Computerization of StumboÕs method of thermal process calculations using neural networks Shyam S. Sablani * , Walid H. Shayya Department of Bioresource and Agricultural Engineering, College of Agriculture, Sultan Qaboos University, P.O. Box-34, Al Khod, P.C.-123, Muscat, Oman Received 7 January 2000; accepted 24 July 2000 Abstract The four heat penetration parameters in StumboÕs method of thermal process calculations were correlated using arti®cial neural networks (ANN). The process involved the development of two dierent arti®cial neural network models, one named ANNG for the parameter g (the dierence between the retort and food center temperatures) and the other named ANNFU for the parameter f h /U (the ratio of heating rate index to the sterilizing value). Both these models replace the 57 tables developed by Stumbo for assessing sterilizing eects. The ANNG model deals with estimating the process time for a given process lethality and involves g as the de- pendent (output) variable while f h /U, z (representing the temperature interval dierence that causes a tenfold change in decimal reduction time), and j cc (the cooling rate lag factor) are taken as the independent (input) variables. The ANNFU model involves the prediction of the lethality of a given process with the f h /U being taken as the dependent variable and z, j cc , and g as the independent variables. In developing each of the ANN models, several con®gurations were evaluated: (i) the input and output parameters were taken on a linear scale, (ii) the input and output parameters were taken after the transformation of some or all the input and output parameters using a logarithmic scale to the base 10, and (iii) all input and output parameters were transformed using a logarithmic scale to the base two. The optimum ANN models, ANNG and ANNFU, were those of the third con®guration. ANNG involved a network with six neurons in each of the three hidden layers while ANNFU included 16 neurons in each of the two hidden layers. The two optimal ANN models are capable of predicting the g and f h /U parameters in the range given in StumboÕs tables. In each in- stance, the predicted values were in close agreement with those listed in the tables. In addition, the developed ANN models can predict the intermediate values of any combination of inputs. Therefore, they eliminate the need for excessive storage requirements of tables and interpolations while computerizing thermal process calculations using StumboÕs method. Ó 2000 Elsevier Science Ltd. All rights reserved. Keywords: Thermal process calculations; Formula methods; Neural network modeling 1. Introduction Existing methods involving the solution of formulae for thermal process calculations have been widely used for many years in the food industry. The purpose of these is to estimate the process lethality of a given pro- cess, or alternatively to arrive at an appropriate process time under a given set of heating conditions to result in a given process lethality. The basic ideas of thermal pro- cess calculations are well presented in several published articles and textbooks (Ball & Olson, 1957; Stumbo, 1973; Hayakawa, 1978; Merson, Singh, & Carroad, 1978; Ramaswamy, Abdelrahim, & Smith, 1992). Pro- cess calculation methods are broadly divided into two classes, namely, general methods and formula methods. The general methods integrate the lethal eects by a graphical or numerical integration procedure based on the time±temperature data obtained from test containers processed under actual commercial processing condi- tions. On the other hand, the formula methods make use of heat penetration parameters with several mathemat- ical procedures to integrate the lethal eects of heat (Stumbo, 1973; Hayakawa, 1978; Ramaswamy et al., 1992). The general methods are accurate since no as- sumptions are made in relation to the nature of heating and cooling curves. However, the process time calcu- lated using such methods is speci®c for a given set of processing conditions. Alternatively, the formula meth- ods are used for convenience and have greater ¯exibility since there is no need to obtain experimental data for Journal of Food Engineering 47 (2001) 233±240 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). 0260-8774/00/$ - see front matter Ó 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 0 - 8 7 7 4 ( 0 0 ) 0 0 1 2 1 - 7