Using Fuzzy Logic Methods for Carbon Dioxide Control in Carbonated Beverages

Transcription

1 International Journal of Electrical & Computer Sciences IJECS-IJENS Vol: 11 No: Using Fuzzy Logic Methods for Carbon Dioxide Control in Carbonated Beverages İman Askerbeyli 1 and Juneed S.Abduljabar 2 1 Department of Computer Engineering, Ankara University, Ankara, Turkey Iman.Askerbeyli@eng.ankara.edu.tr 2 Department of Computer Engineering, Ankara University, Ankara, Turkey Juned_s83@yahoo.com Abstract-- In this paper, this article is about one of the applications of fuzzy logic and neuro-fuzzy in field of control, it is how to measuring the percentage of carbon dioxide gas which is contained in sugary solution of Fizzy drink by using computer system depended on the concept of fuzzy logic and neuro-fuzzy mechanism, by these two methods the percentage of carbon dioxide can be measured in sugary solution of fizzy drink, at last the comparison can be done among result in order to know which one of methods has less ratio than another to measuring the real value of carbon dioxide of AL- TAMIM company for food stuff. consist of two entries: temperature, pressure and one output which the percentage of carbon dioxide gaz. In this project, a mechanism based on Adaptive Network Fuzzy Interface System (ANFIS) is proposed to be used to control of the percentage of carbon dioxide gas which is contained in sugary solution of seven-up fizzy drink. ANFIS is a neuro-fuzzy algorithm that needs only initial membership functions which are trained using a hybrid learning algorithm. Index Term-- Fuzzy logic, adaptive network fuzzy inference system, carbonated beverages, control application. 1. INTRODUCTION Control system is required, it is actually available in many fields like medicine, economy, engineering and agriculture etc. result of rapid process of science & technology which lead to make the field of control theory in reactions create with mentioned fields specially in engineering and computers fields. The subject of control is specialized to study of natural & artificial fields, control rules organize. Control theory developed to get analyze tools & installing control system. Control science is related to modification of dynamic system conduct to realize the required targets, many physical systems are controlled by treating it s entries depending on the outputs in the same time. Control theory has two main targets, the first includes describing the concepts in mathematical way which allows to use it in calculating of control entries in the system, the second is designing system which allow to automatic control system [1]. Later many modern methods had been developed in this field, fuzzy logic which is discovered by Azerian scientist Lutfi Zade on 1965 [2]. The fuzzy logic doesn t mean fuzzy thinking but it is the followed method to treating of mysteries & uncertainty conditions in our life. By merging control theory with fuzzy logic field which produce fuzzy control that is application of fuzzy logic in control field. It is common that the carbonated beverages recently are favored by all people because of the good taste. This article deals with the measure of the percentage of carbon dioxide gas which is contained in sugary solution of seven-up carbonated beverages depending upon fuzzy logic and neuro-fuzzy. The fuzzy logic and neuro-fuzzy systems 2. BACKGROUND WORK 2.1 Carbonated Beverages The definition of carbonated beverages According to the Turkish Food Codex Alcohol Free Beverages Notification, carbonated beverages are drinks such as fruity, aromatic, coke or tonic which are gassed with carbon dioxide. Coke drink; is the beverage which is prepared with potable water, sugar, caffeine, other components, allowed additives, distinctive aromatic substances according to its own technique and gassed with carbon dioxide. [3] The production of carbonated beverages The production of the fizzy beverages is quite a complex process. Heat of the product, gas pressure and filling level are the factors affecting the system and they should be continuously controlled at any stage of the process. The first stage in the production of carbonated beverages is the preparation of the water which constitutes a large amount of the beverage. Depending on the feature of the drink, sugar or sweetener is mixed with the water under appropriate conditions and a homogenous sugary water mixture (sugar syrup) is prepared. Depending on the feature of the drink, color substance, aromatic substances, thickeners, acids and chemical protectors are added into the prepared syrup. The sugar and acid rate of the mixture is determined and water is added if required. Water is cooled down and sent to the carburizer. Here, the carbon dioxide is added. The purpose for cooling down the water is to increase the solubility of the gas. As the carbon dioxide gas has a quite big effect in constituting the flavor profile of the drink, carburizing conditions are important. As the solubility of the carbon dioxide under lower temperatures shall be better, the temperature should be kept under control during all the

