1384 JOURNAL OF FOOD SCIENCE—Vol. 68, Nr. 4, 2003 © 2003 Institute of Food Technologists Further reproduction prohibited without permission Food Engineering and Physical Properties JFS: Food Engineering and Physical Properties Modeling Selected Properties of Extruded Waxy Maize Cross-Linked Starches with Neural Networks G.M. GANJYAL, M.A. HANNA, AND D.D. JONES ABSTRACT: Extrusion process is described as a complex multiple input, multiple output system. Various cross- linked waxy maize starches were extruded at initial moisture contents of 20, 24, and 28% (dry basis) and screw speeds of 110, 150, and 190 rpm. Multiple Input, Single Output neural network models were developed for predicting individual product properties, and Multiple Input, Multiple Output models were developed for pre- dicting selected product properties at 1 time from selected input process parameters. Models varied only in the number of hidden neurons, ranging between 8 and 14. Models had R 2 values of 0.89 and greater. Models ex- plained the process and the influence of selected process parameters on selected product properties. Keywords: extrusion modeling, neural networks, cross-linked starches Introduction E XTRUSION PROCESSING IS STILL CONSIDERED TO BE MORE OF AN ART than a science. Numerous studies have been reported to date on the complexities of the extrusion process and modeling the same. Extrusion cooking of foods can be described as a process whereby moistened, starchy, and/or proteinaceous materials are cooked and worked into viscous, plastic-like dough. Cooking is ac- complished through the application of heat, either directly by steam injection or indirectly through jacketed barrels, and by dis- sipation of mechanical energy through shearing of the dough (Harper 1981a). Extrusion processing is used by manufacturing industries with materials such as rubber, plastics, polymers, and pharmaceutical products and is being used increasingly in food and feed process- ing. Research continues to develop new extrusion applications, with the emphasis on development of new products. Extrusion process still has not been described scientifically. Our inability to describe the process and to understand well the phenomena that occur in- side the extruder are major drawbacks to its adequate modeling. Just like extrusion technology, its modeling has evolved from achievements in the area of plastics extrusion theory. Olivera (1992) predicted that the special case of extruding foods, or more generally biological materials, is on the verge of separating off on its own. Myriad of experimental and numerical studies have reported the physical phenomena involved in the thermal processing of polymeric materials in extrusion (Tadmor and Klein 1978; Tadmor and Gogos 1979; Fenner 1980). Food extrusion has developed rap- idly during the past 50 y, with applications continually increasing in new areas of food processing (Harper 1981a). Good reviews on different aspects of extrusion of foods have been published (Harp- er 1981a, 1981b; Mercier and others 1989; Kokini and others 1992; Frame 1994; Ganjyal and Hanna 2002). Extrusion processing involves (1) process parameters (namely, raw material, moisture content in the raw material, screw speed, and barrel temperature), which are input parameters, (2) system parameters (residence time distribution, mean residence time, specific mechanical energy, and so on), and (3) product properties (namely, radial expansion, product densities, chemical properties, and mechanical properties), which are output parameters (Figure 1). Thus, extrusion cooking is a multiple input and multiple output process (Olkku and others 1984), which is difficult to reduce to a single output situation (Kulshrestha and others 1991). General predictive modeling is very difficult in the case of food processing applications because ingredients are diverse and can vary considerably. The 3 generally neglected differences between food extrusion and synthetic polymers extrusion are as follows: (1) A slip layer often forms during food extrusion. (Grooves in the barrel prevent the material from rotating with the screw but affect the mechanics of the process considerably.) (2) Physical and chemical changes during the process can affect flow and introduce instabil- ity, and (3) a minimal level of shear is needed during food extru- sion, contrary to plastics processing where, in general, only an av- erage level of shear has to be maintained. Thus food extrusion modeling tends to be product- and ma- chine-specific, and new product development tends to be by trial and error and good fortune. Modeling of the food extrusion process has benefited from available information on plastics extrusion. Nevertheless, food extrusion is much more complex than synthetic plastic polymer extrusion and, therefore, more difficult to express as simple mathematical models (Eerikainen and Linko 1989). Approaches that have been followed in modeling extrusion op- erations are mainly dynamic modeling and steady state modeling. Dynamic modeling (Levine and others 1986, 1987) describes the reaction of a process immediately after a perturbation (10 to 15 s) and is particularly useful for control and automation, whereas steady state modeling describes the state of the process after a period long enough for machine stabilization. Between the dynam- ic and steady state models lies the domain of long period (a few minutes) instabilities and metastable states (Roberts and Guy 1986, 1987), which can probably be explained by qualitative mod- els. Many of the research efforts on understanding the transforma- tions in extruders have been empirical. The easiest and most widely used approach has been response surface methodology, which al- lows one to establish mathematical relationships between operat-