An Integrated Approach of GRA Coupled with Principal Component Analysis for Multi-Optimization of Shielded Metal Arc Welding (SMAW) Process
Abstract
:1. Introduction
2. Materials and Methods
2.1. Work Piece Material
2.2. Parameters and Response Variables
2.2.1. Tensile Strength
2.2.2. Impact Energy
2.2.3. Hardness
2.2.4. Angular Distortion (AD)
3. Experimental Design
3.1. Groove Angle
3.2. Preheating
3.3. Electrode Diameter
3.4. Root Gap
4. Optimization Methodology
Principal Component Analysis (PCA)
5. Results and Discussion
5.1. Probability Plots
5.2. ANOVA and Main Effect Plots of Means for Individual Responses
5.2.1. Groove Angle
5.2.2. Preheating
5.2.3. Electrode Diameter
5.2.4. Root Gap
5.3. Single Objective Optimization
5.4. Multi Response Optimization based on GRA and PCA
6. Confirmation Experiment
7. Microstructure
8. Conclusions
- To achieve multiple objective optimization of SMAW process for pressure vessel steel SA 516 grade 70, the optimal combination of parameters is GA3PHT1ED3RG3.
- The percentage contributions of each quality response for principal component in decreasing order are angular distortion (28.40%), tensile strength (27.79%), hardness (27.14%), and impact energy (16.72%) respectively.
- The analysis of the average of GRG revealed that groove angle has the maximum influence, followed by electrode diameter, root gap, and preheat temperature, respectively.
- The analysis of the average of W-GRG revealed that groove angle has maximum influence, followed by root gap, preheat temperature, and electrode diameter, respectively.
- GRA and W-GRG identified identical optimal combination of input parameters as: groove angle 70°; preheat temperature 75 °C; electrode diameter 4 mm; and root gap 4 mm.
- Significant improvement in GRG from initial condition to optimal setting is found as 0.2898 as is achieved by GRA approach.
- Finally, a confirmatory experiment on GRG/W-GRA based optimal settings showed an improvement of 23.80% in tensile strength, 64.38% in impact energy, 3.01% in hardness, and 7.14% in angular distortion.
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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Element | C | Al | V | Cr | P | Mn | Si | Sn | N | As | S | Cu |
---|---|---|---|---|---|---|---|---|---|---|---|---|
% by weight | 0.22 | 0.039 | 0.002 | 0.03 | 0.018 | 0.99 | 0.18 | 0.002 | 0.005 | 0.002 | 0.008 | 0.02 |
Exp. No. | Coded Matrix | Un-Coded Matrix | Experimental Result | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
A | B | C | D | GA | PHT | ED | RG | TS (MPa) | IE (J) | H (HB) | AD (θ) | |
1 | 1 | 1 | 1 | 1 | 50 | 75 | 2.6 | 2 | 445 | 62.88 | 158 | 4.01 |
2 | 1 | 2 | 2 | 2 | 50 | 100 | 3.2 | 3 | 518 | 66.59 | 156 | 3.91 |
3 | 1 | 3 | 3 | 3 | 50 | 125 | 4.0 | 4 | 605 | 72.28 | 156 | 3.71 |
4 | 2 | 1 | 2 | 3 | 60 | 75 | 3.2 | 4 | 503 | 70.77 | 165 | 4.4 |
5 | 2 | 2 | 3 | 1 | 60 | 100 | 4.0 | 2 | 643 | 85.10 | 151 | 3.72 |
6 | 2 | 3 | 1 | 2 | 60 | 125 | 2.6 | 3 | 538 | 71.80 | 158 | 3.95 |
