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A Review on Residence Time Distribution (RTD) in Food Extruders and Study on the Potential of Neural Networks in RTD Modeling

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A Review on Residence Time Distribution (RTD) in Food Extruders and Study on the Potential of Neural Networks in RTD Modeling
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  1996  JOURNAL OF FOOD SCIENCE —Vol. 67, Nr. 6, 2002© 2002 Institute of Food Technologists  C   o  n   c  i    s   e  R   e  v  i    e  w  s  i   n  F    o   o   d    S   c  i    e  n   c   e    JFS:   Concise Reviews and Hypotheses in Food Science A Review on Residence Time Distribution (RTD)in Food Extruders and Study on the Potential of Neural Networks in RTD Modeling G. G  ANJYAL    AND  M. H  ANNA   ABSTRACT: Residence time distribution and mean residence time depend on process variables, namely feed rate,screw speed, feed moisture content, barrel temperature, die temperature and die diameter. Flow in an extruder hasbeen modeled by simulating residence time distribution, assuming the extruder to be a series of continuous-stirred-tank or plug-flow reactors. Others have developed relationships for mean residence time as functions of process variables. Better models can be developed using neural networks. As an example, data from the literature were used to model mean residence time as a function of process variables using statistical regression and neuralnetworks. Neural network models performed better than regression models.Keywords: extrusion modeling, residence time distribution, mean residence time, neural networks Introduction E  XTRUSION   COOKING   OF   FOODS   CAN   BE   DESCRIBED    AS    A    PROCESS  whereby moistened, starchy, and/or proteinaceous materialsare cooked and worked into a viscous, plastic-like dough. Cooking is accomplished through the application of heat, either directly by steam injection or indirectly through jacketed barrels, and by dissi-pation of mechanical energy through shearing of the dough (Harp-er 1981). One can expect that there is a certain residence-time dis-tribution (RTD) in an extruder, which may influence the quality of the food product; because the rates of desirable and undesirablechemical reactions are influenced differently by changes in processconditions. RTD is a measure of the length of time material spendsin the extruder. From the characteristics of the distribution it is pos-sible to derive information about the flow pattern in the extruder.Process variables such as the temperature, screw speed, andthroughput, along with screw configuration, control the mechanicaland thermal energy inputs and the RTD during twin-screw extru-sion (Meuser and others 1992; Choudhary and others 1997; Gogoiand Yam 1994). RTD is a function of extruder size (Colonna and oth-ers 1983).RTD in an extruder is a useful means of determining optimal pro-cessing conditions for mixing, cooking, and shearing reactions dur-ing the process. From knowledge of the RTD function one can esti-mate the degree of mixing, the residence time of mass flow, and theaverage total strain exerted on the mass during its transition andthus provide a clearer picture of how an extruder behaves as achemical reactor (Fichtali and Van de Voort 1989). These results,coupled with the knowledge of the operating variables such as tem-perature, screw speed, screw configuration, and moisture content,provide necessary information to predict what fraction of the mate-rial will undergo specific reactions. RTD studies are needed to char-acterize mixing conditions, flow patterns, and the extent of conver-sions and reactions of the biopolymers in any plasticating or cooking extruder (Singh and Rizvi 1998a).To date the control of the extrusion process has been consideredmore of an art than a science. There are a few references on thecontrol of the extrusion process using neural networks for modeling the process. Extrusion has been identified as a multiple input-out-put system. Modeling the extrusion process using neural networksand taking into account the RTD as a system parameter would proveto be a powerful tool for extrusion process control.The objectives of this study were to review the methods fordetermining residence time in an extruder, to review the effectsof process variables on residence time distribution and mean res-idence time, to review the modeling aspects of residence