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Fuzzy inference system to modeling of crossflow milk ultrafiltration
Applied Soft Computing 8 (2008) 456–465 www.elsevier.com/locate/asoc
Fuzzy inference system to modeling of crossflow milk ultrafiltration J. Sargolzaei a,*, M. Khoshnoodi b, N. Saghatoleslami a, M. Mousavi a a b
Department of Chemical Engineering, Ferdowsi University of Mashhad, P.O. Box 9177948944, Mashhad, Iran Department of Chemical Engineering, University of Sistan and Baluchestan, P.O. Box 98164-161, Zahedan, Iran Received 23 June 2005; received in revised form 1 February 2007; accepted 8 February 2007 Available online 20 March 2007
Abstract Fuzzy inference systems (FISs) have been adopted as a powerful tool to adequately model and simulate the crossflow ultrafiltration of milk. It primary aim of this research was to predict the permeate flux, total hydraulic resistance and the milk components rejection as a function of different physicochemical properties. Dynamic modeling of ultrafiltration performance of colloidal systems (such as milk) is an important criterion in designing of a new process, due to the complex nature of milk in a dynamic manner. Such processes exhibit complex nonlinear behavior due to unknown interactions between compounds and colloidal system, thus the theoretical approaches were not being able do successfully model and simulate the processes. In addition, it has been attempted to test the FIS ability to predict new data that is not normally available. To obtain this objective, fuzzy output with a threshold of 1.2 was constructed in order to predict rejections from the limited number of accessible experimental data. The findings of this work also reveal that there exist an excellent agreement between the experimental data and predicted values. Furthermore, the experimental results shows that the total hydraulic resistance and solutes rejection (except for protein) increased significantly with time for every corresponding value of the hydrodynamic parameters. On the other hand, the permeate flux decreased sharply. However, the fat rejection does not change with time for every value of the pH. # 2007 Elsevier B.V. All rights reserved. Keywords: Milk ultrafiltration; Protein; Fat; Modeling and simulation; Fuzzy inference system
1. Introduction Ultrafiltration is an important process in the food industry, particularly for dairy applications such as concentration of milk. Membrane processing of dairy fluids can reduce the operational expenses incurred from power consumption improve plant processing capacity and efficiency, and increase quality of product. The efficiency and cost of membrane processing is dependent on flux and rejection, which is a function of different factors. The membrane type, processing parameters and fluid properties will determine flux and
Abbreviations: H, high; I, increase; kg, kilogram; L, low; l, liter, volume unit; LOM, largest of maxima; M, medium; m, meter; Max, maximum (logic operator); min, minute; Min, minimum (logic operator); MO, moderate; MOM, mean of maxima; Probor, logic operator; Prod, product (logic operator); s, second; SOM, smallest of maxima; Std, standard deviation; u, unit; VH, very high; VI, very increase; VL, very low; VMO, very moderate; Wtsum, operator * Corresponding author. Tel.: +98 915 512 4591; fax: +98 511 8816840. E-mail addresses: [email protected] (J. Sargolzaei), [email protected] (M. Khoshnoodi), [email protected] (N. Saghatoleslami), [email protected] (M. Mousavi). 1568-4946/$ – see front matter # 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.asoc.2007.02.007
concentration of components in retentate and permeate. Therefore, permeation flux and solute rejection data are necessary for the design of a specified or new membrane separation process. In the simplest method, some laboratory or pilot plant tests are carried out over a wide range of conditions. This method is often usual in industry, which is both time consuming and expensive. Meanwhile this leads to a simple calculation of the membrane area though thereliability of the result is questionable, because the conditions are not the same in all stages of the process. A precise estimation of the membrane area can be made by using the equations describing the dependence of permeate flux and rejection on the process variables. In fact, there have been some theoretical approaches to predict the ultrafiltration performance of colloidal solutions (e.g., milk). These are based on some models such as mass transfer model (film theory), gel-polarisation model, osmotic pressure model, boundary layer-adsorption model, Brownian diffusion model, shear-induced diffusion model, inertial lift model and surface transport model [1,2]. In addition to the complexity of mathematical equations involved, each of these models has a number of limitations: (i) they demand some experimental
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Nomenclature FAT fat (%) FIS fuzzy inference system FL fuzzy logic J permeate flux (m/s) min minute MWCO molecular weight cut off (kDa) P pressure (kPa) pH power hydrogen R total hydraulic resistance (m1) Temp temperature (8C) time(min) time (minute) Time time (minute) TMP transmembrane pressure (kPa) V variable used in Eq. (4) x input to a fuzzy system y output of fuzzy system Greek letters m viscosity (kg/m s) D normalization margins Subscripts i inlet to fuzzy system, input j number of sigma L lower max maximun min minimum n normalized value o outlet of fuzzy system, output P permeate t total U upper
data for determining the input parameters. Perhaps this is always possible in practice, but the equipment required are especially sensitive instruments, which might not be readily available. (ii) None of the methods can describe the full flux– time behavior of process; they often predict the steady or pseudo-steady-state flux. (iii) Each one has been shown to be valid for certain feeds under special conditions. Hence, modeling methods based on direct analysis of experimental data appear to be good alternative to the models based on phenomenological hypotheses. One of these methods is Fuzzy Inference Systems (FISs). The main purpose of a fuzzy system is to achieve a set of local input–output relationships that describe a process. As is well known, the problem of system modeling requires two main stages: structure identification and parameter optimization. Structure identification deals with the problem of determining the input–output space partition and how many rules must be used by the fuzzy system. Parameter optimization finds the optimum value of all the parameters involved in the fuzzy system; that is, it locates the membership functions in the premise and consequent of each rule [3–6].
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In this research, we present a fuzzy logic based method to identify the forecasting model. In practical systems, the knowledge of expert humans used for information sources that defined with natural languages. Basically, a fuzzy system converts this language to mathematics model using concept of fuzzy logic theory [5]. Fuzzy logic (FL) is a synthesis of mathematics and common sense introduced by Lotfi Zadeh in the 1960s [6–8]. The advantage of prediction methods based on fuzzy set theory is to be able to express the models obtained in the form of fuzzy rules which are very close to human language. This allows easily explain and justify the predictions made by the models [9]. A fuzzy set is characterized by a membership function mF 2 [0, 1], which associates each element with a grade of membership in the fuzzy set. The main purpose of a fuzzy system is to achieve a set of local input–output relationships describing a process [10]. Fuzzy models have excellent capabilities to describe a given system. Many studies regarding fuzzy modeling have been reported [11]. Some of them are based on pattern recognition [12,13] and some others are based on system programming theory [13]. One of the most outstanding models among them is the model suggested by Takagi and Sugeno in 1985 [13]. Also, Sugeno and Yasukawa proposed a new model based on pattern recognition techniques [12]. In this study, the ability of FIS applied to modeling and simulation the cross ultrafiltration process of milk and predict permeate flux and total hydraulic resistance under different hydrodynamics parameters and operating time. In addition, the role of each property tested specifies on flux decline and fouling development during the process. 2. Materials and methods 2.1. Experimental set-ups The pilot plant membrane system adopted in this study was equipped to a feed tank (20 l), centrifugal pump, flow meter, spiral wound module, two pressure gauges, tubular heat exchanger, two control valves and temperature sensor. Fig. 1 shows schematic diagram of the ultrafiltration unit used. The membrane was composed of polysulfone amide, molecular weight cut-off [MWCO] 20u (20 kDa), with external diameter 0.52 m, membrane length 0.47 m providing membrane area of
Fig. 1. Schematic diagram of the ultrafiltration unit used in this study.