7 | 3 | 1 | 3 | 2 | 70 | 75 | 4.0 | 3 | 599 | 88.84 | 163 | 4.2 |
8 | 3 | 2 | 1 | 3 | 70 | 100 | 2.6 | 4 | 535 | 76.56 | 169 | 4.3 |
9 | 3 | 3 | 2 | 1 | 70 | 125 | 3.2 | 2 | 620 | 98.48 | 152 | 3.81 |
Parameters | Symbol | Units | Level 1 | Level 2 | Level 3 |
---|---|---|---|---|---|
Groove Angle | A | Θ | 50 | 60 | 70 |
Pre-Heat Temperature | B | °C | 75 | 100 | 125 |
Electrode Diameter | C | mm | 2.6 | 3.2 | 4 |
Root Gap | D | mm | 2 | 3 | 4 |
Component | PC 1 | PC 2 | PC 3 | PC 4 |
---|---|---|---|---|
Eigen Value | 2.4549 | 1.1014 | 0.2804 | 0.1634 |
Variation (%) | 0.614 | 0.275 | 0.070 | 0.041 |
Cumulative (%) | 0.614 | 0.889 | 0.959 | 1.000 |
Eigen Vector | −0.527 | 0.390 | −0.705 | −0.272 |
−0.409 | 0.662 | 0.592 | 0.207 | |
0.521 | 0.461 | −0.371 | 0.615 | |
0.533 | 0.444 | 0.121 | −0.710 |
Source | DoF | Adj SS | Adj MS | F-Value | p-Value | % Contribution | |
---|---|---|---|---|---|---|---|
Tensile strength | Groove angle | 1 | 5504.6 | 5504.6 | 23.98 | 0.008 | 16.55 |
Preheat temperature | 1 | 7776 | 7776 | 33.88 | 0.004 | 23.38 | |
Electrode diameter | 1 | 18351.4 | 18351.4 | 79.97 | 0.001 | 55.18 | |
Root gap | 1 | 704.2 | 704.2 | 3.07 | 0.155 | 2.11 | |
Error | 4 | 918 | 229.5 | 2.76 | |||
Total | 8 | 33253.6 | 100 | ||||
Impact energy | Groove angle | 1 | 648.99 | 648.99 | 80.68 | 0.001 | 61.03 |
Preheat temperature | 1 | 67.13 | 67.13 | 8.35 | 0.045 | 6.31 | |
Electrode diameter | 1 | 194.79 | 194.79 | 24.21 | 0.008 | 18.32 | |
Root gap | 1 | 120.154 | 120.154 | 14.94 | 0.018 | 11.3 | |
Error | 4 | 32.18 | 3.02 | ||||
Total | 8 | 1063.24 | 100 | ||||
Hardness | Groove angle | 1 | 34.105 | 34.105 | 17.24 | 0.014 | 12 |
Preheat temperature | 1 | 66.667 | 66.667 | 33.7 | 0.004 | 23.47 | |
Electrode diameter | 1 | 35.149 | 35.149 | 17.77 | 0.014 | 12.37 | |
Root gap | 1 | 140.167 | 140.167 | 70.86 | 0.001 | 49.35 | |
Error | 4 | 7.913 | 1.978 | 2.78 | |||
Total | 8 | 284 | 100 | ||||
Angular distortion | Groove angle | 1 | 0.0731 | 0.0731 | 20.57 | 0.011 | 14.64 |
Preheat temperature | 1 | 0.2166 | 0.2166 | 60.95 | 0.001 | 43.38 | |
Electrode diameter | 1 | 0.06923 | 0.06923 | 19.48 | 0.012 | 13.86 | |
Root gap | 1 | 0.12615 | 0.12615 | 35.5 | 0.004 | 25.26 | |
Error | 4 | 0.01421 | 0.00355 | 2.84 | |||
Total | 8 | 0.49929 | 100 |
Exp. No. | S/N Ratios of Responses | |||
---|---|---|---|---|
Tensile Strength | Impact Energy | Hardness | Angular Distortion | |
1 | 52.97 | 35.97 | −43.97 | −12.06 |
2 | 54.29 | 36.47 | −43.86 | −11.84 |
3 | 55.64 | 37.18 | −43.86 | −11.39 * |
4 | 54.03 | 37.00 | −44.35 | −12.87 |
5 | 56.16 * | 38.60 | −43.58 * | −11.41 |
6 | 54.62 | 37.12 | −43.97 | −11.93 |
7 | 55.55 | 38.97 | −44.24 | −12.46 |
8 | 54.57 | 37.68 | −44.56 | −12.67 |
9 | 55.85 | 39.87 * | −43.64 | −11.62 |
Optimum | A2B2C3D1 | A3B3C2D1 | A2B2C3D1 | A1B3C3D3 |
Exp No. | Normalization | Grey Relational Coefficient | GRG | Rank | W-GRG | Rank | ||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
TS | IE | H | AD | TS | IE | H | AD | |||||