timedistribution and mean residence time, and to explore the po-tential of neural networks in modeling of residence time. Determination of residence time distribution RTD is usually determined by a stimulus response techniqueusing a tracer. RTD is generally described by E(t)- and F(t)-dia-grams (Levenspiel 1972), which represent the age distribution of the material in the extruder.RTD are characterized by their mean residence times (MRT) andPeclet numbers (Pe). The Peclet number, which was discussed by  Van Zuilichem and others (1988a), characterized the spread of RTDas(1)in which l is the extruder length, De is the axial dispersion coeffi-cient, and is the axial velocity in the extruder chambers. The great-er the Pe, the smaller the spread of the residence time. Peclet num-bers are usually determined by calculating the ratio of theresidence times for which 16% and 64% of the tracer have passed by the detector (Todd 1975). But, MRT is usually used to characterizeRTD. Experimental measurement of residence timedistribution Stimulus response techniques are typically used for the mea-surement of RTD. A stimulus is provided by a tracer (some colordye) and the response is measured by spectrophotometry or by reflectance colorimetry as the dye concentration in the extrudate(Colonna and others 1983). Online measurement of RTD using ra-dioactive tracers, electrical conductivity (Choudhary and Gautam  Vol. 67, Nr. 6, 2002 —   JOURNAL OF FOOD SCIENCE 1997     C    o    n    c    i    s    e    R    e    v    i    e    w    s    i    n    F    o    o    d    S    c    i    e    n    c    e Residence time distribution in extruders . . . 1998), dielectric properties (Golba 1980), and optical properties of the tracer have been reported.Colonna and others (1983) measured the RTD by means of aBlue No. 517-11 Givaudan- ‘Cogilor’ tracer. A tracer pellet (0.5 g) wasadded to the feeding zone. Samples were collected every 5 s andabsorbance at 610 nm of the extrudate was determined after stir-ring the ground starch (600 ± 1 mg) in 20 ml of 1 M KOH for 40 minat + 4 °C. RTD was represented as the residence time probability distribution showing probability that a flow element had a resi-dence time t as a function of time. Mange and others (1987) used aradioactive tracer technique with 42 K isotope in the form of nitrate.Irradiated potassium nitrate was mixed intimately with 5 g of flour.The mixture was poured instantaneously into the feed chute using remote-action pliers. Provision was made for measurement of RTDthroughout the length of the barrel by means of 4 scintillation scan-ners equipped with land collimators. Signals received by the indi-cator probes were transmitted to a data-acquisition unit and re-corded on magnetic media under microprocessor control. The RTDplots were obtained by plotting radioactivity of the tracer versusthe residence time.These post run methods measure the dye concentration in theextrudates after completing the extrusion experiment. Thoughthese methods are accurate, considerable time is needed for sam-ple preparation and determination of tracer concentration. More-over, manual sample collection and preparation increase experi-mental errors (Choudhary and Gautam 1998).Choudhary and Gautam (1998) developed a technique of mea-suring the RTD online based on the electrical conductivity of mate-rial in the die and used a series circuit consisting of a 5 mm dia die,a 10 Ohm resistor and a 15 V DC power supply. Change in the cur-rent flow was measured as a proportional voltage response acrossthe resistor.The dielectric properties of carbon black for online measurementof RTD were used by Golba (1980). The test cell consisted of a spe-cially designed parallel plate capacitor incorporated in a slit die. Various studies on measurement of RTD in extruders are sum-marized in Table 1. It becomes obvious that, when online measure-ment of RTD is possible using some of the techniques, as indicat-ed above, it would be of use for developing online process control,since RTD is an important system parameter which can be used inthe development of 2 step models (Gogoi and Yam 1994) for extru-sion process control.Different process variables, namely screw speed, feed rate, feedmoisture content, screw configuration, die temperature, and diepressure reportedly influence RTD and MRT. There has been vari-ability in the results reported on level of influence of these processvariables. A brief review