WEDM Process Parameter Optimization of Cu/ WC/SiC Composites Using Artificial Immune System
R.Meenakshi1, P.Suresh2 and M.Siva Kumar3
1 Research Scholar, Mechanical Engineering Department, Dhirajlal Gandhi College of Technology, Salem, Tamilnadu, India. E-mail: r.meenakshi77@gmail.com
2 Mechanical Engineering Department, Muthyammal College of Engineering, Rasipuram, Tamilnadu, India. E-mail: suresh.me2004@gmail.com
3 Mechanical Engineering Departmentm, Sree Sowdambika College of Engineering, Aruppukottai, Tamilnadu, India. E-mail: lawan_sisa@yahoo.com
Abstract
A systematic read about evaluating the machining characteristics of Wire Cut Electrical Discharge Machining (WEDM) using ANOVA and multilinear regression model based single objective optimization is provided during this analytical article. The current work explores, the surface roughness of copper metal matrix composite (MMCs) are minimized by optimizing the process parameters like Spark on time (TON), Spark off time (TOFF), peak current (PC) and wire feed (Wf). Taguchi’s L9 orthogonal array has been used to conduct the experiments for two samples having a different composition to measure the surface roughness. The order of significance of parameters on surface roughness (Ra) for sample 1 and 2 MMCs was found using analysis of variance (ANOVA) and a multilinear regression model (MLRM) was developed to predict the Ra value. The new contribution in the present work is that, the coefficients of MLRM were optimized using an Artificial Immune System (AIS) algorithm with the objective of minimizing the mean absolute percentage error (MAPE). Finally, the optimum process parameters were obtained to minimize the surface roughness and reported that the reduced value of Ra of 2.5% and 5% WC Copper MMCs were 0.9μm and 1.1μm respectively later which were established by confirmation experiments.
Keywords: WEDM; Composites; Powder; ANOVA; AIS; MAPE; MLRM; Surface; Roughness;
Introduction
Metal matrix composites (MMCs), reinforced with particulate WC/SiC are potential candidate materials for various utilization. The importance of those composites could be attributed to their high stiffness, elevated temperature strengths, progressed wear resistance and low coefficient of thermal expansion [1–3]. During the fabrication process, processing techniques could be classified as two main routes: liquid and solid routes. Production of MMCs with the aid of liquid metal processing has been receiving a whole lot attention because of its low value; however, it suffers from the subsequent drawbacks: non-uniform distribution of ceramic debris or fibers to agglomeration and unwanted chemical response of the interface due to the high temperature. Those drawbacks might be minimized by the use of P/M route [4, 5].
Further, WEDM is a multi-faceted machining process stressed at different process parameters for machining, which expect a significant part in making enhancements over machining execution [6]. By tradition, the method parameter change overwhelmingly depends upon the experience of the mechanical specialist and furthermore, the thumb rules or the machine producers' imaginative, which commonly end up with clashing shows. Copper reinforced with WC/SiCp is an example of a copper-based composite which widely used for heat sink materials due to its high thermal conductivity. In the present work, reinforced particulates WC/SiC was mixed with Cu powder to improve the SiC/Cu interface. The reason for selecting tungsten carbide material is that WC has good adhesion with Cu and can prevent Cu from reacting with SiC [7, 8]. The physical and mechanical properties of Cu composites were studied in the present paper.
Gopal et al. analyzed on WEDM experiments and grey relative analysis (GRA) based on multi-criteria improvement and machining characteristics for decreased surface roughness (Ra) and improved fabric elimination rate (MRR). Taguchi-based orthogonal array manner is used to formulate the experimental diagram for WEDM considering reinforcement degree and size, spark on time (Ton), spark off time (Toff) and wire feed (Wf) as processing parameters. ANOVA results divulge that Ton and wt% of reinforcement has more impact on Ra and MRR than any different regarded parameters [9]. Authors showed that the values calculated from the mathematical model of Ra and MRR values were comparable to that of experimental results.
