1 Introduction
2 Related work
2.1 CNC milling process optimization
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Multi-response models are being considered for the CNC milling, where Ra, MRR, cutting forces, vibration, energy consumptions, etc., are considered as the process responses [20].
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Some multi-response models are solved using the GRA or fuzzy-GRA-based single-objective techniques. The multiple regression, RSM, MLP, RBF, etc., are used for predictive modeling of process response [32].
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Metaheuristic algorithms such as the GA, PSO, and ACO are used as the optimization tools. Mostly mathematical formulations are being used as the objective functions. Limited studies could be seen, where response surface or regression equations are used as the objective functions [21].
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In true sense, the surrogate-assisted optimization (the deep learning and metaheuristic algorithms in combined form) has not yet been utilized for the manufacturing process optimization.
2.2 Surrogate-assisted optimization
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Surrogate-assisted optimization is useful for computationally expensive and many-objective optimization problems. These problems are based on real-world data, which are not readily available in the literature. Therefore, this area of research is less explored [44].
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Different surrogate models are available in literature such as GP, kriging, and RBF for the surrogate-assisted optimization. Many other predictive models, such as MLP, BRNN, SVM, decision tree, Gaussian kernel, and deep belief network, could also be explored for the surrogate-assisted optimization [42].
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Metaheuristic techniques are being evolved every day. Recently, researchers exhibit great enthusiasm in transforming bionic phenomenon into the computer algorithm. As a result, various new and promising methods have appeared, such as the grey wolf optimization (GWO), African buffalo optimization (ABO), beetle antennae search (BAS) algorithm, ant-lion optimization (ALO), Harris hawks optimization algorithm (HHO), the grasshopper optimization algorithm (GOA), and the multi-verse optimization algorithm (MVO) [45‐49]. These latest methodologies are capable enough to outperform popular EAs and these are not much exploited for the surrogate-assisted optimization. Hence, a missing link exists between the deep learning and bio-inspired metaheuristic research, which is an innovation issue. This further shows immense research scope on the hybridization of methodologies.
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Many different real-world problems are considered for the surrogate-assisted optimization. However, manufacturing or machining processes are not very popular yet for the said purpose. The reason could be that the manufacturing researchers have not yet shown their interest in the said approaches, or some communication gap exists among machine learning, optimization, and manufacturing researchers.
3 Experimental setup and materials
3.1 Materials
Tensile strength | Yield strength | Shear strength | Elastic modulus | Poisson’s ratio | Elongation |
---|---|---|---|---|---|
150 MPa | 130 MPa | 97 MPa | 70–80 GPa | 0.33 | 7% |
3.2 Experiments
Factors | Units | Level 1 | Level 2 | Level 3 | Level 4 |
---|---|---|---|---|---|
Codes | 1 | 2 | 3 | 4 | |
TD | mm | 6 | 7 | 8 | 10 |
SS | Rpm | 1500 | 1750 | 2000 | 2250 |
FR | mm/s | 2 | 3 | 4 | 5 |
DOC | mm | 0.5 | 1.0 | 1.5 | 2.0 |
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The MRR is directly correlated and proportionate with the TD and DOC. This means the higher is the TD and DOC scores, the better is the MRR score, whereas the SS and FR are inversely related to the MRR, i.e., the MRR score is higher at the low-level settings of the SS and FR. MRR is dependent mostly on DOC and FR. Hence, a higher DOC indicates lower FR to achieve a level of MRR. Furthermore, the low FR demands lower SS in order to improve the tool life [15]. Therefore, the ideal setting for the MRR is TD4-SS1-FR3-DOC4 which produces better mean value for MRR (Fig. 5).
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Three cutting force components (Fx, Fy, and Fz) change their values abruptly with small changes on parameters. For the Fx, TD4-SS4-FR2-DOC1 would be the ideal setting, and for the Fy, TD2-SS2-FR1-DOC1 yields best result, whereas for the Fz, TD4-SS2-FR1-DOC1 is the optimal combination. It could be concluded that determining the exact levels of the process parameters is a combinatorial task while attaining the near-optimal force components together with the MRR and Ra.