of the effects of these variables on RTDfollows. Effects of screw speed Screw speed is one of the process parameters which has a strong effect on RTD and MRT. Screw speed determines the amount of time the material resides in the extruder. Obviously, with everything else held constant, when screw speed is increased, the residencetime is reduced. This has been validated by De Ruyck (1997), Singhand Rizvi (1998a), Ainsworth and others (1997), Yeh and Jaw (1998),Ollett and others (1989), Yeh and others (1992), Fichtali and others(1995), Van Zuilichem and others (1973), Lee and McCarthy (1996),Mange and others (1987), Olkku and others (1984), and Gogoi and Yam (1994).High screw speed resulted in short residence time and large dis-persion number (Yeh and others 1992; Yeh and Jaw 1998). The av-erage residence time in the feed zone was inversely proportional tothe rotational speed of the screws (Van Zuilichem and others1988b). According to Altomare and Ghossi (1986), throughput,screw speed, and screw profile had strong effects on MRT. Themost significant process variable affecting MRT was screw speed,followed by throughput (Gogoi and Yam 1994). As screw speed in-creased MRT decreased and RTD increased (De Ruyck 1997). A study by Lee and McCarthy (1996) showed that screw speedhad a strong effect on the E(t)- and F(t)-diagrams, with MRT vary-ing inversely with screw speed (62.5 to 162.5 rpm) from 206 s to 256s. The P estimates, which express the fraction of material in plug flow, varied inversely with screw speed from 0.41 to 0.55 for theoperating conditions in their study. Ollett and others (1989)showed that MRT decreased from about 80 s at 75 rpm to 40 to 50 sat 300 rpm. Singh and Rizvi (1998b) showed that average resi-dence time decreased sharply from 119.2 s to 80.8 s when screw speed was increased from 150 to 200 rpm, but decreased only mod-erately from 80.8 s to 74.8 s when the screw speed was further in-creased from 200 rpm to 250 rpm.But, there are some conflicting results reported in literature. Ainsworth and others (1997) reported that MRT decreased as thescrew speed increased whereas variance of the RTDs changed only slightly. Further, Altomare and Ghossi (1986) confirmed that varia-tion in screw speed, despite its influence on temperature and vis-cosity, did little to alter the shape of the dimensionless RTD andoverall mixing pattern.Empirical models have been developed to model the changes inRTD with changes in screw speed. Gogoi and Yam (1994) fitted asimple empirical equation to their data as(2) where a and b were empirical parameters and N was the screw speed(rpm); with value of b ranging from 0.3 to 0.4 Yeh and others (1992) developed an empirical correlation to ex-press the dispersion number as a power law function of Fr/Sp for atwin-screw extruder as(3) where k was coefficient, D was diffusivity (cm 2 /s), u was flow rate(cm/s), L was length of vessel (cm), F r  was feed rate (rpm), S p  wasscrew speed (rpm), and n was the power of F r /S p . This equation isrelevant to a specific material and extruder and gives some idea of the axial mixing from the operating conditions. They found thevalue of n to be 0.513 and that of k to be 0.014 with a correlationcoefficient of 0.813 for wheat flour.Mange and others (1987) concluded that effects of screw speed,screw configuration, screw speed, and screw dia must be observedin common. Other researchers have reported contradictory resultssaying that the effect of feed rate on the mean residence time wasmore pronounced than that of screw speed (Ainsworth and others1997). From varied results reported in literature on the effects of screw speed, it is concluded that the effects of different variablescan be confounding and complex. Effects of feed rate Feeding rate is the input rate of the material into the extruder. Itis another process parameter which has a pronounced effect onresidence time. MRT and RTD have been reported to decrease withincrease in feed rates (De Ruyck 1997; Ainsworth and others 1997; Yeh and others 1992; Fichtali and others 1995; Van Zuilichem andothers 1973; Olkku and others 1984; Gogoi and Yam 1994). Ainsworth and others (1997) reported that the effect of feed rateon the mean residence time was more pronounced than that of   1998  JOURNAL OF FOOD SCIENCE — Vol. 67, Nr. 6, 2002  C   o  n   c  i    s   e  R   e  v  i    e  w  s  i   n  F    o   o   d    S   c  i    e  n   c   e   Residence time distribution in extruders . . . Table 1—Summary of selected studies on residence time distribution in extruders AuthorExtruder type and feed usedRTD determination method used Ainsworth and othersCo-rotating twin-screw extruder andStimulus response technique. Indigocarmine (blue dye) and(1997)tarhanaextrudate analyzed by spectrophotometer.Altomare and GhossiIntermeshing co-rotating twin-screwRed dye (FD&C No. 40).