Prediction of Squeeze Cast Density Using Fuzzy Logic Based Approaches

J. Manuf. Sci. Prod. 2014; 14(2): 125 – 140

Manjunath Patel G. C., Prasad Krishna and Mahesh B. Parappagoudar*

Prediction of Squeeze Cast Density Using Fuzzy Logic Based Approaches

Abstract: In the present work, efforts are made to develop the input-output relationships for squeeze casting pro-cess by utilizing the fuzzy logic based approaches. Cast-ing density in Squeeze casting is expressed as function of process parameters, such as time delay before pres-surizing the metal, pressure durations, squeeze pressure, pouring temperature and die temperature. It is to be noted that, Mamdani based model and Takagi and Sugeno’s model have been developed to model density in squeeze casting process. Manually constructed Mamdani based fuzzy logic controller and Takagi and Sugeno’s based fuzzy logic controller have been used in approach 1 and approach 2 respectively. Training of FLC is carried with the help of five hundred input-output data set generated artificially through regression equations, obtained earlier by the same authors. The performance of the developed models was tested for both the linear and non-linear membership function distributions with the help of ten test cases. Moreover, the test data was collected by con-ducting the experiments and not used in training of FLCs. It is interesting to note that both approaches are capable to make accurate predictions. However, the performance of approach 2 with G bell shape membership function dis-tribution is found to outperform approach 1 and other type of membership function distributions. The findings are useful to foundry-men, since it provides information on casting density in squeeze casting process for the dif-ferent combination of process parameters without con-ducting any experiments.

Keywords: squeeze casting process, density, fuzzy logic, adaptive network based fuzzy interface system (ANFIS)

PACS® (2010). 83.50.Uv, 81.20.Hy

DOI 10.1515/jmsp-2014-0011Received March 19, 2014; accepted June 15, 2014.

1 IntroductionSqueeze casting process is one of the hybrid metal cast-ing process developed using the pressurized solidifica-tion concept suggested by D. K. Chernov (1878). Squeeze casting is known for producing castings with high yield and dense structure. However, it is required to have precise control of process parameters. The major drawbacks of conventional casting processes such as porosity, shrink-age and segregations are addressed by combining the desirable features of gravity, pressure die casting and forging processes in a single step process in squeeze casting. During squeeze casting process the quality of the parts depends largely on the process variables such as die temperature, pouring temperature, applied pressure, pressure duration and time delay before pressurization. Inappropriate choice of the said process variables may lead to the possible squeeze casting defects, such as oxide inclusions, under/over filling, cold laps, poor surface finish, dimensional accuracy, hot tearing, sticking, extru-sion, segregations and case de-bonding [1]. It is important to note that the aforementioned defects finally affects the casting density, which can be minimized by proper control of the squeeze cast process variables. Higher casting density is always desirable because the casting density is directly decides the mechanical and the micro-structure properties. Hence it is of paramount importance to develop the squeeze cast process model and analyse the input- output relationships of the process.

The rapid development of the squeeze casting process had drawn much attention for researchers towards the improvement of the mechanical and micro-structure prop-erties during 1990’s and 2000’s across the globe. How-ever, most research works carried out during that period was theoretical analysis and conventional engineering experimental approach. The effect of different casting temperatures on density, impact and tensile strength of LM6 alloy and ZA3 alloys processed under gravity and squeeze casting method were studied by Yang [2]. Fur-ther, it was mentioned that, the experiments conducted by keeping the die temperature, compression holding time and applied pressure as constant. Later, Yang [3] studied the effects of solidification time on the density, fracture energy, tensile strengths, yield and ultimate

*Corresponding author: Mahesh B. Parappagoudar: Department of Mechanical Engineering, Chhatrapati Shivaji Institute of Technology, Durg (C.G.) 491001, India. E-mail: [email protected] Patel G. C., Prasad Krishna: Department of Mechanical Engineering, National Institute of Technology, Karnataka-Surathkal 575025, India

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126 Manjunath Patel G. C. et al., Prediction of Squeeze Cast Density Using Fuzzy Logic Based Approaches

tensile strengths of LM6 and ZA3 alloys by using two analytical models, namely steady state heat flow model and gracia’s virtual model. The analytical models showed an average deviation of 27% for LM6 and 20% for ZA3 alloys, when compared with test cases. In addition it was observed that shorter solidification time was re-sponsible to achieve better mechanical properties. Maleki et al. [4] used a classical approach to study the effects of squeeze pressure, melt temperature and die temperature on density, macrostructure, hardness and tensile strengths of LM13 alloy, by varying one process variable at a time and keeping the rest of the parameters at their mid values. However, it is important to note that the effects of pressure duration and time delay before pressurization was left out in their research work. It is to be noted that, conventional approaches, discussed need more number of experiments and the combined (interaction) effect of parameters is lost. Optimizing squeeze casting process requires the input-output relationships expressed in the mathematical form. The statistical regression analyses allow the re-searchers to study effect of process variables, estimates significant contributions on the measured responses and develop input-output relationship with less number of experiments [5].

To the best of the authors’ knowledge, limited re-search work has been reported in the literature on squeeze casting process using statistical regression and taguchi tools. Vijian and Arunachalam [6] utilized taguchi method to study the effect of squeeze pressure, pressure duration and die temperature on hardness and tensile strengths of LM24 alloy. In addition they established separate multi variable linear regression equations for hardness and tensile strength. The developed regression equations in-cluded only linear terms and neglected the square and interaction terms. Moreover, they did not considered pouring temperature variations in their analysis. Senthil and Amirthagadeswaran [7] used taguchi method to con-duct experiments and developed mathematical input- output relationship, which included all linear, square and interaction terms. Later on Senthil and Amirthagades-waran [8] extended their research efforts to study the yield strengths via taguchi method and developed the input-output relationships. However, the time delay before pressurizing the metal and percentage contribution estimation of square and interaction terms towards the responses was left out in their analysis. More recently, Bin et al. [9] investigated the influence of squeeze casting parameters on the strength and ductility of AlSi9Cu3 alloys. However, they did not develop the model to predict the responses and they did not consider the important machine related parameter like pressure duration, in their

analysis. Soft computing modelling approaches can be used to effectively handle the complex problems and to overcome the limitations of Parappagoudar and Vunda-villi [10].

