Neural Network and Regression Modeling of Extrusion Processing Parameters and Properties of Extrudates containing DDGS

Transcription

1 Iowa State University From the SelectedWorks of Kurt A. Rosentrater June, 7 Neural Network and Regression Modeling of Extrusion Processing Parameters and Properties of Extrudates containing DDGS Nehru Chevanan, South Dakota State University Kasiviswanathan Muthukumarappan, South Dakota State University Kurt A. Rosentrater, United States Department of Agriculture Available at:

2 An ASABE Meeting Presentation Paper Number: 7667 Neural Network and Regression Modeling of Extrusion Processing Parameters and Properties of Extrudates containing DDGS Nehru Chevanan South Dakota State University, Brookings, SD. Muthukumarappan K Professor, South Dakota State University, Brookings, SD. muthukum@sdstate.edu Kurt A Rosentrater Bioprocess Engineer, North Central Agricultural Research Station, USDA, ARS, Brookings, SD krosentr@ngirl.ars.usda.gov. Written for presentation at the 7 ASABE Annual International Meeting Sponsored by ASABE Minneapolis Convention Center Minneapolis, Minnesota 7 - June 7 Abstract. Two extrusion experiments using a single screw extruder were conducted with an ingredient blend containing 4% DDGS, along with soy flour, corn flour, fish meal, vitamin mix, and mineral mix, with the net protein content adjusted to 8%. The variables controlled in the first experiment included 7 levels of die size, 3 levels of moisture content, 3 levels of temperature gradient in the barrel, and one screw speed. The variables altered in the second experiment included 3 levels of moisture content, 3 levels of temperature gradient in the barrel, 5 levels of screw speed, and one die size. Regression models and Neural Network (NN) models were then developed using the data pooled from the two experiments to predict extrudate properties and extrusion processing parameters. In general, both regression and NN models predicted the extrusion processing parameters with better accuracy than the extrudate properties. With the regression modeling, even though increasing the number of input variables from 3 to 6 resulted in better R values, there was no significant decrease in the coefficient of variation between the measured and predicted variables. On the other hand, the NN models developed with 3 input variables (L/D ratio of die, moisture content and temperature gradient) predicted the extrusion processing parameters and extrudate properties with better accuracy than the regression models developed with the same 3 input variables. Furthermore, increasing the number of input variables resulted in better accuracy of prediction for both extrudate properties and extrusion processing parameters, and the standard error and coefficient of variation were also found to decrease. The highest accuracy of prediction was observed for the NN models developed to predict the extrusion processing parameters with 6 input variables (D, L, L/D ratio of die, moisture content, temperature gradient and screw speed). Because of its ability to account for variation, NN modeling has great potential for developing robust models for extrusion processing. The authors are solely responsible for the content of this technical presentation. The technical presentation does not necessarily reflect the official position of the American Society of Agricultural and Biological Engineers (ASABE), and its printing and distribution does not constitute an endorsement of views which may be expressed. Technical presentations are not subject to the formal peer review process by ASABE editorial committees; therefore, they are not to be presented as refereed publications. Citation of this work should state that it is from an ASABE meeting paper. EXAMPLE: Author's Last Name, Initials. 7. Title of Presentation. ASABE Paper No. 7xxxx. St. Joseph, Mich.: ASABE. For information about securing permission to reprint or reproduce a technical presentation, please contact ASABE at rutter@asabe.org or (95 Niles Road, St. Joseph, MI USA).

3 Keywords. Modeling, neural network regression, extrusion, extrudate, properties, processing parameters. The authors are solely responsible for the content of this technical presentation. The technical presentation does not necessarily reflect the official position of the American Society of Agricultural and Biological Engineers (ASABE), and its printing and distribution does not constitute an endorsement of views which may be expressed. Technical presentations are not subject to the formal peer review process by ASABE editorial committees; therefore, they are not to be presented as refereed publications. Citation of this work should state that it is from an ASABE meeting paper. EXAMPLE: Author's Last Name, Initials. 7. Title of Presentation. ASABE Paper No. 7xxxx. St. Joseph, Mich.: ASABE. For information about securing permission to reprint or reproduce a technical presentation, please contact ASABE at rutter@asabe.org or (95 Niles Road, St. Joseph, MI USA).

