Abstract
To apply laser forming process in reality, it is required to know the relationships between the deformed shape and scanning paths along with heating conditions. The deformation due to laser scanning depends on various factors, namely laser power, scan speed, spot diameter, scan position, number of scans, and many others. This article presents soft computing-based methods to predict deformations for a set of heating conditions, and also to determine the heating lines and heat conditions, in order to get a desired shape (i.e., inverse analysis). A novel attempt has been made in this paper to carry out analysis and synthesis (inverse analysis) of laser forming process using both genetic-neural network (GA-NN) and genetic adaptive neuro-fuzzy inference system (GA-ANFIS). During the analysis, laser power, scan speed, spot diameter, scan position and number of scans are taken as inputs and bending angle is considered as the output. A batch mode of training has been used for both the approaches with the help of some experimental data. The performances of the developed approaches have been tested on some real experimental data. Both the approaches are found to be effective to predict the bending angles and carry out the process synthesis successfully. GA-NN approach is found to perform better than the GA-ANFIS approach in predicting the bending angles, and both the approaches are able to provide comparable predictions in inverse analysis.
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References
Akbilgic O, Bozdogan H (2011) Predictive subset selection using regression trees and RBF neural networks hybridized with the genetic algorithm. Eur J Pure Appl Math 4(4):467–485
Carlone P, Palazzo GS, Pasquino R (2008) Inverse analysis of the laser forming process by computational modeling and methods. Comput Math Appl 55:2018–2032
Casalino G, Ludovico AD (2002) Parameter selection by an artificial neural network for a laser bending process. IMechE Part B J Eng Manuf 216:1517–1520
Chen DJ, Xiang YB, Wu SC, Li MQ (2002) Application of fuzzy neural network to laser bending process of sheet metal. Mater Sci Technol 18:677–680
Cheng PJ, Lin SC (2000) Using neural networks to predict bending angle of sheet metal formed by laser. Int J Mach Tools Manuf 40:1185–1197
Cheng PJ, Lin SC (2001) An analytical model to estimate angle formed by laser. J Mater Process Technol 108:314–319
Cheng JG, Yao YL (2004) Process synthesis of laser forming by genetic algorithm. Int J Mach Tools Manuf 44:1619–1628
Dragos V, Dan V, Kovacevic R (2000) Prediction of the laser sheet bending using neural network. In: IEEE international symposium on circuits and systems, pp 686–689
Du Y, Wang X (2010) Improved BP network to predict bending angle in the laser bending process for sheet metal. In: International conference on intelligent system design and engineering application, Cairo, Egypt, pp 839–843
Gisario A, Barletta M, Conti C, Guarino S (2011) Springback control in sheet metal bending by laser-assisted bending: experimental analysis, empirical and neural network modeling. Opt Lasers Eng 49:1372–1383
Griffiths J, Edwardson SP, Dearden G, Watkins KG (2010) Finite element modeling of laser forming at macro and micro scales. Phys Procedia 5:371–380
Guarino S, Ucciardello N, Tagliaferri V (2007) An application of neural network solutions to modeling of diode laser assisted forming process of AA6082 thin sheets. Key Eng Mater 344:325–332
Herrera F, Lozano M, Verdegay JL (1995) Tuning fuzzy logic controllers by genetic algorithms. Int J Approx Reason 12:293–315
Hu Z, Labudovic M, Wang H, Kovacevic R (2001) Computer simulation and experimental investigation of sheet metal bending using laser beam scanning. Int J Mach Tools Manuf 41:589–607
Hu J, Dang D, Shen H, Zhang Z (2012) A finite element model using multi-layered shell element in laser forming. Opt Laser Technol 44:1148–1155
Jang JSR (1993) ANFIS: adaptive-network-based fuzzy inference system. IEEE Trans Syst Man Cybern 23(3):665–685
Keller JM, Yager RR, Tahani H (1992) Neural nework implementation of fuzzy logic. Fuzzy Sets Syst 45(1):1–12
Khashei M, Bijari M (2010) An artificial neural network (p, d, q) model for time series forecasting. Expert Syst Appl 37:479–489
Kuo HC, Wu LJ (2002) Automation of heat bending in shipbuilding. Comput Ind 48:127–142
Kyrsanidi AK, Kermanidis TB, Pantelakis SG (2000) An analytical model for the prediction of distortions caused by the laser forming process. J Mater Process Technol 104:94–102
Liu C, Yao YL (2002) Optimal and robust design of the laser forming process. J Manuf Processes 4:52–66
Maji K, Pratihar DK (2010) Forward and reverse mappings of electrical discharge machining process using adaptive network-based fuzzy inference system. Expert Syst Appl 37:8566–8574
Maji K, Pratihar DK, Nath AK (2012) Experimental investigations, modeling and optimization of multi-scan laser forming of AISI 304 stainless steel sheet. Int J Adv Manuf Technol (under review)
Martino FD, Loia V, Sessa S (2010) Fuzzy transforms method and attribute dependency in data analysis. Inf Sci 180:493–505
Martino FD, Loia V, Sessa S (2011) Fuzzy transforms method in prediction data analysis. Fuzzy Sets Syst 180:146–163
Montgomery DC (2001) Design and analysis of experiments. Wiley, New York
Nasrabadi E, Hashemi SM (2008) Robust fuzzy regression analysis using neural networks. Int J Uncertain Fuzziness Knowl Based Syst 16(4):579–598
Nguyen TT, Yang YS, Bae KY, Choi SN (2009) Prediction of deformations of steel plate by artificial neural network in forming process with induction heating. J Mech Sci Technol 23:1211–1221
Pratihar DK (2008) Soft computing. Narosa Publishing House, New Delhi
Pratihar DK, Deb K, Ghosh A (1999) A genetic-fuzzy approach for mobile robot navigation among moving obstacles. Int J Approx Reason 20:145–172
Shen H, Vollertsen F (2009) Modeling of laser forming—a review. Comput Mater Sci 46:834–840
Shen H, Shi Y, Yao Z, Hu J (2006a) An analytical model for estimating deformation in laser forming. Comput Mater Sci 37:593–598
Shen H, Shi YJ, Yao ZQ, Hu J (2006b) Fuzzy logic model for bending angle in laser forming. Mater Sci Technol 22:981–986
Vollertsen F (1994) An analytical model for laser bending. Lasers Eng 2:261–276
Vollertsen F, Geiger M, Li WM (1993) FDM-and FEM simulation of laser forming: a comparative study. In: Proceedings of the fourth international conference on technology of plasticity, pp 1793–1798
Wang X, Xu W, Chen H, Wang J (2008) Parameter prediction in laser bending of aluminum alloy sheet. Front Mech Eng China 3(3):293–298
Whitley D, Starkweather T, Bogart C (1990) Genetic algorithms and neural networks: optimizing connections and connectivity. Parallel Comput 14:347–361
Wu S, Ji Z (2002) FEM simulation of the deformation field during the laser forming of sheet metal. J Mater Process Technol 121:269–272
Zhang L, Michaleris P (2004) Investigation of Lagrangian and Eulerian finite element methods for modeling the laser forming process. Finite Element Anal Des 40:383–405
Zhang P, Guo B, Shan DB, Ji Z (2007) FE simulation of laser curve bending of sheet metals. J Mater Process Technol 184:157–162
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Appendices
Appendix A: Experimental data collected according to CCD to develop the model of bending angle
SL. no. | Input parameters | Output: bending angle (°) | ||||||
---|---|---|---|---|---|---|---|---|
p (W) | v (mm/s) | d (mm) | r | n | A 1 | A 2 | A 3 | |
1 | 225 | 250.0 | 0.500 | 0.25 | 5 | 4.81 | 5.34 | 5.07 |
2 | 275 | 250.0 | 0.500 | 0.25 | 5 | 6.71 | 6.61 | 6.82 |
3 | 225 | 283.0 | 0.500 | 0.25 | 5 | 4.06 | 4.52 | 3.76 |
4 | 275 | 283.0 | 0.500 | 0.25 | 5 | 4.56 | 4.20 | 5.00 |
5 | 225 | 250.0 | 0.750 | 0.25 | 5 | 3.97 | 3.74 | 3.55 |
6 | 275 | 250.0 | 0.750 | 0.25 | 5 | 5.69 | 5.85 | 6.04 |
7 | 225 | 283.0 | 0.750 | 0.25 | 5 | 2.14 | 1.95 | 2.18 |
8 | 275 | 283.0 | 0.750 | 0.25 | 5 | 6.45 | 6.29 | 6.68 |
9 | 225 | 250.0 | 0.500 | 0.75 | 5 | 4.12 | 4.21 | 4.19 |
10 | 275 | 250.0 | 0.500 | 0.75 | 5 | 4.41 | 4.73 | 4.56 |
11 | 225 | 283.0 | 0.500 | 0.75 | 5 | 2.22 | 2.27 | 2.17 |
12 | 275 | 283.0 | 0.500 | 0.75 | 5 | 5.05 | 4.95 | 5.00 |
13 | 225 | 250.0 | 0.750 | 0.75 | 5 | 3.56 | 3.63 | 3.73 |
14 | 275 | 250.0 | 0.750 | 0.75 | 5 | 6.12 | 6.23 | 5.94 |
15 | 225 | 283.0 | 0.750 | 0.75 | 5 | 1.74 | 1.58 | 1.66 |
16 | 275 | 283.0 | 0.750 | 0.75 | 5 | 3.89 | 4.08 | 4.20 |
17 | 225 | 250.0 | 0.500 | 0.25 | 15 | 11.30 | 11.50 | 11.06 |
18 | 275 | 250.0 | 0.500 | 0.25 | 15 | 15.21 | 14.47 | 14.83 |
19 | 225 | 283.0 | 0.500 | 0.25 | 15 | 8.58 | 8.65 | 8.79 |
20 | 275 | 283.0 | 0.500 | 0.25 | 15 | 13.00 | 12.40 | 12.80 |
21 | 225 | 250.0 | 0.750 | 0.25 | 15 | 8.07 | 8.28 | 7.90 |
22 | 275 | 250.0 | 0.750 | 0.25 | 15 | 15.47 | 15.28 | 15.40 |
23 | 225 | 283.0 | 0.750 | 0.25 | 15 | 7.16 | 7.21 | 7.26 |
24 | 275 | 283.0 | 0.750 | 0.25 | 15 | 12.24 | 12.47 | 11.93 |
25 | 225 | 250.0 | 0.500 | 0.75 | 15 | 11.70 | 11.06 | 11.25 |
26 | 275 | 250.0 | 0.500 | 0.75 | 15 | 14.20 | 14.34 | 14.47 |
27 | 225 | 283.0 | 0.500 | 0.75 | 15 | 9.48 | 9.54 | 9.36 |
28 | 275 | 283.0 | 0.500 | 0.75 | 15 | 12.53 | 12.46 | 12.5 |
29 | 225 | 250.0 | 0.750 | 0.75 | 15 | 7.98 | 8.09 | 8.28 |
30 | 275 | 250.0 | 0.750 | 0.75 | 15 | 15.20 | 15.28 | 15.10 |
31 | 225 | 283.0 | 0.750 | 0.75 | 15 | 6.46 | 6.30 | 6.38 |
32 | 275 | 283.0 | 0.750 | 0.75 | 15 | 12.25 | 12.31 | 12.37 |
33 | 225 | 266.5 | 0.625 | 0.50 | 10 | 6.33 | 6.45 | 6.21 |
34 | 275 | 266.5 | 0.625 | 0.50 | 10 | 11.13 | 10.84 | 10.95 |
35 | 250 | 250.0 | 0.625 | 0.50 | 10 | 8.87 | 8.95 | 9.04 |
36 | 250 | 283.0 | 0.625 | 0.50 | 10 | 8.67 | 8.84 | 8.56 |
37 | 250 | 266.5 | 0.500 | 0.50 | 10 | 9.30 | 8.78 | 9.02 |
38 | 250 | 266.5 | 0.750 | 0.50 | 10 | 7.44 | 7.75 | 8.35 |
39 | 250 | 266.5 | 0.625 | 0.25 | 10 | 8.88 | 9.00 | 8.60 |
40 | 250 | 266.5 | 0625 | 0.75 | 10 | 9.25 | 8.78 | 8.97 |
41 | 250 | 266.5 | 0.625 | 0.50 | 5 | 4.60 | 4.85 | 5.08 |
42 | 250 | 266.5 | 0.625 | 0.50 | 15 | 13.67 | 13.80 | 13.56 |
43 | 250 | 266.5 | 0.625 | 0.50 | 10 | 9.24 | 9.13 | 9.19 |
Appendix B: Data collected for testing the models of bending angle
SL. no. | Input parameters | Output: bending angle | ||||
---|---|---|---|---|---|---|
p (W) | v (mm/s) | d (mm) | r | n | A (°) | |
1 | 230 | 258.33 | 0.550 | 0.30 | 6 | 5.93 |
2 | 270 | 275.00 | 0.700 | 0.60 | 6 | 5.82 |
3 | 240 | 275.00 | 0.550 | 0.40 | 8 | 6.37 |
4 | 260 | 258.33 | 0.700 | 0.70 | 14 | 11.85 |
5 | 240 | 258.33 | 0.700 | 0.70 | 8 | 5.72 |
6 | 230 | 275.00 | 0.550 | 0.40 | 6 | 5.91 |
7 | 270 | 258.33 | 0.550 | 0.60 | 8 | 8.18 |
8 | 240 | 275.00 | 0.700 | 0.30 | 14 | 8.93 |
9 | 270 | 275.00 | 0.700 | 0.30 | 6 | 6.95 |
10 | 260 | 258.33 | 0.550 | 0.40 | 8 | 8.29 |
11 | 230 | 258.33 | 0.550 | 0.70 | 12 | 8.70 |
12 | 240 | 275.00 | 0.700 | 0.60 | 14 | 8.41 |
13 | 230 | 258.33 | 0.550 | 0.30 | 12 | 8.61 |
14 | 260 | 258.33 | 0.700 | 0.40 | 6 | 6.08 |
15 | 270 | 275.00 | 0.550 | 0.60 | 12 | 10.48 |
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Maji, K., Pratihar, D.K. & Nath, A.K. Analysis and synthesis of laser forming process using neural networks and neuro-fuzzy inference system. Soft Comput 17, 849–865 (2013). https://doi.org/10.1007/s00500-012-0949-7
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DOI: https://doi.org/10.1007/s00500-012-0949-7