The major soft computing tools namely artificial neural networks (ANNs), genetic algorithms (GA) and fuzzy logic (FL) approaches and their different combina-tions were used in various manufacturing processes. Vijian and Arunachalam utilized GA to solve the multi- objective optimization problems related to squeeze casting process, however they fail to include the square and inter-action terms in their objective functions [6]. ANNs em-ployed to predict the effects of process parameters on temperature difference of the squeeze cast part [11]. It is important to note that some research efforts were made to develop the hybrid systems (combining the desirable fea-tures of two or more approaches) Genetic algorithm based neural network (GA-NN) and back propagation neural network (BPNN) models were developed for foundry ap-plications, namely, different moulding sand systems and pressure die casting [12–15]. The authors made efforts to to model and analyse important manufacturing processes with the help of fuzzy logic based approaches [16–20]. It is to be noted that fuzzy logic based approaches can be successfully implemented in various manufacturing processes and proved as a cost effective tool to analyze, control and model the complex non-linear input-output relationship.

To the authors’ best knowledge, not much of the work is reported to address the problems related to the squeeze casting process utilizing fuzzy logic based approaches. Casting density is the important quality characteristic, since; it is directly related to the internal casting de-fects such as micro-porosity, segregation, shrinkages and micro-voids. The amount of porosity present in the cast-ings decreases the available load area, provoke stress concentration, crack initialization leads to poor tensile strength and ductility of the alloy [21]. In the present work, an attempt has been made to predict the casting density using two fuzzy models, namely Mamdani based fuzzy logic and Takagi Sugeno based fuzzy logic. Approach 1: Development of manually constructed Mamdani based fuzzy logic system deals with construction of rule base, consequent and antecedent parts with the help of human expertise. Approach 2: Development of adaptive network based fuzzy interface system (ANFIS) a Takagi and Sugeno’s model deals with automatic evolution of rule base, consequent and antecedent parts.



Manjunath Patel G. C. et al., Prediction of Squeeze Cast Density Using Fuzzy Logic Based Approaches 127

2 Modelling of squeeze casting process using fuzzy logic

Modelling refers to the method of identifying, analysing and establishing the input-output relationship of the phy-sical system. Squeeze casting is one of the most economi-cal routes to process from liquid metal stage to the final solidification stage. However, density of the components in squeeze casting is largely influenced by squeeze cast technical parameters. Figure 1 shows the inputs (time delay, pressure duration, squeeze pressure, pouring and die temperature) and output (density) of the squeeze casting process.

The input parameters of squeeze casting process and their respective levels used in the current study are shown in Table 1.

2.1 Data collection

The prediction capabilities of any training algorithm rely on the accuracy of the data collected and the amount of data used for training. The collection of huge data through real experiments is impractical, because it leads to mate-rial wastage, high labour costs and time consuming. It is to be noted that five hundred input-output data sets used for training generated artificially through regression equation obtained earlier by the same authors [22]. The performance of the developed models has been tested with the help of ten test cases. It is also important to mention that the test cases used to check the model performances are separate from those used in training.

The non-linear regression equation for casting density in terms of squeeze cast process parameters is shown in Eq. (1).

d d

p t t2 2d d

2 2 2p t t

1.21121 0.0120733T 8.80233E 05P0.000270477S 0.00354289P 0.001781D6.77354E 05T 4.03295E 06P 1.32509E07S 2.47673E 06P 3.89751E 06D .

Density = − + −+ + ++ − + − −− − − − − (1)

Five hundred sets of input-output data have been gen-erated at random using the above equation by selecting the squeeze cast process variables within their respective ranges.

2.2 Fuzzy modelling

The fuzzy concept was used to develop the input-out relationship for the squeeze casting process as shown in the Fig. 2. The aim of the fuzzy modelling is to predict the output for the known set of inputs. In the present work, squeeze cast process casting density is expressed as a function of input parameters. Takagi and Sugeno’s ap-proach of FLC and Mamdani approach of FLC has been developed to model the squeeze casting process.

3 Fuzzy logic controllerIn manufacturing processes the researchers/investigators are more interested to establish accurate input-output re-lationships. The human brain behaviour (thinking and

Fig. 1: Input-output model for squeeze casting process

Table 1: Squeeze cast process parameters and their respective levels

Process parameters Notation Unit Level-1 Level-2 Level-3 Level-4 Level-5

Squeeze pressure (Sp ) A MPa 0.1 50 100 150 200Pressure duration (Dp ) B s 10 20 30 40 50Time delay ( Td) C s 03 05 07 09 11Pouring temperature (Pt ) D °C 630 660 690 720 750Die temperature (Dt ) E °C 100 150 200 250 300




reasoning) can be used to develop such input-output rela-tionship using the concept of fuzzy set theory namely fuzzy logic controller (FLC). Fuzzy logic controller widely used in many applications might be due to many ad-vantages, such as, easy to understand and implement, capable of handling uncertainty and imprecise data and exact mathematical formulation is not required to develop the FLC [23]. The performance of the developed models rely on the use of knowledge base approach, majorly con-sists of both data bases and rule base. In data base ap-proach, the membership function is decided, based on the variability of distributed data in the process. Triangular and trapezoidal membership function is used if the data distributions are assumed to be linear, whereas sigmoid, gaussian and bell-shaped membership functions are used for non-linear. In FLC the variables are expressed in the form of linguistic terms (low, medium, high, etc.) and the input-output relationships are expressed in the form of rules. Since the rules were expressed in the form of lin-guistic terms and number of rules increases with the in-crease in linguistic terms and the process variables. Fuzzy logic controllers are majorly categorized into two types as shown in Table 2.