(1986)extruder and river rice flour, RM-100Bounie (1988)Twin-screw and white wheat flourStimulus response techniques. Two heat-stable tracers, zincoxide and erythrosine, measuring absorbance of the tracers inthe extrudate by colorimetry.Colonna and othersTwin-screw extruder and maize starchColored tracer (Blue NO 517-11 Givaudan- ‘ Cogilor ’ ) by(1983)ROFECmeasuring its absorbance.Choudhary and GoutamTwin screw extruder and rice flourMeasuring the electrical conductivity of material in a die using(1998)sodium nitrate and erythrosine dye.De Ruyck (1997)Co rotating twin-screw extruder andStimulus response technique with NaCl tracer and responsewheat flourmeasured by IDF standard 17A for screw profile studies andby atomic absorption of Na with a varian spectra AA 30/40after enzymatic treatment for other studies.Fichtali and othersCo-rotating, intermeshing twin screwStimulus response technique with Manganese dioxide at 2:3(1995)extruder and dried caseinMnO 2  as tracer. The amount of 56 Mn isotope measured by g-ray emission with Canberra 8180 multianalyzer with a Ge detector.Gogoi and Yam (1994)Co-rotating twin-screw extruder andStimulus response technique, with FD&C red dye as a tracer.feed material consisted of 4 types ofHunter colorimeter was used to observe the ‘ a values ’ .degerminated yellow corn meal (cc-250,cc-400, pure and thick, and micro crisp)Jager and others (1995)Kneading extruder with commercial mixStimulus response technique with lithium chloride tracer. The Liof 22% protein, 65% starch, 10%content in the extrudate measured by a flame ionizationsugars, 2% fat and 1% ash (db) as feedspectrophotometer.Lee and Mccarthy (1996)Co rotating twin-screw extruder and riceStimulus response technique, with red dye of sodium erythrosinemeal as tracer. Response measured by color spectrophotometer.Mange and others (1987)Three twin screw extrudersStimulus response technique with radioactive isotope potassiumisotope 42 was used as tracer. The response measured by 4scintillation scanners equipped with lead collimators.Olkku and others (1984)Twin-screw cooking extruder and wheatStimulus response technique with 56 Mn tracer. Impulse responseflourmeasured by 6 NEA 1 x 1 in scintillation detectors.Ollett and others (1989)Co-rotating twin screw extruder andStimulus response technique with dye (0.5 g, Permicolwheat starchRed)mixed with 2.0 g starch. Dye concentrationmeasured by sectrophotometer.Peng and others (1994)Twin screw extruder and rice flourStimulus response technique with red dye and responsemeasured by Hunter colorimeter. Showed that the redness colorvalue cannot replace the red dye concentrations to determinethe residence time distribution.Van Zuilichem and othersSingle screw extruder and maizeRadio tracer technique, Isotope 64 Cu was used as a(1973)tracer and response measured by scintillation detector.Van Zuilichem and othersTwin screw extruder and maize gritsMeasured by coincidence technique described in Part II (Van(1988c)containing, 85% starch and 8% proteinZuilichem and others 1988b), which measures the 64 Cu activityon dry basisat the die outlet. Half way along the screws above midpoints, 2single detectors were placed, each normal to the screw.Yeh and Jaw (1998)Single screw extruder and rice flourStimulus response technique used for RTD (Altomare andGhossi 1986; Bounie 1988) with erythrosine as a tracer andconcentrations in extrudate measured by spectrophotometer.Yeh and others (1992)Co rotating twin screw extruder andStimulus response technique used for RTD (Altomare andwheat flour with 40% M.CGhossi 1986; Bounie, 1988) with erythrosine as a tracer andconcentrations in extrudate measured by spectrophotometer. screw speed. As feed supply increased both MRT and RTD de-creased (De Ruyck 1997). Yeh and others (1992) reported that in-creasing the feed rate reduced the MRT. The effect of feed rate wasmore pronounced than that of screw speed.It can be concluded that, for any extrusion process using eithera single or a twin screw extruder at a constant screw speed, when thefeed