2 International Journal of Electrical & Computer Sciences IJECS-IJENS Vol: 11 No: process. The derived carburized water and drink syrup are mixed [4]. The fizzy product derived at the end of this process is sent to packaging department. In the packaging department, the drink is packaged depending on the desired feature by using plastic bottle, glass bottle or cans. The packaged products are sent to the storage department and stored under suitable conditions. The first stage in the packaging is filling. Then, the covers of the carbonated beverages which are filled in the glass bottles, plastic bottles or cans are closed. After packing, shrinking and packaging they are sent to the storage department and stored. In order to maintain the flavor characteristic of the fizzy drink in time, it should be kept under suitable conditions beginning from filling until reaching the consumer [5]. 2.2 Fuzzy Logic Introduction to Fuzzy Logic The concept of fuzzy set is an extension of the concept of an ordinary set, called a crisp set. For a crisp set X, an element either belongs to X, represented by logic 1, or does not, represented by logic 0. Whereas, for a fuzzy set F(X) is defined by membership functions. Each element has a real number in the closed interval [0,1]. Any value between 0 and 1 expresses the grade of membership function which represents how much an element belongs to this fuzzy set. The concept of fuzzy sets makes it possible to use fuzzy interface [6] Fuzzy Interface Fuzzy control denotes the field in control engineering in which fuzzy set theory and fuzzy interface are used to derive control laws [7]. In the method of fuzzy interface, the knowledge of an expert in a field of application is expressed as a set of "IF-THEN" rules, leading to algorithms describing what action should be taken based on currently observed information. Generally, fuzzy controllers are the application of fuzzy sets and fuzzy interface in control theory. Their operation is divided into four phases as follows: 1. fuzzification 2. rule base 3. decision making 4. defuzzification Moreover, there are four basic steps in designing a conventional fuzzy logic controller for a physical system: fuzzification, the decision making of fuzzy control rules, fuzzy interface logic, and defuzzification. The interface operations upon fuzzy if-then rules performed by fuzzy interface systems are as follows [8] In the fuzzification part, the in/out variables of a fuzzy controller can be divided into system variables, and linguistic variables. Most fuzzy controllers employ the error and error rate of system variables as the input and the force, voltage or another variable of the control law as the output. The fuzzy control rule is important to the successful operation of the fuzzy control system. The rule base (knowledge base), containing a number of fuzzy if-then rules, is composed as follows: Fig Fuzzy inference schemas Where x = (x 1,..., x n ) T and y are the input and the output of the fuzzy logic system, respectively. is the label of the fuzzy set in i, for m = 1,2,...,M, and K m is the zero-order Sugeno parameter. The sup-algebraic product compositional rule of inference is used in third part of the fuzzy inference system. In order to obtain the correct control input for this control system, it is necessary to defuzzify the fuzzy sets and aggregate the qualified consequent parts to produce a crisp output at the last part.