3.1 Approach 1: Development of manually constructed Mamdani based FLC

In the present work, Mamdani based fuzzy logic ap-proach has been developed to perform forward mapping

of squeeze casting process. The squeeze cast process parameters considered includes five inputs (time delay, pressure duration, squeeze pressure, pouring tempera-ture and die temperature) and one output (density).

It is interesting to note that in fuzzy logic the input- output parameters need to be expressed as a function of linguistic terms. Three linguistic terms are used for the input-output variables namely low, medium and high. For simplicity, the linear type triangular membership function distributions of input-output variables of the fuzzy logic system are shown in Fig. 3. It is important to note that most of the casting processes are complex in nature and output may behaves non-linear with respect to change in the input. So both linear and non-linear (Gaussian and bell shaped) membership function distributions were tried and the performances of the developed models are compared.

In Fig. 3 the ‘a’ values indicates the half base widths of isosceles triangles and base width of right angled trian-gles. As there are five input variables and each input vari-able is expressed as a function of three linguistic terms. The number of rules to be defined for current study is found to be equal to 35 = 243. The Mamdani based manu-ally constructed rule base of the fuzzy logic system is shown in Table 3. One typical manually constructed rule of the fuzzy logic system will appear as follows:

IF A is M AND B is H AND C is L AND D is H AND E is M, THEN ρ is M

However the knowledge base is comprised of both rule and data base of the fuzzy logic system and the manu-ally constructed rule base is purely rely on the experi-ence of the designer, which is not considered to be optimal in most of the cases. Thus attempts required to automatically determine the rule and data base using better learning capabilities of artificial neural networks (ANNs).

Fig. 2: Model representation of squeeze casting process using fuzzy interface system

Table 2: Fuzzy logic controller modelling approaches [23]

Type Linguistic fuzzy modelling

Precise fuzzy modelling

Approach Mamdani approach Takagi sugeno’s approachAdvantage Better interpretability High accuracyLimitation Low accuracy Low interpretability




3.2 Approach 2: Development of adaptive network based fuzzy interface system to automatically retrieve the data and derive the rule base

Artificial neural networks considered being an excellent modelling tool for mapping the complex manufacturing processes [10]. The use of fuzzy set theory finds major applications in the field of production as well as in opera-tion management [24]. ANNs have potential advantages to model complex non-linear relationship but associated with few limitations namely getting stuck with local op-timal solution instead of global one, output precisions are limited, huge training data which covers entire range of different process variables is required and large number of training epochs [25]. There is no systematic procedure

available to define the fuzzy membership function is the major drawback found in the fuzzy logic controller [26]. The hybrid systems developed by combining the desirable features of learning capabilities of ANNs and reasoning capability of fuzzy logic to limit the weak points of one technology with the strengths of the other. In recent years an embedded type adaptive network based fuzzy interface system (ANFIS) developed and shown better prediction in high pressure water jet cleaning [27], surface roughness in end milling process [28, 29] and Al- and weld bead in submerged arc welding process [30].

ANFIS uses the hybrid learning algorithm which com-bines gradient descent method and method of least square principles to model input-output relationship. Here, the developed rule composed of fuzzy antecedent which in-cludes the membership function parameters and its shape and functional consequent parameter which describe the

Fig. 3: Manually constructed membership function distribution for input-output variables