1 | 0.00 | 0.00 | 0.40 | 0.46 | 0.33 | 0.33 | 0.46 | 0.48 | 0.400 | 9 | 0.408 | 9 |
2 | 0.41 | 0.13 | 0.29 | 0.31 | 0.46 | 0.36 | 0.41 | 0.42 | 0.414 | 8 | 0.419 | 8 |
3 | 0.83 | 0.31 | 0.29 | 0.00 | 0.75 | 0.42 | 0.41 | 0.33 | 0.479 | 6 | 0.485 | 6 |
4 | 0.33 | 0.26 | 0.79 | 1.00 | 0.43 | 0.40 | 0.70 | 1.00 | 0.633 | 4 | 0.661 | 3 |
5 | 1.00 | 0.67 | 0.00 | 0.02 | 1.00 | 0.61 | 0.33 | 0.34 | 0.569 | 5 | 0.565 | 5 |
6 | 0.52 | 0.30 | 0.40 | 0.37 | 0.51 | 0.42 | 0.46 | 0.44 | 0.455 | 7 | 0.459 | 7 |
7 | 0.81 | 0.77 | 0.68 | 0.73 | 0.72 | 0.69 | 0.61 | 0.65 | 0.665 | 2 | 0.664 | 2 |
8 | 0.50 | 0.44 | 1.00 | 0.87 | 0.50 | 0.47 | 1.00 | 0.79 | 0.689 | 1 | 0.712 | 1 |
9 | 0.90 | 1.00 | 0.06 | 0.16 | 0.83 | 1.00 | 0.35 | 0.37 | 0.638 | 3 | 0.598 | 4 |
Parameters | Average of GRG | Average of W-GRG | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
Levels | Delta | Rank | Levels | Delta | Rank | |||||
1 | 2 | 3 | 1 | 2 | 3 | |||||
GA | 0.431 | 0.552 | 0.664 * | 0.2334 | 1 | 0.437 | 0.561 | 0.658 * | 0.220 | 1 |
PHT | 0.566 * | 0.557 | 0.524 | 0.0423 | 4 | 0.577 * | 0.566 | 0.514 | 0.063 | 3 |
ED | 0.515 | 0.562 | 0.571 * | 0.0564 | 3 | 0.526 | 0.560 | 0.571 * | 0.063 | 4 |
RG | 0.535 | 0.511 | 0.601 * | 0.0893 | 2 | 0.524 | 0.514 | 0.619 * | 0.105 | 2 |
Response Variable | Contribution |
---|---|
Tensile Strength | 0.2777 |
Impact Energy | 0.1672 |
Hardness | 0.2714 |
Angular Distortion | 0.2840 |
Initial Condition A2B2C3D2 | Confirmatory Experiment Results | Improvement from Initial Condition (%) | |
---|---|---|---|
GRG/W-GRA | GRG/W-GRA | ||
Tensile Strength (MPa) | 545.6 | 675.5 | 23.80 |
Impact Energy (J) | 60.76 | 99.88 | 64.38 |
Hardness (HB) | 166 | 161 | 3.01 |
Angular Distortion (θ) | 4.2 | 3.9 | 7.14 |
Optimal Condition | - | A3B1C3D3 | |
Grey Relational Grade | 0.5417 | 0.7645 |
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Qazi, M.I.; Akhtar, R.; Abas, M.; Khalid, Q.S.; Babar, A.R.; Pruncu, C.I. An Integrated Approach of GRA Coupled with Principal Component Analysis for Multi-Optimization of Shielded Metal Arc Welding (SMAW) Process. Materials 2020, 13, 3457. https://doi.org/10.3390/ma13163457
Qazi MI, Akhtar R, Abas M, Khalid QS, Babar AR, Pruncu CI. An Integrated Approach of GRA Coupled with Principal Component Analysis for Multi-Optimization of Shielded Metal Arc Welding (SMAW) Process. Materials. 2020; 13(16):3457. https://doi.org/10.3390/ma13163457
Chicago/Turabian StyleQazi, Mohsin Iqbal, Rehman Akhtar, Muhammad Abas, Qazi Salman Khalid, Abdur Rehman Babar, and Catalin Iulian Pruncu. 2020. "An Integrated Approach of GRA Coupled with Principal Component Analysis for Multi-Optimization of Shielded Metal Arc Welding (SMAW) Process" Materials 13, no. 16: 3457. https://doi.org/10.3390/ma13163457
APA StyleQazi, M. I., Akhtar, R., Abas, M., Khalid, Q. S., Babar, A. R., & Pruncu, C. I. (2020). An Integrated Approach of GRA Coupled with Principal Component Analysis for Multi-Optimization of Shielded Metal Arc Welding (SMAW) Process. Materials, 13(16), 3457. https://doi.org/10.3390/ma13163457