(\mathrm{MR}(t)\) :
-
Moisture ratio at specific time \(t\)
- \(N\) :
-
Number of observations
- \({N}_{z}\) :
-
Number of model constants
- \(p\) :
-
Number of neurons
- \(q\) :
-
Number of input variables
- \({R}_{g}\) :
-
Universal gas constant (kJ·mol−1 K−1)
- \({\mathrm{RI}}_{j}\) :
-
Relative importance of input \(j\)
- \(\mathrm{RMSE}\) :
-
Root mean squared error
- \({R}^{2}\) :
-
Coefficient of determination
- \(t\) :
-
Drying time (\(\mathrm{s}\))
- \(T\) :
-
Air temperature (°C)
- \(V\) :
-
Air velocity (\(\mathrm{m}/\mathrm{s}\))
- \({W}^{\langle 1\rangle }\) :
-
Weight matrix between input and hidden layers
- \({W}^{\langle 2\rangle }\) :
-
Weight matrix between hidden and output layers
- \(x\) :
-
Artificial Neural Network inputs
- \({y}_{i}\) :
-
i-th Experimental value
- \({\widehat{y}}_{i}\) :
-
i-th Model output value
- \(z\) :
-
Diffusion path (\(\mathrm{m}\))
- \({\chi }^{2}\) :
-
Reduced chi-squared
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Bannoud, M.A., Gomes, B.P., Abdalla, M.C.S.P. et al. Mathematical modeling of drying kinetics of ground Açaí (Euterpe oleracea) kernel using artificial neural networks. Chem. Pap. 78, 1033–1054 (2024). https://doi.org/10.1007/s11696-023-03142-2
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DOI: https://doi.org/10.1007/s11696-023-03142-2