Table 3: Manually constructed rule base of the fuzzy logic system

Rule No. A B C D E ρ Rule No. A B C D E ρ Rule No. A B C D E ρ

1 L L L L L L 57 L H L L H M 113 M M L M M M2 L L L L M M 58 L H L M L M 114 M M L M H M3 L L L L H M 59 L H L M M M 115 M M L H L M4 L L L M L L 60 L H L M H M 116 M M L H M M5 L L L M M M 61 L H L H L M 117 M M L H H M6 L L L M H M 62 L H L H M M 118 M M M L L L7 L L L H L L 63 L H L H H M 119 M M M L M M8 L L L H M M 64 L H M L L M 120 M M M L H M9 L L L H H M 65 L H M L M M 121 M M M M L M10 L L M L L M 66 L H M L H M 122 M M M M M M11 L L M L M M 67 L H M M L M 123 M M M M H M12 L L M L H M 68 L H M M M H 124 M M M H L M13 L L M M L M 69 L H M M H H 125 M M M H M M14 L L M M M H 70 L H M H L M 126 M M M H H M15 L L M M H M 71 L H M H M H 127 M M H L L M16 L L M H L M 72 L H M H H H 128 M M H L M M17 L L M H M H 73 L H H L L M 129 M M H L H M18 L L M H H H 74 L H H L M H 130 M M H M L M19 L L H L L M 75 L H H L H H 131 M M H M M M20 L L H L M H 76 L H H M L M 132 M M H M H M21 L L H L H M 77 L H H M M H 133 M M H H L M22 L L H M L M 78 L H H M H H 134 M M H H M M23 L L H M M H 79 L H H H L M 135 M M H H H M24 L L H M H H 80 L H H H M H 136 M H L L L L25 L L H H L M 81 L H H H H H 137 M H L L M M26 L L H H M H 82 M L L L L L 138 M H L L H M27 L L H H H H 83 M L L L M M 139 M H L M L L28 L M L L L M 84 M L L L H M 140 M H L M M M29 L M L L M M 85 M L L M L L 141 M H L M H M30 L M L L H M 86 M L L M M M 142 M H L H L L31 L M L M L M 87 M L L M H M 143 M H L H M M32 L M L M M M 88 M L L H L L 144 M H L H H M33 L M L M H M 89 M L L H M M 145 M H M L L M34 L M L H L M 90 M L L H H M 146 M H M L M M35 L M L H M M 91 M L M L L L 147 M H M L H M36 L M L H H M 92 M L M L M M 148 M H M M L M37 L M M L L M 93 M L M L H M 149 M H M M M M38 L M M L M M 94 M L M M L M 150 M H M M H M39 L M M L H M 95 M L M M M M 151 M H M H L M40 L M M M L M 96 M L M M H M 152 M H M H M M41 L M M M M H 97 M L M H L M 153 M H M H H M42 L M M M H M 98 M L M H M M 154 M H H L L M43 L M M H L M 99 M L M H H M 155 M H H L M M44 L M M H M H 100 M L H L L M 156 M H H L H M45 L M M H H H 101 M L H L M M 157 M H H M L M46 L M H L L M 102 M L H L H M 158 M H H M M M47 L M H L M H 103 M L H M L M 159 M H H M H M48 L M H L H H 104 M L H M M M 160 M H H H L M49 L M H M L M 105 M L H M H M 161 M H H H M M50 L M H M M H 106 M L H H L M 162 M H H H H M51 L M H M H H 107 M L H H M M 163 H L L L L L52 L M H H L M 108 M L H H H M 164 H L L L M L53 L M H H M H 109 M M L L L L 165 H L L L H L54 L M H H H H 110 M M L L M M 166 H L L M L L55 L H L L L M 111 M M L L H M 167 H L L M M L56 L H L L M M 112 M M L M L L 168 H L L M H L




network output. During training cycle, in forward calcula-tion the antecedent parameters are fixed and the conse-quent parameters are determined using least square prin-ciple. The obtained ANFIS output using the consequent parameters is compared with the target value to determine the error. The objective is to minimize the error by up-dating the network parameters in the backward step. In backward step, the consequent parameters were fixed and the output error is back propagated and the anteced-ent parameters are updated using the gradient descent method [26]. The procedure adapted in ANFIS model is shown in Fig. 4.

The ANFIS model developed for the squeeze casting process is capable to predict the casting density at differ-ent squeeze casting conditions. Squeeze cast process pa-rameters, namely, time delay (Td), pressure duration (Dp), squeeze pressure (Sp), pouring temperature (Pt) and die temperature (Dt) are considered as input parameters in the input layer and casting density is the output param-eter in the output layer (see Fig. 5). Each squeeze cast process parameters are represented using three linguistic terms, since five input parameters used in the current study 35 = 243 combination of rules exists. According to

first order Takagi and Sugeno’s model of FLC, the typical output of each rule is expressed in Eqs. (2) to (4):

Rule 1: If (Td is A1) and (Dp is B1) and (Sp is C1) and (Pt is D1) and (Dt is E1), then

1 1 1 1 1 1 1d p p t tf p T q D r S s P t D u= + + + + + (2)

Rule 2: If (Td is A2) and (Dp is B2) and (Sp is C2) and (Pt is D2) and (Dt is E2), then

2 2 2 2 2 2 2d p p t tf p T q D r S s P t D u= + + + + + (3)

Rule 3: If (Td is Ai) and (Dp is Bi) and (Sp is Ci) and (Pt is Di) and (Dt is Ei), then

i i d i p i p i t i t if pT q D rS s P t D u= + + + + + (4)

where i = 1, 2, 3, . . . , 243, pi, qi, ri, si, ti and ui are the coeffi-cients, f is the output parameter, Ai, Bi, Ci, Di and Ei are the linguistic terms used to divide the membership function.

The network architecture of adaptive network based fuzzy interface system is shown in Fig. 5. The entire

Table 3 (cont.)

Rule No. A B C D E ρ Rule No. A B C D E ρ Rule No. A B C D E ρ

169 H L L H L L 194 H M L M M L 219 H H L L H L170 H L L H M L 195 H M L M H L 220 H H L M L L171 H L L H H L 196 H M L H L L 221 H H L M M M172 H L M L L L 197 H M L H M L 222 H H L M H L173 H L M L M L 198 H M L H H L 223 H H L H L L174 H L M L H L 199 H M M L L L 224 H H L H M M175 H L M M L M 200 H M M L M L 225 H H L H H L176 H L M M M M 201 H M M L H L 226 H H M L L L177 H L M M H M 202 H M M M L L 227 H H M L M M178 H L M H L L 203 H M M M M M 228 H H M L H M179 H L M H M M 204 H M M M H M 229 H H M M L L180 H L M H H M 205 H M M H L L 230 H H M M M M181 H L H L L L 206 H M M H M M 231 H H M M H M182 H L H L M M 207 H M M H H M 232 H H M H L L183 H L H L H M 208 H M H L L L 233 H H M H M M184 H L H M L L 209 H M H L M M 234 H H M H H M185 H L H M M M 210 H M H L H M 235 H H H L L L186 H L H M H M 211 H M H M L L 236 H H H L M M187 H L H H L L 212 H M H M M M 237 H H H L H M188 H L H H M M 213 H M H M H M 238 H H H M L L189 H L H H H M 214 H M H H L L 239 H H H M M M190 H M L L L L 215 H M H H M M 240 H H H M H M191 H M L L M L 216 H M H H H M 241 H H H H L L192 H M L L H L 217 H H L L L L 242 H H H H M M193 H M L M L L 218 H H L L M L 243 H H H H H M




network architecture is a combination of 6 layers namely, input layer, fuzzification layer, product layer, normaliza-tion layer, de-fuzzification layer and the output layer. The systematic procedure in developing the input-output rela-tionship is described as follows:

Layer 1: The network architecture of layer 1 is expressed as a function of squeeze cast process variables, since five inputs used in the current study and this layer consists of five nodes only. The output nodes of the layer 1 are same as the input of the corresponding layer and are directly passed to the input layer 2.