Kulkeci et al. attempted to revise the penalties of surface roughness, depended on the feed rate, the modern-day and pulse duration of the WEDM machining process. Mathematical modeling of response variables (surface roughness) is accustomed, by employing a full factorial layout and also the experimental results were in distinction with the calculated values of the response variables to resolve the closeness of the predictions to the experimental values. The priority order of WEDM parameters for the surface roughness was once found and to be as follows: the feed rate, the modern and the pulse duration [10]. In the current case, the results showed that the anticipated values calculated with a regression calculation were very close to the experimental values, with R2 = 0.87.
The literature on Cu MMC machining and the effect of reinforcement in WEDM were moreover rare. For this reason, an experimental assignment on WEDM of a novel Cu based MMC with consideration of input approach parameters, viz. reinforcement size, reinforcement wt%, Ton, Toff, Peak current, and Wire feed, were undertaken to tackle this research slackness[11,12].
Special Vocabulary
AIS Artificial Immune System
MAPE Mean Absolute Percentage Error
MLRM Multi linear Regression Model
PWM Pair wise mutation
AFF Affinity rates
CR Cloning rates
Ra Surface roughness (μm)
Ton Spark on time (μs)
Toff Spark off time (μs)
PC Peak Current (A)
Wf Wire feed (m/min)
yi Response value of ith run
µ Mean value
σ Standard deviation
n Number of run
ƞ S/N Ratio
k Index for number of runs
a,b,c,d,e Coefficients of MLRM equation
Pij Value of ith parameter of jth antibody
Li, Ui Lower and upper limit of ith parameter
abij ith gene/molecule of jth antibody
i &j Index for parameter & antibody
MATERIALS AND METHODS
One of the most promising and at ease route for the manufacturing MMC is P/M, although the fundamental parametric comparisons were done with the relative MMC manufacturing practice on hand as of now. P/M technique ensures MMCs with extra uniform microstructure when compared with other different methods [13]. The composition of Copper composite considered is presented in Table 1. The specimen was fabricated through powder metallurgy method, where the tungsten carbide and silicon carbide in particulate form were reinforced to pure Copper < 75 µm (230 mesh ASTM). EDAX pattern of WC/SiCp is given in figure 1 filling its compositional elements: facility to refer WC/SiCp as an easily acceptable and promising reinforcement. The analysis reveals the dimensions and a weight percentage of WC/SiCp to vary in the range of 15–50 μm (200 meshes ASTM) and 10–20%, respectively. Alumina-graphite is a lubricating material which is capable of increasing the wear resistance and machinability of the fabric and therefore is mixed in a constant quantity of 1.5 %.
Figure 2, illustrates the step-by-step P/M method (1 – 4) for composite fabrication, which begins by using mechanically alloying a measured quantity of base and reinforcement substances with the useful resource of the planetary ball mill (Fritsch Planetary Ball Mill) roughly for 2 h with a denoted rotation speed of 220 rpm and milling was once achieved in a cycle of 20 min and used to be put on relaxation for next 15 min. This cycle persevered until 2 h of high-quality milling time. Water was used as wetting media. Ball milling was carried out with the use of stainless metal and the ball to powder mass ratio 5:1 was maintained. The mixture then compacted the use of hydraulic compaction press potential 40 tons in an die 40 mm diameter, where the load and dwell time were maintained at 482 MPa and 15 min two respectively. Finally, the compacted specimens were allowed to get sintered beneath argon surroundings of 800-950°C at 10°c/min for 2 hrs by means of a vacuum furnace and then allowed to cool down inside the furnace till the room temperature is attained [14]. Experimental outcomes confirmed that adding WC should effectively improve the thermal conductivity and increase the bonding between Silicon carbide and Copper.
