Estimation of liquid viscosities of oils using associative neural networks

Transcription

1 Indan Journal of Chemcal Technology Vol. 18, November 2011, pp Estmaton of lqud vscostes of ols usng assocatve neural networks P Neelamegam 1* & S Krshnaraj 2 1 School of Electrcal and Electroncs Engneerng, Shanmugha Arts, Scence, Technology & Research Academy (SASTRA) Unversty, Thrumalasamudram, Thanjavur , Taml Nadu, Inda 2 Ponnayah Ramajayam Insttute of Scence and Technology (PRIST) Unversty, Thanjavur , Taml Nadu, Inda Receved 9 December 2010 ; accepted 7 October 2011 Dynamc vscostes of a number of vegetable ols (castor ol, palm ol, sunflower ol and coconut ol) and lubrcant ols (2T and 4T) have been determned at temperature range 30 o - 90 o C usng Ubbelohde vscometer. An assocatve neural network s used to compute the vscostes of ols for unknown temperatures after tranng the neural network wth type of ol, temperature as nput and vscosty as output. Predcted results agree well wth the expermental results. Smplfed and modfed form of Andrade equatons that descrbe the temperature dependence of dynamc vscostes are ftted to the expermental data and correlatons for the best ft are presented. The results obtaned from assocatve neural network and best correlaton equaton show that both predct the vscostes very well wth correlaton coeffcent R 2 = Keywords: Andrade equaton, Assocatve neural network, Ol, Regresson, Vscosty In the food ndustry, vscosty s one of the most mportant parameters requred n desgnng the technologcal processes. On the other sde, vscosty s also an mportant factor that determnes the overall qualty and stablty of a food system. Lubrcant ol s used for lubrcaton n varous nternal combuston engnes whle the man functon s to lubrcate movng parts. It also cleans nhbt corroson, mproves sealng and cools the engne by carryng heat away from the movng parts. From physco chemcal pont of vew, vscosty means measure of the resstance to flow that a flud offers when t s subjected to shear stress. Therefore, vscosty must be closely correlated wth the structural parameters of flud partcles. Vscosty s one of the mportant propertes of ol whch needs to be determned as t nfluences the ease of handlng, transport and nature of storage. The vscosty of the ols strongly depends on temperature. When the temperature s ncreased, the vscosty of the ols rapdly decreases 1. In the present study, the vscostes of some vegetable ols (castor ol, palm ol, sunflower ol and coconut ol) and lubrcant ols 2 (2T, 4T) are measured n the temperature range 30 o - 90 o C expermentally. An assocatve neural network (ASNN) has been developed to predct the dynamc vscostes of vegetable ols at unknown temperatures. The neural network s used to *Correspondng author. E-mal: neelkeer@yahoo.com tran (type of ol, temperature as nput, and dynamc vscosty as output) the nput and output data and the traned neural network s used to compute dynamc vscosty of ols (castor ol, palm ol ) at unknown temperature whch s not used for tranng. The varaton of dynamc vscosty wth temperature s ftted to the experment data and statstcal analyss s performed. The qualtes of predctons are determned from correlaton constant (R 2 ) and root mean square error (RMSE). Andrade equatons whch descrbe the varaton of dynamc vscosty wth temperature are ftted to the expermental data and the correlaton constants for the best ft are determned. The results of ASNN and best ftted Andrade equaton are compared wth expermental data. Expermental Procedure Vegetable ols (castor ol, palm ol, sunflower ol and Coconut ol) are obtaned from a supermarket n Chenna. Lubrcant ols (2T, 4T) are purchased from a local ol dealer. Vscosty determnaton The knematc vscosty (ν) s measured followng the establshed procedure n the ASTM D 445. The dynamc vscosty η (Pa.s) of the ol sample s determned wth a calbrated Cannon-ubbelohde vscometer at temperatures rangng from 30 o - 90 o C at 10 o C ntervals. The vscometer s placed n a temperature controlled vessel equpped wth a