3 International Journal of Electrical & Computer Sciences IJECS-IJENS Vol: 11 No: ANFIS Introduction to ANFIS In 1993 Roger Jang, suggested Adaptive neuro fuzzy Inference system (ANFIS) [9]. ANFIS can serve as a basis for constructing a set of fuzzy if-then rules with appropriate membership functions in order to generate the stipulated input and output pairs. Here, the membership functions are tuned to the input-output data and getting excellent results is possible. Basically, ANFIS is about taking an initial fuzzy inference (FIS) system and tuning it with a back propagation algorithm based on the collection of input-output data. The basic structure of a fuzzy inference system consists of three conceptual components. The first one is a rule base, which contains a selection of fuzzy rules. The second one is a database, which defines the membership functions used in the fuzzy rules. The third one is a reasoning mechanism, which performs the inference procedure upon the rules and the given facts to derive a reasonable output or conclusion. These intelligent systems combine knowledge, techniques and methodologies from various sources. They possess human-like expertise within a specific domain. They can adapt themselves and learn to do better in changing environments. In ANFIS, neural Networks recognize patterns, and help adaptation to environments. Fuzzy inference systems incorporate human knowledge and perform interfacing and decision-making. ANFIS is tuned with a back propagation algorithm based on the collection of input output data [10] The Hybrid Learning Algorithm Used in the ANFIS Network In the update of the parameters belonging to the ANFIS network, which is used in the identification, hybrid algorithm, which is a two-staged learning algorithm, is used. In the hybrid learning algorithm the parameters belonging to the ANFIS network structure are divided into two as input and output parameters. If we define the total set of parameters as ; S = S1 + S2; S1 is equivalent to input parameters and S2 is equivalent to output parameters. With the first stage or the advanced route transition of the hybrid algorithm input parameters and with the second stage or the backward route transition the result parameters of the ANFIS network is updated. In the section of the hybrid learning algorithm constituting the advanced route transition which is realized by using the least square estimate (LSE) method, the membership parameters at the entry of the network or briefly input parameters defined as S1 are kept constant. So, the output of the network becomes a linear combination of the output parameters found in the S2 set of parameters. The output of the network can be stated as in the mathematical form when a number of P input output data of the system to be modeled or education data are used as S1. The θ vector is an unknown vector in the matrix equivalency is consisted of S2 output parameters. This equivalence shows the standard linear least squares problem and the best solution for θ is the least squares estimation θ*,, 2 Aθ-B which is the minimum value of (3) θ* = (A T A) 1 A T B Here, if the A T is the transpose of the matrix A and if A T A is not singular, A T, is the fake inverse of A. Instead of this, the LSE formula can also be used as recursive. Let the equivalence (2) to be shown as the row numbered i of the A matrix as, and row numbered i of the B matrix as. In this case, the θ vector can be iteratively calculated as below. Here, the least squares estimate θ* equals to θ P. The initial conditions required at the equivalence numbered (4) are those; = 0 ve = γ I. Here, γ is a positive large number and I is a identity matrix having a dimension of MxM [11]. In the hybrid learning algorithm, S2 output parameters are kept constant and the error signal at the output of the network spreads backward and input parameters are updated with the gradient descent method. The update formula for the input parameters for the backward route transition is as follows: Here, α shows any input parameter, η shows learning rate and E shows the error value at the output of the network [12]. 3. CONTROLLER DESIGN Just like in any control system, we also need inputs and outputs in the fuzzy logic and neuro-fuzzy control systems. Fuzzy logic and neuro-fuzzy shall determine the carbon dioxide amount in the production of sugar syrup of the carbonated beverages they are applied. According to the recommendations of the engineers working in the Iraq-Al TA MIM food industry, the carbon dioxide values, which are our output, changes between 2 and 6 and our inputs shall be heat and pressure. According to the results we obtained, we see that under low heat and high pressure the carbon dioxide amount is the highest, under normal heat and normal pressure the carbon dioxide amount is average, and under high heat and low pressure the carbon dioxide amount is the lowest. 3.1 Conventional Fuzzy Controller In the fuzzification step of the fuzzy inference system, we have two inputs, temperature and pressure. Triangular membership function type is used for temperature input. Figure 3.1 shows that the temperature range [7-16] and temperature is defined by three linguistic term; Verycold, Cold, Normal, Hot, Veryhot.