Ex# | TD | SS | FR | DOC | MRR (mm3/s) | Ra (μm) | Fx (N) | Fy (N) | Fz (N) |
---|---|---|---|---|---|---|---|---|---|
1 | 6 | 1500 | 2 | 0.5 | 5.263 | 0.08 | 1.115 | 3.081 | 11.44 |
2 | 6 | 1750 | 3 | 1 | 11.080 | 0.06 | 1.079 | 4.047 | 10.7 |
3 | 6 | 2000 | 4 | 1.5 | 18.100 | 0.06 | 0.391 | 0.586 | 0.171 |
4 | 6 | 2250 | 5 | 2 | 7.299 | 0.05 | 0.662 | 0.2448 | 0.0287 |
5 | 7 | 1500 | 3 | 1.5 | 6.652 | 0.29 | 1.546 | 4.342 | 12.35 |
6 | 7 | 1750 | 2 | 2 | 20.690 | 0.25 | 0.138 | 6.675 | 12.72 |
7 | 7 | 2000 | 5 | 0.5 | 5.848 | 0.05 | 1.148 | 3.719 | 13.49 |
8 | 7 | 2250 | 4 | 1 | 18.018 | 0.04 | 1.401 | 2.158 | 6.924 |
9 | 8 | 1500 | 4 | 2 | 41.379 | 0.18 | 0.1233 | 0.0195 | 7.094 |
10 | 8 | 1750 | 5 | 1.5 | 20.000 | 0.22 | 0.1333 | 0.5187 | 7.368 |
11 | 8 | 2000 | 2 | 1 | 13.043 | 0.29 | 0.079 | 0.579 | 7.45 |
12 | 8 | 2250 | 3 | 0.5 | 7.477 | 0.62 | 0.703 | 0.643 | 7.585 |
13 | 10 | 1500 | 5 | 1 | 25.641 | 0.075 | 1.09 | 1.823 | 11.755 |
14 | 10 | 1750 | 4 | 0.5 | 6.390 | 0.27 | 1.1225 | 2.038 | 11.884 |
15 | 10 | 2000 | 3 | 2 | 40.000 | 0.89 | 1.103 | 2.05 | 12.096 |
16 | 10 | 2250 | 2 | 1.5 | 24.390 | 0.72 | 1.181 | 1.99 | 12.198 |
3.3 KSOM analysis
4 Research methodologies
4.1 Taguchi’s OAD coupled with grey relational analysis
4.2 Taguchi’s OAD coupled with VIKOR method
4.3 BRNN-BSA technique
4.3.1 BRNN model
4.3.2 BAS algorithm
4.3.3 Performance metric
4.4 Regression model-assisted BAS technique
MRR | Ra | Fx | Fy | Fz | ||
---|---|---|---|---|---|---|
p values for decision variables | TD | 0.022 | 0.001 | 0.637 | 0.452 | 0.053 |
SS | 0.530 | 0.055 | 0.923 | 0.266 | 0.077 | |
FR | 0.947 | 0.011 | 0.972 | 0.163 | 0.115 | |
DOC | 0.005 | 0.193 | 0.192 | 0.874 | 0.179 | |
R2 | 64.69%* | 75.66%* | 16.54%§§ | 27.85%§§ | 55.08%* |
5 Results and discussions
5.1 GRA analysis
Normalized responses | Deviation sequence | GRC | GRG | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
MRR | Ra | Fx | Fy | Fz | MRR | Ra | Fx | Fy | Fz | MRR | Ra | Fx | Fy | Fz | |
0.000 | 0.953 | 0.294 | 0.540 | 0.152 | 1.000 | 0.047 | 0.706 | 0.460 | 0.848 | 0.333 | 0.914 | 0.415 | 0.521 | 0.371 | 0.5107 |
0.161 | 0.976 | 0.318 | 0.395 | 0.207 | 0.839 | 0.024 | 0.682 | 0.605 | 0.793 | 0.373 | 0.955 | 0.423 | 0.452 | 0.387 | 0.5182 |
0.355 | 0.976 | 0.787 | 0.915 | 0.989 | 0.645 | 0.024 | 0.213 | 0.085 | 0.011 | 0.437 | 0.955 | 0.702 | 0.855 | 0.979 | 0.7855 |
0.056 | 0.988 | 0.603 | 0.966 | 1.000 | 0.944 | 0.012 | 0.397 | 0.034 | 0.000 | 0.346 | 0.977 | 0.557 | 0.937 | 1.000 | 0.7634 |