2 464 INDIAN J. CHEM. TECHNOL., NOVEMBER 2011 thermostat whch mantaned the temperature wth an accuracy of ±0.1 o C. The temperature error n vscosty determnaton s less than 0.5%. Densty vs temperature s measured usng a 25CC pycnometer mmersed n a temperature - controlled crculatng water bath. The knematc vscosty values at each temperature are determned by multplyng the measured flow tme of the ol through the vscometer capllary wth a calbraton constant 3. The dynamc vscosty (η) s estmated by the product of knematc vscosty (ν) and the correspondng densty (ρ) of the ols usng the followng equaton for each temperature: η = ρ ν (1) The measured values of dynamc vscostes of ols for dfferent temperatures are gven n Table 1. The data s used as nput pattern for tranng the assocatve neural network and regresson analyss. Neural network method An artfcal neural network (ANN) has ts orgn n efforts to produce a computer model of the nformaton processng that takes place n the nervous system. In many applcatons, ncludng the present work, the bologcal relevance of neural networks of nervous system functon s unmportant. A neural network may smply be vewed as a hghly parallel computatonal devce and s found to be useful n a varety of tasks ncludng solvng certan optmaton problems and pattern recognton. The ANN are traned to perform a partcular functon by adjustng the values of the connectons, or weghts, between elements untl a partcular nput leads to a specfc output 4-7. The ANN conssts of three layers: nput layer, hdden layer, and output layer. These three layers are connected wth each other. The nput layer receves the nput data outsde the network and sends them to the hdden layer. The hdden layer contans nterconnected neurons for the pattern recognton and the relevant nformaton nterpretaton for adjustng the weghts on the connectons. Afterwards, the results from the hdden layer are sent to the output layer for the outputs. The neurons contan several functons and varables ncludng weghts, non-lnear transfer functons, methods to add up all nputs and bas values. The sum of all products of all the nputs multpled wth the weghts and the bas values passes through a non-lnear transfer functon as the output of each neuron 8. Assocatve neural network The tradtonal artfcal feed forward neural network s a memory-less approach. Ths means that after tranng s complete, all nformaton about the nput patterns s stored n the neural network weghts and nput data are no longer needed,.e. there s no explct storage of any presented example n the Table 1 Expermental data for the dynamc vscosty of ols as a functon of temperature (Tranng pattern for ASNN and regresson analyss) Name of ol Temperature, o C Vscosty 10-1, Pa.s Castor ol (Type 1) Palm ol (Type 2) Sunflower ol (Type 3) Coconut ol (Type 4) Lubrcant ol (4T) (Type 5) Lubrcant ol (2T) (Type 6)

3 NEELAMEGAM & KRISHNARAJ: ESTIMATION OF LIQUID VISCOSITIES OF OILS 465 system. Contrary to that, ASNN s a combnaton of memory-based and memory-less methods. It offers an elegant approach to ncorporate on the fly the user s data 9. The ASNN s an extenson of the commttee of machnes that goes beyond a smple/weghted average of dfferent models. An ASNN represents a combnaton of an ensemble of feed forward neural networks (memory-less) and the K nearest neghbour technque (memory-based). It uses the correlaton between ensemble responses as a measure of dstance among the analyed cases for the nearest neghbour technques. An assocatve neural network has a memory that can concde wth tranng set. If new data s avalable the network mproves ts predctve ablty and gves a good approxmaton of unknown functon wthout a need to retran the neural network ensemble. Ths method dramatcally enhances ts predctve ablty over tradtonal neural network and K nearest neghbour technques. In K nearest neghbour approach, t keeps the entre database of examples n memory and ther predctons are based on some local approxmaton of the stored examples. The neural network can be consdered global models, whle the other approach s usually consdered local model. Let us consder a tranng set consstng of N nputoutput pars {(x 1, y 1 ),(x 2,y 2 ),,(x N, y N )}, where x s a vector of nput parameters. Our purpose s to predct y-value of a new data case x. Let us consder an ensemble of M neural networks [ ANNE ] M = ANN. ANN ANN 1 j M (2) The predcton of a case x, =1,.., N can be represented by a vector of output values = { j } M j =1, where j=1,, M s the ndex of the network wthn the ensemble [ X ].[ ANNE ] M = [ I ] 1 Z = j M (3) A smple average = 1 M j j= 1, M (4) s usually used to predct the test case wth neural network ensemble. Ths average gnores the predctons (varatons) of ndvdual neural networks. These varatons can be used to ntroduce a measure of smlarty of data cases n the output space, e.g. usng Pearson s lnear correlaton coeffcent (r j 2 ) (ref. 9), between the vectors of predcted values and j. The ASNN corrects the ensemble value accordng to the followng formula: ' 1 = + ( y j ) K j Nk ( x ) (5) where y are the expermental values and the summaton s over the k nearest neghbour cases determned usng Pearson s r j 2, as descrbed above. Snce the varance of ensemble predcton can become suffcently small by analyss of a suffcent number of neural networks n the ensemble, the dfference (y ) corresponds manly to the bas of the ANNE for the case x. Thus, ths formula explctly corrects the bas analyed case accordng to the observed bases calculated for the neghborng cases. KNN method was used as (x) = 1 k j N ( x) k y( x j ) (6) where (x) s a predcted value for case x; and N k (x) s the collecton of the k nearest neghbour of x among the nput vectors n the tranng set {x } N =1 usng the Eucldan metrc d(x,x ) = x x. The memory of both KNN and ASNN s represented by the tranng set {x }N =1 and the number of nearest neghbours (k) s selected to provde lowest leave-one-out (LOO) error for ths set. The performance of both these methods for the tranng set s estmated usng the LOO error. The neural networks used n the current study are traned usng early stoppng over ensemble (ESE) method. In ths method, the ntal tranng set s randomly dvded nto equal se learnng and valdaton sets for each neural network n the