4 Introduction Extrusion processing is a very complex process, involving numerous interdependent input parameters (both process and system variables) and output parameters. Process parameters are the operating conditions that can be controlled and manipulated directly, such as raw material characteristics, moisture content, screw speed, screw configuration, barrel temperature, etc. System parameters are influenced by the process parameters and subsequently affect the output parameters, and include residence time, specific mechanical energy, pressure build up, viscosity of the dough, etc. Output parameters include extrudate expansion, bulk density, mechanical and chemical properties such as breaking strength, pellet durability, water solubility index, water absorption index, nutrient content, extent of gelatinization, etc. Various models have been developed to understand the extrusion process in order to quantify and predict product characteristics. Two approaches are generally followed in extrusion processing. In the first, models have been developed to predict the system parameters applying well understood engineering and scientific principles, and then the output parameters can be predicted based on the system parameters. In the second approach, the output parameters are predicted directly from the process parameters without considering the physical/chemical phenomena occurring inside the extruder. Numerous modeling studies have been carried out by applying engineering fundamentals, such as flow modeling, thermal modeling, and product transformation modeling, to understand the biochemical/thermomechanical changes occurring inside the barrel and their influences upon resulting final product properties (Barres et al. 99; Bruin et al. 978; Dallevalle 993; Frazier et al. 98; Jager et al. 99; Levine and Rockwood, 985; Levine et al. 987; Li and Hsieh, 994; Li et al. 997; Mohamed et al. 99; Moysey and Thompson, 5; Olkku et al. 98; Vanionpaa, 99, 995; Vergnes et al. 99; Zuilichem, 99). Most models predict the various system parameters from the processing parameters. There are only a few modeling studies published on prediction of output parameters based on system parameters (Yacu, 985; Tayeb et al. 988; Kirby et al. 988; Mueser and Van, 987). In this approach, the output parameters were typically predicted directly from process parameters. Most often regression modeling and response surface modeling were employed for this purpose. All mathematical modeling by response surface and regression techniques are product specific and machine specific. Response surface modeling is an empirical model building technique where the physical relationships are not known (Box and Draper, 987), and is used to determine optimum conditions for obtaining the maximum or minimum response within the operating conditions. Regression modeling is also widely used to determine the relationships between the input and output variables in extrusion processing, which are often nonlinear in nature. Hence the nonlinear regression equations will generally contain many cross product terms and higher order terms. Due to this, there is the possibility of introducing very large error when there is actually little variation in the operating conditions. In regression modeling, mathematical relationships are established to obtain good results through approximation, without necessarily understanding the actual process. This also increases the possibility of introducing error. Neural Network (NN) modeling, on the other hand, is an alternative modeling tool and can be used successfully for extrusion processing (Batchelor et al. 997; Ganjyal et al. 6) to overcome some of these problems. NN is a type of mathematical algorithm which has the capability of relating the input and output parameters, learning from examples through iteration, without requiring prior knowledge of the specific relationships between the parameters (Torrecilla et al. 5). The main advantages of NN over mathematical modeling are its fast processing, learning and adopting to new or changed environments, and application to

5 unlearned data (Torrecilla et al. 4; Gonclaves, 6). NN has performed well even in noisy, incomplete, and inconsistent data (Bochereau et al. 99; Biollereaux et al. 3). For example, in extrusion processing, Linko et al. (99) used NN for control of specific mechanical energy on the basis of screw speed in flat bread production. Eerikainan used NN for modeling torque, specific mechanical energy, and pressure using two independently trained feed forward NN. Ganjyal et al. (6) used NN and reported that it performed better than the regression model for predicting the extrudate properties. These studies have shown that NN has greater potential to be used in extrusion processing for modeling both system parameters and output parameters than either response surface or regression modeling. Some of the commonly varied variables in extrusion processing include moisture content of the ingredient blend, screw speed, temperature gradient in the barrel, die dimensions, screw configuration, etc. To develop a robust model, it may not be possible to vary all these variables in an experiment to study the extrusion process. Usually two to three variables are varied in a given experiment, while all other variables are kept constant; many such experiments are then conducted to understand the effect of all the parameters. Since NN models are developed through learning by iteration and training, it is possible to obtain a robust prediction model with many input variables from data collected from different experiments. Hence the objectives of this study were to compare the effectiveness of NN models and regression models, using data collected from two unique experiments, to vary the number of input variables into these models, and to predict extrudate properties and extrusion processing parameters with the developed models. Materials and Methods Sample preparation An ingredient blend containing 4% DDGS, along with appropriate quantities of soy flour, corn flour, Menhaden fish meal, whey, vitamin mix, and mineral mix, with the net protein adjusted to 8%, was prepared following Chevanan et al. (5a, b). DDGS was provided by Dakota Ethanol LLC (Wentworth, SD), and was ground to a particle size of approximately µm using a laboratory grinder (S5 Disc Mill, Genmills Inc., Clifton, NJ). Corn flour was provided by Cargill Dry Ingredients (Paris, IL), and soy flour was provided by Cargill Soy Protein Solutions (Cedar Rapids, IA). The ingredients were mixed in a laboratory scale mixer (N5 Mixer, Hobart Corporation, Troy, OH) for min, and then stored overnight at refrigerated conditions ( + C) for moisture stabilization. The moisture content of the ingredient mix was adjusted by adding required quantities of water during mixing. Experimental Design The extrusion studies were carried out using a single screw extruder (Brabender Plasti- Corder, model PL, South Hackensack, NJ), which had a barrel length of 37.5 mm, with a length to diameter ratio of :. The die assembly had an internal conical section, and had a length of.6 mm. A screw with a uniform pitch of 9.5 mm was used in the experiments. The screw had variable flute depth, with the depth at the feed portion of 9.5 mm, and near the die of 3.8 mm. The compression ratio achieved inside the barrel was 3:. The speed of the screw and the temperature inside the barrel were controlled by a computer control system. The extruder barrel s band heaters allowed the temperature of the feed zone, transition zone in the barrel, and the die section to be controlled. Compressed air cooling was provided in the barrel section as well, but not in the die section. The extruder had a 7.5 HP motor, and the computer system could control the speed of the screw between to rpm ( to rad/s).