4 (7) International Journal of Electrical & Computer Sciences IJECS-IJENS Vol: 11 No: Fig. 3.1 Membership function of the Temperature input Fig. 3.2 triangular membership function axbisexaba 1 ( 1 )/( 1 ) (;,,) xaba 1 2 bxaiseax 2 ( 2 )/( ab 2 ) xaveyaxaise 2 10 Triangular membership function type is used for Pressure input, as well. The graphic of the Pressure member ship function is shown in the figure 3.4. In here, [1.7-4] range is chosen for 5 Linguistic variables are Very low,low, Normal, Good, Very good. If Temperature is Verycold and Pressure is Bad Then CO2 measure is Normal If Temperature is Verycold and Pressure is Normal Then CO2 measure is Good If Temperature is Verycold and Pressure is Good Then CO2 measure is Verygood If Temperature is Verycold and Pressure is Verygood Then CO2 measure is Verygood If Temperatur is Cold and Pressure is Verybad Then CO2 measure is Bad If Temperatur is Cold and Pressure is Bad Then CO2 measure is Good If Temperatur is Cold and Pressure is Normal Then CO2 measure is Good If Temperatur is Cold and Pressure is Good Then CO2 measure is Good If Temperatur is Cold and Pressure is Verygood Then CO2 measure is Verygood If Temperatur is Normal and Pressure is Verybad Then CO2 measure is Bad If Temperatur is Normal and Pressure is Bad Then CO2 measure is Normal If Temperatur is Normal and Pressure is Normal Then CO2 measure is Normal If Temperatur is Normal and Pressure is Good Then CO2 measure is Good If Temperatur is Normal and Pressure is Verygood Then CO2 measure is Verygood If Temperatur is Hot and Pressure is Verybad Then CO2 measure is Bad If Temperatur is Hot and Pressure is Bad Then CO2 measure is Bad If Temperatur is Hot and Pressure is Normal Then CO2 measure is Normal If Temperatur is Hot and Pressure is Good Then CO2 measure is Good If Temperatur is Hot and Pressure is Verygood Then CO2 measure is Good If Temperatur is Veryhot and Pressure is Verybad Then CO2 measure is Verybad If Temperatur is Veryhot and Pressure is Bad Then CO2 measure is Bad If Temperatur is Veryhot and Pressure is Normal Then CO2 measure is Normal If Temperatur is Veryhot and Pressure is Good Then CO2 measure is Normal If Temperatur is Veryhot and Pressure is Verygood Then CO2 measure is Good Fig. 3.3 Membership function of the Pressure input Second step is rule base in fuzzy inference system. We have 25 fuzzy rules come by 5 linguistic terms for Temperature and 5 terms for Pressure. Following if-then rules shows these fuzzy rules constituted. If Temperature is Verycold and Pressure is Verybad Then CO2 measure is Normal Third part of the FIS is Fuzzy inference logic. In here for applying AND logic to inputs the sup-algebraic product compositional rule of inference is employed in this work. Last part of FIS is defuzzification. Takagi-surgeno fuzzy inference system is used in this Project. Crisp values are calculated using weighted average method. 3.2 ANFIS Controller The input membership functions are initially same with the classical fuzzy controller membership functions in section

5 International Journal of Electrical & Computer Sciences IJECS-IJENS Vol: 11 No: Therefore the result of two models can be more comparable. Fig. 3.4 Membership function of the temperature Rule Matrix Fig. 3.5 Membership function of the pressure Fuzzy rules and if-then rules are same with classical fuzzy controller, too. These rules can be seen from Table 3.1 and they are table form of classical fuzzy controller fuzzy rules at mentioned in section 3.1 Difference of the models is starting in here; output variable is not created at this time. It will create after training step with neural network so two output data of the models will be comprised after training. Table 3.1 Rule matrix of the ANFIS Verycold Cold Normal Hot Veryhot Verybad Normal Bad Bad Bad Verybad Bad Normal Good Normal Bad Bad Normal Good Good Normal Normal Normal Good Verygood Good Good Normal Normal Verygood Verygood Verygood Verygood Good Good Design ANFIS architecture Integrated neuro-fuzzy system combines the advantages of ANN and FIS. While the learning capability is an advantage from the viewpoint of FIS, formation of knowledge base is an advantage from the viewpoint of ANN. One such neuro-fuzzy algorithm is called as Adaptive Neuro Fuzzy Inference System (ANFIS). It is used to build neuro-fuzzy controllers. ANFIS is a feed forward type adaptive network. Its functionally equivalent to an FIS. It basically consists of five layers. These layers are shown in Figure 3.6 Fig. 3.6 ANFIS Architecture Layer I: Every node in this layer computes the degree of membership of the input. Each node is using triangular membership function as given in equation.