4 466 INDIAN J. CHEM. TECHNOL., NOVEMBER 2011 ensemble. Thus, each neural network has ts own learnng and valdaton sets. The learnng set s used to adjust neural network weghts. The tranng s stopped when mnmum error for the valdaton set s calculated (early stoppng pont). The updatng of neural network weghts s performed usng Levenberg-Marquardt algorthm. Followng ensemble learnng, a smple average of all networks gven by Eq. (4) s used to predct the test patterns 10. Andrade equatons Several studes have been carred out on vscosty of ols and fats. The effect of hydrogenaton has been nvestgated on the densty and vscosty of sunflower-seed ol. Topallar and Bayrak have studed the effect of temperature on dynamc vscosty of acetone sunflower-seed ol mxtures. Modelng of the temperature effect on the dynamc vscosty of ols s mportant and has been nvestgated by some researchers. For ths temperature dependence, many emprcal relatons have been proposed. Smple form of Andrade equaton s represented by the followng equaton: ln(η) = A + B/T... (7) We also used followng modfed versons of the Andrade Eqs (8) and (9): ln(η) = A + B/T + C/T 2... (8) Table 2 Predcted vscostes of ols at dfferent temperatures by usng ASNN and Eq.9 Name of ol Temperature Predcted vscosty 10-1, Pa.s Name of ol Temperature Predcted vscosty 10-1, Pa.s o C ASNN Eq.(9) o C ASNN Eq.(9) Type Type Coconut ol Castor ol Type Type Palm ol Lubrcant ol (4T) Type Sunflower Type ol Lubrcant ol (2T)

5 NEELAMEGAM & KRISHNARAJ: ESTIMATION OF LIQUID VISCOSITIES OF OILS 467 and ln(η) = A + B/T + C.T (9) where T s the temperature n K; and A, B and C n the Eqs (7), (8) and (9) are the correlaton coeffcents. Results and Dscusson Assocatve neural network represents an nnovatve method to calculate non-lnear models between temperatures and vscosty. In the present study, the network nvolves two neurons (type of ol and temperature) n the nput layers, seven neurons n the hdden layer and one neuron (vscosty) n the output layer. The network s traned usng the LevenBerg Marquardt algorthm. Numbers of hdden neurons are decded by tranng and predctng the tranng data and testng data by varyng the number of hdden neurons n the hdden layer. A sutable confguraton has to be chosen for the best performance of the network 17. Out of the dfferent confguraton tested, a hdden layer wth 7 neurons produced the best result for predcton of vscostes for unknown temperatures. Table 1 shows the dynamc vscostes of castor ol, palm ol, sunflower ol, coconut ol and lubrcant ols (2T, 4T) measured at varous temperatures whch s used as tranng pattern for assocatve neural network and for regresson analyss. The traned ASNN s used to compute dynamc vscosty of ols at unknown temperatures whch are not used for tranng as gven n Table 2. The sutablty of Eqs (7), (8) and (9) n descrbng the temperature dependence of vscosty of ols s studed by utlng the vscosty data gven n Table 1. Usng expermental vscosty data for vegetable and lubrcant ols, the constants A, B and C are calculated by regresson methods and these values are then used to calculate the vscostes of ols for unknown temperatures. The calculated vscostes of ols usng Eq. (9) of Andrade equatons are also presented n Table 2. Experments are carred out to measure vscosty at varous temperatures to check the predcted values by ASNN and regresson analyss K-nearest neghbour (KNN) Number of hdden neurons Table 3 Statstcal analyss of ASNN results R 2 methods. A comparson of expermental results to the results obtaned from ASNN and Eq. (9) s gven n Fgs 1. Fgure 1a compares expermental data for castor and palm ols wth predcted results from ASNN and Eq. (9). Smlarly, Fg. 1b compares sunflower and coconut ol and Fg. 1c compares lubrcant ols 2T and 4T. It s observed that the expermental and predcted results from ASNN and Eq. (9) are very close to each other wth neglgbly small error. Table 3 gves the statstcal analyss of ASNN. A close look at Table 3 shows that R 2 value s 0.99 and Fg.1 Comparson between expermental vscosty values and the values predcted by ASNN and Eq.(9) [(a) castor, palm; (b) sunflower, coconut; and (c) lubrcants 4T, 2T] RMSE Learnng Valdaton LOO Learnng Valdaton LOO

