ELECTRONIC JOURNAL OF POLISH AGRICULTURAL UNIVERSITIES

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1 Electroic Joural of Polish Agricultural Uiversities (EJPAU) fouded by all Polish Agriculture Uiversities presets origial papers ad review articles relevat to all aspects of agricultural scieces. It is target for persos workig both i sciece ad idustry, regulatory agecies or teachig i agricultural sector. Covered by IFIS Publishig (Food Sciece ad Techology Abstracts), ELSEVIER Sciece - Food Sciece ad Techology Program, CAS USA (Chemical Abstracts), CABI Publishig UK ad ALPSP (Associatio of Leared ad Professioal Society Publisher - full membership). Preseted i the Master List of Thomso ISI. ELECTRONIC JOURNAL OF POLISH AGRICULTURAL UNIVERSITIES 00 Volume 3 Issue Topic AGRICULTURAL ENGINEERING Copyright Wydawictwo Uiwersytetu Przyrodiczego we Wroclawiu, ISSN J. KRÓLCZYK, D. MATUSZEK, M. TUKIENDORF. 00. MODELLING OF QUALITY CHANGES IN A MULTICOMPONENT GRANULAR MIXTURE DURING MIXING, EJPAU, 3(), #. Available Olie MODELLING OF QUALITY CHANGES IN A MULTICOMPONENT GRANULAR MIXTURE DURING MIXING Jolata Królczyk, Domiika Matuszek, Marek Tukiedorf Departmet of Agricultural ad Forest Techology Opole Uiversity of Techology, Polad ABSTRACT The paper presets results of modellig of quality chages i a muliticompoet o-homogeous graular mixture durig mixig i a idustrial worm mixer. The aalysis was carried out for three graular mixtures: ie-compoet, te-compoet ad twelve-compoet. Modellig was performed with the use of oliear regressio. Depedet variable was a residual sum of squares (mixture quality parameter), whereas idepedet variables were: umber of compoets ad mixig time. Twodimesioal depedece was costituted by square fuctio formula. The aim of the study was to describe quality chages of muliticompoet, o-homogeous graular mixtures (ie, te ad twelve compoet) durig mixig i a vertical mixer with worm agitator, with the use of oliear regressio model. Atypical aspect of the mixig process was a specific recirculatio of the mixed compoets with the use of bucket coveyor durig the process. Key words: graular materials, graular mixture, muliticompoet graular mixture, residual sum of squares, oliear regressio INTRODUCTION Mixig process course, that is its developmet i time, is oe of more importat issues related to theory ad practice of techologies cocerig obtaiig mixtures of possibly homogeous compositio [3]. Due to its complexity, the mixig process is difficult to describe with the use of simple aalytical methods. Depedig o mixig methods ad types of mixed compoets, the course of this process may possess qualities of various models. I agricultural ad food practice the use of artificial itelligece as a tool for modellig may be ecoutered icreasigly ofte, it is used amog others for modellig of: family agricultural holdig s productivity [], agricultural productio process [9] or techical objects operatio process [4]. Usefuless of eural etworks i describig quality chages of graular systems mixed with the use of ormal pour out method ad i a static device was described by Tukiedorf [5]. It was proved, that the results of process modellig with the use of reverse propagatio method do ot differ from the oes estimated by the Markov chai [4]. Iterpretatio of chages occurrig i time, with the use of artificial eural etworks is certaily oe of the latest methods, which use eables simulatio of very complex fuctios. The issue of modellig of o-homogeous graular systems mixig process