6 Two sets of experiments were conducted using same ingredient mix with the following experimental designs. Experiment Experiments were conducted with a 3x3x7 full factorial design: three levels of moisture content (MC) (5,, and 5% (wb)); three levels of temperature gradient in the barrel (T) (9- -, 9--, and C), and seven levels of die geometry (with a length-todiameter ratio (L/D) ranging from 3.3 to.). The screw speed was maintained at 3 rpm (3.6 rad/s) throughout the experiment. In this experiment, both extrusion processing parameters and extrudate properties were measured. Experiment Experiments were conducted using a 3x3x5 full factorial design: three levels of moisture content (5,, and 5%,wb), three levels of temperature gradient in the barrel (9--, 9-3-3, and C), and five levels of screw speed (8,,, 4 and 6 rpm). The only die insert used in these experiments had a diameter of.7 mm and a length of 3 mm. In this experiment only the extrusion processing parameters were measured. Measurement of Extrudate Properties After processing, extrudates were cut into mm lengths. Unit density (UD) was determined as the ratio of extrudate mass to the calculated volume of each piece by assuming cylindrical shapes for each extrudate, following Jamin and Flores (998). Bulk density (BD) was measured using a standard bushel tester (Seedburo Equipment Co., Chicago, IL) following the method prescribed by USDA (999). Pellet durability (PD) was determined following ASAE standard method S69.4 (996), where g of the extrudates were tumbled inside a pellet durabilty tester (Seedburo Equipment Co., Chicago, IL) for min, and then hand sieved through a No.6 screen. PD was calculated as: Mass of pellets after tumbling Pellet Durability (%) = x () Mass of Pellets before tumbling Water absorption index (WAI) was determined according to Jones et al. (). To determine WAI,.5 g of finely ground sample was suspended in 3 ml of distilled water at 3 C in 5 ml tarred centrifuge tubes. The tubes were stirred intermittently over a period of 3 min, and then centrifuged at 3 x g for min. The supernatant water was transferred into tarred aluminum dishes. The mass of the remaining gel was weighed, and WAI was calculated as the ratio of gel mass to the original sample mass. Water solubility index (WSI), on the other hand, was determined as the water soluble fraction in the supernatant, expressed as a percentage of the dry sample (Jones et al. ). The WSI was determined from the amount of dried solids recovered by evaporating the resulting supernatant in an oven at 35 C for h, and was calculated as the mass of solids in the extract to the original sample mass (%). Sinking velocity (SV) was measured following the method used by Himadri et al. (993), by recording the time taken for an extrudate of mm length to travel from the surface of water to a depth of 45 mm in a ml graduated cylinder. Color of the extrudates was determined using a spectrophotometer (Portable model CM 5d, Minolta Corporation, Ramsey, NJ) using the L- a-b opposable color space, where L* quantified the brightness / darkness, a* quantified redness / greenness, and b* quantified yellowness / blueness of the samples.

7 Measurement of Extrusion Processing Parameters The temperature of the ingredient melt at the end of the barrel (TB) was measured with a Type J thermocouple, which had a range of to 4 C. The absolute pressure (P) inside the die was recorded with a pressure transducer, which had a range of to 68.9 MP. The temperature of the melt in the die section (TD) was recorded with a thermocouple that was integral to the pressure transducer. The net torque ( Ω ) was measured with a torque transducer, which had a range of to 39 N-m. During experimentation, extrudate samples were collected for 3 s intervals, and the mass flow rate (MFR) was then calculated (g/min). Based on the torque and the mass flow rate data, other processing variables were then determined. Specific mechanical energy (SME) (J/g) was calculated according to Harper (98) and Martelli (983) as: SME = ( Ω * ω *6) / () where Ω is the net torque exerted on the extruder drive (N-m), ω is the angular velocity of the screw (rad/s) and m feed is the mass flow rate (g/min). Apparent viscosity (η) of the dough in the extruder (Pa-s) was calculated by approximating the barrel and screw as a concentric cylinder viscometer arrangement, and then incorporating corrections for the tapered screw geometry following Konkoly (997), Lam and Flores (3), Lo and Moreira (996), Rogers (97), and Rosentrater et al.( 5). The apparent viscosity was determined as the ratio of shear stress (τ s ) at the screw surface (N/m ) to the shear rate (γ s ) at the screw (/s), and was calculated using: m feed τ Ω /(* π *( r ) * L ) = C Ω (3) s = coor s ss γ s coor = ( * ω * r ) /( r ( r ) = C b b sr ω (4) where r corr is the radius correction due to the frustum geometry ( ( r eff + reff reff + reff ) / 3,m), r eff is the effective radius including the screw root radius and half of the flight height (m), L is the screw length in the axial direction (m), C ss is a correction factor for shear stress ( for the specific screw used in this study), γ s is the shear rate at the screw (/s), r b is the barrel radius (m) and C sr is the correction factor for shear rate (6.3 for the specific screw used in this study). Regression modeling To analyze the data, multiple linear regression models were then developed using SAS v.8 (SAS Institute, Cary, NC) software. Die dimensions, temperature profile in the barrel, and moisture content of the ingredient mix were input variables for the models. During analysis, it was determined that L/D predicted extrudate properties and extrusion processing parameters with higher R values compared to L or D alone as primary geometric parameters. Thus, for the data collected from experiment, the regression models were developed to examine the extrusion processing parameters and extrudate properties. Regression models were also developed for the extrusion processing parameters only, using six input variables, namely L, D, and L/D ratio of die nozzle, moisture content, temperature, and screw speed, using the data obtained from both experiment and together. Only statistically significant terms were included in the final models, which were determined using a step-wise selection method (Neter et al. 99) with inclusion and exclusion p values of. and.5, respectively. Thus the criteria used for selection of a particular regression model were: () include only statistically significant (p<.) parameters in the model, () maximize R value, and (3) minimize coefficient of variation (CV) and standard error (SE) values.

