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Nature-Inspired Optimization Algorithm-Tuned Feed-Forward and Recurrent Neural Networks Using CFD-Based Phenomenological Model-Generated Data to Model the EBW Process

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Abstract

To automate the electron beam welding process, the identification of its contributing parameters is a must, for which it is required to establish the input–output correlations in both forward and reverse directions as accurately as possible. In the present investigation, both feed-forward and recurrent neural networks are developed for the said purposes, which have been trained using the welding data collected from an existing computational fluid dynamics (CFD)-based phenomenological model with the help of some natured-inspired optimization tools like cuckoo search, firefly, flower pollination, crow search algorithms, particle swarm optimization, covariance adaptation evolution strategy and spider monkey optimization, separately. The results of the trained networks have been validated using some real experimental data. The novelty of this study lies with the applications of these newly developed nature-inspired optimization algorithms to tune the neural networks using the CFD-based phenomenological model-generated welding data. In addition, the performances of these neural networks tuned using the said nature-inspired optimization algorithms have been compared through some statistical tests. In general, flower pollination-tuned recurrent neural network is found to provide the best predictions.

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References

  1. Roy, G.G.; Zhang, Z.; Mishra, S.; He, X.; Fan, Y.; Kumar, A.; DebRoy, T.: A computer program to calculate fluid flow and heat transfer during fusion welding with free surface. Department of Materials Science and Engineering, Pennsylvania State University, University Park, Pennsylvania—16802 (2002)

  2. Das, D.; Pratihar, D.K.; Roy, G.G.: Cooling rate predictions and its correlation with grain characteristics during electron beam welding of stainless steel. Int. J. Adv. Manuf. Technol. (2018). https://doi.org/10.1007/s00170-018-2095-6

    Article  Google Scholar 

  3. Ganjigatti, J.P.; Pratihar, D.K.; Roychoudhury, A.: Modeling of the MIG welding process using statistical approaches. Int. J. Adv. Manuf. Technol. 35, 1166–1190 (2008). https://doi.org/10.1007/s00170-006-0798-6

    Article  Google Scholar 

  4. Datta, S.; Pratihar, D.K.; Bandyopadhyay, P.P.: Modeling of plasma spray coating process using statistical regression analysis. Int. J. Adv. Manuf. Technol. 65, 967–980 (2013). https://doi.org/10.1007/s00170-012-4232-y

    Article  Google Scholar 

  5. Pratihar, D.K.: Soft Computing Fundamentals and Applications. Narosa Publishing House Pvt. Ltd, New Delhi (2015)

    Google Scholar 

  6. Dutta, P.; Pratihar, D.K.: Modeling of TIG welding process using conventional regression analysis and neural network-based approaches. J. Mater. Process. Technol. 184, 56–68 (2007). https://doi.org/10.1016/j.jmatprotec.2006.11.004

    Article  Google Scholar 

  7. Parappagoudar, M.B.; Pratihar, D.K.; Datta, G.L.: Forward and reverse mappings in green sand mould system using neural networks. Appl. Soft Comput. J. 8, 239–260 (2008). https://doi.org/10.1016/j.asoc.2007.01.005

    Article  Google Scholar 

  8. Malviya, R.; Pratihar, D.K.: Tuning of neural networks using particle swarm optimization to model MIG welding process. Swarm Evol. Comput. 1, 223–235 (2011). https://doi.org/10.1016/j.swevo.2011.07.001

    Article  Google Scholar 

  9. Jha, M.N.; Pratihar, D.K.; Bapat, A.V.; Dey, V.; Ali, M.; Bagchi, A.C.: Knowledge-based systems using neural networks for electron beam welding process of reactive material (Zircaloy-4). J. Intell. Manuf. 25, 1315–1333 (2014). https://doi.org/10.1007/s10845-013-0732-3

    Article  Google Scholar 

  10. Das, A.K.; Pratihar, D.K.: Performance improvement of a genetic algorithm using a novel restart strategy with elitism principle. Int. J. Hybrid Intell. Syst. 15, 1–15 (2018). https://doi.org/10.3233/HIS-180257

    Article  Google Scholar 

  11. Yang, X.-S.: Firefly algorithm, levy flights and global optimization. In: Bramer, M., Ellis, R., Petridis, M. (eds.) Research and Development in Intelligent Systems XXVI, pp. 209–218. Springer, London (2010)