2 has bee the object of the authors iterest for years. I the previous works, the possibility of usig artificial eural etworks ad oliear regressio i descriptio of quality chages of a graular mixture durig mixig was poited out [5, 0]. Despite the fact, that may research works have bee devoted to this field, mixig of graular materials is a curret issue. It is a complex process depedet o may parameters such as: characteristics of mixed materials, mixig device type, process coditios. May research carried out i laboratory coditios explai partial mechaisms which gover the mixig. The majority of real graular mixtures, which ca be ecoutered i idustry, e.g. i feed mixig plats, are costituted by muliticompoet o-homogeous systems. I particular, mixig processes related to this field have ot yet bee thoroughly studied. Muliticompoet system is a system i which the umber of solid compoets amouts to at least 3. At the same time, mixig of k compoets (k > ) creates problems of a completely ew quality []. This system may be examied as a two-compoet system, assessig the mixture s state from the poit of view of the A compoet, ad all of the remaiig compoets may be treated as oe B compoet. The majority of real graular mixtures ecoutered i idustrial practice are o-homogeous systems. Descriptio of this mixture s state ad kietics of the process belog to the mai problems of mixig []. Most research that has bee coducted before, cocers maily two ad three-compoet mixtures. There are oly few works describig mixig of muliticompoet o-homogeous graular systems. Regressio aalysis costitutes the most widely ad frequetly used statistical method of modellig of depedeces betwee variables []. Simple model of liear regressio may be applied oly whe depedece betwee variables is liear. I practice, however, this situatio is very ucommo. Aalysis of empirical values of variables ofte iclies to the use of oliear regressio. Noliear regressio allows to determie ay type of depedece betwee variables. Relative measure of adjustmet of regressio lies to data may be the square of sample correlatio coefficiet r, called coefficiet of determiatio. It is the most commo measure of adjustmet []. The coefficiet of determiatio may be defied as this part of Y variable, which is explaied by occurrece of the assumed depedece betwee X ad Y. Whe r equals, variable X explais 00% of variable Y s variace, which meas that the observatio results lie exactly o the regressio lie ad errors are zero. Whe the value of coefficiet equals 0, the all deviatios from the regressio lie are due to errors. The paper presets the possibility of oliear regressio model s use i descriptio of quality chages of muliticompoet graular mixtures durig mixig with the use of a vertical mixer. AIM OF THE STUDY The aim of the study was to describe quality chages of muliticompoet, o-homogeous graular mixtures (iecompoet, te-compoet ad twelve-compoet) durig mixig i a vertical mixer with worm agitator with the use of oliear regressio model. RESEARCH METHOD Experimetal research was coducted i idustrial coditios i the feed mixig plat Ovigor i Opole, which is egaged i the productio ad distributio of feed for pigeos. Productio of feeds is composed of several idividual operatios of techological process, which iclude the followig:. charge of idividual mixture compoets with the use of eight-way separators to the appropriate silos,. storage of crop seeds i the silos, 3. trasport of the selected compoets with the use of worm coveyors to the belt strai gauge scales, 4. dosage ad mass cotrol of idividual compoets by a employee of the mixig plat with the use of cotrol pulpit, 5. charge of mixture compoets with the use of belt coveyor ad vibratig screes to the feed mixer s itake hopper, 6. trasport of graular materials from the itake hopper to iside of the mixer with the use of bucket coveyor, 7. mixig i the temporal operatio mixer with a immovable chamber ad a vertical worm agitator with compoets recirculatio takig place simultaeously (Fig., Tab. ), 8. packagig of fiished products to bags. I the experimetal research the temporal operatio mixer with a immovable chamber ad a vertical agitator was used. The feed mixer s dimesios have bee provided i Table ad the schematic drawig have bee preseted i Figure. The mixer s power equals 5.5 kw. Mass of the graular material charged to the mixer equalled: 000 kg i case of a ie-compoet mixture with the trade ame Ovigor Ekoomik Z witer, 00 kg i case of a te-compoet mixture with the trade ame Ovigor Ekoomik RL breedig-flight, kg i case f a twelve-compoet mixture with the trade ame Ovigor Ekoomik BP without wheat.