6 International Journal of Electrical & Computer Sciences IJECS-IJENS Vol: 11 No: axbisexaba 1 ( 1 )/( 1 ) (;,,) xaba 1 2 bxaiseax 2 ( 2 )/( ab 2 ) xaveyaxaise Training After designing ANFIS architecture, the module basically requires rough initial premise parameters for the membership functions of the first layer and the training data [8]. Consequent parameters are learnt during forward pass of the hybrid learning algorithm using recursive least square estimator and the premise parameters are trained using the gradient descent method [7]. The initial premise parameters and consequent parameters after designed ANFIS controller are shown in Table 3.3. The member ship functions of ANFIS controller are changed after trained. These are can be seen from Figure 3.7 and Figure 3.8. where, {a 1i, b i, a 2i } is a parameter set. The parameters in this layer are referred to as premise parameters. The hybrid algorithm adjusts these premise parameters to achieve the optimal shape of the member functions. Layer II: Every node in this layer is a fixed node labeled II, whose output is the product of all the incoming signals. Layer III: Here, the node calculates the ratio of the rule s firing strength to the sum of all rule s firing strengths. Fig. 3.7 Membership function of the temperature Layer IV: Every node i in this layer is an adaptive node with a node function Where is a normalized firing strength from layer 3 and {pi, qi, ri} is the parameter set of the node. The parameters {p i,q i,r i } are adjusted through RLSE (Recursive Least Square Estimator)[13]. Layer V: The single node in this layer is a fixed node labeled Σ, which computes the overall output as the summation of all incoming signals: Table 3.2 Premise parameters Premise parameters Fig. 3.8 Membership function of the pressure a1i b i a 2i

7 International Journal of Electrical & Computer Sciences IJECS-IJENS Vol: 11 No: Table 3.3 Consequent Parameters Consequent parameters α i ß i γ i p i q i r i RESULT After applying all these fuzzy inference system steps to our inputs, and the result is the value of the gas carbon dioxide in the form of crisp. The result Carbon dioxide values are shown at the figure 4.1 and 4.2 with respect to input values, Temperature and Pressure. Fig. 4.2 Output of the ANFIS controller Fig. 4.1 Output of the fuzzy contrloller Fig. 4.3 Fuzzy controller output respect to desired data

8 International Journal of Electrical & Computer Sciences IJECS-IJENS Vol: 11 No: Table 4.3 Error values of fuzzy controller Classical fuzzy Check Error Fig. 4.4 ANFIS controller output respect to desired data Sample data is tested on classic Fuzzy inference system and results can be seen from figure 4.3. Result is not bad but there is some not match point at the plot. The data that is used in the classical controller is tested in trained ANFIS controller. The plot shows this data and controller output. Match results in here is better if we compare the results of classical fuzzy controller Table 4.2 Error values of ANFIS controller ANFIS Train Error Check Error When we compare the tables 4.1 and 4.2, we see that we could obtain better results with the ANFIS method. Its error rate is lesser than the fuzzy logic method. Because the membership functions are established once in the fuzzy logic method, but in the ANFIS method process the membership functions are updated again according to that problem after the education. If we look the ANFIS controller result with a graph shown in Figure 4.5, we can see clearly ANFIS controller error values (red points) are smaller than fuzzy controller error values (black points). 5. CONCLUSIONS According to results, we see that the results of the ANFIS method are more close to the reality when compared with the results of the fuzzy logic method, in other words the ANFIS method is more reliable. We can list the reasons for the reliability of the ANFIS method as such: firstly the number of rules is limited and there are only 25 rules, there are only 10 membership variables. Secondly, while the values of the rules and membership functions are selected by an expert in the fuzzy logic, in the ANFIS method they are first selected by the expert but after the training it Fig. 4.5 Error values of fuzzy controller and ANFIS controller updates itself. It doesn t stay constant in that state like in the fuzzy logic. The rules and the membership variables are the same in the fuzzy logic and ANFIS methods. The reason for that is that when we compare them with each other the result of the comparison is one hundred per cent reliable. ANFIS method uses the advantages of the artificial neuron networks and fuzzy logic and obtains perfect result. When we consider all the results stated above, we see that the ANFIS method is better than the fuzzy logic in the carbon dioxide control of the fizzy drinks.

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