Machining Conditions
The experiments were carried out on Ecocut EX4 WEDM machine, as shown in the figure 3 surrounding copper of diameter 0.25 mm as the wire material was operated by the wire feed mechanism. Dielectric fluids (deionized water) were passed over the workpiece and the wire (tool) by using pump [15, 16]. The fundamental machining conditions are tabulated in Table 2 for the EX4 WEDM machine.
The methodology is formed by taking the process parameter for optimization to maximize surface finish of copper MMCs is carried out in four stages. In the first stage, Taguchi's L9 Orthogonal Array has been used to conduct experiments with different levels of process parameters for two samples and the corresponding surface finish is measured. In the second stage, using ANOVA the parameter which influence surface finish is determined for both the sample separately. MLRM is established in the third stage and its coefficients are optimized using the AIS algorithm to minimize the MAPE. In the final stage, the optimized process parameters are obtained using MLRM by AIS algorithm and were verified by confirmation experiments.
The machining parameters, especially Ton, Toff, PC, and Wf, are optimized based on the ground of lookup hypothesis; their associated level for the sake of the Taguchi layout of experiments is given in Table 3.In this method, the experimental data are transferred into signal to noise ratio (S/N Ratio), a measure of quality characteristic takes the value of lower the better (LtB), normal the better (NtB) and higher the better (HtB) forms and represented in equations (1) – (3).
LtB S/N Ratio:
(1)
NtB S/N Ratio:
(2)
HtB S/N Ratio:
(3)
Taguchi's L9 Orthogonal Array has been selected for conducting the experiments which are represented in Table 4. Since, the response is surface roughness, lower the better quality characteristic is considered to calculate the S/N ratio [17, 18]. The effects of parameters were analyzed using MINITAB 15, statistical analysis done by Taguchi method and ANOVA analysis. Table 5 represents the measurements of surface roughness for different parameters. The contribution of each parameter influencing the response and they are significant is obtained using ANOVA analysis. Tables 6 and 7 represent response tables of S/N Ratio and Means, for both the MMCs samples.
Establishing MLRM Equation
MLRM is fitted for the surface roughness values as an output variable and TON, TOFF, PC and Wf as input parameters using ‘regstats' MATLAB function. Equation (4), (5) & (6) represents a linear MLRM equation fitted for the values given in Table 4. Table 8 represents the coefficients of the MLRM equation obtained from MATLAB along with R2 and the mean absolute percentage error (MAPE).
(4)
(5)
(6)
AIS Algorithm to Optimize the Coefficients of MLRM Equation using process parameters
In this work, the coefficients are optimized using the AIS algorithm based on the objective of minimizing the MAPE to enhance the accuracy of the MLRM. This algorithm is impressed by the behavior of the human immune system against foreign particles [19]. This is basically done by clone selection and affinity maturation of the immune system. This concept becomes a decent tool in finding optimization issues in engineering fields [20]. To eliminate or neutralize the antigens, the new cloned cells need to perform the method of mutation that will increase the affinity of the antibodies. The process of cloning, mutation, and receptor editing process, the immune system show the learning and recognition properties attracted the researchers to implement this algorithm in combinatorial optimization problems [21-23]. In this stage, using the coefficients obtained from the earlier stage, the process parameters are optimized by minimizing the surface roughness value using the AIS algorithm. The implementation of the AIS algorithm in the present work is presented in figure 4.
Step 1: Read the lower and upper values of the process parameter which is presented in Table 9 and the coefficients of the MLRM equation which is shown in Table 8.
Step 2: For demonstrating purpose, randomly 5 antibodies with four molecules/variables are generated and presented in Table 10. It is converted into the parameter values using Equation (7).
(7)
Substituting the values of Li & Ui from Table 9 and M1, M2, M3 & M4 values from Table 10 in Equation (7), the process parameters of antibody is calculated as,
Step 3: The surface roughness values are calculated by substituting the coefficient values from Table 8 and parameter values from Table 9. The surface roughness (Ra), affinity rates (AFF) and cloning rates (CR) of antibodies are calculated from Equation (4), (5) & (6) were formed to predict the response parameters shown in Table 10.
