Modified Flower Pollination Algorithm to Optimize WEDM parameters while Machining Inconel-690 alloy

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ScienceDirect Materials Today: Proceedings 5 (2018) 7864–7872

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IMME17

Modified Flower Pollination Algorithm to Optimize WEDM parameters while Machining Inconel-690 alloy Sreenivasa Rao Ma*, Venkata Naresh Babu Aa, Venkaiah Nb a

DVR & Dr HS MIC College of Technology, Kanchikacherla, A.P., India-521180 b Indian Institute of Technology, Tirupati, A.P., India-517506

Abstract Flower Pollination algorithm (FPA) is one of the global optimization algorithms and was found to outperform genetic algorithm (GA) and particle swarm optimization (PSO) algorithm. In order to improve the performance of existing FP algorithm, a modified FPA has been proposed in the present work. Further, super alloys are finding wide range of applications including power generation turbines, aircraft, nuclear power, automobiles, rocket engines, and chemical processing plants. These materials exhibit superior mechanical and chemical properties. They are found to retain hardness at elevated temperatures, be resistant to corrosion and have low thermal conductivity. Machining of these alloys with conventional processes is very difficult. Wire electrical discharge machining (WEDM) is one of the modern machining techniques and it can machine materials, irrespective of their hardness, as it is a non-contact machining process. Inconel-690, one of the nickel-based alloys is widely used in nuclear power and aerospace applications. The influence of WEDM process parameters such as pulse on time, pulse off time, peak current and servo voltage on responses such as material removal rate (MRR) and surface roughness (SR) has been studied while machining Inconel-690. Mathematical models are developed to predict these responses. The proposed modified FPA has been used to optimize WEDM process parameters. Further, this method has also been applied for simultaneous optimization of the responses. As the current method is found to yield encouraging results, it can be extended to solve other optimization problems also. © 2017 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of International Conference on Emerging Trends in Materials and Manufacturing Engineering (IMME17). Keywords: Optimization; Flower pollination algorithm; WEDM; Inconel-690; Super alloy; Material removal rate; Surface roughness

* Sreenivasa Rao M. Tel.: 91-8678273535. E-mail address: [email protected] 2214-7853 © 2017 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of International Conference on Emerging Trends in Materials and Manufacturing Engineering (IMME17).