rate is increased there will be more material going into theextruder with time, leading to a decrease in the time the material will stay in the extruder, thus decreasing the residence time. Effects of screw configuration Screw configuration is another process parameter which hasbeen proven to have a pronounced effect on RTD and MRT.Gautam and Choudhary (1999) reported that the type, length, andposition of mixing elements significantly affected the RTD andmixing. A systematic increase in MRT was observed as mixing ele-ments were moved farther away from the die, as elements weremade longer, and as the spacing between the 2 elements was in-creased. They reported that by manipulation of the screw config-  Vol. 67, Nr. 6, 2002 —   JOURNAL OF FOOD SCIENCE 1999     C    o    n    c    i    s    e    R    e    v    i    e    w    s    i    n    F    o    o    d    S    c    i    e    n    c    e Residence time distribution in extruders . . . uration the residence time and mixing could be altered, which af-fected the type and the extent of reactions during extrusion, influ-encing extrudate characteristics. According to Altomare and Ghossi(1986), screw configuration influenced RTD the most. Greater pro-file differences were needed to induce a significant effect on resi-dence time, indicating that screw configuration had an effect onRTD (De Ruyck 1997).Ollett and others (1989) reported that RTD, for closely inter-meshing and self-wiping screws, were similar. Olkku and others(1984) reported that inclusion of a counter screw element broughtabout a remarkable broadening of the RTD, affecting the homoge-neity of the product. Thus, we can conclude that the screw config-uration has a significant effect on the RTD and MRT. Effects of moisture content, die configuration, andbarrel temperature Moisture content of the feed material is another process variable which affects the residence time. It has been reported that themoisture content has nominal effect on the residence time (Al-tomare and Ghossi 1986). Gogoi and Yam (1994) showed that mois-ture content had only borderline effect and die pressure and tem-perature had no significant effects. At a certain moisture contentand die dia the MRT and the dead time were approximately pro-portional (Van Zuilichem and others 1973).Other factors which are considered to have effects on the RTDare die configuration and barrel temperature. De Ruyck (1997)showed that as the die dia increased MRT and RTD decreased to asmall extent. The RTD appeared to depend mainly on the die dia(Olkku and others 1984). But contradictory to some of the abovestudies, Altomare and Ghossi (1986) reported die size and temper-ature had no effects on residence time.Thus, it can be seen that, according to the literature, the processvariables of screw speed, feed rate, and screw configuration havesignificant affects on RTD and MRT, though there have been somecontradictory results as to the most effective parameter. From theseresults it is clear that the relationships between the process vari-ables and the RTD, or the MRT, are complex, and will depend on theprocess. It may be important to highlight the fact that feed moisturecontent, die dia, and barrel temperature or product temperatureare confounding variable, namely changing any of these willchange the back pressure which will change the melt viscosity, which can change the pumping characteristics of a specific screw. Modeling residence time distribution and meanresidence time  A thorough understanding of the flow behavior in an extruder ismost useful when producing extruded food products or designing extruders (Bounie 1988). The modeling of flow conditions may beused (1) to quantify the effect of each successive screw element onthe flow behavior under different process conditions; (2) to predictthe extent of a continuous chemical reaction, especially when sys-tem transfer functions are available and when the kinetics of reac-tion are known; (3) to compare the flow characteristics and the ef-ficacy of different extruders; (4) to optimize the sequence of screw elements; and (5) to design and scale up extruders.Bounie (1988) reviewed modeling of the extrusion process. Hereported that one possible approach would be to determine exper-imentally the RTD of the food mix particles in the extruder. Concep-tual flow models may then be envisioned which represent the mainfeatures of the physical flow pattern, such as the positive