8 NN modeling NN models were developed using commercially available software (Neurosolutions TM V.4, Neurodimensions, Inc., Gainesville, FL). Networks were built using the Neural Builder for Excel sub-program in the software. A generalized feed forward model using a back propagation algorithm was used for model development, because it resulted in better R values and minimized error compared to other models available in the software. Variables altered in the program included momentum rate (. to.7), initial step size (. to.3), and the default decay weight of.. These values were used for all models. In preliminary investigations of the data set, it was observed that good R values could be achieved using one hidden layer and by varying the number of neurons and other parameters. Hence all subsequent models were developed using one hidden layer. The data set was then randomized, and the first 7% of the data set were used for training and the remaining 3% were used for performance testing. Highest R values and minimum coefficient of variation and standard error were used as criterion for selecting the best models. The software could be used to develop NN models to predict each output variable using multiple input variables individually, or MIMO (Multiple Input and Multiple Output) simultaneously. For comparison of different models, standard training steps of epochs, for 3 times, was followed for all models. NN models were developed to predict each extrudate property, each extrusion processing parameter, all extrudate properties, and all extrusion processing parameters simultaneously. In order to determine the effect of the number of input variables on accuracy, NN models were developed using 3 input variables (L/D ratio, moisture content and temperature) and 5 input variables (L, D, L/D ratio, moisture content and temperature) for the extrudate properties and extrusion processing parameters of experiment. NN models were also developed for the extrusion processing parameters for the combined data in experiments and using 6 input variables (L, D, L/D ratio, moisture content, screw speed and temperature). Results and Discussion Regression modeling using 3 input variables predicted the extrusion processing parameters with higher R values compared to the extrudate properties using the same three input variables (Table ). This was true with NN modeling also. In regression modeling, even though increasing the number of input variables resulted in better R values, there was not much reduction in the error between the measured and predicted values (Table and ). In general, NN models predicted the extrusion processing parameters and extrudate properties with better accuracy, as evidenced by the coefficient of variation between the measured and predicted values, which were all less compared to the regression models. In the NN models, higher R values were exhibited for extrusion processing parameters compared to the extrudate properties for a particular network with the same number of training steps. Regression models Most of the regression models achieved R values greater than.6 and used first and second order terms (both cross product and square terms) from the data collected from experiment. But, regression models to predict WSI, a* value, and SME resulted in R values of only.4,.9, and.56, respectively (Table ). The WAI and temperature of dough in the die resulted in R values of.65 and.97, respectively, but contained only 3 significant terms, namely, L/D ratio, MC, and T. All other dependent variables contained cross product terms, squared terms, or both. Pellet durability, WSI, pressure in the die, and apparent viscosity, on the other hand, had 6 significant terms in the regression models. Bulk density, L* value, a* value,