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1. Introduction Machining of super alloys is difficult with conventional processes due to high hardness and low thermal conductivity. Wire cut Electrical Discharge Machining (WEDM) is one of the advanced processes; it can cut any material irrespective of its hardness [1]. As there are number of process parameters such pulse-on time, pulse –off time, peak current and servo voltage wire tension, wire feed, dielectric pressure etc. it is very difficult to identify optimal working conditions. A back propagation Neural network modeling was used by Spedding et al. [2] and Saha et al. [3], further these models are used for optimization. Sarkar et al. [4] applied Taguchi experimental design to conduct experiments, and neural network to develop predictive models for WEDM responses such as cutting speed, wire off-set and surface roughness (SR). Mahapatra and patnaik [5] and Sadeghi et al.[6] used Taguchi technique for experimental plan and mathematical models for WEDM responses and these models are further optimized using genetic algorithms and Tabu search respectively. Tosun [7] applied a full factorial experimental design for experimentation and mathematical models are generated for responses using regression analysis. Response Surface Methodology was used by Shandilya et al.[8], Garg et al.[9], Zhange et al. [10] and Narendranath et al. [11] etc. for experimental plan and also to model the WEDM responses while machining different materials. Multi-response optimization algorithms such as grey relational analysis [12], multi response signal to noise ratio (MRSN) method [13] are used to optimize responses such as material removal rate (MRR), wire wear rate (WWR) and SR. Desirability function of RSM was used by Ghodsiyeh et al. [14] for multi-objective optimization of WEDM process in machining Titanium alloy. NSGA-II was applied by Kondayya and Gopalakrishna [15] in optimization of MRR and SR simultaneously. Particle swarm optimization (PSO) and artificial bee colony (ABC) algorithms are used by Rao and Pawar [16, 17] to find the optimal WEDM process parameters for machining speed at desired level of finish. It can be observed from the literature that attempts have been made by researchers to model the WEDM process and optimize the parameters using various techniques. Flower pollination algorithm (FPA) was found to outperform GA and PSO [18]. In the present work a flower pollination algorithm has been used to optimize WEDM responses such as MRR and SR. However, in order to improve the performance of the FPA, a modified flower pollination algorithm has been proposed in this paper. Furthermore, Inconel-690 is a high chromium nickel alloy and due to its excellent resistance to corrosion, high strength and metallurgical stability at high temperatures, it is extensively used in aerospace, automotive and nuclear power applications. RSM has been used for experimental plan and also to develop predictive models. These models are used for further optimization using FPA and modified FPA. 2. Flower pollination algorithms The FPA was introduced by Xin-She Yang in 2012, it is inspired by the pollination process of flowering plants. It is estimated that there are over a quarter of a million types of flowering plants in nature and that about 80 % of all plant species are flowering species. The main purpose of any flower is ultimately reproduction through pollination. This process involves transfer of pollen with pollinators such as birds, bats, insects and other animals. There are two major pollination forms: abiotic and biotic. If the pollen is transferred by any insects or animals, it is called as biotic pollination and 90 % of the flowers fall under this group. The remaining 10 % of the flowers fall under abiotic pollination, it does not require any pollinators. This abiotic pollination will be done with the help of wind and diffusion and the example of this pollination is grass [19]. Pollinators also called pollen vectors, can be very diverse, honeybees are a good example of pollinators. They have also developed the flower constancy [20], that is, these pollinators visit specific flower species exclusively, bypassing the others. This flower constancy may also have evolutionary advantages because it maximizes the transfer of flower pollen to the same or specific plants, thus increase the reproduction of the same kind of flower species. Pollinators find that flower constancy requires minimum investment costs and more likely guaranteed intake of nectar [21]. In Biotic cross-pollination, pollinators such as birds, bees, bats, and flies can fly a long distance, leads to global pollination. In addition, bees and birds may exhibit Lévy flight behavior with jump or fly distance steps obeying a Lévy distribution. From the biological evolution point of view, flower pollination objective is the survival of the fittest and the reproduction of plants in terms of numbers. The characteristics of pollination process, flower constancy and pollinator behavior has the following rules [18, 22]:

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 Biotic and cross-pollination is considered as global pollination with pollinators performing L´evy flights.  Abiotic and self-pollination are considered as local pollination.  Flower constancy can be considered as the reproduction probability  Local pollination and global pollination is controlled by a switch probability p ∈ [0, 1]. 3. Proposed method In this paper, a two stage initialization based flower pollination algorithm has been presented. It tries to approach the target in an optimal manner for finding the optimal solution to any mathematical optimization problem. The major stages of the proposed algorithm are briefly described as follows: The population is generated using the following equation

xi , j = x j min + rand ( 0, 1) ( x j max − x j min )

(1)

where i = 1, 2,.., ps ; j = 1, 2,.., ncv.

ps = population size.

ncv = number of control variables. xj

min

& xj

max

are the lower and upper bounds of

j th control variable.

rand ( 0,1 ) is a uniformly distributed random number between 0 and 1. The two stage initialization process provides better probability of detecting an optimal solution. In the first stage, initial population is generated as a multi-dimensional vector of size (spv × ncv). Evaluate the value of objective function for each string in the population vector and select the best string from the population vector corresponding to optimal function value. Repeat the procedure for number of population vectors (n). In the second stage, combine all the best strings to form multi-dimensional vector of size (n ×ncv) and this new population is used for further evolutionary operations. According to FPA, each flower changes its position according to its constancy and the previous positions in the problem space. The individual best and the global best is calculated during iterative process till the stopping criteria is satisfied. The flower constancy is updated using the Eqn. (2) - (3). Local pollination and global pollination is controlled by a switch probability. In the global pollination step, flower pollen gametes are carried by pollinators such as insects, and pollen can travel over a long distance because insects can often fly and move in a much longer range. The flower population is updated using the equation (2):

xit +1 = xit + L ( xit − g* )

(2)