transportzones, mixing zones, dead zones, recirculating loops, by-passes,and segregated flows. Numerous flow models including perfectplug flow (PFR-plug flow reactor), perfect mixing (CSTR-continuousstirred tank reactors), partial PFR and partial CSTR, CSTRs in series,GAMMA model (PFR + CSTRs in series), laminar pipe flow, disper-sion model, Wolf-Resnick model, and Levenspiel-Levich model,have been tested for single screw extruders (Van Zuilichem andothers 1973; Wolf and White 1976; Bruin and others 1978; Davidsonand others 1983). Other studies by Todd (1975), Janssen (1978), Werner and Eise (1979), Olkku and others (1984), Rauwendaal(1981), Walk (1982), and Kao and Allison (1984) examined RTDs intwin-screw extruders, but only a few of those suggested realisticflow models. Incomplete knowledge of the exact behavior in twin-screw extruders and the multivariate adjustment of most of theproposed combined models resulted in unsatisfactory model per-formance.Jager (1992) presented a numeric RTD model for corotating andcounter rotating twin-screw extruders. De Ruyck (1997) developeda RTD model by means of ISIM (interactive simulation) softwareprogram for a screw profile consisting of a positive screw element ina corotating twin-screw extruder. The extruder was simulated as acomplex reactor consisting of different subreactors of continuously stirred tanks, providing for recycling flows to compensate for theback flow that occurred just before the die. A mathematical model was developed by Van Zuilichem andothers (1988c) to simulate axial mixing in a twin-screw extruder. A comparison was made between the RTD predicted by the modeland the measurements on an actual counter-rotating, twin-screw extrusion of maize grits. The model contained an infinite seriesCSTR, each one representing 4 chambers. The leakage flows be-tween the screw chambers were described in the model as back mixed flows. With this model a fairly close simulation of the RTDcould be made. Singh and Rizvi (1998b) modeled exit age distribu-tions, E-curves using the approach of Wolf-White model, a cascadeof CSTRs. and a plug-flow in series with CSTR model. They reportedthat the last model of a plug-flow in series with CSTRs gave the bestfit for the observed E curves including their tails, and was used tomodel residence time curves in extrusion. A mathematical modelconsisting of plug flow reactors in series with a CSTR, cross flowing  with a dead volume, fitted with the experimental data with r 2  valueof 0.988 for a single screw extrusion (Yeh and Jaw 1998).Residence time is considered to be a system parameter that is alink between process variables such as screw speed and moisturecontent and product parameters such as texture and taste. Resi-dence time is characterized by MRT. MRT can be used more easily to develop links between the process variables and the productproperties. From a practical point of view, it is useful to be able tomanipulate the process variables to produce a desirable productquality attribute. Such a task is difficult because we lack a goodunderstanding of even simple food extrusion processes, let alonethose involving significant physico-chemical changes. Therefore,instead of relating process variables directly to the quality at-tributes, it is more sensible to take a 2-step approach: the first stepis to relate process variables with system parameters, and the sec-ond step is to relate system parameters with quality attributes of extrudate (Gogoi and Yam 1994). The first step should be taken by both theoretical and experimental means. The second step re-quires tests to determine how useful residence time is along withother system parameters such as specific mechanical energy forcorrelating quality attributes with parameters such as gelatiniza-tion/melting ratio and starch conversion.Gogoi and Yam (1994) developed regression models for MRT asa function of screw speed, throughput, moisture content, and dietemperature with an r 2  value of 0.84. The details of the models arepresented in Table 2. When the model was developed taking intoconsideration only screw speed and throughput, the model gave r 2  2000  JOURNAL OF FOOD SCIENCE — Vol. 67, Nr. 6, 2002  C   o  n   c  i    s   e  R   e  v  i    e  w  s  i   n  F    o   o   d    S   c  i    e  n   c   e   Residence time distribution in extruders . . . Table 3 — Neural network model results for selected data with different independent variables RStandardAuthorANN