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0.33 m2. The two pressure gauges are used to measure the pressure at the inlet [Pi] and outlet [Po] of the module. To monitor the temperature probe was attached to the feed tank. The temperature of the feed was continuously controlled by a heat exchanger. In addition, the weight of permeate was recorded with an electronic scale every 30 s for the computation of flux. 2.2. Total hydraulic resistance and permeate flux By assuming that the osmotic pressure is very small, the total hydraulic resistance (Rt) can be expressed by Darcy’s law [2]: Rt ¼
TMP mP J P
(1)
and the permeate flux by [14]: JP ¼
1 TMP mP Rt
(2)
where mP is the permeate viscosity, JP the permeate flux and TMP is the transmembrane pressure which can be calculated by the following equation: TMP ¼ 12ðPi þ Po Þ PP
(3)
where Pi, Po and PP are inlet, outlet and permeate pressures, respectively. 2.3. Analytical methods Protein, lactose, fat, minerals and total solids contents of skim milk, permeate and retentate samples were measured using an apparatus called Lactostar instrument after each 3, 15 and 30 min in each run. Viscosity and density of permeate samples were measured using an Ostwald U-tube capillary viscometer and a densitometer, respectively, at given temperature (30, 40 and 50 8C) after each run. The acidity of skim milk, permeate, retentate and flashing solutions (distillate water and NaOH solution) samples were measured using pH meter. All measurements were repeated to ensure reproducibility of the results.
2.4. Experimental procedure Generally speaking, ultrafiltration operation is carried out in the following steps:
Distillate water filtration from clean membrane for 10 min. Milk filtration from clean membrane for 30 min. Distillate water filtration from closed membrane for 10 min. Cleaning-In-Place [CIP] cycle was done either according to the manufacturer’s instructions or by acid nitric, NaOH and detergents for 1.5–2 h.
Reconstituted skim milk was prepared by adding moderate temperature skim milk powder to warm water (about 50 8C) in blender with fast agitation. The average composition of the skimmed milk samples is shown in Table 1. The same batch of powdered milk was used in all experiments to ensure that changes in measured parameters did not result from variation in the milk composition. The effect of transmembrane pressure (TMP) variations (51, 101.33, 152, 203 and 253 kPa) and temperature (30, 40 and 50 8C) on flux (JP), total hydraulic resistance (Rt) and solutes rejection {i.e., protein (RP), fat (RF), lactose (RL), minerals (RM) and total solids (RTS)} have been considered in this work. The experiment were carried out in batch mode, constant feed concentration and flow rate (15 l/ min). Twelve kilograms of reconstituted skim milk was used in each run. Before conducting each experiment, the feed tank was first washed with hot distilled water to warm up the system and to assess the water flux. The permeate flux was measured and recorded every 30 s. After each 30 min, the membrane unit was flushed with distillate water, NaOH solution and distillate water, respectively (according to manufacturer’s instructions). The difference between the two measured data must not exceed more than 3–5%, otherwise the fouling was not completely removed and the flushing cycle must be repeated. The conventional method for calibrating the system are Micro-colloidal method for protein, Lin-Anion method for lactose, Gerber method for fat and Weight method for minerals and suspension solids total.
Table 1 Input–output values samples used in this work TMP (kPa)
Temp (8C)
Fat (%)
MWCO (kDa)
pH
Time (min)
JP (106 m/s)
Rt (1013 m1)
150 150 150 200 150 150 150 50 100 150 150 150 100
30 40 50 40 30 30 30 40 40 40 40 40 40
0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 1.2 2.4 3.3 0.1
20 20 20 20 20 20 20 20 20 20 20 20 10
6.67 6.67 6.67 6.67 6.43 6.25 5.97 6.67 6.67 6.67 6.67 6.67 6.67
4.5 9.5 28 8.5 30 0 7.5 1 5.5 10.5 13 23 22
6.75 6.5 5.5 7.7 5 5 3.9 5.5 4.75 6 5.8 5.5 2.1
2.4 3.25 4.25 3.65 3.25 3.25 4 1.25 2.85 3.5 3.5 3.7 6.55
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Fig. 2. Membership function of input and output variables used in this study (VL: very low, L: low, VMO: very moderate, MO: moderate, M: medium, I: increase, VI: very increase, H: high, VH: very high).
fuzzy inference system. It consists of fuzzifier, defuzzifier and fuzzy inference engine.
3. The structure of FIS and modeling methods 3.1. Fuzzy inference system
3.2. Modeling methods Fuzzy inference system use if-then rules as do conventional AI techniques [15,16]. A fuzzy rule is of form X IS A, where X is a linguistic variable of a fuzzy type Tand A is a fussy set (linguistic) defined on. The if part of a fuzzy if-then rule is called the antecedent (or premise), whereas the then part is called the consequent. The antecedent part of a fuzzy rule is a conjunction and/or a disjunction of fuzzy propositions. A fuzzy implication is viewed as describing a fuzzy relation between the fuzzy sets forming the implication [17]. A fuzzy rule, such as ‘‘if X IS A then Y IS B’’ is implemented by a fuzzy implication (fuzzy relation) which has a membership function mA!B(x, y) 2 [0, 1]. Therefore, Data are normalized by the following relationship: V n ¼ ð1 DU DL Þ
V V min þ DL V max V min
(4)
where Vn is the normalized value of V. Vmax and Vmin are the minimum and maximum values of V, respectively. From experience the authors have found that a better fit will be achieved if Du and DL (small margins) are kept a value of 0.05. Note that mA!B(x, y) 2 [0, 1] measures the degree of truth of the implication relation between x and y. In this study Gaussian membership function was applied that as follows: mA0 ðXÞ ¼ exp
x x s
2 (5)
where s, x* are function parameters. Fig. 2 shows membership function of input and output variables in the model. A set of related fuzzy rules forms a fuzzy rule base that can be used to infer fuzzy results in the form of fuzzy sets. A fuzzy result can be further refined to a more useful crisp result in the process called defuzzification. The most common mean of defuzzification is called the center of gravity method in which the center of gravity of the fuzzy set is measured and projected to the x-axis to get the crisp and clear result [18]. Fig. 3 shows a
The most commonly used fuzzy inference method is the Max-Min inference method or Mamdani inference method [16]. Another popular fuzzy model structure is called the TakagiSugeno model [19,2,20,16]. An overview of both the methods is given in this Section. 3.2.1. Mamdani model Consider the following rule base (where X, Y and Z are linguistic variables): If X is Ai and Y is Bi and . . . then Z is Ci and . . . i ¼ 1; 2; . . . ; n (6) Given the input fact (x0, y0), the goal is to determine the output ‘‘Z is C’’. The first step to make is to fuzzify the given input. The fuzzifier maps the inputs data x0 into the fuzzy set A and y0 into the fuzzy set B and etc. The next step is to evaluate the truth-value for the premise of each rule, and then apply the result to the conclusion part of each rule using the fuzzy implication. The membership functions defined on the input variables are applied to their actual values to determine the degree of truth for each rule premise. The degree of the truth for a rule’s premise is computed in Mamdani rule base as follows: ai ¼ min ðmAi ðx0 Þ; mBi ðy0 ÞÞ
Fig. 3. A schematic of fuzzy inference system (FIS).