Step 4: The antibodies are sorted based on CR and the order is shown in Table 11. Usually, a certain % of antibodies are selected for clonal selection, but in this paper all the antibodies are subjected to the clonal selection process.
Step 5: For each antibody, two random numbers (R1 and R2) are generated within the number of process parameters (in this case it is 4 i.e TON, TOFF, PC and Wf), are presented in Table 12. The molecules within the random numbers are mutated in inverse order and the new cloning antibody is generated. For the demonstrated purpose, the new cloning of the third antibody (3') is shown in Table 13.
Step 6: Similar to step 2 and 3, the parameter values and its surface roughness (Ra'') of each antibody is calculated and presented in Table 14.
Step 7: The surface roughness values of the original antibody (1',2',3'..5') are compared with the inverse mutated antibody (1'',2'',3''…5''). The inverse mutated antibody which has more surface roughness than the original antibody will go for a pairwise mutation (PWM) shown in Table 15.
Interchanging the molecule from the location of random numbers R1' and R2', the new cloning of antibody is obtained. PWM process is explained for 3rd antibody (3'') given in Table 16 and the antibodies after the PWM process is shown in Table 17. (Ra''') is greater than the original surface roughness (Ra) value, the original molecules are considered as cloned antibody otherwise the molecules of PWM are considered as a cloned antibody. The outcomes of new cloned antibodies and molecules are presented in Tables 18 and 19.
Step 9: The antibodies shown in the above Table 19 are sorted in ascending order based on surface roughness and ranked accordingly. In receptor editing process, it is considered that amount of 20% of worst antibodies are removed and the same percentages of newly generated antibodies are inserted for the next iteration presented in Table 20.
Step 10: The step 2 to step 9 are repeated for a specified number of iterations or reached the specific condition. Table 21 represents the improved coefficients after the implementation of the AIS algorithm with the aim of minimizing the MAPE.
Results and discussion
The process parameters on surface roughness for sample 1, MMCs material is shown in terms of main effects plot for S/N Ratio and Means in figure 5. It is understood that TON process parameter is the primary factor affects the surface roughness followed by TOFF, PC and Wf.
For sample 2, MMCs material, TOFF is the primary factor that influences in getting good surface finish followed by a TON, PC and Wf shown in Figure 6. It is also understood from the Figures 5 and 6 that Peak Current has the least effect on the surface roughness of the materials as compared to the other parameters.
The MLRM equation for samples 1 and 2 are given in Equations (8) and (9). The value of surface roughness obtained using MLRM equation, both before and after implementation of AIS algorithm is compared with the experimental value along with their absolute percentage error (APE) for samples 1 & 2 MMCs shown in Figures 7 and 8 . It is understood that the APE values of surface roughness are reduced after the coefficients are optimized using the AIS algorithm in both the samples.
(8)
(9)
The percentage improvement in R2 and MAPE values both in Sample 1 and 2, MMCs are presented in Figure 9. The optimum process parameters after the successful implementation of the AIS algorithm are presented in Table 22 for both the samples. The affirmation test is performed to take a look at the durability of the envisioned optimum parameter stipulations toward reliability. Therefore the most likely suitable parameter degree can be used to machine the WC/SiCp reinforced copper MMC for achieving best-performance measures. The confirmation test experiments have been conducted for every two samples to test the process parameters received from AIS algorithm
Conclusion
Copper Surface composites with a varying volume percentage of Showcased particles were developed through powder metallurgy and the WEDM process conducted over an L9 OA trial revealed below-given the results.
• WC particles have a significant effect on governing the surface roughness (Ra) values along with the WEDM machining parameters which include TON, TOFF, PC, and Wf.
• The process parameter TON used to be the major factor influenced the surface roughness value in 2.5% WC than 5% WC, Copper MMCs; the parameter TOFF was the principal issue that influences the response.
• The result showed that nearly about 12% to 16% improvement in R2 value and 2% to 9% improvement in MAPE values.