0.038 | 0.706 | 0.000 | 0.351 | 0.085 | 0.962 | 0.294 | 1.000 | 0.649 | 0.915 | 0.342 | 0.630 | 0.333 | 0.435 | 0.353 | 0.4187 |
0.427 | 0.753 | 0.960 | 0.000 | 0.057 | 0.573 | 0.247 | 0.040 | 1.000 | 0.943 | 0.466 | 0.669 | 0.926 | 0.333 | 0.347 | 0.5482 |
0.016 | 0.988 | 0.271 | 0.444 | 0.000 | 0.984 | 0.012 | 0.729 | 0.556 | 1.000 | 0.337 | 0.977 | 0.407 | 0.474 | 0.333 | 0.5056 |
0.353 | 1.000 | 0.099 | 0.679 | 0.488 | 0.647 | 0.000 | 0.901 | 0.321 | 0.512 | 0.436 | 1.000 | 0.357 | 0.609 | 0.494 | 0.5791 |
1.000 | 0.835 | 0.970 | 1.000 | 0.475 | 0.000 | 0.165 | 0.030 | 0.000 | 0.525 | 1.000 | 0.752 | 0.943 | 1.000 | 0.488 | 0.8366 |
0.408 | 0.788 | 0.963 | 0.925 | 0.455 | 0.592 | 0.212 | 0.037 | 0.075 | 0.545 | 0.458 | 0.702 | 0.931 | 0.870 | 0.478 | 0.6879 |
0.215 | 0.706 | 1.000 | 0.916 | 0.449 | 0.785 | 0.294 | 0.000 | 0.084 | 0.551 | 0.389 | 0.630 | 1.000 | 0.856 | 0.476 | 0.6701 |
0.061 | 0.318 | 0.575 | 0.906 | 0.439 | 0.939 | 0.682 | 0.425 | 0.094 | 0.561 | 0.348 | 0.423 | 0.540 | 0.842 | 0.471 | 0.5248 |
0.564 | 0.959 | 0.311 | 0.729 | 0.129 | 0.436 | 0.041 | 0.689 | 0.271 | 0.871 | 0.534 | 0.924 | 0.420 | 0.649 | 0.365 | 0.5784 |
0.031 | 0.729 | 0.289 | 0.697 | 0.119 | 0.969 | 0.271 | 0.711 | 0.303 | 0.881 | 0.340 | 0.649 | 0.413 | 0.622 | 0.362 | 0.4773 |
0.962 | 0.000 | 0.302 | 0.695 | 0.104 | 0.038 | 1.000 | 0.698 | 0.305 | 0.896 | 0.929 | 0.333 | 0.417 | 0.621 | 0.358 | 0.5318 |
0.530 | 0.200 | 0.249 | 0.704 | 0.096 | 0.470 | 0.800 | 0.751 | 0.296 | 0.904 | 0.515 | 0.385 | 0.400 | 0.628 | 0.356 | 0.4567 |
(a) | (b) | ||||||||
---|---|---|---|---|---|---|---|---|---|
Level | TD | SS | FR | DOC | Level | TD | SS | FR | DOC |
1 | 0.6444 | 0.5867 | 0.5473 | 0.5046 | 1 | 0.7892 | 0.6167 | 0.8092 | 0.9253 |
2 | 0.5132 | 0.5592 | 0.4994 | 0.5869 | 2 | 0.8529 | 0.7895 | 0.9293 | 0.7278 |
3 | 0.6812 | 0.6246 | 0.6699 | 0.5896 | 3 | 0.5852 | 0.8084 | 0.5670 | 0.7667 |
4 | 0.5138 | 0.5821 | 0.6360 | 0.6714 | 4 | 0.8050 | 0.8177 | 0.7269 | 0.6125 |
Delta | 0.1680 | 0.0654 | 0.1705 | 0.1667 | Delta | 0.2678 | 0.2010 | 0.3623 | 0.3128 |
Rank | 2 | 4 | 1 | 3 | Rank | 3 | 4 | 1 | 2 |
Source | DF | Seq. SS | Contribution | Adj. SS | Adj. MS | F value | R-Sq | R-Sq (adj.) |
---|---|---|---|---|---|---|---|---|
TD (mm) | 3 | 0.09189 | 39.44% | 0.09189 | 0.03063 | 2.61 | 39.44% | 24.31% |
SS (rpm) | 3 | 0.008818 | 3.79% | 0.008818 | 0.002939 | 0.16 | 3.79% | 0.00% |
FR (mm/s) | 3 | 0.07405 | 31.79% | 0.07405 | 0.02468 | 1.86 | 31.79% | 14.73% |
DOC (mm) | 3 | 0.05562 | 23.88% | 0.05562 | 0.01854 | 1.25 | 23.88% | 4.84% |
