A Novel Data Preprocessing Method for the Modeling and Prediction of Freeze-Drying Behavior of Apples: Multiple Output-Dependent Data Scaling (MODDS)

Abstract

In the present study, the freeze drying behavior of apples have been modeled and predicted. Because freeze-drying is a very expensive and complex process, modeling of the freeze-drying process is a challenging task. In this study, a novel data scaling method called multiple output-dependent data scaling (MODDS) has been proposed and combined with an adaptive neuro-fuzzy inference system (ANFIS) to forecast the moisture content (MC), moisture ratio (MR), and drying rate (DR) values, which are outputs of freeze-drying behavior of apples. The input parameters of the freeze drying system are the sample thicknesses, drying time, pressure, relative humidity, chamber temperature, and sample temperature. Using the input parameters, the outputs of the freeze-drying process of apples were predicted using a hybrid system based on MODDS and ANFIS. In the first stage, only input parameters were scaled using MODDS. In the second stage, the outputs of freeze drying of apples were predicted with the scaled input parameters using ANFIS algorithm. Ninety-two samples were included in the data set, including 10-, 7-, and 5-mm samples. In order to evaluate the performance of the proposed model, the mean absolute error (MAE), mean square error (MSE), root mean square error (RMSE), coefficient of determination (R-2), index of agreement (IA), and mean absolute percentage error (MAPE) were used. Though MSE values of 2.48, 0.035, and 0.011 and IA values of 0.887, 0.887, and 0.466 were obtained for MC, MR, and DR, respectively, using the ANFIS prediction algorithm the hybrid MODDS-ANFIS model achieved MSE values of 0.003, 0.00005, and 0.00007 and IA values of 0.999, 0.999, and 0.993 for the prediction of MC, MR, and DR, respectively. The results obtained demonstrate that the proposed hybrid system is a robust and efficient method for the modeling and prediction of freeze-drying behavior of apples.