9 Table. Regression models for extrudate properties and extrusion processing parameters using moisture content (M), barrel temperature (T) and length-to-diameter ratio of die (L/D) Property Regression model SE CV (%) UD BD PD WAI WSI SV L* a* B*.4 +.3*(L/D) -.5*MC +.8*T.3*(L/D)*MC *(L/D) +.*MC +.6*T +.*(L/D) -.3MC *(L/D)-.3*MC-.*T-.33*(L/D)*MC+.4*T*MC-.54*(L/D).99-.*(L/D)+.3*MC+.*T.4+.57*(L/D)-.5*MC+.4*T+.*(L/D)*T-.7*(L/D)*MC+.*T*MC *(L/D)-.5*MC-.*T+.6*(L/D) *(L/D)+3.*MC-.3*T-.9*(L/D)*MC-.9*(MC).4+.4*(L/D)-.3*MC+.*T-.3*(L/D)*T+.*(L/D)*MC *(L/D)-.67*MC-.7*T+.4*T*MC MFR TB TD P SME Ω *(L/D)+8.4*MC+.7*T-.6*MC *(L/D)-.9*MC+.39*T-.4*(L/D)*T-.59*(L/D) *(L/D)+.48*MC+.7*T *(L/D)-.7*MC-4.*T-.3*(L/D)*MC+.9*T*MC-3.*(L/D) *(L/D)+8.6*MC-3.6*T-3.3*(L/D) -7.4*MC *(L/D)+59.6*MC-.47*T-.53*MC *(L/D)+449*MC-8.8*T-.*(L/D)*T-5.3*(L/D)*MC-6.5*(L/D) -.3*MC UD - Unit density, BD - Bulk density, PD - Pellet durability, WAI - Water soluble index, WSI - Water soluble index, SV - sinking velocity, L* - Brightness, a* - Redness, b* - Yellowness, MFR - Mass flow rate, TB - Temperature of dough at the barrel, TD - Temperature of dough at die, P - Pressure developed in the die, SME - Specific mechanical energy, Ω - Torque, η - Viscosity of dough Table. Regression models for extrusion processing parameters using moisture content (MC), barrel temperature (T), length (L), diameter(d), length-to-diameter ratio of die (L/D), and screw speed (rpm) Prop Regression model R SE CV Erty MFR *D 5.9*L *(L/D) + 4.3*MC.3*T +.4*rpm -.36*D*L -.6*D*MC + 3.5*L*(L/D) +.3*L*T +.55*L*MC -.4*(L/D)*T -.7*(L/D)*MC +.*T*MC +.*T*rpm -.*MC*rpm *(L/D) -.4*T -.537*MC -.9*rpm TB *D 3.34*L +.4*(L/D)-.86*MC +.8*T +.33*rpm + 6.9*D*(L/D).49*D*T +.9*D*MC +.6*L*T.*L*MC.*(L/D)*T +.*MC*T.*T*rpm.*rpm TD *D *L 9.77*(L/D).33*MC +.3*T.*rpm +.44 * (D/L) +.86*D*T.8*D*MC 6.5*L*(L/D).3*L*T +.5*(L/D)*T +.*T*rpm +.4*MC*rpm *(L/D).5*T +.35*MC -.5*rpm P *D 73.5*L 43.5*(L/D) 3.89*MC.6*T.*rpm 4.45*D*L +.8*D*L +.*D*(L/D).*D*T +.84*D*MC.*L*T.6*L*MC +.*(L/D)*T +.49*(L/D)*MC +.9*T*MC +.7*T +.3*D +.9*MC SME *D 445.5*L + 93.*(L/D) + 3.*MC +.66*T 6.4*rpm *D(L/D).63*D*T + 7.7*D*MC +.78*L*T 5.3*L*MC.5*(L/D)*T *(L/D)*MC +.*T*rpm +.7*MC*rpm *L 56.67*(L/D).3*T 7.5*MC +.4*rpm Ω *D 36.8*L 3.6*(L/D) + 5.6*MC.75*T.63*rpm *D*(L/D) +.8*D*T +.*D*MC-.4*L*MC +.78*(L/D)*MC +.*T*MC +.*T +.36*MC + 4.4*D.5*T.55*MC +.*rpm η *D 33*L 49*(L/D) *MC 46.3*T 68.6*rpm + 645*D*(L/D) + 6.*D*T *(L/D)*MC +.*T*MC +.*T*rpm + 3.8*MC*rpm *D *D.346*T 7.39*MC +.8*rpm MFR - Mass flow rate, TB - Temperature of dough at the barrel, TD - Temperature of the dough at the die, P - Absolute pressure, SME - Specific mechanical energy, Ω - Torque, η - Apparent viscosity. (%)

10 temperature of dough in the barrel, and SME had 5 significant terms in the regression model. Unit density, sinking velocity, b* value, mass flow rate and torque had 4 significant terms in the regression model (Table ). Ultimately, regression modeling was marginally adequate for summarizing most of the dependent variables in the study. And, higher cross product terms and square terms in the models may lead to the possibility of a geometric increase in error. By increasing the input variables from 3 to 6, and combining the data collected from the two different experiments, it was observed that the R value to predict the extrusion processing parameters increased for all, except for mass flow rate (Table ). But the numbers of significant terms in the models increased substantially, and were in the range of 8 to. Additionally, there was no significant reduction in the coefficient of variation between the measured and predicted values (Table and ) as the models expanded in size. Moreover, rigid mathematical models, with many cross product terms, increase the possibility of introducing large error. NN models from experiment The R, CV, and SE values of the resulting NN models for predicting each extrudate property individually, and for the MIMO models (to predict all properties of extrudates simultaneously) from 3 input variables are given in Tables 3 and 4. The R, CV, and SE values of the NN models for predicting each extrusion processing parameter individually, and the MIMO models (to predict all extrusion processing parameters simultaneously) from 3 input variables are given in Tables 5 and 6. Results from NN models to predict all properties of extrudates from 5 input variables are given in Tables 7 and 8, whereas results for all the extrusion processing parameters are given in Tables 9 and. In general, lower R values in the regression models corresponded to lower R values in the NN models for particular properties. Similarly, higher R values in the regression models correspond to higher R values in the NN models. The lowest and highest R values of.9 and.97 were observed for a* value and TD using regression models with 3 input variables (Table ). In the same way, lowest and highest R values of.6 and.984 were observed for the same two variables namely, a* value and TD with NN models using 3 input variables (Table 3 and 5). But, the R values of all the neural network models were always higher than those of the corresponding regression model for a particular property. This was true for the NN models for each parameter individually, as well as for the models to predict all parameters simultaneously. Moreover, the R value of each NN model using 5 input variables was always higher than those using 3 input variables. The R values of the NN models to predict the extrudate properties individually using 3 input variables were in the range of.7 to.94 (Table 3), and the R values of the NN models to predict the extrudate properties individually with 5 input variables were in the range of.785 to.938 (Table 7). In the same way, the R value of the NN models to predict extrusion processing parameters individually using 3 input variables were in the range of.89 to.984 (Table 5), and the R values of the NN models to predict the extrusion processing parameters individually using 5 input variables were in the range of.86 to.984 (Table 9). This was true for the MIMO NN models as well. Table 3. Neural network models for each extrudate property (3 input parameters) Output UD BD PD WAI WSI SV L* a* b* R SE CV(%) Network Initial step size =., Momentum rate =., UD - Unit density, BD - Bulk density, PD - Pellet durability, WAI - Water absorption index, WSI - Water solubility index, L* - Brightness, a* - Redness, b* - Yellowness Number of input variables - Number of neurons in the hidden layer - Number of output variables