Layer 2: The function of the layer 2 is to determine the membership values for the given set of inputs correspond-ing to the assigned linguistic terms shown in Eqs. (5) to (9). Td, Dp, Sp, Pt and Dt are the input nodes expressed as membership functions in terms of Ai, Bi, Ci, Di and Ei of layer 2. O2,i is the output of ith node of layer 2.

O2,i = μAi(Td) for i = 1, 2, 3 (5)

O2,i = μBi−3(Dp) for i = 4, 5, 6 (6)

O2,i = μCi−6(Sp) for i = 7, 8, 9 (7)

O2,i = μDi−9(Pt) for i = 10, 11, 12 (8)

O2,i = μEi−12(Dt) for i = 13, 14, 15 (9)

The most commonly used membership functions are tri-angular, bell shaped and gaussian membership functions and the values are always lies between maximum of 1 and a minimum of zero corresponding to the input parameter setting.

Layer 3: The layer 3 contains the 35 = 243 nodes, which determines the number of possible rules and is usually labelled using the term Π. For the particular set of input pairs a maximum of 32 nodes will be activated in the third layer and each node is a possible combination of input variables. In this layer the information received from the layer 2 is multiplied and the obtained output as a firing strength shown in Eq. (10).

3, 3 6 9 12( ). ( ). ( ). ( ). ( )i i i d i p i p i t i tO w A T B D C S D P E Dµ µ µ µ µ− − − −= =(10)

Layer 4: Each node present in the layer 4 is labelled as N. The function of this layer is to normalize the weight func-tions using Eq. (11). The calculation of the ith node is the ratio of ith rule firing strength to the summation of all the fired rules.

4, 1 2 3 243/( )i i iO w w w w w w= = + + + + (11)

Layer 5: 243 nodes present in the layer 5 and maximum of 32 nodes will be activated for the particular input vari-ables combination. This layer considered as the defuzzifi-cation (centroid area method) layer and the output node is calculated using the product of the normalized firing strength and the output of the corresponding fired rule shown in Eq. (12).

5, ( )i i i i i d i p i p i t i t iO w f w pT q D rS s P t D u= = + + + + + (12)

Layer 6: Since only one output used in the present case the output layer has only one node and is denoted by a symbol Σ, hence the present output is the combination of summation of all the received signals from the 5th layer shown in Eq. (13).

6,i ii

i i ii ii

w fO w f

w= = ∑∑ ∑

(13)

Fig. 4: Flow chart representing methodology followed for predicting casting density using ANFIS




4 Results and discussionThe performance of the developed models to predict the casting density at different squeeze casting conditions is carried using the forward mappings. Ten different squeeze casting conditions were taken to evaluate the model performances using both linear and non-linear type membership function distributions. The following section presents the information regarding results ob-

tained and comparison of the developed models used in the current study.

4.1 Approach 1

The rule base and data base of the fuzzy logic system is constructed manually with the help of experience of human experts. For simplicity, the linear type triangular

Fig. 5: ANFIS network architecture for predicting the casting density




membership function distribution is shown in Fig. 3. The values of a1, a2, a3, a4, a5 and a6 are kept equal to 4, 20, 75, 60, 100 and 0.8 respectively. It is interesting to note that three different membership functions were used and the results were compared with the experimental values as shown in Table 4. The construction of the rules plays vital role in accurate prediction of the responses, since it purely rely on the knowledge of the human expertise. The developed manually constructed rule base is presented in Table 3.

4.2 Approach 2

Five hundred data sets have been collected from the re-gression equation carried out by earlier authors. The steps followed to predict the casting density via ANFIS is shown in Fig. 4. Five inputs namely, squeeze pressure, pressure duration, time delay, pouring temperature and die tem-perature and one output such as density have been con-sidered for the present study as shown in Fig. 5. Table 5 presents ten different test cases used for the present study to compare the predicted and the observed values. Linear type, triangular membership function distribution and non-linear type gaussian and generalized bell shaped membership function distributions have been adopted and the performance of the developed models are com-pared with experimental values as shown in Table 4. The root mean squared error (RMSE) obtained at the end of the training for different membership functions are shown in Fig. 6.

4.3 Comparison of the developed models

The performances of the developed models are compared with different membership function distributions in pre-dicting the casting density, as shown in Figs. 7 and 8.

4.3.1 Approach 1

It is interesting to note that for approach 1 shown in Fig. 7(a), the best-fit line of triangular shape membership function distributions are close to the ideal line as com-pared to Fig. 7(b) and Fig. 7(c) and many data points falls close to the trend line. The summary results of test cases in predicting the casting density is shown in Table 4. The accuracy and prediction capability of the developed

Table 4: Summary results of test cases for the response density

Test case no.