architectureSquaredError Zuilichem and others (1973)Three layered network, 2-4-1, with logistic function for both hiddenand output layersLR = 0.5, MO = 0.4, IW = 0.30.90631.688Gogoi and Yam (1994) DT, MC, SS and TPThree layered network, 4-7-1, with Gaussian function for both hiddenand output layersLR = 0.4, MO = 0.3, IW = 0.30.91050.1265SS and TPThree layered network, 2-3-1, with logistic function for both hiddenand output layersLR = 0.4, MO = 0.3, IW = 0.10.86450.2121 MC: moisture content (% w.b.); SS: screw rotational speed (rpm); DT: die temperature ( ° C); TP: throughput (g/min); DP: die pressure (psi);LR: learning rate, MO: momentum, IW: initial weights value of 0.83. Finally, another model developed relating spread of RTD curves as a function of screw speed and throughput, moisturecontent, and die temperature, showed a weak fitting of data with r 2 value of 0.49.Jager and others (1991) developed a regression equation for thedetermination of the average residence time as(4) where t was the average residence time (s), B was the barrel-valveposition (rad), Sp was the screw speed (s -1 ), Q was the feed rate (kg/s), and T was the barrel temperature used (0 = low and 1 = high).The different process variables are related to RTD and also withextrudate properties in a complex manner. Taking into considerationthe nonlinear relationships between the process parameters, sys-tem parameters, and the extrudate properties, it should be possibleto model the extrusion process more effectively using neural net- works (NN). An attempt is made to study the usefulness of NN inextrusion process modeling using selected data from the literature. Neural network modeling Neural networks have the capabilities of learning from the in-puts and outputs and developing relationships between them, which can be used for the further predictions of the outputs giventhe inputs. For nonlinear problems, NN are a most promising alter-native technique (Borggard and Thodberg 1992). The advantage of NN over rule-based models is that if the process under analysischanges, new examples can be added and NN can be trained again.This is much easier than determining new models or rules. More-over, no statistical assumptions are made on the behavior of thedata. Artificial neural networks (ANN) are the mathematical modelsof biological neural systems (Vallejo-Cordoba and others 1995). NNlearn from examples through iteration, without requiring a prioriknowledge of relationships between variables under investigation(Eerikainen and others 1994).Linko and others (1992) used NN with output feedback and timedelays for the control of specific mechanical energy on the basis of screw speed for flat bread production via twin-screw extrusioncooker. Because a food extruder is a multiple input/multiple out-put (MIMO) system, dynamic changes in torque, specific mechan-ical energy, and pressure were modeled and subsequently con-trolled using 2 independently taught feedforward artificial NN(Eerikainen and others 1994). Linko (1998) presented a review onthe potential of some novel tools in food process control. NNs wereshown to have great potential as ‘ software ’  sensors for online, real-time state estimation and prediction in complex process controlapplications. Backpropagation learning  A NN consists of a large number of highly interconnected pro-cessing elements called neurons. Each neuron receives input sig-nals from multiple neurons in proportion to their connection weights (W  ij ). Within each neuron a threshold value (bias, Bi) isadded to the weighted sum and nonlinearly transformed using anactivation function to generate the output signals. A fully connect-ed 3-layer network is illustrated in Figure 1. The response (O) of eachneuron (i) to input signals (I) from the connecting neurons (j) canbe mathematically expressed as:(5)The transfer function (f) can be any linear or nonlinear function.Commonly used functions are sigmoidal and hyperbolic tangentfunctions. The learning process starts with randomly initialized weights. A set of input data is presented to this network and theresulting output is compared with a corresponding desired output.Errors associated with the output neurons are transmitted fromoutput layer to the input layer through the hidden layers using aback-propagation algorithm, hence the name backpropagation Figure 1 —  A typical single layered neural network 
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