    Chapter  Google Scholar 

  12. Yang, X.S.; Deb, S.: Cuckoo search via Levy flights. In: Abraham, A., Carvalho, A., Herrera, F., Pai, V. (eds.) Nature and Biologically Inspired Computing (NABIC), pp. 210–214. IEEE, Coimbatore, India (2009). https://doi.org/10.1109/NABIC.2009.5393690

    Google Scholar 

  13. Yang, X.-S.: Flower pollination algorithm for global optimization. In: Durand-Lose, J., Jonoska, N. (eds.) Unconventional Computation and Natural Computation: 11th International Conference, UCNC 2012, pp. 240–249. Springer, Orléans (2012)

  14. Askarzadeh, A.: A novel metaheuristic method for solving constrained engineering optimization problems: crow search algorithm. Comput. Struct. 169, 1–12 (2016). https://doi.org/10.1016/j.compstruc.2016.03.001

    Article  Google Scholar 

  15. Bag, S.; De, A.; DebRoy, T.: A genetic algorithm-assisted inverse convective heat transfer model for tailoring weld geometry. Mater. Manuf. Process. 24, 384–397 (2009). https://doi.org/10.1080/10426910802679915

    Article  Google Scholar 

  16. Manvatkar, V.D.; Arora, A.; De, A.; Debroy, T.: Neural network models of peak temperature, torque, traverse force, bending stress and maximum shear stress during friction stir welding. Sci. Technol. Weld. Join. 17, 460–466 (2012). https://doi.org/10.1179/1362171812Y.0000000035

    Article  Google Scholar 

  17. Das, D.; Pratihar, D.K.; Roy, G.G.; Pal, A.R.A.: Phenomenological model-based study on electron beam welding process, and input–output modeling using neural networks trained by back-propagation algorithm, genetic algorithms, particle swarm optimization algorithm and bat algorithm. Appl. Intell. 48, 2698–2718 (2018). https://doi.org/10.1007/s10489-017-1101-2

    Article  Google Scholar 

  18. Nandan, R.; DebRoy, T.; Bhadeshia, H.K.D.H.: Recent advances in friction-stir welding—process, weldment structure and properties. Prog. Mater Sci. 53, 980–1023 (2008). https://doi.org/10.1016/j.pmatsci.2008.05.001

    Article  Google Scholar 

  19. He, X.; Elmer, J.W.; Debroy, T.: Heat transfer and fluid flow in laser microwelding. J. Appl. Phys. 97, 084909 (2005). https://doi.org/10.1063/1.1873032

    Article  Google Scholar 

  20. Roy, G.G.; Elmer, J.W.; DebRoy, T.: Mathematical modeling of heat transfer, fluid flow, and solidification during linear welding with a pulsed laser beam. J. Appl. Phys. 100, 034903 (2006). https://doi.org/10.1063/1.2214392

    Article  Google Scholar 

  21. Rai, R.; Roy, G.G.; Debroy, T.: A computationally efficient model of convective heat transfer and solidification characteristics during keyhole mode laser welding. J. Appl. Phys. 101, 054909 (2007). https://doi.org/10.1063/1.2537587

    Article  Google Scholar 

  22. Rai, R.; Elmer, J.W.; Palmer, T.A.; DebRoy, T.: Heat transfer and fluid flow during keyhole mode laser welding of tantalum, Ti–6Al–4 V, 304L stainless steel and vanadium. J. Phys. D Appl. Phys. 40, 5753–5766 (2007). https://doi.org/10.1088/0022-3727/40/18/037

    Article  Google Scholar 

  23. Rai, R.; Palmer, T.A.; Elmer, J.W.; Debroy, T.: Heat transfer and fluid flow during electron beam welding of 304L stainless steel alloy. Weld. J. 88, 54–61 (2009)

    Google Scholar 

  24. Khorram, A.; Ghoreishi, M.; Yazdi, M.R.S.; Moradi, M.: Optimization of bead geometry in CO2 laser welding of Ti 6Al 4 V using response surface methodology. Engineering 03, 708–712 (2011). https://doi.org/10.4236/eng.2011.37084

    Article  Google Scholar 

  25. Srivastava, S.; Garg, R.K.: Process parameter optimization of gas metal arc welding on IS:2062 mild steel using response surface methodology. J. Manuf. Process. 25, 296–305 (2017). https://doi.org/10.1016/j.jmapro.2016.12.016

    Article  Google Scholar 

  26. Torres-Treviño, L.M.; Reyes-Valdes, F.A.; López, V.; Praga-Alejo, R.: Multi-objective optimization of a welding process by the estimation of the Pareto optimal set. Expert Syst. Appl. 38, 8045–8053 (2011). https://doi.org/10.1016/j.eswa.2010.12.139