3 Fig.. Scheme of the feed mixer used to carry out the research a temporal mixer with immovable chamber ad a vertical worm agitator Table. Dimesios of the feed mixer (mm) used i the research Height of the cylidrical part A Height of the coic part B Height of the pour out outlet C Iside diameter of the cylidrical part D Iside diameter of the pour out outlet E 550 mm 600 mm 300 mm 800 mm 300 mm Compositio of graular mixtures, their mass ad percetage share, ad the mass of compoets charged to the mixer have bee preseted i Table. Characteristic properties of the mixed materials have bee preseted i Table 3. Statistical bulk desity ρ was determied i coformity to the PN-80/C-0453 stadard. The average size of seeds was determied with the use of a set of cotrol sieves by meas of sieve aalysis. Measuremet procedure was based o the PN-7/C-0450 stadard. Table. Compositio of the examied graular mixtures, their percetage ad mass share at the charge Mixture ame Ekoomik Z Ekoomik RL Ekoomik BP Compoets of graular mixtures percetage share, % mass share, kg percetage share, % mass share kg percetage share, % mass share, kg Dari (white sorghum) Gree peas Yellow peas Barley Kardi (carthamus ) Maize Hulled oat (hull-less) Field pea Yellow millet Wheat White rice Black suflower Sorghum Brow vetch Total

4 Table 3. Characteristic properties of the mixed graular materials Compoets of graular mixtures Bulk desity Average size of particles kg/m 3 mm Dari (white sorghum) Gree peas Yellow peas Barley Kardi (carthamus ) Maize Hulled oat (hull-less) Field pea Yellow millet 73.6 Wheat White rice Black suflower Sorghum Brow vetch Mixig of the charged graular material was performed by meas of movemets of the mixer s worm agitator ad recirculatio of the compoets with the use of the bucket coveyor. The charged graular material was poured out at the bottom outlet, ad ext directed to the bucket coveyor, from where it was trasported back to the mixer. The compoets mixig time amouted to 30 miutes. Test samples were collected i a discrete way at the mixer s bottom outlet at 30-secod itervals. I this way 60 samples were obtaied ad the aalyzed takig ito accout seed species compositio. The tests were coducted i three measuremet series. Cosecutive samples of the feed mixture were divided ito separate compoets ad the the obtaied results were aalyzed. STATISTICAL ANALYSIS Residual sum of squares mixture quality As a parameter used i descriptio of the mixture s quality the residual sum of squares was used. Aalysis of percetage chages of the compoets share i the mixture iclied to searchig for a parameter, which would determie with oly oe uiversal umerical value the mixture s quality i a certai uit of time. I this way, the quality of graular mixtures were described i the authors previous articles [6, 7]. I descriptio of the mixig process used for the feed mixture beig examied a classical liear regressio model was used. Basic equality of variace aalysis is the depedece: ( y j y) ( ŷ j y) ( y j ŷ j ) ( y y) = ( ŷ y) + ( y ŷ ) j the total sum of squares of the respose variable s deviatios (SST), j the sum of the Y depedet variable s deviatios explaied by square regressio (SSR), the residual sum of squares of the Y respose variable s deviatios (SSE) [8]. The sum o the right side is the total sum of squares. It is the sum of two compoets. The first compoet is the estimated sum of squares, whereas the secod compoet is the residual sum of squares. I descriptio of the process, oe parameter of liear regressio was used the residual sum of squares: SSE ( y j ŷ i ) = i= y i target decompositio of compoets frequecy, ŷ value predicted from evaluatio obtaied from simple regressio. i j j () ()