(7)
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If a rule’s premise has nonzero degree of truth then the rule is activated. The next step is to find the output, Ci, of each of the rules: mCi ðwÞ ¼ mðAi and BiÞ ! Ci ðx0 ; y0 ; wÞ;
8w2W
(8)
In Min inference (or Mamdani implication rule) the implication is interpreted as a fuzzy And operator: mAi and Bi ðx0 ; y0 Þ and mCi ðwÞ ¼ min ðmAi and Bi ðx0 ; y0 Þ; mCi ðwÞÞ (9) In the rule aggregation step, all fuzzy subsets assigned to each output variable are combined together to form a single fuzzy subset for each output variable. The purpose is to aggregate all individual rule outputs to obtain the overall system output. In the Max composition, the combined output fuzzy subset C* is constructed by taking the maximum over all of the fuzzy subsets assigned to the output variable by the inference rule: mC ðwÞ ¼ max ðmC0 1 ðwÞ; mC0 2 ðwÞ; . . . ; mC0 n ðwÞÞ
(10)
Normally, the defuzzification step is executed as the last step. In this investigate, the Centriod, Bisector, smallest of maxima (SOM), mean of maxima (MOM) and largest of maxima (LOM) defuzzification methods used that the best method described in this study. 3.2.2. Takagi-Sugeno model The Takagi-Sugeno fuzzy model differs from the Mamdani model by introducing crisp functions as the consequences of the rules. This structure offers a systematic approach to generate fuzzy rules from a given input–output data set. A TakagiSugeno rule set is of the form: If X is Ai and Y is Bi and then Z ¼ f ðx0 ; y0 Þ;
(11)
i ¼ 1; 2; . . . ; n; ðx0 ; y0 Þ is input The antecedent of each rule is a set of fuzzy propositions connected with the AND operator. The consequent of each rule is a crisp function of the input vector (x0, y0). By means of the fuzzy sets of the antecedent propositions the input domain is softly partitioned in smaller regions where the mapping is locally approximated by the crisp functions f i. Combining the rules and their effects differ from the Mamdani method considerably. One variation of the Takagi-Sugeno inference system uses the weighted mean criterion to combine all the local representations in a global approximator, like this: Pr i¼1 mi zi z¼ P mi
Fig. 4. The built fuzzy inference system.
4. Results and discussion The objectives of this work were to study the ability of FIS to predict JP and Rt under different operating conditions with respect to time and to specify the role of each component on the flux decline and fouling development during the process. The results obtained from the dynamic simulation of this work are presented as follows for the flux and total resistance: 4.1. Permeate flux (JP) The results of the dynamic simulation permeate flux is shown in Fig. 5. The result reveals that there is high degree of agreement between the experimental data and the dynamic simulation of this work. This figure shows the variations of each physicochemical property versus 126 rules that applied in this study. It also exhibit that the permeate flux decreases as the time increases too. Likewise, Fig. 6 shows the results of Mamdani and Sugeno model for JP versus input variables. It can be clearly seen from these results that FISs system can effectively simulate the dynamic and non-linearity behavior of JP under different conditions. Furthermore, it is apparent that the rules (made of
(12)
where mi is the degree of fulfillment of the ith rule and r is the number of rules in the rule base. Finally, Fig. 4 shows the FIS built with two models as follow:
Fig. 5. Comparison between the dynamic simulation of this work and experimental data for the permeate flux (JP).
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Fig. 6. Effects of the input variables (Fat, pH, TMP, MWCO, Temp, time) on the permeate flux (JP) and the fouling resistance (Rt) according to: (a) Mamdani and (b) Sugeno models.
linguistic statement) in FIS structure had a significant effect on its decline. Fig. 6 shows the effect of different input variables on the pseudo-steady-state flux. It is evident that the permeate flux of the milk systems were quite different during the ultrafiltration process. Furthermore, it is found that permeate flux are influenced by modifying the input variables (e.g., TMP and fat of milk). These results are correct, as they are compatible with the Mamdani model. However, the results obtained from the Sugeno model shows that it can not be adopted for this process as it is inaccurate (in view of the fact that, the fouling is increased in the Mamdani model as the TMP and fat percent increases too. While, the results obtained from the Sugeno model shows the opposite). Therefore, the results of Mamdani model show that it can enable us to predict the ultrafiltration process accurately.
exhibits the simulation results using fuzzy system for Rt as a function of pH, Fat, MWCO, Temp, TMP and operating time. These figures confirm the complex behavior of Rt which are well reproduced by the FIS model. This figure also shows that how the variation of different properties can affect the fouling resistance. It also evident from these figures that Rt increases with time. These results suggest that fouling occurs with an increase of Rt during the first few minutes and as a result the flux will be greatly reduced. Therefore, as the result reveals, the modeling and simulation of the fouling resistance are compatible with Mamdani model and it can effectively predict the ultrafiltration process. However, the results obtained from
4.2. Total hydraulic resistance The results of Mamdani and Sugeno model for Rt versus input variables are plotted in Figs. 6 and 7 shows the variation of the total hydraulic resistance at the total index. In Fig. 6 the changes of Rt with each physicochemical properties are demonstrated in which it has been increased with time. It
Fig. 7. Comparison between the dynamic simulation of this work and experimental data for the fouling resistance (Rt).
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Fig. 8. Comparison between the result of this work and the experimental data at 0.1 fat percent for the: (a) permeate flux and (b) the fouling resistance.
Fig. 9. The effects of variations of transmembrane pressure (TMP) on the protein (RP), lactose (RL), fat (RF), mineral materials (RM) and total solids (RTS) on rejection.
the Sugeno model shows that it cannot be adopted for this process as it is inaccurate as explained earlier. 4.3. Simulation results and the foremost structure of FIS To achieve this objective, we used two models of Mamdani and Sugeno, with an automatic extraction of data from FIS [GENFIS2]. The MATLAB software was adopted for comparison purposes. We generated a dataset of 1600 samples and split them in a set of GENFIS2 and a test set. Moreover, we fixed the coverage threshold to 0.05. In
addition, we adopted product with adjustable threshold. Fig. 8 shows a comparison between the simulation results (FIS) and the experimental data (actual data). The result reveals that there is an excellent agreement between the simulation data from Genfis2 and the actual data. The simulation data FIS are resulted from two models of Mamdani and Sugeno. The results reveals that the curves could be well reproduced based upon the right selection of the data points by fuzzy system, although the data are not linear. In this study, different degree of accuracy was achieved through varying the structure of the model.
