Modeling of thermodynamic properties of carrot product using ALO, GWO, and WOA algorithms under multi-stage semi-industrial continuous belt dryer

In this paper, multi-stage continuous belt (MSCB) dryer was used for carrot slices drying. Experiments were performed at three air speeds (1, 1.5, and 2 m/s) three belt linear velocities (2.5, 6.5, and 10.5 mm/s), and three air temperatures (40, 55, and 70 °C) in triplicate. Three intelligent systems including Ant-Lion-Optimizer (ALO), Grey-Wolf-Optimizer (GWO) and Whale-Optimization-Algorithm (WOA) models were developed to predict the thermodynamic properties of carrot slices including of effective moisture diffusivity (D_eff) and specific energy consumption (SEC). The results revealed that D_eff and SEC values were in the range of 1.77–2.90 × 10⁻⁹ m²/s and 169.77–551.19 MJ/kg, respectively. The models of ALO, GWO, and WOA were able to predict the value of D_eff and SEC. The amounts of correlation coefficient (\(R\)), root-mean-square error (\({\text{RMSE}}\)), and mean absolute error (\({\text{MAE}}\)) for ALO, GWO, and WOA models for predication D_eff were obtained (0.9989, 7.81 × 10⁻¹², and 1.50 × 10⁻¹²), (0.9993, 5.39 × 10⁻¹², and 1.03 × 10⁻¹²) and (0.9994, 4.95 × 10⁻¹², and 9.54 × 10⁻¹³), respectively. In addition, The amounts of \(R\), \({\text{RMSE}}\), and \({\text{MAE}}\) for ALO, GWO, and WOA model for predication SEC were obtained (0.9983, 0.6700, and 0.1289), (0.9988, 0.5274, and 0.0715) and (0.9996, 0.2566, and 0.0060), respectively. Therefore, model of WOA can be used to easily and accurately predict D_eff and SEC values.