Neural networks for predicting thermal conductivity of bakery products Shyam S. Sablani a, * , Oon-Doo Baik b,1 , Michele Marcotte b a Department of Bioresource and Agricultural Engineering, College of Agriculture, Sultan Qaboos University, P.O. Box-34, Al-Khod P.C. 123 Muscat, Oman b Food Research and Development Center, Agriculture and Agri-Food Canada, 3600 Boulvard Casavant, St. Hyacinthe, Que., Canada J2S 8E3 Received 14 October 2000; accepted 27 May 2001 Abstract An artificial neural network (ANN) approach was used to model the thermal conductivity of bakery products as a function of product moisture content, temperature and apparent density. The bakery products considered in this work were bread, bread dough, French bread, yellow cake, tortilla chip, whole wheat dough, baked chapati and cup cake. Data on thermal conductivity of bakery products were obtained from the literature for a wide range of product moisture contents, temperatures and apparent densities resulted from different baking conditions. In developing the ANN model, several configurations were evaluated. The optimal ANN model was found to be a network with six neurons in each of the two hidden layers. This optimal model was capable of predicting the thermal conductivity values of various bakery products for a wide range of conditions with a mean relative error of 10%, a mean absolute error of less than 0.02 W/m K and a standard error of about 0.003 W/m K. The simplest ANN model, which had one hidden layer and two neurons, predicted thermal conductivity values with a mean relative error of less than 15%. Ó 2002 Elsevier Science Ltd. All rights reserved. Keywords: Baking; Modeling; Thermo-physical properties 1. Introduction Thermal conductivity is one of the most important thermal properties of food/biological materials since it is needed in the analysis of heat transfer during processing. Data on thermal conductivity are required for math- ematical modeling and computer simulation of heat and moisture transport (Rask, 1989). In recent years, mathematical modeling and computer-based numerical analyses have become the main tools for understanding and predicting processing phenomena (Baik, Marcotte, Sablani, & Castaigne, 2001). Models can also incorpo- rate time/temperature-dependent thermal properties in- stead of average values for the whole process. The baking process results in a series of physical, chemical and biochemical changes in a product. These changes include volume expansion, evaporation of water, formation of a porous structure, denaturation of protein, gelatinization of starch, crust formation and browning reaction. During baking, heat is transferred mainly by convection from the heating media, and by radiation from oven walls to the product surface fol- lowed by conduction to the geometric center. At the same time, moisture diffuses outward to the product surface. The temperature and moisture distribution within the porous product can be predicted using dif- fusion equations of heat and water. In order to predict the temperature and water distribution in the product during baking, a knowledge of the product properties, including thermal conductivity as a function of pro- cessing conditions, is needed (Rask, 1989; Sablani, Marcotte, Baik, & Castaigne, 1998). Data on thermo- physical properties of dough and bakery products dur- ing baking are scarce as compared to fruits, vegetables, meat and meat products. Rask (1989) reviewed data and prediction models of thermal properties of bakery products, and Lind (1991) presented measurement techniques and models of thermal properties of dough Journal of Food Engineering 52 (2002) 299–304 www.elsevier.com/locate/jfoodeng * Corresponding author. Tel.: +968-515-289; fax: +968-513-418. E-mail address: shyam@squ.edu.om (S.S. Sablani). 1 Present address: School of Engineering, University of Guelph, Guelph, ON, N1G 2W1. 0260-8774/02/$ - see front matter Ó 2002 Elsevier Science Ltd. All rights reserved. PII:S0260-8774(01)00119-4