Table 2 Comparison and selection of the best structures of FIS by Mamdani and Sugeno Models
Mamdani Sugeno
Operators and Std And
Or
Implication
Aggregation
Defuzzification
Std (JP 106)
Std (Rt 10+13)
Min Min Min
Max Max Probor
Prod – –
Max – –
Centroid Wtsum Wtsum
0.7248 0.3247 0.3247
0.2967 0.156 0.156
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In particular, 14 and 8 fuzzy systems were tested corresponding to Mamdani and Takagi-Sugeno [TS] models, respectively. Furthermore, in this work the foremost of operators AND and OR, if-then implication, ELSE aggregation, defuzzification methods and standard deviation were computed. The results demonstrate that the precision of simulation could be improved by using appropriate selection of methods. A comparison between the results obtained from the Mamdani and Sugeno models are highlighted in Table 2. Table 2 shows the FIS operators results the best fit for each set of data. The result also demonstrates that the Centroid and
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Wtsum defuzzification for Mamdani and Sugeno models produces the best model performance in terms of the drop in the quantity of standard deviation. Therefore, as also mentioned earlier, the Mamdani model will be able to predict this process with a high degree of accuracy. 4.4. Components rejection In this part of study, we wanted to examine the ability of FISs to model the milk components rejection (i.e., protein, fat, lactose and total solids) by considering the effect of MWCO,
Fig. 10. The effects of variations of: (a) molecular weight cut off (MWCO), (b) fat, (c) pH and d) temperature (Temp) on the rejection (protein (RP), lactose (RL), fat (RF), mineral materials (RM) and total solids (RTS) on rejection.
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TMP, pH, Fat and Temp variation on rejection. The results obtained are shown in Figs. 9 and 10 which reveals the ability of FISs approach in modeling the process. In this work, the FIS system was also adopted to predict the solutes rejection by considering the effect of MWCO (10, 20, 50 kDa), TMP (50, 100, 150, 200, 250 kPa), pH (6.67, 6.43, 6.25, 5.97), Fat (3.3, 2.4, 1.2, 0.1%) and Temp (30, 40, 50 8C). For this work, fuzzy output values were based upon the coverage threshold of 1.2. These figures also exhibit that there is a good degree of agreement between the experimental data and the predictions values. These figures also demonstrate that the protein (RP) is almost constant with time for each parameter. However, the rejection of other components (such as RF, RL, RM and RTS) has increased significantly with time for the same set of condition. Thus, it can be concluded that for a flux decline, the increase of total resistance with time is probably due to decreasing transmission of small soluble compounds (such as lactose, salts) and fat through the membrane and their adsorption on the surface. The fouling resistance can be considered as a direct consequence of adsorption of small soluble compounds on the surface of the membrane which may increase with time; however, its value would be small in comparison to the total hydraulic resistance. Furthermore, the result exhibit that by rising the transmembrane pressure up to 250 kPa, it will results in a small increase in the rejection of each component. It can also be concluded that despite the increase of TMP flux, the rejection of each component has not been changed to a large extent. This can be caused by an increase of compounds migration toward membrane surface by convective transport (permeate flux) and their deposition on the membrane which causes a reduction in effective pore size [21,22]. As a consequence, the fouling or total hydraulic resistance has increased with time (Fig. 10a) for the Mamdani model. Fig. 10c also reveals that the fat rejection at each value of pH does no vary with time. 5. Conclusions In this research, the ability of FIS was investigated for modeling and simulation of cross ultrafiltration process of milk in order to predict permeate flux and total hydraulic resistance under different hydrodynamics parameters and time. Furthermore, we have also been assessed the role of each property on flux decline and fouling development during the process. Due to the complexity of the milk ultrafiltration process, instead of predicting the permeate flux, fouling and the milk components rejection in a conventional manner, an alternative approach have been adopted to allow a unified approach that could be used for analysis of the process and design of a new application. The simulation results reveals that the full-time profiles of the milk ultrafiltration performance could be predicted with a high degree of accuracy. As a result, it is unnecessary to carry out extensive pilot plant testing for collection of the data which on the other hand can be interpolated with potentially great savings both in time and cost. The results also show that the permeate flux decreases, while the total resistance increase significantly with time. In order to obtain these objectives, the MATLAB
software was adopted in this work. The input and output data were normalized and de-normalized before and after each simulation runs. The results also reveals that the permeate flux and the fouling resistance vary with time for each variables. Furthermore, the protein rejection is almost constant for each parameter with time; however, the rejection of other components has been raised significantly with time. In addition, the fouling has been picked up at the beginning and then lowered with the TMP. This could be caused by the blockage of the membrane pores. It is also worth noting that the fat rejection for each value of pH does not vary with time. Therefore, fuzzy inference systems can be used adequately to model and simulate the crossflow ultrafiltration of milk in a dynamic manner with a high degree of precision. Acknowledgements The authors would like to thank the Universities of Ferdowsi and Sistan & Baluchestan for funding this research work and also the Food Industrial complex of the agricultural faculty for providing the laboratory facilities. References [1] M. Cheryan, Ultrafiltration and Microfiltration Handbook, Lancaster, 1998. [2] A.S. Grandison, W. Youravong, M.J. Lewis, Hydrodynamics factors affecting flux and fouling during ultrafiltration of skimmed milk, Lait 80 (2000) 165–174. [3] T.E. Clarke, C.A. Heath, Ultrafiltration of skim milk in flat-plate and spiral-wound modules, J. Food Eng. 33 (1997) 373–383. [4] G. Samuelsson, I.H. Huisman, G. Tragardh, M. Paulsson, Predicting limiting flux of skim milk in crossflow microfiltration, J. Membr. Sci. 129 (1997) 277–281. [5] L.-X. Wang, A Course in Fuzzy Systems and Control, Englewood Cliffs, USA, 1994. [6] L.A. Zadeh, G.J. Klir, B. Yuan, Shadows of Fuzzy Sets, World Scientific, 1996. [7] L.A. Zadeh, Outline of a new approach to the analysis of complex systems and decision processes, IEEE Trans. Man. Cyber. 3 (1973) 28–44. [8] L.A. Zadeh, Theory of Fuzzy Sets, Memo, No. UCB/ERLM77/1, California, Berkeley, CA, 1977. [9] N. Peton, G. Dray, D. Pearson, M. Mesbah, B. Vuillot, Modeling and analysis of ozone episodes, Environ. Model. Software 15 (2000) 647–652. [10] M. Hiirsalmi, E. Kotsakis, A. Pesonen, A. Wolski, Discovery of Fuzzy Models from Observation Data, VTT Information Technology, Finland, 2000. [11] R. Ronald, P. Dimitar, Essentials of Fuzzy Modeling and Control, USA, New York, 1994. [12] M. Sugeno, T. Yasukawa, A fuzzy logic based approach to qualitative modeling, IEEE Trans. Fuzzy Syst. 1 (1993) 7–31. [13] L.-X. Wang, Adaptive Fuzzy Systems and Control: Design and Stability Analysis, Englewood Cliffs, USA, 1994. [14] A.G. Fane, Ultrafiltration Factors Influencing Flux, Progress in Filtration and Separation, vol. 4, Amsterdam, 1986, pp. 101–179. [15] L.A. Zadeh, The Calculus of Fuzzy If-Then Rules, vol. 7, AI Expert, USA, New York, 1992, pp. 22–27. [16] F. Esragh, E.H. Mamdani, in: E.H. Mamdani, B.R. Gaines (Eds.), A General Approach to Linguistic Approximation, in Fuzzy Reasoning and Its Application, London, 1981. [17] T. Munakata, Y. Jani, Fuzzy Systems: An Overview, Communications of the ACM, 7 (March 1994) pp. 69–76.