11 Table 4. MIMO neural network models for all extrudate properties (3 input parameters) Output UD BD PD WAI WSI SV L* A* b* R SE CV (%) Network Initial step size =., Momentum rate =., UD - Unit density, BD - Bulk density, PD - Pellet durability, WAI - Water absorption index, WSI - Water solubility index, L* - Brightness, a* - Redness, b* - Yellowness Number of input variables - Number of neurons in the hidden layer - Number of output variables Table 5. Neural network models for each extrusion processing parameter (3 input parameters) Output MFR TB TD P SME Ω η R SE CV (%) Network Initial step size =., Momentum rate =., MFR - Mass flow rate, TB - Temperature of dough at the barrel, TD - Temperature of dough at the die, P - Absolute pressure inside the die, SME - Specific mechanical energy, Ω - Torque, η - Apparent viscosity of the dough Number of input variables - Number of neurons in the hidden layer - Number of output variables Table 6. MIMO neural network models for all extrusion processing parameters (3 input parameters) Output MFR TB TD P SME Ω η R SE CV (%) Network Initial step size =., Momentum rate =., MFR - Mass flow rate, TB - Temperature of dough at the barrel, TD - Temperature of dough at the die, P - Absolute pressure inside the die, SME - Specific mechanical energy, Ω - Torque, η - Apparent viscosity of the dough Number of input variables - Number of neurons in the hidden layer - Number of output variables Table 7. Neural network models for each extrudate property (5 input parameters) Output UD BD PD WAI WSI SV L* a* b* R SE CV (%) Network Initial step size =., Momentum rate =., UD - Unit density, BD - Bulk density, PD - Pellet durability, WAI - Water absorption index, WSI - Water solubility index, L* - Brightness, a* - Redness, b* - Yellowness Number of input variables - Number of neurons in the hidden layer - Number of output variables

12 Table 8. MIMO neural network models for all extrudate properties (5 input parameters) Output UD BD PD WAI WSI SV L* a* b* R SE CV (%) Network Initial step size =., Momentum rate -., UD - Unit density, BD - Bulk density, PD - Pellet durability, WAI - Water absorption index, WSI - Water solubility index, L* - Brightness, a* - Redness, b* - Yellowness Number of input variables - Number of neurons in the hidden layer - Number of output variables Table 9. Neural network models for each extrusion processing parameter (5 input parameters) Output MFR TB TD P SME Ω η R SE CV (%) Network Initial step size =., Momentum rate =., MFR - Mass flow rate, TB - Temperature of dough at the barrel, TD - Temperature of dough at the die, P - Absolute pressure inside the die, SME - Specific mechanical energy, Ω - Torque, η - Apparent viscosity of the dough Number of input variables - Number of neurons in the hidden layer - Number of output variables Table. MIMO neural network models for all extrusion processing parameters (5 input parameters) Output MFR TB TD P SME Ω η R SE CV (%) Network Initial step size =., Momentum rate =., MFR - Mass flow rate, TB - Temperature of dough at the barrel, TD - Temperature of dough at the die, P - Absolute pressure inside the die, SME - Specific mechanical energy, Ω - Torque, η - Apparent viscosity of the dough Number of input variables - Number of neurons in the hidden layer - Number of output variables The ingredients components in the feed ingredient mix play an important role in deciding the extrudate properties. In all the NN models developed in our experiments there was no input parameter pertaining to constituents of the ingredient mix like starch, protein, fat, fiber and ash content. Even though the accuracy of prediction of the NN models was very high compared to the regression models, R value as low as.6 and.7 were observed for a* value and WSI (with 3 input variables). This might be due to the fact that the neural network models developed in this study does not include any parameter for ingredient components such as starch, protein, fat, fiber, ash content and the interaction between these components with the machine parameters like screw speed, temperature gradient in the barrel, die dimensions significantly affected a* value and WSI. There is a possibility that the R values to predict extrudate properties can be further increased by incorporating constituents such as starch, protein, fat, fiber and ash content as input parameters in the NN model. The higher R values for extrusion processing parameters indicated that the extrusion processing parameters such as mass flow rate, temperature of dough, pressure inside the barrel, specific mechanical energy, torque and apparent viscosity depends on the machine parameters such as temperature gradient in the barrel, screw speed, die dimensions, residence time etc. and the interaction effect between