λΓ ( λ ) sin ( πλ / 2 ) 1 S 1+λ π xit = Solution vector xi at iteration t

where L ~

g* = Current best solution Γ ( λ ) = Standard Gamma function Due to physical proximity and other factors such as wind, local pollination can have a significant fraction p in the overall pollination activities.

xit +1 = xit + ε ( x tj − xkt )

(3)

t k

where x tj and x are pollen from different flowers of the same plant species. This essentially mimics the flower constancy in a limited neighborhood. Mathematically if x tj and xkt come from the same species or selected from

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the same population, this equivalently becomes a local random walk if ε is drawn from a uniform distribution in [0,1]. In any evolutionary algorithm, the optimization process starts with initialization step. Once the initialization is done, all the operators of the algorithm are applied in a sequence to find feasible solutions in each generation. In order to guide the search to global optimal solution, the optimization process will be repeated until a stopping criterion is met. This procedure is followed in the existing FPA also. However, the accuracy and the convergence rate will heavily depend upon the initial population and its location from the target value. Furthermore, this method applies all the operators of the algorithm at every iteration and this could delay the convergence. However, the modified FPA proposed in this work involves two-stage initialization process. This process enhances the probability of finding global optimal solution. In the first stage, a sub population vector of size (sspv×ncv) is formed. The value of objective function for each string is evaluated in the sub population vector. The best string from the sub population vector based on its fitness is selected. This procedure is repeated for all the sub-population vectors. In the second stage, all the best strings from the sub population vectors are combined to form a new population vector of size (nspv×ncv) and the evolutionary operators are applied on this newly formed population vector. Therefore, accuracy and fast convergence resulted from the proposed method can be attributed to the following reasons: (1) The newly formed population vector will be closer to the global optimal solution and therefore, overall number of generations required to reach the target value will be reduced significantly. Evolutionary operators are applied from the second stage of the process instead of initial sub-populations. 4. Results and Analysis The experiments were conducted on Inconel-690 material as per the RSM (face centered central composite design) experimental plan and the results have been presented in Table 1. Pulse-on time (Ton), pulse-off time (Toff), peak current (Ip) and servo voltage (Sv) are considered as input parameters, MRR and SR are considered as the responses. The chemical composition of Inconel-690 material includes C:0.017, S:0.0013, Mn:0.21, Si:0.25, Cr:29.58, Cu:0.01, Ti:0.2, Nb:0.02, Fe:9.05 and Ni:60 in % of weight. ANOVA has been applied for each response to investigate the significance of process parameters and also to model the response parameters in relation to their influencing parameters. 4.1. ANOVA Results of MRR ANOVA has been applied for MRR to investigate the significance of process parameters and their contributions for the Inconel-690 work material and also used to model the response MRR in relation with their influencing process parameters. The results of ANOVA for MRR are presented in Table 2. ANOVA Tables depict the influencing parameters along with their percentages of contribution. Cor. Total

5.30

29

100.00

From the ANOVA results of it can be observed that Ton, Toff, Ip, Sv and interaction effect of Ton and Ip are influencing the MRR (Figure 1(a) to (e)). Pulse-on time is the time allowed to discharge energy. At high Ton the energy applied will also high and more amount of heat energy will be generated, thereby MRR increase. Pulse-off time is the interval between discharges. The effect of Toff is inverse to the effect of Ton. Peak current is the maximum current and energy supplied for machining is directly proportional to current. At high Ip, the discharge power is also high thereby MRR increases. Servo voltage is used to control the tool advance and retract. At smaller value of Sv, the mean gap will be narrowed which leads to an increase in number of electric sparks and also intensity of the sparks these leads to speed up the machining rate. The acceptance of the model will be decided by the R-Squared, Adjusted R-Squared and Predicted R-Squared values, which are 97.3 %, 96.6 % and 95 % respectively. The mathematical model developed for MRR from ANOVA in coded form is given by Eq. (4).

(

MRR = 1.67 - 0.25A + 0.074B - 0.38C + 0.049D - 0.12AC - 0.4C 2

)

−1

2

(4)

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Sreenivasa Rao et al., / Materials Today: Proceedings 5 (2018) 7864–7872 Table 1. Experimental results S. No.

Ton

Toff

Ip

Sv

MRR

SR

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

(µs) 115 115 125 115 105 115 125 115 115 105 115 125 125 105 115 105 115 105 105 105 125 105 115 105 125 125 115 125 115 125

(µs) 55 60 50 55 60 55 60 55 55 50 55 60 50 60 55 50 50 50 60 60 55 55 55 50 50 60 55 60 55 50

(A) 11 11 12 10 12 11 10 11 11 10 12 10 10 12 11 10 11 12 10 10 11 11 11 12 12 12 11 12 11 10

(V) 50 50 60 50 60 60 40 50 50 40 50 60 40 40 50 60 50 60 40 60 50 50 50 40 40 60 50 40 40 60

(mm3/min) 0.3722 0.34049 4.06502 0.3648 0.499 0.345 0.4113 0.35309 0.3753 0.33727 1.71822 0.39578 0.58931 0.54517 0.36988 0.36228 0.37504 0.53466 0.27822 0.28444 0.43536 0.31819 0.3457 0.8808 5.843 2.1615 0.32263 3.44124 0.35897 0.38071

(µm) 0.354 0.357 2.585 0.336 0.559 0.373 0.571 0.371 0.348 0.378 1.842 0.377 0.595 0.669 0.322 0.371 0.407 0.447 0.332 0.276 0.431 0.317 0.392 0.761 3.253 2.786 0.422 3.012 0.533 0.436

4.2. ANOVA Results of SR

From the ANOVA results of SR as presented in Table 3, it is observed that Ton, Ip, Sv and interaction effect of Ton and Ip are influencing the SR as shown in figure 2 (a) to (d). When Ton increases, the energy applied will also increases and more amount of heat energy will be generated during this period MRR increases, it leads to increase the SR. When Ip decreases it leads to less discharge power thereby decrease the machining rate and SR. At higher values of Sv, the mean gap becomes wider which leads to decrease in number of electric sparks, thereby reducing the machining rate and increase in surface finish. R-Squared, Adjusted R-Squared and Predicted RSquared values were 94.4 %, 93.2 % and 91.3 % respectively. The mathematical model developed for SR from ANOVA in coded form is given in Eq. (5).

(

SR = 1.62 − 0.24 A − 0.34 + 0.085D − 0.11AC − 0.36C 2

)

−1

2

(5)

Table 2 ANOVA results of MRR Source Model A- Ton B- Toff C-Ip D-Sv AC C2 Resid.

SS 5.16 1.08 0.10 2.56 0.04 0.25 1.13 0.14

DOF 6 1 1 1 1 1 1 23

MS 0.860 1.080 0.100 2.560 0.044 0.250 1.130 6.20E-03

F value 138.80 174.64 16.11 413.00 7.06 40.03 181.95

p-value < 0.0001 < 0.0001 0.0005 < 0.0001 0.0141 < 0.0001 < 0.0001

% Contribution 97.358 20.377 1.8868 48.302 0.8302 4.7169 21.321 2.6415

Sreenivasa Rao et al., / Materials Today: Proceedings 5 (2018) 7864–7872

(a) Effect of Ton on MRR

(c) Effect of Ip on MRR

(b)Effect of Toff on MRR

(d) Effect of Sv on MRR

(e) Interaction effect of Ip and Ton on MRR Figure 1. Effect of WEDM process parameters on MRR while machining Inconel-690

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Table 3 ANOVA results of SR Source Model A- Ton C-Ip D-Sv AC C2 Resid. Cor. Total

SS

DOF

MS

F value

p-value

% Contribution

4.326 1.002 2.070 0.129 0.182 0.942 0.256 4.583

5 1 1 1 1 1 24 29

0.865 1.002 2.070 0.129 0.182 0.942 0.011

81.027 93.867 193.88 12.161 17.035 88.195

< 0.0001 < 0.0001 < 0.0001 0.0019 0.0004 < 0.0001

94.407 21.874 45.179 2.834 3.969 20.552 5.593 100.00

(a) Effect of Ton on SR

(c) Effect of Sv on SR

(b) Effect of Ip on SR

(d) Interaction effects of Ip and Ton on SR

Figure 2. Effect of WEDM process parameters on SR while machining Inconel-690

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Table 4 Optimal results of proposed methods Technique/Response

RSM

Existing FPA

Proposed method

MRR (mm3/min)

5.8912 (Ton: 125, Toff: 50.28, Ip: 12, Sv: 40)

5.9493 (Ton: 125, Toff: 50, Ip: 12, Sv: 40.75)

6.0584 (Ton: 125, Toff: 50, Ip: 12, Sv: 40)

Computational time (s)

-

0.2097

0.1589

SR (µm)

0.2713 (Ton: 106, Toff: 50.41, Ip: 10.98, Sv: 59.82)

0.2673 (Ton: 105, Toff:55.33, Ip: 10.67, Sv: 60)

Computational time (s)

-

0.1712

0.2550 (Ton: 105, Toff: 59.61, Sv: 60)

Ip: 10.7,

0.1584

Figure 3. Pareto optimal front for MRR and SR Table 5. Multi-objective optimization of MRR and SR S. No.

W1 (MRR)

W2 (SR)

Ton (µs)

Toff (µs)

Ip (A)

Sv (V)

MRR (mm3/min)

SR (µm)

1

0

1

105

59.6

10.7

60

0.2319

0.25501

2

0.1

0.9

107.8

50

10

60

0.3398

0.31653

3

0.2

0.8

105.3

50

11.9

60

0.5818

0.50326

4

0.3

0.7

107.9

50

12

60

0.7777

0.6437

5

0.4

0.6

111.7

50

12

60

1.0094

0.80014

6

0.5

0.5

114.7

50

12

60

1.2734

0.96718

7

0.6

0.4

117.4

50

12

60

1.6209

1.17261

8

0.7

0.3

120

50

12

60

2.1126

1.44065

9

0.8

0.2

122.9

50

12

60

2.9487

1.84987

10

0.9

0.1

125

50

12

60

3.9234

2.27206

11

1

0

25

50

12

40

6.0584

4.10532

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Results obtained using RSM, existing FPA and the proposed methods are presented in Table 4 along with machining conditions. From the results it is observed that, MRR values using RSM, existing FPA and proposed method are 5.8912 mm3/min, 5.9493 mm3/min and 6.0584 mm3/min respectively. Whereas SR values obtained using these methods are 0.2713 µm, 0.2673 µm and 0.2550 µm respectively. Therefore, by applying the proposed method better results can be attained. Furthermore, the modified flower pollination algorithm is extended for simultaneous optimization of MRR and SR. The simultaneous optimum values of MRR and SR at different weights are presented in the Table 5 and also the Pareto front between MRR and surface finish (SF) has been shown in Figure 3. Surface finish is simply inverse of SR Based on the requirements, the user may fix weights for the responses and select the corresponding optimal solutions. 5. Conclusions Flower pollination algorithm, one of the global optimization algorithms, was found to outperform some popular algorithms such as GA and PSO. However, there is a need to further improve the FPA with regard to its accuracy and speed. A modified FPA has been proposed in the present work to estimate the global optimal response value accurately. The proposed method has been successfully tested on standard bench-mark problems for its robustness before applying it on the WEDM data. The proposed algorithm was found to be accurate and fast as compared to existing FPA and RSM methods. The proposed method is able to perform better than the existing FPA technique in terms of accuracy and speed because of the novel two-stage initialization concept introduced in this work. Since the best strings, after the first generation, are grouped and further search is made around these solutions, the convergence rate is much faster. Though the proposed algorithm has been applied for optimizing the WEDM process, it can also be used for other applications. Furthermore, an attempt has been made in this work to study the machining behavior for Inconel-690 using WEDM. By conducting the trial experiments, feasible ranges for process parameters have been identified for the material in order to avoid problems such as wire breakage and wire short. A face centered central composite design of RSM was used for the experimental design. Effects of process parameters and their interaction effects on performance measures such as MRR and SR have been investigated. Percentage contributions of each process parameter on various responses have been estimated using ANOVA. MRR and SR values are significantly influenced by Ton, Ip and their interaction. 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