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[21] J. Sargolzaei, N. Saghatoleslami, M. Mousavi, M. Khoshnoodi, Comparative study of artificial neural networks and statistical methods for predicting the performance of ultrafiltration process in milk industry, Iranian J. Chem. Chem. Eng. 25 (2006) 67–76. [22] J. Sargolzaei, Modeling and Simulation of Milk Ultrafiltration Process Using Adaptive Neuro-Fuzzy Inference Systems, Ph.D. Thesis, Department of Chemical Engineering, University of Sistan & Baluchestan, 2006.
Fuzzy inference system to modeling of crossflow milk ultrafiltration J. Sargolzaei a,*, M. Khoshnoodi b, N. Saghatoleslami a, M. Mousavi a a b
Department of Chemical Engineering, Ferdowsi University of Mashhad, P.O. Box 9177948944, Mashhad, Iran Department of Chemical Engineering, University of Sistan and Baluchestan, P.O. Box 98164-161, Zahedan, Iran Received 23 June 2005; received in revised form 1 February 2007; accepted 8 February 2007 Available online 20 March 2007
Abstract Fuzzy inference systems (FISs) have been adopted as a powerful tool to adequately model and simulate the crossflow ultrafiltration of milk. It primary aim of this research was to predict the permeate flux, total hydraulic resistance and the milk components rejection as a function of different physicochemical properties. Dynamic modeling of ultrafiltration performance of colloidal systems (such as milk) is an important criterion in designing of a new process, due to the complex nature of milk in a dynamic manner. Such processes exhibit complex nonlinear behavior due to unknown interactions between compounds and colloidal system, thus the theoretical approaches were not being able do successfully model and simulate the processes. In addition, it has been attempted to test the FIS ability to predict new data that is not normally available. To obtain this objective, fuzzy output with a threshold of 1.2 was constructed in order to predict rejections from the limited number of accessible experimental data. The findings of this work also reveal that there exist an excellent agreement between the experimental data and predicted values. Furthermore, the experimental results shows that the total hydraulic resistance and solutes rejection (except for protein) increased significantly with time for every corresponding value of the hydrodynamic parameters. On the other hand, the permeate flux decreased sharply. However, the fat rejection does not change with time for every value of the pH. # 2007 Elsevier B.V. All rights reserved. Keywords: Milk ultrafiltration; Protein; Fat; Modeling and simulation; Fuzzy inference system
1. Introduction Ultrafiltration is an important process in the food industry, particularly for dairy applications such as concentration of milk. Membrane processing of dairy fluids can reduce the operational expenses incurred from power consumption improve plant processing capacity and efficiency, and increase quality of product. The efficiency and cost of membrane processing is dependent on flux and rejection, which is a function of different factors. The membrane type, processing parameters and fluid properties will determine flux and
Abbreviations: H, high; I, increase; kg, kilogram; L, low; l, liter, volume unit; LOM, largest of maxima; M, medium; m, meter; Max, maximum (logic operator); min, minute; Min, minimum (logic operator); MO, moderate; MOM, mean of maxima; Probor, logic operator; Prod, product (logic operator); s, second; SOM, smallest of maxima; Std, standard deviation; u, unit; VH, very high; VI, very increase; VL, very low; VMO, very moderate; Wtsum, operator * Corresponding author. Tel.: +98 915 512 4591; fax: +98 511 8816840. E-mail addresses: [email protected] (J. Sargolzaei), [email protected] (M. Khoshnoodi), [email protected] (N. Saghatoleslami), [email protected] (M. Mousavi). 1568-4946/$ – see front matter # 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.asoc.2007.02.007
concentration of components in retentate and permeate. Therefore, permeation flux and solute rejection data are necessary for the design of a specified or new membrane separation process. In the simplest method, some laboratory or pilot plant tests are carried out over a wide range of conditions. This method is often usual in industry, which is both time consuming and expensive. Meanwhile this leads to a simple calculation of the membrane area though thereliability of the result is questionable, because the conditions are not the same in all stages of the process. A precise estimation of the membrane area can be made by using the equations describing the dependence of permeate flux and rejection on the process variables. In fact, there have been some theoretical approaches to predict the ultrafiltration performance of colloidal solutions (e.g., milk). These are based on some models such as mass transfer model (film theory), gel-polarisation model, osmotic pressure model, boundary layer-adsorption model, Brownian diffusion model, shear-induced diffusion model, inertial lift model and surface transport model [1,2]. In addition to the complexity of mathematical equations involved, each of these models has a number of limitations: (i) they demand some experimental
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Nomenclature FAT fat (%) FIS fuzzy inference system FL fuzzy logic J permeate flux (m/s) min minute MWCO molecular weight cut off (kDa) P pressure (kPa) pH power hydrogen R total hydraulic resistance (m1) Temp temperature (8C) time(min) time (minute) Time time (minute) TMP transmembrane pressure (kPa) V variable used in Eq. (4) x input to a fuzzy system y output of fuzzy system Greek letters m viscosity (kg/m s) D normalization margins Subscripts i inlet to fuzzy system, input j number of sigma L lower max maximun min minimum n normalized value o outlet of fuzzy system, output P permeate t total U upper
data for determining the input parameters. Perhaps this is always possible in practice, but the equipment required are especially sensitive instruments, which might not be readily available. (ii) None of the methods can describe the full flux– time behavior of process; they often predict the steady or pseudo-steady-state flux. (iii) Each one has been shown to be valid for certain feeds under special conditions. Hence, modeling methods based on direct analysis of experimental data appear to be good alternative to the models based on phenomenological hypotheses. One of these methods is Fuzzy Inference Systems (FISs). The main purpose of a fuzzy system is to achieve a set of local input–output relationships that describe a process. As is well known, the problem of system modeling requires two main stages: structure identification and parameter optimization. Structure identification deals with the problem of determining the input–output space partition and how many rules must be used by the fuzzy system. Parameter optimization finds the optimum value of all the parameters involved in the fuzzy system; that is, it locates the membership functions in the premise and consequent of each rule [3–6].
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In this research, we present a fuzzy logic based method to identify the forecasting model. In practical systems, the knowledge of expert humans used for information sources that defined with natural languages. Basically, a fuzzy system converts this language to mathematics model using concept of fuzzy logic theory [5]. Fuzzy logic (FL) is a synthesis of mathematics and common sense introduced by Lotfi Zadeh in the 1960s [6–8]. The advantage of prediction methods based on fuzzy set theory is to be able to express the models obtained in the form of fuzzy rules which are very close to human language. This allows easily explain and justify the predictions made by the models [9]. A fuzzy set is characterized by a membership function mF 2 [0, 1], which associates each element with a grade of membership in the fuzzy set. The main purpose of a fuzzy system is to achieve a set of local input–output relationships describing a process [10]. Fuzzy models have excellent capabilities to describe a given system. Many studies regarding fuzzy modeling have been reported [11]. Some of them are based on pattern recognition [12,13] and some others are based on system programming theory [13]. One of the most outstanding models among them is the model suggested by Takagi and Sugeno in 1985 [13]. Also, Sugeno and Yasukawa proposed a new model based on pattern recognition techniques [12]. In this study, the ability of FIS applied to modeling and simulation the cross ultrafiltration process of milk and predict permeate flux and total hydraulic resistance under different hydrodynamics parameters and operating time. In addition, the role of each property tested specifies on flux decline and fouling development during the process. 2. Materials and methods 2.1. Experimental set-ups The pilot plant membrane system adopted in this study was equipped to a feed tank (20 l), centrifugal pump, flow meter, spiral wound module, two pressure gauges, tubular heat exchanger, two control valves and temperature sensor. Fig. 1 shows schematic diagram of the ultrafiltration unit used. The membrane was composed of polysulfone amide, molecular weight cut-off [MWCO] 20u (20 kDa), with external diameter 0.52 m, membrane length 0.47 m providing membrane area of
Fig. 1. Schematic diagram of the ultrafiltration unit used in this study.