Approach 1 Approach 2

Triangular G bell shape Gaussian Triangular G bell shape Gaussian

Pre- dicted

Abs.% deviation

Pre- dicted

Abs.% deviation

Pre- dicted

Abs.% deviation

Pre- dicted

Abs.% deviation

Pre- dicted

Abs. % deviation

Pre- dicted

Abs. % deviation

1 2.608 0.231 2.620 0.692 2.617 0.577 2.576 0.999 2.588 0.538 2.589 0.4992 2.623 0.038 2.621 0.038 2.621 0.038 2.608 0.534 2.617 0.191 2.619 0.1143 2.625 0.114 2.622 0.228 2.622 0.228 2.632 0.152 2.629 0.038 2.624 0.1524 2.640 0.901 2.635 1.089 2.637 1.013 2.671 0.263 2.681 0.638 2.728 2.4025 2.613 0.495 2.609 0.648 2.614 0.457 2.615 0.419 2.611 0.571 2.61 0.6096 2.622 0.306 2.622 0.307 2.621 0.268 2.609 0.191 2.607 0.268 2.607 0.2687 2.615 0.771 2.620 0.963 2.618 0.886 2.591 0.154 2.594 0.039 2.594 0.0398 2.621 0.114 2.622 0.153 2.622 0.152 2.601 0.649 2.604 0.535 2.606 0.4589 2.649 1.009 2.662 0.523 2.651 0.934 2.674 0.075 2.677 0.037 2.682 0.22410 2.635 1.051 2.646 0.638 2.638 0.939 2.651 0.451 2.662 0.038 2.676 0.488MAPE 0.503 0.528 0.549 0.388 0.289 0.523R2 0.856 0.693 0.828 0.928 0.949 0.843

Table 5: Summary results of input-output results of the test cases

Exp. no.

Squeeze casting process parameters Responses

Td Pd Sp Pt Dt SDAS ρ

1 11 30 101 671 263 48.43 2.6022 7 14 110 635 192 49.74 2.6223 6 37 63 674 236 47.64 2.6284 5 40 142 731 254 33.78 2.6645 5 10 71 723 142 46.86 2.6266 9 33 110 738 261 48.33 2.6147 9 48 96 637 174 50.63 2.5958 11 32 172 712 189 44.86 2.6189 4 21 196 646 213 35.66 2.67610 4 23 89 742 284 41.34 2.663




models have been evaluated using coefficient of cor-relation determination (R2) and mean absolute percent error (MAPE) using Eqs. (14) and (15) respectively. The co-efficient of determination is expressed as the square ratio of covariance and the multiplied standard deviation between the observed and predicted values. The R2 values always fall in the range of 0 to 1. Higher R2 value indicates a strong co-relation between the observed and the pre-dicted values and there is no co-relation, if R2 value is zero. However it is interesting to note that for approach 1, R2 value is found to be equal to 0.856 for triangular mem-bership function, 0.693 for bell shape membership func-tion and 0.828 for gaussian function distribution and is shown in Table 4. The mean absolute percentage error (MAPE) in prediction of casting density for the approach 1 is found to be 0.503 for triangular membership function, 0.528 for bell shaped membership function and 0.549 for gaussian membership distribution (see Table 4).

2

12

2 21 0

( )( )

( ) ( )

ni ii

n ni ii i

O O P PR

O O P P

=

= =

− −

= − −

∑∑ ∑

(14)

1

1 ni i

i i

O PMAPEn O=

−= ∑ (15)

where P is the predicted, n is the number of data sets and O is the observed values.

4.3.2 Approach 2

The artificial neural networks are fused together in the second approach in order to improve the prediction per-formance of the developed models. In this approach the better learning capabilities of artificial neural networks is utilized to automatically define the rule and the mem-bership function distributions of the data bases. As re-ported in the previous literatures the performance of the developed models can be further enhanced with differ-ent membership function distributions [16, 17]. It is also important to note that the performance of the devel-oped models rely on the number of training data used and closeness of the actual and the predicted network values and is usually determined by the root mean squared

Fig. 6: Convergence of ANFIS training (RMSE v/s Number of training epoch) for response-density: (a) Triangular membership function, (b) bell shaped membership function, and (c) Gaussian membership function




error at the end the end of the training. Five hundred data sets used for training the network and the network training were terminated once the error value becomes steady. The network convergence during the ANFIS train-ing is studied for different membership function distri-butions and the minimum root mean square values are found to be equal to 0.00209 for triangular member-ship function distributions, 0.00205 for bell shaped membership function and 0.00211 for gaussian member-ship function distributions (see Fig. 6). It is interesting to note that the initial input-output membership func-tion distributions at the beginning of the training phase of the fuzzy logic system are seen similar to Fig. 3. How-ever, a small change in the input-output membership function distributions of the fuzzy logic system has been observed at the end of training. The optimized “a” values of six variables such as a1, a2, a3, a4, a5 and a6

are found to be equal to 2.9941, 19.5594, 74.3348, 59.4485, 99.6776 and 2.61385 respectively for bell shaped mem-bership function distributions. Similarly for gaussian membership function distributions the “a” values are found to be equal to 3.3835, 19.6299, 74.3831, 59.3588,

98.9817 and 2.61385 respectively. It is interesting to note that there is no significant change in the input mem-bership distributions for triangular shape. However, the slight change in the output membership distribution and the corresponding a6 value is found to be equal to 2.60415.

The performance of the developed models with dif-ferent membership function distributions in predicting the casting density using approach 2 is shown in Fig. 8. The best fit line method is used to compare the model pre-dicted and the actual values. However it is interesting to note that line of best fit for all the models is found to be close to the ideal line. However, bell shape membership function distribution shown in Fig. 8(b) outperforms the triangular (see Fig. 8(a)) and gaussian membership dis-tributions (see Fig. 8(c)). It is interesting to observe that majority of the data points of bell shape membership function of the fuzzy logic system falls on the best fit line compared to gauss and triangular shaped membership distribution of fuzzy logic system. Summary results of the results of the test cases for predicting the casting density is shown in Table 4.