• The minimum surface roughness values were obtained by optimizing the process parameter using the AIS algorithm and reported that 0.97 μm for 2.5% WC and 1.1 μm for 5% WC Copper MMCs.
• Developed the MLRM equation and their coefficients were optimized using the AIS algorithm with the objective of minimizing the MAPE which predicts the Ra values using the developed regression model were closer with real-time WEDM experimental results.
References
[1] Bains, P. S.; Sidhu, S. S.; & Payal, S. Fabrication and machining of metal matrix composites: a review. Materials and Manufacturing Processes 2016, 31(5), 553-573.
[2] Jawalkar, C. S.; Verma, A. S.; & Suri, N. M. Fabrication of aluminium metal matrix composites with particulate reinforcement: a review. Materials Today: Proceedings 2017, 4(2), 2927-2936.
[3] Manohar, G.; Dey, A.; Pandey, K. M.; & Maity, S. R. Fabrication of metal matrix composites by powder metallurgy: A review. In AIP Conference Proceedings 2018, 1952(1), 020041.
[4] Haghshenas, M. Metal–matrix composites. Reference Module in Materials Science and Materials Engineering 2016, 03950-3.
[5] Rajkovic, V.; Bozic, D.; Stasic, J.; Wang. H.; & Jovanovic, M. T. Processing, characterization and properties of copper-based composites strengthened by low amount of alumina particles, Powder Technology 2014 , 268, 392-400.
[6] Venkateswarlu, G.; and Devaraj, P. Optimization of Machining Parameters in Wire EDM of Copper Using Taguchi Analysis, International Journal of Advanced Materials Research 2015,,1(24), 126-131.
[7] De Mello, J. D. B.; Binder, C.; Hammes, G.; Binder, R.; & Klein, A. N. Tribological behaviour of sintered iron based self-lubricating composites. Friction 2017, 5(3), 285-307.
[8] Wu, D.; Wu, S. P.; Yang, L.; Shi, C. D.; Wu, Y. C.; & Tang, W. M. Preparation of Cu/Invar composites by powder metallurgy. Powder Metallurgy 2015, 58 (2), 100-105.
[9] Gopal, P. M.; Soorya Prakash, K.; and Jayaraj, S. WEDM of Mg/CRT/BN composites: Effect of materials and machining parameters. Materials and Manufacturing Processes 2018, 33 (1), 77-84.
[10] Kulekci, M. K.; Akkurt, A.; Esme, U.; & Ozkul, I.; Multiple regression modeling and prediction of the surface roughness in the Wedm process. Material in Tehnology 2014, 48(1), 9-14.
[11] Bains, P. S.; Sidhu, S. S.; & Payal, H. S. Fabrication and machining of metal matrix composites: a review. Materials and Manufacturing Processes 2016, 31(5), 553-573.
[12] Soorya, Prakash, K.; Sathiya, Moorthy, R.; Gopal, P.M.; Kavimani, V. Effect of reinforcement, compact pressure and hard ceramic coating on aluminium rock dust composite performance. International Journal of Refractory Metals and Hard Materials 2016, 54, 223–229.
[13] Dhakad, A, K.; & Vimal, J. Multi responses optimization of wire EDM process parameters using Taguchi approach coupled with principal component analysis methodology. International Journal of Engineering Science and Technology 2017, 9(2), 61-74.
[14] Gill, A. S.; & Kumar, S. Investigation of Micro-Hardness in Electrical Discharge Alloying of En31 Tool Steel with Cu–W Powder Metallurgy Electrode. Arabian Journal for Science and Engineering 2018, 43(3), 1499-1510.
[15] Kataria, Ravinder.; Kumar, Jatinder.; Pabla, B.S. Experimental investigation and optimization of machining characteristics in ultrasonic machining of WC-Co composite using GRA method. Materials and Manufacturing Processes 2016, 31(5), 685–693.
[16] Thankachan, T.; Soorya Prakash, K.; & Loganathan, M. WEDM process parameter optimization of FSPed copper-BN composites. Materials and Manufacturing Processes 2018, 33(3), 350-358.
[17] Hanjie, X.; Dalin, R.; and Shibo, W. EDM machining quality control and parameters optimization. The International Journal of Advanced Manufacturing Technology 2017, 89(5-8), 1307-1315.
[18] Jangra, K.; Grover, S.; & Aggarwal, A. Optimization of multi machining characteristics in WEDM of WC-5.3% Co composite using integrated approach of Taguchi, GRA and Entropy method. Frontiers of Mechanical Engineering 2012, 7(3), 288–299.
[19] Rao, R. V.; Rai, D. P.; & Balic, J. A multi-objective algorithm for optimization of modern machining processes. Engineering Applications of Artificial Intelligence 2017, 61, 103-125.
[20] Li, X.; & Jiang, H. Artificial Intelligence Technology and Engineering Applications. Applied Computational Electromagnetics Society Journal 2017, 32(5).
[21] Schmidt, B.; Al-Fuqaha, A.; Gupta, A.; & Kountanis, D. Optimizing an artificial immune system algorithm in support of flow-Based internet traffic classification. Applied Soft Computing 2017, 54, 1-22.
[22] Garg, Mohinder, Pal.; Ajai, Jain.; and Gian, Bhushan.; On process analysis and optimization of wire electric discharge machining of Ti 6-2-4-2 using regression modelling and genetic algorithms, International Journal of Machining and Mach inability of Materials 2015, 17(3-4), 185-210.
[23] Sharma, Neeraj.; Rajesh, Khanna.; and Rahul, Dev, Gupta. WEDM process variables investigation for HSLA by response surface methodology and genetic algorithm, International journal of Engineering science and technology 2015, 18(2), 171-177.
Figure 1. EDAX pattern of Cu composites
Figure 2. Composite fabrication process
Figure 3. Working zone of WEDM setup
Figure 4. Implementation of AIS Algorithm
Figure 5. Effect of process parameters on surface roughness for Sample 1
Figure 6. Effect of process parameters on surface roughness for Sample 2
Figure 7. Sample 1 – Surface Roughness and APE
Figure 8. Sample 2 – Surface Roughness and APE
Figure 9. % Improvement of R Square and MAPE
Table 1. Chemical Composition of Copper based MMCs
S.No. % Weight of Composition Weight (g) of Composition
Cu WC SiC Cu WC SiC
Sample 1 87.5 2.5 10 55.289 2.791 2.268
Sample 2 85 5 10 53.114 5.583 2.268
Table 2. Experimental Range of WEDM Parameters.
Parameters of WEDM Range /Values
Discharge current 10 A
Gap voltage 20 V
T ON 120-131 μs
T OFF 40 -50 μs
Wire Material copper
Wire Diameter Ф 0.25 mm
Wire Feed 70-110 m/min
Wire Tension 10 N
Ht. of Work piece 40 mm
Dielectric fluid Deionized water
Table 3. Levels of Process Parameters
S No. Parameter Unit Level 1 Level 2 Level 3
1 TON μs 120 125 131
2 TOFF μs 40 45 50
3 PC A 200 215 230
4 Wf m/min 80 100 120
Table 4. L9 Orthogonal Array with Response Variables.
S.No TON TOFF PC Wf
1 1 1 1 1
2 1 2 2 2
3 1 3 3 3
4 2 1 2 3
5 2 2 3 1
6 2 3 1 2
7 3 1 3 2
8 3 2 1 3
9 3 3 2 1
Table 5. Measurement of Surface Roughness for Samples SA1 and SA2
S.No TON TOFF PC Wf Ra
SA1 SA2
1 120 40 200 80 1.10 1.5
2 120 45 215 100 1.05 1.18
3 120 50 230 120 1.00 1.40
4 125 40 215 120 0.95 1.33
5 125 45 230 80 1.06 1.20
6 125 50 200 100 1.01 1.18
7 131 40 230 100 1.02 1.20
8 131 45 200 120 1.12 1.11
9 131 50 215 80 1.15 1.23
Table 6. Response Table for S/N Ratio
Level Sample 1 Sample 2
TON TOFF PC Wf TON TOFF PC Wf
1 -0.41721 -0.18478 -0.63288 -0.84931 -2.627 -2.527 -1.955 -2.301
2 -0.04901 -0.63809 -0.3974 -0.22741 -1.833 -1.309 -1.904 -1.486
3 -0.79011 -0.43346 -0.22604 -0.17961 -1.429 -2.053 -2.030 -2.102
Delta 0.74110 0.45331 0.40684 0.66970 1.198 1.218 0.126 0.815
Rank 1 3 4 2 2 1 4 3
Table 7. Response Table for Means
Level Sample 1 Sample 2
TON TOFF PC Wf TON TOFF PC Wf
1 1.05 1.023 1.077 1.103 1.360 1.343 1.263 1.310
2 1.007 1.077 1.05 1.027 1.237 1.163 1.247 1.187
3 1.097 1.053 1.027 1.023 1.180 1.270 1.267 1.280
Delta 0.090 0.053 0.050 0.080 0.180 0.180 0.020 0.123
Rank 1 3 4 2 2 1 4 3
Table 8. Coefficients of MLRM Equation
Sample No. a b c d e R2 MAPE
SA1 0.89830 0.00460 0.00300 -0.001700 -0.00200 0.570800 3.220
SA2 3.66232 -0.01614 -0.00733 0.000111 -0.00075 0.452773 5.938
Table 9. Lower and Upper Values of Process Parameters
S No. Parameter Unit Lower (Li) Upper (Ui)
1 TON μs 120 131
2 TOFF μs 40 50
3 PC A 200 230
4 Wf m/min 80 120
Table 10. Antibodies (ab) and Process Parameters
ab M1 M2 M3 M4 TON TOFF PC Wf
1 0.81472 0.09754 0.15761 0.14189 128.962 40.9754 204.728 85.6755
2 0.90579 0.2785 0.97059 0.42176 129.964 42.785 229.118 96.8705
3 0.12699 0.54688 0.95717 0.91574 121.397 45.4688 228.715 116.629
4 0.91338 0.95751 0.48538 0.79221 130.047 49.5751 214.561 111.688
5 0.63236 0.96489 0.80028 0.95949 126.956 49.6489 224.008 118.38
Table 11. Ra, AFF and CR values
ab Ra AFF CR
1 1.11838 0.89415 0.94397
2 1.06225 0.9414 0.99385
3 0.99347 1.00657 1.06265
4 1.07813 0.92753 0.97921
5 1.03468 0.96648 1.02033
Sum of Affinity 4.73613
Table 12. Sorted Antibodies based on CR
ab M1 M2 M3 M4 Ra’ CR R1 R2
1' 0.126987 0.546882 0.957167 0.915736 0.993471 1.062652 2 3
2' 0.632359 0.964889 0.80028 0.959492 1.034682 1.020327 2 3
3' 0.905792 0.278498 0.970593 0.421761 1.062251 0.993846 1 3
4' 0.913376 0.957507 0.485376 0.792207 1.078133 0.979206 1 2
5' 0.814724 0.09754 0.157613 0.141886 1.118378 0.943969 1 2
Table 13. Inverse Mutation of Antibody
Before inverse Mutation of 3’ R1 R2 After inverse mutation of 3’ (3’’)
M1 M2 M3 M4 M1’ M2’ M3’ M4’