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0.33 m2. The two pressure gauges are used to measure the pressure at the inlet [Pi] and outlet [Po] of the module. To monitor the temperature probe was attached to the feed tank. The temperature of the feed was continuously controlled by a heat exchanger. In addition, the weight of permeate was recorded with an electronic scale every 30 s for the computation of flux. 2.2. Total hydraulic resistance and permeate flux By assuming that the osmotic pressure is very small, the total hydraulic resistance (Rt) can be expressed by Darcy’s law [2]: Rt ¼
TMP mP J P
(1)
and the permeate flux by [14]: JP ¼
1 TMP mP Rt
(2)
where mP is the permeate viscosity, JP the permeate flux and TMP is the transmembrane pressure which can be calculated by the following equation: TMP ¼ 12ðPi þ Po Þ PP
(3)
where Pi, Po and PP are inlet, outlet and permeate pressures, respectively. 2.3. Analytical methods Protein, lactose, fat, minerals and total solids contents of skim milk, permeate and retentate samples were measured using an apparatus called Lactostar instrument after each 3, 15 and 30 min in each run. Viscosity and density of permeate samples were measured using an Ostwald U-tube capillary viscometer and a densitometer, respectively, at given temperature (30, 40 and 50 8C) after each run. The acidity of skim milk, permeate, retentate and flashing solutions (distillate water and NaOH solution) samples were measured using pH meter. All measurements were repeated to ensure reproducibility of the results.
2.4. Experimental procedure Generally speaking, ultrafiltration operation is carried out in the following steps:
Distillate water filtration from clean membrane for 10 min. Milk filtration from clean membrane for 30 min. Distillate water filtration from closed membrane for 10 min. Cleaning-In-Place [CIP] cycle was done either according to the manufacturer’s instructions or by acid nitric, NaOH and detergents for 1.5–2 h.
Reconstituted skim milk was prepared by adding moderate temperature skim milk powder to warm water (about 50 8C) in blender with fast agitation. The average composition of the skimmed milk samples is shown in Table 1. The same batch of powdered milk was used in all experiments to ensure that changes in measured parameters did not result from variation in the milk composition. The effect of transmembrane pressure (TMP) variations (51, 101.33, 152, 203 and 253 kPa) and temperature (30, 40 and 50 8C) on flux (JP), total hydraulic resistance (Rt) and solutes rejection {i.e., protein (RP), fat (RF), lactose (RL), minerals (RM) and total solids (RTS)} have been considered in this work. The experiment were carried out in batch mode, constant feed concentration and flow rate (15 l/ min). Twelve kilograms of reconstituted skim milk was used in each run. Before conducting each experiment, the feed tank was first washed with hot distilled water to warm up the system and to assess the water flux. The permeate flux was measured and recorded every 30 s. After each 30 min, the membrane unit was flushed with distillate water, NaOH solution and distillate water, respectively (according to manufacturer’s instructions). The difference between the two measured data must not exceed more than 3–5%, otherwise the fouling was not completely removed and the flushing cycle must be repeated. The conventional method for calibrating the system are Micro-colloidal method for protein, Lin-Anion method for lactose, Gerber method for fat and Weight method for minerals and suspension solids total.
Table 1 Input–output values samples used in this work TMP (kPa)
Temp (8C)
Fat (%)
MWCO (kDa)
pH
Time (min)
JP (106 m/s)
Rt (1013 m1)
150 150 150 200 150 150 150 50 100 150 150 150 100
30 40 50 40 30 30 30 40 40 40 40 40 40
0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.1 1.2 2.4 3.3 0.1
20 20 20 20 20 20 20 20 20 20 20 20 10
6.67 6.67 6.67 6.67 6.43 6.25 5.97 6.67 6.67 6.67 6.67 6.67 6.67
4.5 9.5 28 8.5 30 0 7.5 1 5.5 10.5 13 23 22
6.75 6.5 5.5 7.7 5 5 3.9 5.5 4.75 6 5.8 5.5 2.1
2.4 3.25 4.25 3.65 3.25 3.25 4 1.25 2.85 3.5 3.5 3.7 6.55
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Fig. 2. Membership function of input and output variables used in this study (VL: very low, L: low, VMO: very moderate, MO: moderate, M: medium, I: increase, VI: very increase, H: high, VH: very high).
fuzzy inference system. It consists of fuzzifier, defuzzifier and fuzzy inference engine.
3. The structure of FIS and modeling methods 3.1. Fuzzy inference system
3.2. Modeling methods Fuzzy inference system use if-then rules as do conventional AI techniques [15,16]. A fuzzy rule is of form X IS A, where X is a linguistic variable of a fuzzy type Tand A is a fussy set (linguistic) defined on. The if part of a fuzzy if-then rule is called the antecedent (or premise), whereas the then part is called the consequent. The antecedent part of a fuzzy rule is a conjunction and/or a disjunction of fuzzy propositions. A fuzzy implication is viewed as describing a fuzzy relation between the fuzzy sets forming the implication [17]. A fuzzy rule, such as ‘‘if X IS A then Y IS B’’ is implemented by a fuzzy implication (fuzzy relation) which has a membership function mA!B(x, y) 2 [0, 1]. Therefore, Data are normalized by the following relationship: V n ¼ ð1 DU DL Þ
V V min þ DL V max V min
(4)
where Vn is the normalized value of V. Vmax and Vmin are the minimum and maximum values of V, respectively. From experience the authors have found that a better fit will be achieved if Du and DL (small margins) are kept a value of 0.05. Note that mA!B(x, y) 2 [0, 1] measures the degree of truth of the implication relation between x and y. In this study Gaussian membership function was applied that as follows: mA0 ðXÞ ¼ exp
x x s
2 (5)
where s, x* are function parameters. Fig. 2 shows membership function of input and output variables in the model. A set of related fuzzy rules forms a fuzzy rule base that can be used to infer fuzzy results in the form of fuzzy sets. A fuzzy result can be further refined to a more useful crisp result in the process called defuzzification. The most common mean of defuzzification is called the center of gravity method in which the center of gravity of the fuzzy set is measured and projected to the x-axis to get the crisp and clear result [18]. Fig. 3 shows a
The most commonly used fuzzy inference method is the Max-Min inference method or Mamdani inference method [16]. Another popular fuzzy model structure is called the TakagiSugeno model [19,2,20,16]. An overview of both the methods is given in this Section. 3.2.1. Mamdani model Consider the following rule base (where X, Y and Z are linguistic variables): If X is Ai and Y is Bi and . . . then Z is Ci and . . . i ¼ 1; 2; . . . ; n (6) Given the input fact (x0, y0), the goal is to determine the output ‘‘Z is C’’. The first step to make is to fuzzify the given input. The fuzzifier maps the inputs data x0 into the fuzzy set A and y0 into the fuzzy set B and etc. The next step is to evaluate the truth-value for the premise of each rule, and then apply the result to the conclusion part of each rule using the fuzzy implication. The membership functions defined on the input variables are applied to their actual values to determine the degree of truth for each rule premise. The degree of the truth for a rule’s premise is computed in Mamdani rule base as follows: ai ¼ min ðmAi ðx0 Þ; mBi ðy0 ÞÞ
Fig. 3. A schematic of fuzzy inference system (FIS).