Fig. 7: Comparison of predicted and actual density values using approach 1: (a) Triangular membership function distributions, (b) bell shape membership function distributions, and (c) Gaussian membership function distributions




In addition, the performance of the developed models is evaluated using MAPE and R2 values. It is interesting to note that R2 value is found to be equal to the 0.949 for bell shape membership function distribution. This indicates, the model can map with actual values accurately with a probability equal to 94.9%. For triangular and gauss shaped membership function distribution the R2 value is found to be equal to 0.928 and 0.843 respectively (see Table 4). However, the MAPE value is also calculated for the developed membership function distributions and the values are found to be equal to 0.388 for triangular shape membership function distribution, 0.289 for bell shape membership function distribution and 0.523 for gaussian membership function distributions of fuzzy logic system (see Table 4).

4.4 Comparison of the developed approaches

The percent deviation in prediction of the density as obtained for the developed approaches with different

membership function distributions are shown in Fig. 9 and Fig. 10.

It has been observed that for the response density, the percentage deviation values for both the approaches using triangular shape membership function distribution are found to lie in the range of (−0.771, +1.051)% for approach 1 and (−0.263, +0.999)% for approach 2 respectively. Similarly for gaussian membership function distributions percent deviation is found to lie in the range of (−0.886, +1.0135)% for approach 1 and (−0.638, +0.571)% for ap-proach 2 and for bell shape (−0.963, +1.088)% for approach 1 and (−2.402, +0.609)% for approach 2 respectively (see Fig. 9).

4.5 Comparison of the developed approaches using average absolute percent deviation

Fig. 10 compares the performances the developed ap-proach 1 and approach 2 with different membership function distributions in terms of mean absolute percent

Fig. 8: Comparison of predicted and actual density values using approach 2: (a) Triangular membership function distributions, (b) bell shape membership function distributions, and (c) Gaussian membership function distributions




Fig. 9: Comparison of different approaches of the developed models with different membership function distribution in terms of percent deviation in prediction for the response-density: (a) Manually constructed fuzzy logic system and (b) adaptive network based fuzzy logic system

Fig. 10: Comparison of different models performances in terms of average absolute percent deviation in prediction for the responses-density




deviation in prediction of density of the squeeze casting process. It is important to note that the performance of approach 2 would be slightly better than approach 1 in predicting both of the responses. However, the results showed that the performance of approach 2 also varies with different membership function distributions, the reason might be due to the nature of error surface. In case of approach 1 the consequent part of the rule base has been developed with the help of the human expertise and may not be optimal in all cases. On the other-hand, in case of approach 2, the evolution of optimal fuzzy logic system is through the better learning capabilities of arti-ficial neural networks. The reason might be due to the in-herent adaptability of the automatically defined fuzzy logic system to evolve consequent part, rule and data bases utilizing artificial neural networks. It is interesting to note that, the approach 2 of bell shaped member-ship function distributions outperforms all other models with minimum average absolute percentage deviation as shown in Fig. 10.

5 Concluding remarksAn attempt has been made to carry out forward mapping of squeeze casting process to predict density utilizing the fuzzy logic based approaches. Two different approaches, namely manually constructed Mamdani based fuzzy logic and automatically designed Takagi and Sugeno’s (ANFIS) approaches, have been utilized for this purpose. Batch mode of training has been employed, with huge (500) amount of training data. The training data is generated artificially through response equation obtained through regression analysis. Two different approaches with three different membership function distribution are developed and their performances are compared with the help of ten test cases. It is to be noted that the test case data is col-lected by conducting experiments and are not used during the learning phase of ANFIS. It is interesting to note that the approach 2 performed better compared to approach 1. It is important to note that the triangular membership function distributions of approach 1 and bell shape membership function distributions of approach 2 made better predictions in the present case. The improved per-formance of approach 2 relies majorly on the member-ship function distribution and the nature of the error surface. In addition it also depends on the behaviour (linear or non-linear) of the response with variation of the process parameters. Moreover the developed approaches are capable of making better predictions with the experi-mental test cases with different membership function dis-

tributions. However, the prediction of the approach 1 can be further enhanced by increasing the number of linguis-tic terms. The fuzzy logic models developed are found to be useful to make accurate prediction of casting density in squeeze casting for the different combination of process parameters. The present work is useful to foundry-men, since, it provides an insight about selection of process parameters for good quality casting in squeeze casting process.

NomenclatureFLC Fuzzy logic controllerL LowM MediumH HighA Time delayB Pressure durationC Squeeze pressureD Pouring temperatureE Die temperatureρ Densityμ Membership functiona1, . . . , a6 Half base widths pi, qi, ri and ui Coefficient of consequent partGA Genetic algorithmsANNs Artificial neural networksGA-NN Genetic algorithm neural networkBPNN Back propagation neural networkFL Fuzzy logicANFIS Adaptive network based fuzzy interface

systemRMSE Root mean square errorMAPE Mean absolute percent errorR2 Co-efficient of correlation determination

References[1] Britnell DJ and Neailey K (2003), Macrosegregation in thin

walled castings produced via the direct squeeze casting process, Journal of Materials Processing Technology, 138(1), 306–310.

[2] Yang LJ (2003), The effect of casting temperature on the properties of squeeze cast aluminium and zinc alloys, Journal of Materials Processing Technology, 140(1), 391–396.

[3] Yang LJ (2007), The effect of solidification time in squeeze casting of aluminium and zinc alloys, Journal of Materials Processing Technology, 192, 114–120.

[4] Maleki A, Niroumand B and Shafyei A (2006), Effects of squeeze casting parameters on density, macrostructure and




hardness of LM13 alloy, Materials Science and Engineering: A, 428(1), 135–140.