Error | 12 | 0.1754 | 75.28% | 0.1754 | 0.0146 | |||
Total | 15 | 0.23296 | 100.00% |
5.2 VIKOR analysis
Normalized decision matrix | Utility measure for individual response | Si | Ri | Qi | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
MRR | Ra | Fx | Fy | Fz | MRR | Ra | Fx | Fy | Fz | |||
0.3411 | 0.0044 | 0.3290 | 0.8496 | 3.2906 | 0.3500 | 0.0021 | 0.0519 | 0.0213 | 0.0719 | 0.4972 | 0.3500 | 0.9009 |
1.5119 | 0.0025 | 0.3081 | 1.4659 | 2.8787 | 0.3302 | 0.0009 | 0.0486 | 0.0368 | 0.0629 | 0.4794 | 0.3302 | 0.8545 |
4.0342 | 0.0025 | 0.0405 | 0.0307 | 0.0007 | 0.2877 | 0.0009 | 0.0062 | 0.0008 | 0.0000 | 0.2955 | 0.2877 | 0.6267 |
0.6561 | 0.0017 | 0.1160 | 0.0054 | 0.0000 | 0.3447 | 0.0004 | 0.0181 | 0.0001 | 0.0000 | 0.3633 | 0.3447 | 0.7748 |
0.5449 | 0.0580 | 0.6325 | 1.6874 | 3.8349 | 0.3466 | 0.0365 | 0.1000 | 0.0423 | 0.0838 | 0.6092 | 0.3466 | 0.9941 |
5.2715 | 0.0431 | 0.0050 | 3.9879 | 4.0682 | 0.2668 | 0.0270 | 0.0005 | 0.1000 | 0.0889 | 0.4832 | 0.2668 | 0.7595 |
0.4211 | 0.0017 | 0.3487 | 1.2379 | 4.5756 | 0.3486 | 0.0004 | 0.0550 | 0.0310 | 0.1000 | 0.5351 | 0.3486 | 0.9321 |
3.9980 | 0.0011 | 0.5194 | 0.4168 | 1.2054 | 0.2883 | 0.0000 | 0.0821 | 0.0105 | 0.0263 | 0.4072 | 0.2883 | 0.7259 |
21.0860 | 0.0223 | 0.0040 | 0.0000 | 1.2653 | 0.0000 | 0.0136 | 0.0004 | 0.0000 | 0.0277 | 0.0417 | 0.0277 | 0.0000 |
4.9259 | 0.0334 | 0.0047 | 0.0241 | 1.3650 | 0.2726 | 0.0207 | 0.0005 | 0.0006 | 0.0298 | 0.3243 | 0.2726 | 0.6287 |
2.0951 | 0.0580 | 0.0017 | 0.0300 | 1.3955 | 0.3204 | 0.0365 | 0.0000 | 0.0008 | 0.0305 | 0.3882 | 0.3204 | 0.7590 |
0.6884 | 0.2649 | 0.1308 | 0.0370 | 1.4466 | 0.3441 | 0.1695 | 0.0205 | 0.0009 | 0.0316 | 0.5666 | 0.3441 | 0.9529 |
8.0965 | 0.0039 | 0.3144 | 0.2975 | 3.4743 | 0.2192 | 0.0018 | 0.0496 | 0.0075 | 0.0759 | 0.3539 | 0.2192 | 0.5718 |
0.5028 | 0.0502 | 0.3334 | 0.3718 | 3.5510 | 0.3473 | 0.0316 | 0.0526 | 0.0093 | 0.0776 | 0.5184 | 0.3473 | 0.9152 |
19.7037 | 0.5459 | 0.3219 | 0.3761 | 3.6788 | 0.0233 | 0.3500 | 0.0508 | 0.0094 | 0.0804 | 0.5139 | 0.3500 | 0.9156 |
7.3259 | 0.3573 | 0.3691 | 0.3544 | 3.7411 | 0.2322 | 0.2288 | 0.0582 | 0.0089 | 0.0818 | 0.6099 | 0.2322 | 0.8172 |
Source | DF | Seq. SS | Contribution | Adj. SS | Adj. MS | F value | R-Sq | R-Sq(adj.) |
---|---|---|---|---|---|---|---|---|
TD (mm) | 3 | 0.1683 | 19.77% | 0.1683 | 0.05609 | 0.99 | 19.77% | 0.00% |
SS (rpm) | 3 | 0.1082 | 12.71% | 0.1082 | 0.03608 | 0.58 | 12.71% | 0.00% |
FR mm/s | 3 | 0.2776 | 32.61% | 0.2776 | 0.09255 | 1.94 | 32.61% | 15.77% |
DOC (mm) | 3 | 0.2006 | 23.56% | 0.2006 | 0.06686 | 1.23 | 23.56% | 4.45% |
Error | 12 | 0.66265 | 77.84% | 0.66265 | 0.05522 | |||
Total | 15 | 0.8513 | 100.00% |
5.3 BRNN-BAS and regression-BAS comparison
5.4 Confirmatory test
GRA method | VIKOR method | Regression-BAS | BRNN-BAS | |||||
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Parameters | TD = 8, SS = 2000, FR = 4, DOC = 2 | TD = 7, SS = 2250, FR = 3, DOC = 0.5 | TD = 10, SS = 1876, FR = 5, DOC = 1.93 | TD = 10, SS = 1646, FR = 4.66, DOC = 1.54 | ||||
Predicted | Experimental | Predicted | Experimental | Predicted | Experimental | Predicted | Experimental | |
MRR | 17.69 | 6.49 | 33.73 | 29.822 | 46.027 | 42.042** | ||
Ra | 0.78 | 0.52 | 0.412 | 0.561 | 0.1652 | 0.4651** | ||
Fx | 0.009 | 0.03616 | 0.697 | 0.749 | 0.7823 | 0.7973 | ||
Fy | 0.0527 | 0.04776 | 0.655 | 2.127 | 2.826 | 2.547 | ||
Fz | 0.0128 | 0.03387 | 8.455 | 9.212 | 10.8195 | 2.3727 | ||
GRG/VIKOR index/obj. value | 0.8826 | 0.7791 | 1.2509 | 0.8687 | − 4.7018 | − 3.4346 | − 6.2868 | − 7.172 |
6 Conclusions
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AA3105 shows substantially good machining properties under the end milling on the Proxxon FF 500 BL CNC with proper settings of the parameters. The ideal settings for the parameters are found to be (TD = 10 mm, SS = 1646 rpm, FR = 4.66 mm/s, and DOC = 1.54 mm).
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The ANOVA and response surface plots depict that the FR is the most influential and SS is the least influential process parameters.
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The improved GRG, VIKOR index, and objective values for both the BAS algorithms could be extremely helpful in minimizing the cost of manufacturing, which could improve the machining quality.
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Probabilistic BRNN shows good performance curve and regression fit, which is comparable with the other predictive functions, such as the MLP, RBF, SVM, and Gaussian kernels. The BAS algorithm portrays its capability to obtain the near-optimal solutions promptly while coupled with the trained surrogate.
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The BRNN-BAS technique shows its superior ability to optimize the machining process while compared with the heavily exploited GRA and VIKOR methods and regression-driven BAS algorithm. The BRNN-BAS is shown to outperform all the techniques by obtaining 40.98% improved MRR and 10.56% improved Ra values.