    Article  Google Scholar 

  27. Buffa, G.; Fratini, L.; Micari, F.: Mechanical and microstructural properties prediction by artificial neural networks in FSW processes of dual phase titanium alloys. J. Manuf. Process. 14, 289–296 (2012). https://doi.org/10.1016/j.jmapro.2011.10.007

    Article  Google Scholar 

  28. Mathew, J.; Griffin, J.; Alamaniotis, M.; Kanarachos, S.; Fitzpatrick, M.E.: Prediction of welding residual stresses using machine learning: comparison between neural networks and neuro-fuzzy systems. Appl. Soft Comput. 70, 131–146 (2018). https://doi.org/10.1016/j.asoc.2018.05.017

    Article  Google Scholar 

  29. Vargas, J.A.R.; Pedrycz, W.; Hemerly, E.M.: Improved learning algorithm for two-layer neural networks for identification of nonlinear systems. Neurocomputing 329, 86–96 (2018). https://doi.org/10.1016/j.neucom.2018.10.008

    Article  Google Scholar 

  30. Jha, M.N.; Pratihar, D.K.; Dey, V.; Saha, T.K.; Bapat, A.V.: Study on electron beam butt welding of austenitic stainless steel 304 plates and its input–output modelling using neural networks. Proc. Inst. Mech. Eng. Part B J. Eng. Manuf. 225, 2051–2070 (2011). https://doi.org/10.1177/0954405411404856

    Article  Google Scholar 

  31. Reddy, D.Y.A.; Pratihar, D.K.: Neural network-based expert systems for predictions of temperature distributions in electron beam welding process. Int. J. Adv. Manuf. Technol. 55, 535–548 (2011). https://doi.org/10.1007/s00170-010-3104-6

    Article  Google Scholar 

  32. Gao, X.D.; Zhang, Y.X.: Prediction model of weld width during high-power disk laser welding of 304 austenitic stainless steel. Int. J. Precis. Eng. Manuf. 15, 399–405 (2014). https://doi.org/10.1007/s12541-014-0350-9

    Article  Google Scholar 

  33. Ruiz, L.G.B.; Rueda, R.; Cuéllar, M.P.; Pegalajar, M.C.: Energy consumption forecasting based on Elman neural networks with evolutive optimization. Expert Syst. Appl. 92, 380–389 (2018). https://doi.org/10.1016/j.eswa.2017.09.059

    Article  Google Scholar 

  34. Ge, H.W.; Liang, Y.C.; Marchese, M.: A modified particle swarm optimization-based dynamic recurrent neural network for identifying and controlling nonlinear systems. Comput. Struct. 85, 1611–1622 (2007). https://doi.org/10.1016/j.compstruc.2007.03.001

    Article  Google Scholar 

  35. Zhou, C.; Ding, L.Y.; He, R.: PSO-based Elman neural network model for predictive control of air chamber pressure in slurry shield tunneling under Yangtze River. Autom. Constr. 36, 208–217 (2013). https://doi.org/10.1016/j.autcon.2013.03.001

    Article  Google Scholar 

  36. Nawi, N.M.; Khan, A.; Rehman, M.Z.; Herawan, T.; Deris, M.M.: CSLMEN: a new cuckoo search Levenberg Marquardt Elman network for data classification. In: Recent Advances on Soft Computing and Data Mining, pp. 173–182. Springer, Kluang (2014)

  37. Guo, C.; Yan, J.; Tian, Z.: Analysis and design of an attitude calculation algorithm based on elman neural network for SINS. Clust. Comput. 8, 1–6 (2018). https://doi.org/10.1007/s10586-018-2562-8

    Article  Google Scholar 

  38. Mehrgini, B.; Izadi, H.; Memarian, H.: Shear wave velocity prediction using Elman artificial neural network. Carbonates Evaporites (2017). https://doi.org/10.1007/s13146-017-0406-x

    Article  Google Scholar 

  39. Nayak, J.; Naik, B.; Behera, H.S.; Abraham, A.: Elitist teaching–learning-based optimization (ETLBO) with higher-order Jordan Pi-sigma neural network: a comparative performance analysis. Neural Comput. Appl. 30, 1445–1468 (2018). https://doi.org/10.1007/s00521-016-2738-1

    Article  Google Scholar 

  40. Rather, A.M.; Agarwal, A.; Sastry, V.N.: Recurrent neural network and a hybrid model for prediction of stock returns. Expert Syst. Appl. 42, 3234–3241 (2015). https://doi.org/10.1016/j.eswa.2014.12.003

    Article  Google Scholar 

  41. Krichene, E.; Masmoudi, Y.; Alimi, A.M.; Abraham, A.; Chabchoub, H.: Forecasting using Elman recurrent neural network. In: International Conference on Intelligent Systems Design and Applications, pp. 488–497. Springer, Cham (2016)

  42. Valian, E.; Mohanna, S.; Tavakoli, S.: Improved cuckoo search algorithm for feedforward neural network training. Artif. Intell. 2, 36–43 (2011). https://doi.org/10.5121/ijaia.2011.2304

    Article  Google Scholar 

  43. Vazquez, R.A.: Training spiking neural models using cuckoo search algorithm. In: Evolutionary Computation (CEC), pp. 679–686. IEEE Congress (2011)

  44. Swain, K.B.; Solanki, S.S.; Mahakula, A.K.: Bio inspired cuckoo search algorithm based neural network and its application to noise cancellation. In: Signal Processing and Integrated Networks (SPIN), pp. 632–635. IEEE (2014)

  45. Gotmare, A.; Patidar, R.; George, N.V.: Nonlinear system identification using a cuckoo search optimized adaptive Hammerstein model. Expert Syst. Appl. 42, 2538–2546 (2015). https://doi.org/10.1016/j.eswa.2014.10.040

    Article  Google Scholar 

  46. Goswami, D.; Chakraborty, S.: Optimal process parameter selection in laser transmission welding by cuckoo search algorithm. In: Proceedings of the International Conference on Advanced Engineering Optimization Through Intelligent Techniques (AEOTIT), Gujarat, India, pp. 40–44 (2013)

  47. Chen, G.; Ding, X.: Optimal economic dispatch with valve loading effect using self-adaptive firefly algorithm. Appl. Intell. 42, 276–288 (2015). https://doi.org/10.1007/s10489-014-0593-2

    Article  Google Scholar 

  48. Alweshah, M.; Abdullah, S.: Hybridizing firefly algorithms with a probabilistic neural network for solving classification problems. Appl. Soft Comput. J. 35, 513–524 (2015). https://doi.org/10.1016/j.asoc.2015.06.018

    Article  Google Scholar 

  49. Nayak, J.; Naik, B.; Behera, H.S.: A novel nature inspired firefly algorithm with higher order neural network: performance analysis. Eng. Sci. Technol. Int. J. 19, 197–211 (2016). https://doi.org/10.1016/j.jestch.2015.07.005

    Article  Google Scholar 

  50. Senthilkumar, N.; Tamizharasan, T.; Gobikannan, S.: Application of response surface methodology and firefly algorithm for optimizing multiple responses in turning AISI 1045 steel. Arab. J. Sci. Eng. 39, 8015–8030 (2014). https://doi.org/10.1007/s13369-014-1320-3

    Article  Google Scholar 

  51. Chiroma, H.; Khan, A.; Abubakar, A.I.; Saadi, Y.; Hamza, M.F.; Shuib, L.; Gital, A.Y.; Herawan, T.: A new approach for forecasting OPEC petroleum consumption based on neural network train by using flower pollination algorithm. Appl. Soft Comput. J. 48, 50–58 (2016). https://doi.org/10.1016/j.asoc.2016.06.038

    Article  Google Scholar 

  52. Acherjee, B.; Maity, D.; Kuar, A.S.: Parameters optimisation of transmission laser welding of dissimilar plastics using RSM and flower pollination algorithm integrated approach. Int. J. Math. Model. Numer. Optim. 8, 1–22 (2017). https://doi.org/10.1504/IJMMNO.2017.10004515

    Article  Google Scholar 

  53. Draa, A.: On the performances of the flower pollination algorithm—qualitative and quantitative analyses. Appl. Soft Comput. J. 34, 349–371 (2015). https://doi.org/10.1016/j.asoc.2015.05.015

    Article  Google Scholar 

  54. Singh, D.; Singh, U.; Salgotra, R.: An extended version of flower pollination algorithm. Arab. J. Sci. Eng. 43, 7573–7603 (2018). https://doi.org/10.1007/s13369-018-3166-6

    Article  Google Scholar 

  55. Oliva, D.; Hinojosa, S.; Cuevas, E.; Pajares, G.; Avalos, O.; Gálvez, J.: Cross entropy based thresholding for magnetic resonance brain images using crow search algorithm. Expert Syst. Appl. 79, 164–180 (2017). https://doi.org/10.1016/j.eswa.2017.02.042

    Article  Google Scholar 

  56. Nobahari, H.; Bighashdel, A.: MOCSA: a multi-objective crow search algorithm for multi-objective optimization. In: 2nd Conference on Swarm Intelligence and Evolutionary Computation (CSIEC), pp. 60–65. IEEE, Kerman (2017)

  57. Abdelaziz, A.Y.; Fathy, A.: A novel approach based on crow search algorithm for optimal selection of conductor size in radial distribution networks. Eng. Sci. Technol. Int. J. 20, 391–402 (2017). https://doi.org/10.1016/j.jestch.2017.02.004

    Article  Google Scholar 

  58. Mason, K.; Duggan, M.; Barrett, E.; Duggan, J.; Howley, E.: Predicting host CPU utilization in the cloud using evolutionary neural networks. Fut. Gener. Comput. Syst. 86, 162–173 (2018). https://doi.org/10.1016/j.future.2018.03.040

    Article  Google Scholar 

  59. Mason, K.; Duggan, J.; Howley, E.: Forecasting energy demand, wind generation and carbon dioxide emissions in Ireland using evolutionary neural networks. Energy 155, 705–720 (2018). https://doi.org/10.1016/j.energy.2018.04.192

    Article  Google Scholar 

  60. Cuevas, E.; Galvez, J.: An optimization algorithm guided by a machine learning approach. Int. J. Mach. Learn. Cybern. (2019). https://doi.org/10.1007/s13042-018-00915-0

    Article  Google Scholar 

  61. Veloso De Melo, V.; Iacca, G.: A CMA-ES-based 2-stage memetic framework for solving constrained optimization problems. In: IEEE SSCI 2014–2014 IEEE Symposium Series on Computational Intelligence—FOCI 2014 2014 IEEE Symposium on Foundations of Computational Intelligence Proceedings, pp. 143–150 (2015). https://doi.org/10.1109/FOCI.2014.7007819

  62. Jadon, S.S.; Tiwari, R.; Sharma, H.; Bansal, J.C.: Hybrid artificial bee colony algorithm with differential evolution. Appl. Soft Comput. J. 58, 11–24 (2017). https://doi.org/10.1016/j.asoc.2017.04.018

    Article  Google Scholar 

  63. Kusakci, A.O.; Can, M.: A novel evolution strategy for constrained optimization in engineering design. In: 2013 24th International Conference on Information, Communication and Automation Technologies. ICAT 2013, pp. 1–6 (2013). https://doi.org/10.1109/icat.2013.6684072

  64. Elmer, J.W.; Giedt, W.H.; Eager, T.W.: The transition from shallow to deep penetration during electron beam welding. Weld. J. 69, 167–176 (1990)

    Google Scholar 

  65. Kar, J.; Mahanty, S.; Roy, S.K.; Roy, G.G.: Estimation of average spot diameter and bead penetration using process model during electron beam welding of AISI 304 stainless steel. Trans. Indian Inst. Met. 68, 935–941 (2015). https://doi.org/10.1007/s12666-015-0529-5

    Article  Google Scholar 

  66. Bansal, J.C.; Sharma, H.; Jadon, S.S.; Clerc, M.: Spider monkey optimization algorithm for numerical optimization. Memet. Comput. 6, 31–47 (2014). https://doi.org/10.1007/s12293-013-0128-0

    Article  Google Scholar 

  67. Petrov, P.: Optimization of carbon steel electron-beam hardening. J. Phys. Conf. Ser. 223, 012029 (2010). https://doi.org/10.1088/1742-6596/223/1/012029

    Article  Google Scholar 

  68. Das, D.; Pratihar, D.K.; Roy, G.G.: Electron beam melting of steel plates: temperature measurement using thermocouples and prediction through finite element analysis. In: Mandal, D.K., Syan, C.S. (eds.) CAD/CAM, Robotics and Factories of the Future, pp. 579–588. Springer, New Delhi (2016)

    Chapter  Google Scholar 

  69. Datta, S.; Pratihar, D.K.; Bandyopadhyay, P.P.: Modeling of input–output relationships for a plasma spray coating process using soft computing tools. Appl. Soft Comput. 12, 3356–3368 (2012). https://doi.org/10.1016/j.asoc.2012.07.015

    Article  Google Scholar 

  70. Yang, X.: Recent Advances in Swarm Intelligence and Evolutionary Computation, vol. 585. Springer, London (2015)

    Google Scholar 

  71. Yang, X.S.; Deb, S.: Cuckoo search: recent advances and applications. Neural Comput. Appl. 24, 169–174 (2014). https://doi.org/10.1007/s00521-013-1367-1

    Article  Google Scholar 

  72. Yang, X.S.: Multiobjective firefly algorithm for continuous optimization. Eng. Comput. 29, 175–184 (2013). https://doi.org/10.1007/s00366-012-0254-1

    Article  Google Scholar 

  73. Gupta, K.; Deep, K.; Bansal, J.C.: Spider monkey optimization algorithm for constrained optimization problems. Soft. Comput. 21, 6933–6962 (2017). https://doi.org/10.1007/s00500-016-2419-0

    Article  Google Scholar 

  74. Sharma, H.; Hazrati, G.; Bansal, J.C.: Spider monkey optimization algorithm. In: Bansal, J.C., Singh, P.K., Pal, N.R. (eds.) Evolutionary and Swarm Intelligence Algorithms, pp. 43–59. Springer International Publishing, Cham (2019)

    Chapter  Google Scholar 

  75. Derrac, J.; García, S.; Molina, D.; Herrera, F.: A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol. Comput. 1, 3–18 (2011). https://doi.org/10.1016/j.swevo.2011.02.002

    Article  Google Scholar 

  76. Chakri, A.; Khelif, R.; Benouaret, M.; Yang, X.S.: New directional bat algorithm for continuous optimization problems. Expert Syst. Appl. 69, 159–175 (2017). https://doi.org/10.1016/j.eswa.2016.10.050

    Article  Google Scholar 

  77. Al-Azza, A.A.; Al-Jodah, A.A.; Harackiewicz, F.J.: Spider monkey optimization: a novel technique for antenna optimization. IEEE Antennas Wirel. Propag. Lett. 15, 1016–1019 (2016). https://doi.org/10.1109/LAWP.2015.2490103

    Article  Google Scholar 

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Acknowledgements

The first author would like to thank the Ministry of Human Resource Development (MHRD), Government of India, for their financial support during this study.

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Authors and Affiliations

  1. Indian Institute of Technology Kharagpur, Kharagpur, India

    Debasish Das, Abhishek Rudra Pal & Amit Kumar Das

  2. Department of Mechanical Engineering, Indian Institute of Technology Kharagpur, Kharagpur, India

    Dilip Kumar Pratihar

  3. Department of Metallurgical and Materials Engineering, Indian Institute of Technology Kharagpur, Kharagpur, India

    Gour Gopal Roy

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  1. Debasish Das
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Correspondence to Dilip Kumar Pratihar.

Appendix

Appendix

See Figs. 2, 4, 5, 6, 7, 8, 9, 10 and 11.

Fig. 3
figure 3

Schematic views of ANN models: a feed-forward, b Elman–Jordan recurrent neural networks

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Fig. 4
figure 4

Forward modeling case one studies on experimental results versus soft computing model estimated a penetration depth, b half-width

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Fig. 5
figure 5

Forward modeling case one studies on phenomenological model versus soft computing model estimated a pool length, b cooling time (symbols used are the same with that of Fig. 4)

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Fig. 6
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Forward modeling case two studies on experimental results versus soft computing model estimated a penetration depth, b half-width (symbols used are the same with that of Fig. 4)

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Fig. 7
figure 7

Forward modeling case two studies on phenomenological model versus soft computing model estimated a pool length, b cooling time (symbols used are the same with that of Fig. 4)

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Fig. 8
figure 8

Reverse modeling case one studies on experimental results versus soft computing model estimated a power, b welding speed (symbols used are the same with that of Fig. 4)

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Fig. 9
figure 9

Reverse modeling case one studies on phenomenological model versus soft computing model estimated a beam radius, b power distribution factor (symbols used are the same with that of Fig. 4)

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Fig. 10
figure 10

Reverse modeling case two studies on experimental results versus soft computing model estimated a power, b welding speed (symbols used are the same with that of Fig. 4)

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Fig. 11
figure 11

Reverse modeling case two studies on phenomenological model vs soft computing model estimated a beam radius, b power distribution factor (symbols used are the same with that of Fig. 4)

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Das, D., Pal, A.R., Das, A.K. et al. Nature-Inspired Optimization Algorithm-Tuned Feed-Forward and Recurrent Neural Networks Using CFD-Based Phenomenological Model-Generated Data to Model the EBW Process. Arab J Sci Eng 45, 2779–2797 (2020). https://doi.org/10.1007/s13369-019-04142-9

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