6 468 INDIAN J. CHEM. TECHNOL., NOVEMBER 2011 Table 4 Values of parameters of the best theoretcal model descrbed by Eq.(9) wth the standard error of regresson (SD) Name of ol Eq. (9) A B C SD RSS R 2 Castor ol Palm ol Sunflower ol Coconut ol Lubrcant ol (4T) Lubrcant ol (2T) root mean square error (RMSE) s , whch ndcates that ASNN predcts the vscosty for unknown temperatures very well. The statstcal parameters for theoretcal model as descrbed by Eq. (9) of Andrade equatons s presented n Table 4. It s observed that the emprcal relaton gves the best predcton for the temperature dependence of vscosty of ol as descrbed by the Eq. (9). The correlaton coeffcent (R 2 ) value s almost The resdual sum of squares (RSS) whch measures the devaton of calculated vscosty from the expermental one [Eq. (9)] s maxmum (0.014). On the other hand, relatons shown n Eqs (7) and (8) are less sutable for descrpton of the temperature dependence of ol vscosty, whle the correlaton coeffcent value beng less than 0.98 and the resdual sum of square (RSS) s apprecable. Concluson The ASNN havng an archtecture wth LevenBerg Marquardt algorthm gves an overall root mean square error of n the predcton of vscosty of ols at dfferent temperatures and hence can be consdered neglgbly small and acceptable. On comparng the performance of ASNN and regresson analyss, t s observed that both ASNN and Eq. (9) of Andrade equaton predct the dynamc vscosty effectvely wth correlaton coeffcent (R 2 ) of 0.998, ndcatng a hgh degree of accuracy. References 1 Abramovč H & Klofutar C, Acta Chm Slov, 45 (1) (1998), Klamman Deter, Lubrcants and Related Products (Verlag Cheme), Standard Test Method for Knematc vscosty of transparent and opaque lquds (and the calculaton of Dynamc vscosty) ASTM D ( Amercan Socety for Testng and Materals), Rosenblatt F, Prncples of Neurodynamcs (Spartan, New York), Howard H & Martn K, Proc Nat Acad Sc, USA, 86 (1989) Espnosa G, Yaffe D & Cohen Y, J Chem Inf Comput Sc, 40 (2000) Rosa M G & Cesar H, J Food Mcrobol, 72 (2002) Krapat Cheenkachorn, Predctng propertes of bodesels usng statstcal models and artfcal neural networks, paper presented at the Jont Internatonal Conference on Sustanable Energy and Envronment (SEE), Thaland, 1-3 December Igor V Tetko, J Chem Inf Comput Sc, 42 (2002) Tetko I V &Vlla A E P, Neural Networks, 10(1997) Swern D, Baley s Industral Ol and Fat Products, Vol. I (John Wley and Sons, New York), Topallar H & Bayrak Y, Turk J Chem, 22 (1998) Noureddn H, Teoh B C & Clements L D, J Am Ol Chem Soc, 69 (1992) Lang W, Sokhansanj S & Sosulsk F W, J Am Ol Chem Soc, 69 (1992) Gupta A, Sharma S K & Pal Toor A, Indan J Chem Technol, 14(2007) Andrade E N da C, Nature, 125 (1930) (accessed on September 2010).