[5] Benguluri S, Vundavilli PR, Bhat RP and Parappagoudar MB (2011), Forward and reverse mappings in metal casting – A step towards quality casting and automation, (11-009), AFS Transactions-American Foundry Society, 119(19), 1–15.

[6] Vijian P and Arunachalam VP (2007), Modelling and multi objective optimization of LM24 aluminium alloy squeeze cast process parameters using genetic algorithm, Journal of Materials Processing Technology, 186(1), 82–86.

[7] Senthil P and Amirthagadeswaran KS (2012), Optimization of squeeze casting parameters for non symmetrical AC2A aluminium alloy castings through Taguchi method, Journal of Mechanical Science and Technology, 26(4), 1141–1147.

[8] Senthil P and Amirthagadeswaran KS (2013), Experimental study and squeeze cast process optimization for high quality AC2A aluminium alloy castings, Arabian Journal of Science and Engineering, 1(1), 1–13, doi: 10.1007/s13369-013-0752-5.

[9] Bin SB, Xing SM, Zhao N and Li L (2013), Influence of technical parameters on strength and ductility of AlSi9Cu3 alloys in squeeze casting, Transactions of Nonferrous Metals Society of China, 23(4), 977–982.

[10] Parappagoudar MB and Vundavilli PR (2012), Application of modeling tools in manufacturing to improve quality and productivity with case study, Proceedings in Manufacturing Systems, 7(4), 193–198.

[11] Wang RJ, Zeng J and Zhou DW (2012), Determination of temperature difference in squeeze casting hot work tool steel, International Journal of Material Forming, 5(4), 317–324.

[12] Parappagoudar MB, Pratihar DK and Datta GL (2008), Forward and reverse mappings in green sand mould system using neural networks, Applied Soft Computing, 8(1), 239–260.

[13] Parappagoudar MB, Pratihar DK and Datta GL (2007), Modelling of input–output relationships in cement bonded moulding sand system using neural networks, International Journal of Cast Metals Research, 20(5), 265–274.

[14] Kittur JK and Parappagoudar MB (2012), Forward and reverse mappings in die casting process by neural network-based approaches, J. Manuf. Sci. Prod., 12(1), 65–80.

[15] Parappagoudar MB, Pratihar DK and Datta GL (2008), Neural network-based approaches for forward and reverse mappings of sodium silicate-bonded, carbon dioxide gas hardened moulding sand system, Materials and Manufacturing Processes, 24(1), 59–67.

[16] Surekha B, Vundavilli PR, Parappagoudar MB and Srinath A (2011), Design of genetic fuzzy system for forward and reverse mapping of green sand mould system, International Journal of Cast Metals Research, 24(1), 53–64.

[17] Surekha B, Vundavilli PR and Parappagoudar MB (2012), Forward and reverse mappings of the cement-bonded sand mould system using fuzzy logic, The International

Journal of Advanced Manufacturing Technology, 61(9–12), 843–854.

[18] Vundavilli PR, Parappagoudar MB, Kodali SP and Benguluri S (2012), Fuzzy logic-based expert system for prediction of depth of cut in abrasive water jet machining process, Knowledge-Based Systems, 27, 456–464.

[19] Surender Y and Pratihar DK (2013), Fuzzy logic-based techniques for modeling the correlation between the weld bead dimension and the process parameters in MIG welding, International Journal of Manufacturing Engineering, 2013, http://dx.doi.org/10.1155/2013/230463.

[20] Maji K and Pratihar DK (2010), Forward and reverse mappings of electrical discharge machining process using adaptive network-based fuzzy inference system, Expert Systems with Applications, 37(12), 8566–8574.

[21] Zhao HD, Wang F, Li YY and Xia W (2009), Experimental and numerical analysis of gas entrapment defects in plate ADC12 die castings, Journal of Materials Processing Technology, 209(9), 4537–4542.

[22] Patel GCM, Mathew R and Krishna P (2013), Effects of squeeze casting process parameters on density of LM20 alloy, 4th International Joint Conference on Advances in Engineering and Technology (AET 2013), Dec 13–14th, pp. 776–785, NCR, India.

[23] Pratihar DK (2008), Soft Computing, Narosa Publishing House Pvt. Ltd, India.

[24] Wong BK and Lai VS (2011), A survey of the application of fuzzy set theory in production and operations management: 1998–2009, International Journal of Production Economics, 129(1), 157–168.

[25] Rajasekaran S and Pai GV (2003), Neural networks, fuzzy logic and genetic algorithm: synthesis and applications, PHI Learning Pvt. Ltd.

[26] Yurdusev MA and Firat M (2009), Adaptive neuro fuzzy inference system approach for municipal water consumption modeling: An application to Izmir, Turkey, Journal of Hydrology, 365(3), 225–234.

[27] Daoming G and Jie C (2006), ANFIS for high-pressure waterjet cleaning prediction, Surface and Coatings Technology, 201(3), 1629–1634.

[28] Lo SP (2003), An adaptive-network based fuzzy inference system for prediction of workpiece surface roughness in end milling, Journal of Materials Processing Technology, 142(3), 665–675.

[29] Al-Zubaidi S, Ghani JA and Haron CHC (2013), Prediction of surface roughness when end milling Ti6Al4V alloy using adaptive neurofuzzy inference system, Modelling and Simulation in Engineering, 2013, 10, http://dx.doi.org/10.1155/2013/932094.

[30] Dhas JER and Kumanan S (2007), ANFIS for prediction of weld bead width in a submerged arc welding process, Journal of Scientific and Industrial Research, 66(4), 335.



Prediction of Squeeze Cast Density Using Fuzzy Logic Based Approaches

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