(7)
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If a rule’s premise has nonzero degree of truth then the rule is activated. The next step is to find the output, Ci, of each of the rules: mCi ðwÞ ¼ mðAi and BiÞ ! Ci ðx0 ; y0 ; wÞ;
8w2W
(8)
In Min inference (or Mamdani implication rule) the implication is interpreted as a fuzzy And operator: mAi and Bi ðx0 ; y0 Þ and mCi ðwÞ ¼ min ðmAi and Bi ðx0 ; y0 Þ; mCi ðwÞÞ (9) In the rule aggregation step, all fuzzy subsets assigned to each output variable are combined together to form a single fuzzy subset for each output variable. The purpose is to aggregate all individual rule outputs to obtain the overall system output. In the Max composition, the combined output fuzzy subset C* is constructed by taking the maximum over all of the fuzzy subsets assigned to the output variable by the inference rule: mC ðwÞ ¼ max ðmC0 1 ðwÞ; mC0 2 ðwÞ; . . . ; mC0 n ðwÞÞ
(10)
Normally, the defuzzification step is executed as the last step. In this investigate, the Centriod, Bisector, smallest of maxima (SOM), mean of maxima (MOM) and largest of maxima (LOM) defuzzification methods used that the best method described in this study. 3.2.2. Takagi-Sugeno model The Takagi-Sugeno fuzzy model differs from the Mamdani model by introducing crisp functions as the consequences of the rules. This structure offers a systematic approach to generate fuzzy rules from a given input–output data set. A TakagiSugeno rule set is of the form: If X is Ai and Y is Bi and then Z ¼ f ðx0 ; y0 Þ;
(11)
i ¼ 1; 2; . . . ; n; ðx0 ; y0 Þ is input The antecedent of each rule is a set of fuzzy propositions connected with the AND operator. The consequent of each rule is a crisp function of the input vector (x0, y0). By means of the fuzzy sets of the antecedent propositions the input domain is softly partitioned in smaller regions where the mapping is locally approximated by the crisp functions f i. Combining the rules and their effects differ from the Mamdani method considerably. One variation of the Takagi-Sugeno inference system uses the weighted mean criterion to combine all the local representations in a global approximator, like this: Pr i¼1 mi zi z¼ P mi
Fig. 4. The built fuzzy inference system.
4. Results and discussion The objectives of this work were to study the ability of FIS to predict JP and Rt under different operating conditions with respect to time and to specify the role of each component on the flux decline and fouling development during the process. The results obtained from the dynamic simulation of this work are presented as follows for the flux and total resistance: 4.1. Permeate flux (JP) The results of the dynamic simulation permeate flux is shown in Fig. 5. The result reveals that there is high degree of agreement between the experimental data and the dynamic simulation of this work. This figure shows the variations of each physicochemical property versus 126 rules that applied in this study. It also exhibit that the permeate flux decreases as the time increases too. Likewise, Fig. 6 shows the results of Mamdani and Sugeno model for JP versus input variables. It can be clearly seen from these results that FISs system can effectively simulate the dynamic and non-linearity behavior of JP under different conditions. Furthermore, it is apparent that the rules (made of
(12)
where mi is the degree of fulfillment of the ith rule and r is the number of rules in the rule base. Finally, Fig. 4 shows the FIS built with two models as follow:
Fig. 5. Comparison between the dynamic simulation of this work and experimental data for the permeate flux (JP).
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Fig. 6. Effects of the input variables (Fat, pH, TMP, MWCO, Temp, time) on the permeate flux (JP) and the fouling resistance (Rt) according to: (a) Mamdani and (b) Sugeno models.
linguistic statement) in FIS structure had a significant effect on its decline. Fig. 6 shows the effect of different input variables on the pseudo-steady-state flux. It is evident that the permeate flux of the milk systems were quite different during the ultrafiltration process. Furthermore, it is found that permeate flux are influenced by modifying the input variables (e.g., TMP and fat of milk). These results are correct, as they are compatible with the Mamdani model. However, the results obtained from the Sugeno model shows that it can not be adopted for this process as it is inaccurate (in view of the fact that, the fouling is increased in the Mamdani model as the TMP and fat percent increases too. While, the results obtained from the Sugeno model shows the opposite). Therefore, the results of Mamdani model show that it can enable us to predict the ultrafiltration process accurately.
exhibits the simulation results using fuzzy system for Rt as a function of pH, Fat, MWCO, Temp, TMP and operating time. These figures confirm the complex behavior of Rt which are well reproduced by the FIS model. This figure also shows that how the variation of different properties can affect the fouling resistance. It also evident from these figures that Rt increases with time. These results suggest that fouling occurs with an increase of Rt during the first few minutes and as a result the flux will be greatly reduced. Therefore, as the result reveals, the modeling and simulation of the fouling resistance are compatible with Mamdani model and it can effectively predict the ultrafiltration process. However, the results obtained from
4.2. Total hydraulic resistance The results of Mamdani and Sugeno model for Rt versus input variables are plotted in Figs. 6 and 7 shows the variation of the total hydraulic resistance at the total index. In Fig. 6 the changes of Rt with each physicochemical properties are demonstrated in which it has been increased with time. It
Fig. 7. Comparison between the dynamic simulation of this work and experimental data for the fouling resistance (Rt).
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Fig. 8. Comparison between the result of this work and the experimental data at 0.1 fat percent for the: (a) permeate flux and (b) the fouling resistance.
Fig. 9. The effects of variations of transmembrane pressure (TMP) on the protein (RP), lactose (RL), fat (RF), mineral materials (RM) and total solids (RTS) on rejection.
the Sugeno model shows that it cannot be adopted for this process as it is inaccurate as explained earlier. 4.3. Simulation results and the foremost structure of FIS To achieve this objective, we used two models of Mamdani and Sugeno, with an automatic extraction of data from FIS [GENFIS2]. The MATLAB software was adopted for comparison purposes. We generated a dataset of 1600 samples and split them in a set of GENFIS2 and a test set. Moreover, we fixed the coverage threshold to 0.05. In
addition, we adopted product with adjustable threshold. Fig. 8 shows a comparison between the simulation results (FIS) and the experimental data (actual data). The result reveals that there is an excellent agreement between the simulation data from Genfis2 and the actual data. The simulation data FIS are resulted from two models of Mamdani and Sugeno. The results reveals that the curves could be well reproduced based upon the right selection of the data points by fuzzy system, although the data are not linear. In this study, different degree of accuracy was achieved through varying the structure of the model.