13 ingredient components like starch, protein, fat, fiber and ash content with machine parameters was minimum. This might be due to the fact that the extrudate obtained with an ingredient mix containing 4% DDGS had little or no expansion and the biochemical changes occurring inside the barrel was minimum due to its low starch content. However, the accuracy of prediction of extrusion processing parameters also can be further increased by incorporating constituents in the ingredient mix such as starch, protein, fat, fiber and ash content as input parameters in the NN models, NN Models from both experiments The R, CV, and SE values for NN models for predicting each extrusion processing parameter individually, and MIMO models to predict all the extrusion processing parameters simultaneously, using 6 input variables pooled from both experiments, are given in the Tables and. The R value to predict each extrusion processing parameter separately, using 6 input variables, was always higher than the MIMO model to predict all the extrusion processing parameters simultaneously. The R value for each processing parameter was greater than.9 for all models. The highest R value,.99, was observed for temperature of dough at the die, while the lowest R value of.9, was observed for specific mechanical energy (Table ). The R value of the MIMO models to predict all the extrusion processing parameters simultaneously were in the range of.855 to.968. The highest R value,.975, was observed for temperature of the dough at the die, while the lowest R value of.855 was observed for specific mechanical energy (Table ). As the number of input variables was increased, a continuous decrease in the standard error and coefficient of variation was observed. Using 6 input variables and combining the results of both the experiments, the coefficient of variation were reduced to approximately %. This behavior clearly illustrates the difference in model performance based on the type of model structure used. The accuracy of prediction of NN models with 6 input variables for TB and TD were very high (R values of.988 and.99). In extrusion processing changes occurring in the thermal properties such as thermal conductivity, thermal diffusivity etc of the dough due to interaction between the ingredient components and machine parameters such as screw speed, temperature profile in the barrel, and die dimensions might be minimum and resulted in higher R values compared to other extrusion processing parameters. NN models with 6 input variables predicted the mass flow rate, and absolute pressure inside the barrel with R values of.974 and.98 respectively (Table ). This showed that the changes occurring in mass flow rate, absolute pressure inside the barrel due to interaction effect of ingredient components and machine parameters was more on these parameters compared to thermal properties. During extrusion processing with an ingredient mix containing 4% DDGS, we observed very little or no expansion by varying the screw speed, temperature profile in the barrel, die dimension and moisture content of the ingredient mix due to its low starch content. This might have resulted in lesser interaction effect on pressure developed inside the barrel and mass flow rate compared to specific mechanical energy, torque and apparent viscosity. R values of.9,.93 and.9 were observed for specific mechanical energy, torque and apparent viscosity. This showed that the changes occurring due to the interaction effect between the ingredient components and the machine parameters was maximum for specific mechanical energy consumption, torque and apparent viscosity of dough inside the barrel. Specific mechanical energy was a derived quantity from torque and mass flow rate, apparent viscosity was a derived quantity from torque and screw speed. Hence the minimum R values for these two extrusion processing parameters were expected.

14 Table. Neural network models for each extrusion processing parameters (6 input parameters) Output MFR TB TD P SME Ω η R SE CV (%) Network Initial step size =., Momentum rate =., MFR - Mass flow rate, TB - Temperature of dough at the barrel, TD - Temperature of dough at the die, P - Absolute pressure inside the die, SME - Specific mechanical energy, Ω - Torque, η - Apparent viscosity of the dough Number of input variables - Number of neurons in the hidden layer - Number of output variables Table. MIMO neural network models for all extrusion processing parameters (6 input parameters) Output MFR TB TD P SME Ω η R SE CV (%) Network Initial step size =., Momentum rate =., MFR - Mass flow rate, TB - Temperature of dough at the barrel, TD - Temperature of dough at the die, P - Absolute pressure inside the die, SME - Specific mechanical energy, Ω - Torque, η - Apparent viscosity of the dough Number of input variables - Number of neurons in the hidden layer - Number of output variables Comparison between regression and NN models The relationship between the measured and predicted values for each of the extrusion processing parameters, using six input variables (which was deemed to produce the best performance) and data collected from the experiments, are given in Figures to 7. In general, NN models predicted the extrusion processing parameters with a high degree of accuracy, and exhibited very low variation. In fact, the coefficient of variation between the actual and predicted values were nearly %. On the other hand, even though the R values between the predicted and measured values were fairly high for each parameter, there was a wide deviation between the actual and predicted values using multiple linear regression models. This can be clearly seen by the deviation of the data points in each graph. In fact, the coefficient of variation between the measured and predicted values were in the range of 3. to 4.% for the regression models using 6 input variables. The regression models, however, did predict the mass flow rate, temperature of dough inside the barrel, die, and absolute pressure, with fairly good R values, and the coefficient of variation between the measured and predicted values for these parameters were comparatively low. This might be due to lower degree of interaction between the ingredient components such as starch, protein, fat, fiber and ash content with machine parameters such as screw speed, temperature gradient in the barrel and die dimensions. But, the coefficient of variation between the measured and predicted values for SME, torque, and apparent viscosity were high. This might be due to higher degree of interaction between the ingredient components such as starch, protein, fat, fiber and ash content with the machine parameters such as screw speed, temperature gradient in the barrel and die dimensions. Specific mechanical energy and apparent viscosity were derived quantities from other parameters and hence the higher coefficient of variation between the actual and predicted values was expected. Most of the predicted SME values for the regression models at the lower end of the SME range ( to 4 J/g), were higher than actual, whereas, at higher end of the SME range (4 to 7 J/g), most of the predicted values were found to be lower than actual (Figure 6). The same trend was observed with torque and apparent viscosity as well. Most of the predicted torque values were high for the measured torques values between and