5 The residual sum of squares is a sum of squares of differeces betwee values of the Y variable (target decompositio of frequecy of compoets) ad evaluatios obtaied from simple regressio. Whe the sum of squares equals zero, the all fractios i the particular poit of time equal the target (required) values. Statistical modellig Modellig was carried out for depedet uivariate variable ad two idepedet variables. Depedece betwee the residual sum of squares, the umber of the mixture s compoets (ie, te, twelve compoets) ad the mixig time. ( x, y) z = f (3) z residual sum of squares, depedet variable, x mixig time (s), idepedet variable, y umber of the mixture compoets (ie, te ad twelve compoets), idepedet variable. It was observed, that dispersio of empirical data reflects depedeces of the square fuctio described with the formula: ( x) = ax + bx c f + (4) a, b, c R ad a 0, a, b, c square fuctio coefficiets, x variable. Descriptio of the variables obtaied experimetally was made basig o the proposed form: square fuctio: z = ax + bx + cxy + dy + ey + f (5) z residual sum of squares, x mixig time, s, y umber of the mixture compoets, a, b, c, d, e, f square regressio coefficiets. Evaluatio of parameters was carried out i the oliear estimatio module of the program [3]. The regressio model was estimated with the use of loss fuctio sum of squares, defiig the method of the smallest squares. The ext step was the choice of estimatio method. For the examied case the quasi-newto method was selected, sice it appeared to be a method which allows to fid the best estimators. Durig the ext steps, this method evaluates the fuctios i differet poits i order to estimate derivatives of the first ad secod row. Due to itroductio of the parameters estimatio procedure, obtaied results were i the form of regressio coefficiet values of the assumed model, predicted values, value of adjustmet of the model to empirical data i the form of the coefficiet of determiatio r ad values of residues for each case. O the basis of the obtaied square fuctio formula of specific parameters, modellig of quality chages i a eleve-compoet graular mixture durig mixig was performed. Statistical modellig results As a result of statistical modellig, the equatio of specific parameters was obtaied: z residual sum of squares, x mixig time, s, y umber of compoets. z = *x 0.88x xy 3.9y y (6) The obtaied coefficiet of determiatio equals r = 0.77 Graphic iterpretatio of the adjustmet of theoretical values to empirical data was preseted i the schemes (Fig. a, b).

6 Fig. a. Spatial arragemet of the z = f (x, y) depedece (view a) Fig. b. Spatial arragemet of the z = f (x, y) depedece (view b) I the Figure a spatial arragemet of the z = f(x, y) depedece obtaied as a result of statistical modellig was preseted. The values of residual sum of squares, the mixig time expressed i secods ad the umber of compoets of the mixed feeds, were plotted o the axes. The obtaied model of liear regressio i the form of formula umber 6 was preseted as the plae eclosed betwee three axes of the residual sum of squares, the mixig time ad the umber of compoets. Additioally, empirical poits obtaied as a result of experimetal research were marked i the scheme. The obtaied coefficiet of determiatio which equals r = 0.77 shows that the empirical data were quite properly adjusted to the oliear regressio model. The scheme (Fig. a) shows, that with the greater umber of compoets (twelve) the quality of graular mixture is the worst i the last phase of the mixig process. The best mixture quality is obtaied for a ie-compoet mixture, takig ito accout especially the last stage of the mixig process. The proposed model may costitute a formula for describig quality chages i the muliticompoet graular mixture durig mixig i the aalyzed mixer for differet umber of compoets, eve before commecemet of the mixig process. The liear regressio model (formula o. 6) was used i formulatio of the scheme presetig chages of the residual sum of squares parameter (predictio) durig mixig, for eleve compoets of the mixture (Fig. 3).

