Diameter-independent determination of apple watercore using microwave free-space and finite element methods

Watercore is a physiological disorder that impairs the quality of apples. This study proposed a novel method to determine the apple watercore with different diameters combining microwave free-space and finite element simulation. Firstly, the transmission coefficients (S₁₂, S₂₁) and watercore degrees were collected for 509 'Fuji' apples ranging from 69 to 100 mm in diameter. Then, the antenna-apple coupling simulation model was developed based on the finite element method to acquire the electric field strength on the pulp cross-section, as well as the fitted equations between diameter and transmission coefficients for correcting the transmission coefficients to the same diameter scale. Finally, decision tree (DT), support vector machine (SVM), artificial neural network (ANN), and one-dimensional convolutional neural network (1D-CNN) models for watercore degree classification were established based on the original and corrected spectra, respectively. The experimental results proved negative correlations between transmission coefficients at most frequencies and apple diameter, as well as watercore degree. The simulation results presented that the variations in transmission coefficients at seven equally spaced logarithmic frequencies with diameter followed sin trigonometric functions. The model established using the corrected spectra exhibited higher accuracy than the original spectra. The ANN model built using the corrected S₂₁ spectra exhibited the highest accuracy, with the training, prediction, and validation sets reaching 99.02 %, 97.12 %, and 91.19 %, and the sound, slight, moderate, and severe watercore apples in the validation set was 88.89 %, 92.59 %, 88.89 %, and 100 %, respectively. This study demonstrates that apple watercore degree can be sensed using microwave free-space, finite element simulation, and proper algorithms, regardless of the diameter.