15 8 N-m, but most of the predicted torque values for the measured torque values between 8 to 4 N-m were found to be lower (Figure 7). In the case of apparent viscosity, there was a wide variation between the measured and predicted apparent viscosity observed. Most of the predicted apparent viscosity for the measured apparent viscosity above 8 Pa-s was found to be lower (Figure 8). Overall, these results show that NN models developed using 6 input variables resulted in a drastic reduction in the variation for parameter prediction compared to the multiple linear regression models. (a) NN Model Predicted mass flow rate, g/min Actual mass flow rate, g/min (b) Regression Model Predicted mass flow rate, g/min Actual mass flow rate, g/min Figure. Correlation between actual and predicted mass flow rate using 6 input variables

16 (a) NN Model Predicted temperature of dough at barrel, C Actual temperature of dough at barrel, C (b) Regression Model Predicted temperature of dough a barrel, C Actual temperature of dough at barrel, C Figure. Correlation between actual and predicted temperature of dough at barrel using 6 input variables (a) NN Model Predicted temperature of dough at die, C Actual temperature of dough at die, C Predicted temperature of dough at die, C (b) Regression Model Acutal temperature of dough at die, C Figure 3. Correlation between actual and predicted temperature of dough at die using 6 input variables 8

17 (a) NN Model Predicted pressure at die, MPa Actual pressure at die, MPa (b) Regression Model Predicted pressure at die, MPa Actual pressure at die, MPa Figure 4. Correlation between actual and predicted pressure at die using 6 input variables (a) NN Model 7 6 Predicted SME, J/g Actual SME, J/g 7 (b) Regression Model Predicted SME, J/g Actual SME, J/g Figure 5. Correlation between actual and predicted specific mechanical energy using 6 input variables

18 (a) NN Model 4 Predicted torque, N-m Actual torque, N-m (b) Regression Model 4 Predicted torque, N-m Actual torque, N-m Figure 6. Correlation between actual and predicted torque using 6 input variables 5 (a) NN Model 3 Predicted apparent viscosity, Pa-s Actual apprent viscosity, Pa-s (b) Regression Model Predicted apparent viscosity, Pa-s Actual apparent viscosity, Pa-s Figure 7. Correlation between actual and predicted apparent viscosity using 6 input variables

19 Conclusion Extrusion processing parameters and extrudate properties were analyzed and predicted using die dimensions, ingredient moisture content, and barrel temperature, by both regression modeling and Neural Network modeling. Irrespective of the number of input variables, NN models always predicted the extrudate properties and extrusion processing parameters with better accuracy and lower variation than the regression models. In general, both NN and regression models predicted the extrusion processing parameters with higher R values compared to the extrudate properties. The regression models predicted the extrusion processing parameters using 3 and 5 input variables with R values of.56 to.97 and.75 to.97 respectively. NN models predicted the extrusion processing parameters using 3, 5 and 6 input variables with R values of.89 to.984,.86 to.988 and.9 to.99 respectively. The regression models developed with 3 input variables contained 3 to 6 significant terms, while those with 6 input variables contained 8 to significant terms. In general, lower R value in the regression models corresponded to lower R value with the NN models. In NN modeling, increasing the number of input variables resulted in better accuracy of prediction. Even though the R values to predict the extrusion processing parameters with 6 input variables increased with regression models, there was no significant decrease in the coefficient of variation between the measured and predicted values of extrusion processing parameters. The main benefit of using NN models is the reduction in variation for parameter prediction. This type of analysis should be conducted for a wider range of extrusion settings to develop a more robust model. Acknowledgements We thankfully acknowledge the financial support provided by the Agricultural Experiment Station, South Dakota State University, and the North Central Agricultural Research Laboratory, USDA-ARS, Brookings, SD. References ASAE American Society of Agricultural Engineers Standards, Engineering Practices, and Data. The Society: St. Joseph, MI. Barres, C., B. Vergnes, and J. Tayeb. 99. An improved thermal model for the solid conveying section of a twin screw extrusion cooker. J. Food Eng. 5: Batchelor, W. D., X. B. Yang, and A. T. Tschanz Development of a neural network for soybean rust epidemics. Trans. ASAE 4: Bruin, S., D. J. V. Zuilichem, W. Stolp A review of fundamental and engineering aspects of extrusion of biopolymers in a single screw extruder. J. Food Process Engineering : Bochereacu, L., P. Bourgine, and B. Palagos. 99. A model for prediction by combining data analysis and neural networks: Applications to prediction of apple quality using near infrared spectra. J. Agric. Eng. Res. 5: 7-6. Boillereaux, L., C. Cadet, and A. L. Bail. 3. Thermal properties estimation during thawing via real-time neural network learing. J. Food Eng. 57: 7-3. Box, G. E. P., and N. R. Draper Emprical model building and response surfaces. New York, NY: John Wiley and Sons. Chevanan, N., K. A. Rosentrater, and K. Muthukumarappan. 5a. Physical properties of extruded tilapia feed with distillers dried grains with solubles. Paper No St. Joseph., MI: ASABE. Chevanan, N., Rosentrater, K. A., and Muthukumarappan, K. 5b. Effect of whey protein as a binder during extrusion of fish feed. Paper No. SD5-. St. Joseph., MI: ASABE.

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