Table 2 Comparison and selection of the best structures of FIS by Mamdani and Sugeno Models
Mamdani Sugeno
Operators and Std And
Or
Implication
Aggregation
Defuzzification
Std (JP 106)
Std (Rt 10+13)
Min Min Min
Max Max Probor
Prod – –
Max – –
Centroid Wtsum Wtsum
0.7248 0.3247 0.3247
0.2967 0.156 0.156
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In particular, 14 and 8 fuzzy systems were tested corresponding to Mamdani and Takagi-Sugeno [TS] models, respectively. Furthermore, in this work the foremost of operators AND and OR, if-then implication, ELSE aggregation, defuzzification methods and standard deviation were computed. The results demonstrate that the precision of simulation could be improved by using appropriate selection of methods. A comparison between the results obtained from the Mamdani and Sugeno models are highlighted in Table 2. Table 2 shows the FIS operators results the best fit for each set of data. The result also demonstrates that the Centroid and
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Wtsum defuzzification for Mamdani and Sugeno models produces the best model performance in terms of the drop in the quantity of standard deviation. Therefore, as also mentioned earlier, the Mamdani model will be able to predict this process with a high degree of accuracy. 4.4. Components rejection In this part of study, we wanted to examine the ability of FISs to model the milk components rejection (i.e., protein, fat, lactose and total solids) by considering the effect of MWCO,
Fig. 10. The effects of variations of: (a) molecular weight cut off (MWCO), (b) fat, (c) pH and d) temperature (Temp) on the rejection (protein (RP), lactose (RL), fat (RF), mineral materials (RM) and total solids (RTS) on rejection.
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TMP, pH, Fat and Temp variation on rejection. The results obtained are shown in Figs. 9 and 10 which reveals the ability of FISs approach in modeling the process. In this work, the FIS system was also adopted to predict the solutes rejection by considering the effect of MWCO (10, 20, 50 kDa), TMP (50, 100, 150, 200, 250 kPa), pH (6.67, 6.43, 6.25, 5.97), Fat (3.3, 2.4, 1.2, 0.1%) and Temp (30, 40, 50 8C). For this work, fuzzy output values were based upon the coverage threshold of 1.2. These figures also exhibit that there is a good degree of agreement between the experimental data and the predictions values. These figures also demonstrate that the protein (RP) is almost constant with time for each parameter. However, the rejection of other components (such as RF, RL, RM and RTS) has increased significantly with time for the same set of condition. Thus, it can be concluded that for a flux decline, the increase of total resistance with time is probably due to decreasing transmission of small soluble compounds (such as lactose, salts) and fat through the membrane and their adsorption on the surface. The fouling resistance can be considered as a direct consequence of adsorption of small soluble compounds on the surface of the membrane which may increase with time; however, its value would be small in comparison to the total hydraulic resistance. Furthermore, the result exhibit that by rising the transmembrane pressure up to 250 kPa, it will results in a small increase in the rejection of each component. It can also be concluded that despite the increase of TMP flux, the rejection of each component has not been changed to a large extent. This can be caused by an increase of compounds migration toward membrane surface by convective transport (permeate flux) and their deposition on the membrane which causes a reduction in effective pore size [21,22]. As a consequence, the fouling or total hydraulic resistance has increased with time (Fig. 10a) for the Mamdani model. Fig. 10c also reveals that the fat rejection at each value of pH does no vary with time. 5. Conclusions In this research, the ability of FIS was investigated for modeling and simulation of cross ultrafiltration process of milk in order to predict permeate flux and total hydraulic resistance under different hydrodynamics parameters and time. Furthermore, we have also been assessed the role of each property on flux decline and fouling development during the process. Due to the complexity of the milk ultrafiltration process, instead of predicting the permeate flux, fouling and the milk components rejection in a conventional manner, an alternative approach have been adopted to allow a unified approach that could be used for analysis of the process and design of a new application. The simulation results reveals that the full-time profiles of the milk ultrafiltration performance could be predicted with a high degree of accuracy. As a result, it is unnecessary to carry out extensive pilot plant testing for collection of the data which on the other hand can be interpolated with potentially great savings both in time and cost. The results also show that the permeate flux decreases, while the total resistance increase significantly with time. In order to obtain these objectives, the MATLAB
software was adopted in this work. The input and output data were normalized and de-normalized before and after each simulation runs. The results also reveals that the permeate flux and the fouling resistance vary with time for each variables. Furthermore, the protein rejection is almost constant for each parameter with time; however, the rejection of other components has been raised significantly with time. In addition, the fouling has been picked up at the beginning and then lowered with the TMP. This could be caused by the blockage of the membrane pores. It is also worth noting that the fat rejection for each value of pH does not vary with time. Therefore, fuzzy inference systems can be used adequately to model and simulate the crossflow ultrafiltration of milk in a dynamic manner with a high degree of precision. Acknowledgements The authors would like to thank the Universities of Ferdowsi and Sistan & Baluchestan for funding this research work and also the Food Industrial complex of the agricultural faculty for providing the laboratory facilities. References [1] M. Cheryan, Ultrafiltration and Microfiltration Handbook, Lancaster, 1998. [2] A.S. Grandison, W. Youravong, M.J. Lewis, Hydrodynamics factors affecting flux and fouling during ultrafiltration of skimmed milk, Lait 80 (2000) 165–174. [3] T.E. Clarke, C.A. Heath, Ultrafiltration of skim milk in flat-plate and spiral-wound modules, J. Food Eng. 33 (1997) 373–383. [4] G. Samuelsson, I.H. Huisman, G. Tragardh, M. Paulsson, Predicting limiting flux of skim milk in crossflow microfiltration, J. Membr. Sci. 129 (1997) 277–281. [5] L.-X. Wang, A Course in Fuzzy Systems and Control, Englewood Cliffs, USA, 1994. [6] L.A. Zadeh, G.J. Klir, B. Yuan, Shadows of Fuzzy Sets, World Scientific, 1996. [7] L.A. Zadeh, Outline of a new approach to the analysis of complex systems and decision processes, IEEE Trans. Man. Cyber. 3 (1973) 28–44. [8] L.A. Zadeh, Theory of Fuzzy Sets, Memo, No. UCB/ERLM77/1, California, Berkeley, CA, 1977. [9] N. Peton, G. Dray, D. Pearson, M. Mesbah, B. Vuillot, Modeling and analysis of ozone episodes, Environ. Model. Software 15 (2000) 647–652. [10] M. Hiirsalmi, E. Kotsakis, A. Pesonen, A. Wolski, Discovery of Fuzzy Models from Observation Data, VTT Information Technology, Finland, 2000. [11] R. Ronald, P. Dimitar, Essentials of Fuzzy Modeling and Control, USA, New York, 1994. [12] M. Sugeno, T. Yasukawa, A fuzzy logic based approach to qualitative modeling, IEEE Trans. Fuzzy Syst. 1 (1993) 7–31. [13] L.-X. Wang, Adaptive Fuzzy Systems and Control: Design and Stability Analysis, Englewood Cliffs, USA, 1994. [14] A.G. Fane, Ultrafiltration Factors Influencing Flux, Progress in Filtration and Separation, vol. 4, Amsterdam, 1986, pp. 101–179. [15] L.A. Zadeh, The Calculus of Fuzzy If-Then Rules, vol. 7, AI Expert, USA, New York, 1992, pp. 22–27. [16] F. Esragh, E.H. Mamdani, in: E.H. Mamdani, B.R. Gaines (Eds.), A General Approach to Linguistic Approximation, in Fuzzy Reasoning and Its Application, London, 1981. [17] T. Munakata, Y. Jani, Fuzzy Systems: An Overview, Communications of the ACM, 7 (March 1994) pp. 69–76.
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