0.90579 0.2785 0.97059 0.42176 1 3 0.97059 0.2785 0.90579 0.42176
Table 14. Antibodies after Inverse Mutation (IM)
ab’ M1’ M2’ M3’ M4’ TON’ TOFF’ PC’ Wf’ Ra’’
1'' 0.126987 0.957167 0.546882 0.915736 121.3969 49.57167 216.4064 116.6294 1.027567
2'' 0.632359 0.80028 0.964889 0.959492 126.956 48.0028 228.9467 118.3797 1.021003
3'' 0.970593 0.278498 0.905792 0.421761 130.6765 42.78498 227.1738 96.87045 1.068714
4'' 0.957507 0.913376 0.485376 0.792207 130.5326 49.13376 214.5613 111.6883 1.078866
5'' 0.09754 0.814724 0.157613 0.141886 121.0729 48.14724 204.7284 85.67545 1.106457
Table 15. Selected Antibodies for Pair Wise Mutation Process (PWM)
ab Ra' ab’ Ra'' PWM R1' R2'
1' 0.993471 1'' 1.027567 Yes 3 1
2' 1.034682 2'' 1.021003 No
3' 1.062251 3'' 1.068714 Yes 3 2
4' 1.078133 4'' 1.078866 Yes 3 2
5' 1.118378 5'' 1.106457 No
Table 16. Example for PWM
Before inverse mutation R1' R2' After pair wise mutation
M1' M2' M3' M4' M1'' M2'' M3'' M4''
0.970593 0.278498 0.905792 0.421761 3 2 0.97059 0.90579 0.2785 0.42176
Table 17. Antibodies after PWM Process
ab'' M1'' M2'' M3'' M4'' TON'' TOFF'' PC'' Wf'' Ra'''
1''' 0.54688 0.95717 0.12699 0.91574 126.016 49.5717 203.81 116.629 1.06944
2''
3''' 0.97059 0.90579 0.2785 0.42176 130.677 49.0579 208.355 96.8705 1.12084
4''' 0.95751 0.48538 0.91338 0.79221 130.533 44.8538 227.401 111.688 1.0433
5''
Table 18. Antibodies after IM and PWM Process
ab Ra Outcome of IMP Outcome of PWM ab'''
ab' Ra' ab'' Ra''
1' 0.99347 1'' 1.02757 1''' 1.06944 1'
2' 1.03468 2'' 1.021 2'' 2''
3' 1.06225 3'' 1.06871 3''' 1.12084 3'
4' 1.07813 4'' 1.07887 4''' 1.0433 4'''
5' 1.11838 5'' 1.10646 5'' 5''
Table 19. Molecules after IM and PWM Process
ab’’’ M1'' M2'' M3'' M4'' Ra''' Ranking
1' 0.12699 0.54688 0.95717 0.91574 0.99347 I
2'' 0.63236 0.80028 0.96489 0.95949 1.021 II
3' 0.90579 0.2785 0.97059 0.42176 1.06225 IV
4''' 0.95751 0.48538 0.91338 0.79221 1.0433 III
5'' 0.09754 0.81472 0.15761 0.14189 1.10646 V
Table 20. Antibodies for next iteration
Ranking ab M1 M2 M3 M4
I 1 0.12699 0.54688 0.95717 0.91574
II 2 0.63236 0.80028 0.96489 0.95949
III 3 0.95751 0.48538 0.91338 0.79221
IV 4 0.90579 0.2785 0.97059 0.42176
New 5 0.75127 0.2551 0.50596 0.69908
Table 21. Improved Coefficients of MLRM Equation using AIS Algorithm
Sample No. a b c d e R2 MAPE
SA1 0.976832 0.004287 0.003053 -0.00175 -0.00207 0.6646 2.9384
SA2 3.798005 -0.01712 -0.00798 0.000105 -0.00061 0.510232 5.814803
Table 22. Optimum Process Parameters
Sample Details TON TOFF PC Wf Ra
Sample 1 Experiment 125 40 215 120 0.95
AIS 120.35 40.87 229.97 119.37 0.97
Sample 2 Experiment 131 45 200 120 1.11
AIS 130.99 49. 79 200.2 118.8 1.1