7 This approach is a attempt to fid depedece betwee the umber of mixed compoets ad the quality of obtaied feed. However, it does ot exhaust the issue, i which the mixig process course ad method are iflueced by may parameters, e.g. diameter ad bulk desity of seeds. CONCLUSIONS. Liear regressio model i the form of the described square fuctio well reflects the quality chages of mixtures i time.. It has bee observed, that graular systems with the greatest umber of compoets twelve have the worst mixig qualities, whereas the best mixture quality was obtaied for a mixture with the smallest umber of compoets ie. 3. The developed regressio model eabled predictio of quality chages of a graular mixture i a 30-miute mixig time for a eleve-compoet mixture, which was ot the object of the study. 4. The applied statistical methods residual sum of squares ad o-liear regressio costitute appropriate tools for aalyzig the mixig process i muliticompoet graular systems. REFERENCES. Aczel A. D., 005. Statystyka w zarządzaiu [Statistics i maagemet]. PWN, Warszawa X [i Polish].. Boss J., 987. Mieszaie materiałów ziaristych [Mixig graular materials]. PWN, Warszawa Wrocław ISBN [i Polish]. 3. Boss J., Kapik A., 995. Modele stochastycze procesu mieszaia [Stochastic models of the mixig process]. WSI i Opole 995, Studia i Moografie, 78 [i Polish]. 4. Bartik G., Kusz A., Marciiak A. W., 006. Modelowaie procesu eksploatacji obiektów techiczych za pomocą dyamiczych sieci bayesowskich [Modellig of techical objects operatio process with the use of dyamic Bayesia etworks]. Iż. Rol. (87), 9 6 [i Polish]. 5. Królczyk J., Matuszek D., Tukiedorf M., 008. Wykorzystaie sieci euroowych (FBM) do modelowaia procesu mieszaia dwuskładikowych układów ziaristych [Usig eural etworks (FBM) i modellig of the two-compoet graular systems mixig process]. Iż. Rol. 7(05), 7 [i Polish]. 6. Królczyk J., Tukiedorf M., 007. Ocea jakości wieloskładikowej, iejedorodej mieszaiy ziaristej [Quality assessmet of a muliticompoet o-homogeous graular mixture]. Iż. Rol. (90), 9 7 [i Polish]. 7. Królczyk J., Tukiedorf M., 007. Określeie czasu mieszaia wieloskładikowego układu ziaristego podczas mieszaia z recyrkulacją składików [Determiatio of the muliticompoet graular system s mixig time durig mixig with recirculatio of compoets]. Iż. Rol. 8(96), 7 3 [i Polish]. 8. Lusziewicz A., Słaby T., 00. STATISTICA TM PL. Teoria i zastosowaia [STATISTICA TM PL. Theory ad applicatios]. C.H. Beck Press, Warszawa, ISBN [i Polish].

8 9. Maksym P., Marciiak A.W., Kostecki R., 006. Zastosowaie sieci bayesowskich do modelowaia roliczego procesu produkcyjego [Usig dyamic Bayesia etworks i modellig of agricultural productio process]. Iż. Rol. (87), [i Polish]. 0. Matuszek D., Tukiedorf M., 008. Adaptacja fukcji kwadratowej do opisu zmia jakości mieszaki ziaristej [Adaptatio of square fuctio for describig quality chages i a graular mixture]. Iż. Rol. 9(07), 9 6 [i Polish].. Siejka K., Tukiedorf M., 006. Aaliza wydajości produkcyjej rodziego gospodarstwa rolego przy pomocy sieci euroowej [Aalysis of the agricultural holdig s productio efficiecy with the use of eural etwork]. Iż. Rol. (87), [i Polish].. Staisz A., 00. Przystępy kurs statystyki w oparciu o Statistica Pl a przykładach z medycyy [Accessible course o statistics basig o Statistica Pl o the examples from medicie]. Vol. II StatSoft Polska, Kraków, ISBN [i Polish]. 3. StatSoft, Ic STATISTICA for Widows. Computer program maual. Tulsa, OK: StatSoft, Ic. 4. Tukiedorf M., 00. Porówaie sposobów modelowaia procesu mieszaia jedorodych układów ziaristych przy użyciu modelu stochastyczego oraz metody wsteczej propagacji w techice sztuczych sieci euroowych [Compariso of modellig methods of homogeous graular systems mixig process with the use of stochastic model ad reverse propagatio method i techology of artificial eural etworks]. Iż. Rol. (35), [i Polish]. 5. Tukiedorf M., 003. Modelowaie euroowe procesów mieszaia iejedorodych układów ziaristych [Neural modellig of o-homogeous graular systems mixig process]. Rozpr. Nauk. AR w Lubliie, 7 [i Polish]. Jolata Królczyk Departmet of Agricultural ad Forest Techology Opole Uiversity of Techology 5 Mikołajczyka Street, 45-7 Opole, Polad tel. (+48) j.krolczyk@po.opole.pl Domiika Matuszek Departmet of Agricultural ad Forest Techology Opole Uiversity of Techology 5 Mikołajczyka Street, 45-7 Opole, Polad tel. (+48) d.matuszek@po.opole.pl Marek Tukiedorf Departmet of Agricultural ad Forest Techology Opole Uiversity of Techology 5 Mikołajczyka Street, 45-7 Opole, Polad tel. (+48) m.tukiedorf@po.opole.pl Accepted for prit: