Temperature evolution prediction for laser directed energy deposition enabled by finite element modelling and bi-directional gated recurrent unit

Abstract

In the laser-directed energy deposition (L-DED) process, achieving an efficient temperature evolution prediction of molten pools is critical but challenging. To resolve this issue, this study presents an innovative approach that integrates a high-fidelity finite element (FE) model and an effective machine-learning model. Firstly, a high-fidelity FE model for the L-DED process was developed and subsequently validated through an experimental examination of the cross-sectional geometries of the molten pools and temperature fields of the substrate. Then, a Bi-directional gated recurrent unit (Bi-GRU) was formulated to predict the temperature evolution of the molten pools during L-DED. By training the Bi-GRU model using datasets generated from the FE model, it was deployed to efficiently predict the temperature evolution of the manufactured multi-layer single-bead walls. The results demonstrated that, in terms of the average mean absolute error, this approach outperformed other approaches designed based on the gated recurrent unit (GRU) model, long short-term memory model, and recurrent neural network models by 26.7%, 52.1%, and 65.2%, respectively. The results also showed that the prediction time required by this approach, once trained, was significantly reduced by five orders of magnitude compared with the FE model. Therefore, this approach accurately predicts the temperature evolution of multi-layer single-bead walls in a computationally efficient manner. This approach is a promising solution for supporting the real-time control of the L-DED process in industrial applications.

Keywords

Laser-directed energy deposition (L-DED) / Temperature evolution / Finite element (FE) modelling / Bi-directional gated recurrent unit (Bi-GRU) / Additive manufacturing (AM)

References

[1] GuDD, MeinersW, WissenbachK, et al.. Laser additive manufacturing of metallic components: materials, processes and mechanisms. Int Mater Rev, 2012, 57: 133-164.

[2] ShrivastavaA, MukherjeeS, ChakrabortySS. Addressing the challenges in remanufacturing by laser-based material deposition techniques. Opt Laser Technol, 2021, 144. 107404

[3] DebRoyT, WeiHL, ZubackJS, et al.. Additive manufacturing of metallic components-process, structure and properties. Prog Mater Sci, 2018, 92: 112-224.

[4] WeiHL, MukherjeeT, ZhangW, et al.. Mechanistic models for additive manufacturing of metallic components. Prog Mater Sci, 2021, 116. 100703

[5] LiSH, KumarP, ChandraS, RamamurtyU. Directed energy deposition of metals: processing, microstructures, and mechanical properties. Int Mater Rev, 2023, 68(6): 605-647.

[6] SvetlizkyD, DasM, ZhengB, et al.. Directed energy deposition (DED) additive manufacturing: physical characteristics, defects, challenges and applications. Mater Today, 2021, 49: 271-295.

[7] AhnDG. Directed energy deposition (DED) process: state of the art. Int J Precis Eng Manuf Technol, 2021, 8: 703-742.

[8] SegerstarkA, AnderssonJ, SvenssonLE. Evaluation of a temperature measurement method developed for laser metal deposition. Sci Technol Weld Join, 2017, 22(1): 1-6.

[9] ZhangZ, GeP, LiT, et al.. Electromagnetic wave-based analysis of laser–particle interactions in directed energy deposition additive manufacturing. Addit Manuf, 2020, 34. 101284

[10] YangD, WangG, ZhangG. Thermal analysis for single-pass multi-layer GMAW based additive manufacturing using infrared thermography. J Mater Process Technol, 2017, 244: 215-224.

[11] AnsariM, KhamooshiM, HuangY, et al.. Analytical solutions for rapid prediction of transient temperature field in powder-fed laser directed energy deposition based on different heat source models. Appl Phys A, 2021, 127445.

[12] WangZ, YangW, LiuQ, et al.. Data-driven modeling of process, structure and property in additive manufacturing: a review and future directions. J Manuf Process, 2022, 77: 13-31.

[13] XamesMD, TorshaFK, SarwarF. A systematic literature review on recent trends of machine learning applications in additive manufacturing. J Intell Manuf, 2023, 34: 2529-2555.

[14] RoyM, WodoO. Data-driven modeling of thermal history in additive manufacturing. Addit Manuf, 2020, 32. 101017

[15] ZhangZ, LiuZ, WuD. Prediction of melt pool temperature in directed energy deposition using machine learning. Addit Manuf, 2021, 37. 101692

[16] Cho K, Van Merriënboer B, Gulcehre C et al (2014) Learning phrase representations using RNN encoder-decoder for statistical machine translation. arXiv Prepr arXiv:1406.1078. https://doi.org/10.48550/arXiv.1406.1078

[17] Chung J, Gulcehre C, Cho K et al (2014) Empirical evaluation of gated recurrent neural networks on sequence modeling. arXiv Prepr arXiv:1412.3555. https://doi.org/10.48550/arXiv.1412.3555

[18] ZhangZ, DongZ, LinH, et al.. An improved bidirectional gated recurrent unit method for accurate state-of-charge estimation. IEEE Access, 2021, 9: 11252-11263.

[19] LiX, MaX, XiaoF, et al.. Time-series production forecasting method based on the integration of bidirectional gated recurrent unit (Bi-GRU) network and sparrow search algorithm (SSA). J Pet Sci Eng, 2022, 208. 109309

[20] YuS, WangJ, LiuJ, et al.. Rapid prediction of respiratory motion based on bidirectional gated recurrent unit network. IEEE Access, 2020, 8: 49424-49435.

[21] WangS, ShaoC, ZhangJ, et al.. Traffic flow prediction using bi-directional gated recurrent unit method. Urban Inform, 2022, 116.

[22] ZhangR, ChenT, XiaoF, et al.. Bi-directional gated recurrent unit recurrent neural networks for failure prognosis of proton exchange membrane fuel cells. Int J Hydrog Energy, 2022, 47: 33027-33038.

[23] HashemiSM, ParviziS, BaghbanijavidH, et al.. Computational modelling of process–structure–property–performance relationships in metal additive manufacturing: a review. Int Mater Rev, 2022, 67: 1-46.

[24] BikasH, StavropoulosP, ChryssolourisG. Additive manufacturing methods and modelling approaches: a critical review. Int J Adv Manuf Technol, 2016, 83: 389-405.

[25] ZhuG, ZhangA, LiD, et al.. Numerical simulation of thermal behavior during laser direct metal deposition. Int J Adv Manuf Technol, 2011, 55: 945-954.

[26] LiL, YanL, ZengC, LiuF. An efficient predictive modeling for simulating part-scale residual stress in laser metal deposition process. Int J Adv Manuf Technol, 2021, 114: 1819-1832.

[27] GaoJ, WuC, HaoY, et al.. Numerical simulation and experimental investigation on three-dimensional modelling of single-track geometry and temperature evolution by laser cladding. Opt Laser Technol, 2020, 129. 106287

[28] WuestT, WeimerD, IrgensC, et al.. Machine learning in manufacturing: advantages, challenges, and applications. Prod Manuf Res, 2016, 4: 23-45

[29] HuK, WangY, LiW, et al.. CNN-BiLSTM enabled prediction on molten pool width for thin-walled part fabrication using laser directed energy deposition. J Manuf Process, 2022, 78: 32-45.

[30] WangY, HuK, LiW, et al.. Prediction of melt pool width and layer height for laser directed energy deposition enabled by physics-driven temporal convolutional network. J Manuf Syst, 2023, 69: 1-17.

[31] NessKL, PaulA, SunL, et al.. Towards a generic physics-based machine learning model for geometry invariant thermal history prediction in additive manufacturing. J Mater Process Technol, 2022, 302. 117472

[32] GuoS, GuoW, BianL, et al.. A deep-learning-based surrogate model for thermal signature prediction in laser metal deposition. IEEE Trans Autom Sci Eng, 2022, 20: 482-494.

[33] FariasFWC, da CruzPFJ, e’OliveiraVHPM. Prediction of the interpass temperature of a wire arc additive manufactured wall: FEM simulations and artificial neural network. Addit Manuf, 2021, 48. 102387

[34] KumarHA, KumaraguruS, PaulCP, et al.. Faster temperature prediction in the powder bed fusion process through the development of a surrogate model. Opt Laser Technol, 2021, 141. 107122

[35] MozaffarM, PaulA, Al-BahraniR, et al.. Data-driven prediction of the high-dimensional thermal history in directed energy deposition processes via recurrent neural networks. Manuf Lett, 2018, 18: 35-39.

[36] RenK, ChewY, ZhangYF, et al.. Thermal field prediction for laser scanning paths in laser aided additive manufacturing by physics-based machine learning. Comput Methods Appl Mech Eng, 2020, 362. 112734

[37] BaturynskaI, SemeniutaO, MartinsenK. Optimization of process parameters for powder bed fusion additive manufacturing by combination of machine learning and finite element method: a conceptual framework. Procedia Cirp, 2018, 67: 227-232.

[38] ToyserkaniE, KhajepourA, CorbinSFLaser cladding, 2004, Cambridge. CRC Press. .

[39] DavidzonMI. Newton’s law of cooling and its interpretation. Int J Heat Mass Transf, 2012, 55: 5397-5402.

[40] MontambauxG. Generalized Stefan–boltzmann law. Found Phys, 2018, 48: 395-410.

[41] AkbariM, SaedodinS, ToghraieD, et al.. Experimental and numerical investigation of temperature distribution and melt pool geometry during pulsed laser welding of Ti6Al4V alloy. Opt Laser Technol, 2014, 59: 52-59.

[42] YinJ, ZhuH, KeL, et al.. Simulation of temperature distribution in single metallic powder layer for laser micro-sintering. Comput Mater Sci, 2012, 53: 333-339.

[43] WuY, MaPZ, BaiWQ, et al.. Numerical simulation of temperature field and stress field in 316L/AISI304 laser cladding with different scanning strategies. Chin J Lasers, 2021, 482202002.

[44] KakaçS, YenerY, Naveira-CottaCPHeat conduction, 2018, Cambridge. CRC Press. .

[45] Al HamahmyMI, DeiabI. Review and analysis of heat source models for additive manufacturing. Int J Adv Manuf Technol, 2020, 106: 1223-1238.

[46] FachinottiVD, AncaAA, CardonaA. Analytical solutions of the thermal field induced by moving double-ellipsoidal and double-elliptical heat sources in a semi-infinite body. Int J Numer Method Biomed Eng, 2011, 27: 595-607.

[47] GoldakJ, ChakravartiA, BibbyM. A new finite element model for welding heat sources. Metall Trans B, 1984, 15: 299-305.

[48] ZhanMJ, SunGF, WangZD, et al.. Numerical and experimental investigation on laser metal deposition as repair technology for 316L stainless steel. Opt Laser Technol, 2019, 118: 84-92.

[49] YongY, FuW, DengQ, et al.. A comparative study of vision detection and numerical simulation for laser cladding of nickel-based alloy. J Manuf Process, 2017, 28: 364-372.

[50] GougeM, MichalerisPThermo-mechanical modeling of additive manufacturing, 2018, Oxford. Butterworth-Heinemann.

[51] MishraR, ImamM, ChinthapentaV, et al.. Thermo-mechanical modelling of the wire arc based additively manufactured Inconel 625 superalloy. Mater Today Proc, 2023.

[52] LuX, LinX, ChiumentiM, et al.. Residual stress and distortion of rectangular and S-shaped Ti-6Al-4V parts by directed energy deposition: modelling and experimental calibration. Addit Manuf, 2019, 26: 166-179

[53] YaW, PathirajB, LiuS. 2D modelling of clad geometry and resulting thermal cycles during laser cladding. J Mater Process Technol, 2016, 230: 217-232.

[54] WangY, PerryM, WhitlockD, et al.. Detecting anomalies in time series data from a manufacturing system using recurrent neural networks. J Manuf Syst, 2022, 62: 823-834.

[55] GersFA, SchmidhuberJ, CumminsF. Learning to forget: continual prediction with LSTM. Neural Comput, 2000, 12: 2451-2471.

[56] GreffK, SrivastavaRK, KoutnikJ, et al.. LSTM: a search space odyssey. IEEE Trans Neural Netw Learn Syst, 2016, 28: 2222-2232.

[57] GulliA, PalSDeep learning with Keras, 2017, Birmingham. Packt Publishing Ltd.

[58] LeCunY, BengioY, HintonG. Deep learning. Nature, 2015, 521: 436-444.

[59] ZhouZ-HMachine learning, 2021, Berlin. Springer. .

[60] RongY, HuangY, XuJ, et al.. Numerical simulation and experiment analysis of angular distortion and residual stress in hybrid laser-magnetic welding. J Mater Process Technol, 2017, 245: 270-277.

Funding

National Natural Science Foundation of China(51975444)

RIGHTS & PERMISSIONS

Shanghai University and Periodicals Agency of Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature