Deep learning; Directed energy deposition; Monte-Carlo method; Robust optimization; Uncertainty quantification; Conceptual frameworks; Directed energy; Energy depositions; Melt pool; MonteCarlo methods; Optimization under uncertainty; Uncertainty quantifications; Strategy and Management; Management Science and Operations Research; Industrial and Manufacturing Engineering
Abstract :
[en] This paper introduces a conceptual framework for the robust optimization under uncertainty in the directed energy deposition (DED) of M4 High-Speed Steel. The goal is to identify optimal process parameters for robust manufacturing of printed parts with a stationary melt pool depth and low consumed energy under uncertainty within the multiple layers of a bulk sample. To increase the computational efficiency, a deep learning-based surrogate model is built using the training data generated by a validated high-fidelity DED two-dimensional FE model. The robustness of the optimized result is verified using the Monte-Carlo method and compared with experiments and two other deterministic approaches. Furthermore, we conduct a global sensitivity analysis, which indicates that among six uncertain input variables, the thermal conductivity and the convection have the most significant impact on the melt pool depth variation. This study shows the promising possibilities of the presented framework in optimizing the DED process.
Disciplines :
Mechanical engineering
Author, co-author :
Pham Quy Duc, Thinh ; Université de Liège - ULiège > Aérospatiale et Mécanique (A&M)
Hoang, T.V.; Chair of Mathematics for Uncertainty Quantification, RWTH-Aachen University, Aachen, Germany
Tran, X.V.; Institute of Strategy Development, Thu Dau Mot University, Viet Nam
Fetni, Seifallah; University of Liège, Liège, Belgium
Duchene, Laurent ; Université de Liège - ULiège > Département ArGEnCo > Analyse multi-échelles dans le domaine des matériaux et structures du génie civil
Tran, Hoang Son ; Université de Liège - ULiège > Département ArGEnCo
Habraken, Anne ; Université de Liège - ULiège > Département ArGEnCo > Département Argenco : Secteur MS2F ; Fonds de la Recherche Scientifique de Belgique (F.R.S-FNRS), France
Language :
English
Title :
A framework for the robust optimization under uncertainty in additive manufacturing
Shin, Y.C., Bailey, N., Katinas, C., Tan, W., Predictive modeling capabilities from incident powder and laser to mechanical properties for laser directed energy deposition. Comput Mech, 61, 2018, 10.1007/s00466-018-1545-1.
Pinkerton, A.J., Syed, W. Ul Haq, Li, L., An experimental and theoretical investigation of combined gas- and water-atomized powder deposition with a diode laser. J Laser Appl, 18, 2006, 10.2351/1.2164486.
Mazumder, J., Dutta, D., Kikuchi, N., Ghosh, A., Closed loop direct metal deposition: art to part. Opt Lasers Eng, 34, 2000, 10.1016/S0143-8166(00)00072-5.
Ahn, D.G., Direct metal additive manufacturing processes and their sustainable applications for green technology: a review. Int J Precis Eng Manuf - Green Technol, 3, 2016, 10.1007/s40684-016-0048-9.
Jardin, R.T., Tchoufang Tchuindjang, J., Duchêne, L., Tran, H.S., Hashemi, N., Carrus, R., et al. Thermal histories and microstructures in direct energy deposition of a high speed steel thick deposit. Mater Lett, 236, 2019, 10.1016/j.matlet.2018.09.157.
Pham, T.Q.D., Hoang, T.V., Tran, X.V., Fetni, S., Duchêne, L., Tran, H.S., et al. Characterization, propagation, and sensitivity analysis of uncertainties in the directed energy deposition process using a deep learning-based surrogate model. Probabilistic Eng Mech, 69, 2022, 103297, 10.1016/J.PROBENGMECH.2022.103297.
Wang, Z., Jiang, C., Liu, P., Yang, W., Zhao, Y., Horstemeyer, M.F., et al. Uncertainty quantification and reduction in metal additive manufacturing. NPJ Comput Mater, 6, 2020, 10.1038/s41524-020-00444-x.
Arnst, M., Ponthot, J.P., An overview of nonintrusive characterization, propagation, and sensitivity analysis of uncertainties in computational mechanics. Int J Uncertain Quantif, 4, 2014, 10.1615/Int.J.UncertaintyQuantification.2014006990.
Nath, P., Hu, Z., Mahadevan, S., Multi-level uncertainty quantification in additive manufacturing. Solid freeform fabrication 2017: proceedings of the 28th annual international solid freeform fabrication symposium - an additive manufacturing conference, SFF 2017, 2020.
Hoang, T.V., Wu, L., Golinval, J.C., Arnst, M., Noels, L., Stochastic multiscale model of MEMS stiction accounting for high-order statistical moments of non-Gaussian contacting surfaces. J Microelectromech Syst 27 (2018), 137–155, 10.1109/JMEMS.2018.2797133.
Hoang, T.V., Wu, L., Paquay, S., Golinval, J.C., Arnst, M., Noels, L., A computational stochastic multiscale methodology for MEMS structures involving adhesive contact. Tribol Int, 110, 2017, 10.1016/j.triboint.2016.10.007.
Beyer, H.G., Sendhoff, B., Robust optimization – a comprehensive survey. Comput Methods Appl Mech Eng 196 (2007), 3190–3218, 10.1016/J.CMA.2007.03.003.
Wang, Z., Liu, P., Xiao, Y., Cui, X., Hu, Z., Chen, L., A data-driven approach for process optimization of metallic additive manufacturing under uncertainty. J Manuf Sci E T ASME, 141, 2019, 10.1115/1.4043798.
Laue, V., Schmidt, O., Dreger, H., Xie, X., Röder, F., Schenkendorf, R., et al. Model-based uncertainty quantification for the product properties of lithium-ion batteries. Energ Technol, 8, 2020, 1900201, 10.1002/ENTE.201900201.
Kidane, A., Lashgari, A., Li, B., McKerns, M., Ortiz, M., Owhadi, H., et al. Rigorous model-based uncertainty quantification with application to terminal ballistics, part I: systems with controllable inputs and small scatter. J Mech Phys Solids 60 (2012), 983–1001, 10.1016/J.JMPS.2011.12.001.
Lopez, F., Witherell, P., Lane, B., Identifying uncertainty in laser powder bed fusion additive manufacturing models. J Mech Des Trans ASME, 138, 2016, 10.1115/1.4034103.
Tapia, G., King, W., Johnson, L., Arroyave, R., Karaman, I., Elwany, A., Uncertainty propagation analysis of computational models in laser powder bed fusion additive manufacturing using polynomial chaos expansions. J Manuf Sci E T ASME, 140, 2018, 10.1115/1.4041179.
Haines, M., Plotkowski, A., Frederick, C.L., Schwalbach, E.J., Babu, S.S., A sensitivity analysis of the columnar-to-equiaxed transition for Ni-based superalloys in electron beam additive manufacturing. Comput Mater Sci 155 (2018), 340–349, 10.1016/J.COMMATSCI.2018.08.064.
Kamath, C., Kamath, C. Kamath, Data mining and statistical inference in selective laser melting. Int J Adv Manuf Technol 86 (2016), 1659–1677, 10.1007/S00170-015-8289-2 2016 86:5.
Pham, T.Q.D., Hoang, T.V., Van Tran, X., Pham, Q.T., Fetni, S., Duchêne, L., et al. Fast and accurate prediction of temperature evolutions in additive manufacturing process using deep learning. J Intell Manuf, 2022, 10.1007/s10845-021-01896-8.
Fetni, S., Enrici, T.M., Niccolini, T., Tran, H.S., Dedry, O., Duchêne, L., et al. Thermal model for the directed energy deposition of composite coatings of 316L stainless steel enriched with tungsten carbides. Mater Des, 204, 2021, 10.1016/j.matdes.2021.109661.
Tran, H.S., Tchuindjang, J.T., Paydas, H., Mertens, A., Jardin, R.T., Duchêne, L., et al. 3D thermal finite element analysis of laser cladding processed Ti-6Al-4V part with microstructural correlations. Mater Des, 128, 2017, 10.1016/j.matdes.2017.04.092.
Kistler, N.A., Corbin, D.J., Nassar, A.R., Reutzel, E.W., Beese, A.M., Effect of processing conditions on the microstructure, porosity, and mechanical properties of Ti-6Al-4V repair fabricated by directed energy deposition. J Mater Process Technol, 264, 2019, 10.1016/j.jmatprotec.2018.08.041.
Jardin, R.T., Tuninetti, V., Tchuindjang, J.T., Hashemi, N., Carrus, R., Mertens, A., et al. Sensitivity analysis in the modeling of a high-speed, steel, thin wall produced by directed energy deposition. Metals (Basel), 10, 2020, 10.3390/met10111554.
Ahn, D.G., Directed energy deposition (DED) process: state of the art. Int J Precis Eng Manuf - Green Technol 8 (2021), 703–742, 10.1007/S40684-020-00302-7 2021 8:2.
Ahn, D.G., Applications of laser assisted metal rapid tooling process to manufacture of molding & forming tools - state of the art. Int J Precis Eng Manuf, 12, 2011, 10.1007/s12541-011-0125-5.
Sing, S.L., Tey, C.F., Tan, J.H.K., Huang, S., Yeong, W.Y., 3D printing of metals in rapid prototyping of biomaterials: techniques in additive manufacturing. Rapid prototyping of biomaterials: techniques in additive manufacturing, 2020, 17–40, 10.1016/B978-0-08-102663-2.00002-2.
Moges, T., Ameta, G., Witherell, P., A review of model inaccuracy and parameter uncertainty in laser powder bed fusion models and simulations. J Manuf Sci E T ASME, 141, 2019, 10.1115/1.4042789.
Bennett, J.L., Wolff, S.J., Hyatt, G., Ehmann, K., Cao, J., Thermal effect on clad dimension for laser deposited Inconel 718. J Manuf Process, 28, 2017, 10.1016/j.jmapro.2017.04.024.
Gorissen, B.L., Yanikoğlu, I., den Hertog, D., A practical guide to robust optimization. Omega (Westport) 53 (2015), 124–137, 10.1016/J.OMEGA.2014.12.006.
Bertsimas, D., Gupta, V., Kallus, N., Data-driven robust optimization. Math Program 167 (2018), 235–292, 10.1007/S10107-017-1125-8/TABLES/4.
Niederreiter, H., Random number generation and quasi-Monte Carlo methods. 1992, SIAM.
Sobol, I.M., Uniformly distributed sequences with an additional uniform property. USSR Comput Math Math Phys 16 (1976), 236–242.
Jardin, A.M.H. Rúben Tome, Tuninetti, Víctor, Tchuindjang, Jérôme Tchoufang, Duchêne, Laurent, Hashemi, Neda, Tran, Hoang Son, et al. Optimizing laser power of directed energy deposition process for homogeneous AISI M4 steel microstructure. Opt Laser Technol, 163, 2022, 109426.
Collier, N., Haji-Ali, A.-L., Nobile, F., Von Schwerin, E., Tempone, R., A continuation multilevel Monte Carlo algorithm. BIT Numer Math 55 (2015), 399–432.
Pham, T.Q.D., Hoang, T.-V., Pham, T.Q., Huyng, P.T., Tran, X.V., Fetni, S., et al. Data-driven prediction of temperature evolution in metallic additive manufacturing process. ESAFORM, 2021, 2021, 10.25518/esaform21.2599.
Bilal, M., Pant, H., Zaheer, L., Garcia-Hernandez, A., Abraham, differential evolution: a review of more than two decades of research. Eng Appl Artif Intel, 90, 2020, 103479, 10.1016/J.ENGAPPAI.2020.103479.
Opara, K.R., Arabas, J., Differential evolution: a survey of theoretical analyses. Swarm Evol Comput 44 (2019), 546–558, 10.1016/J.SWEVO.2018.06.010.
Saltelli, A., Annoni, P., Azzini, I., Campolongo, F., Ratto, M., Tarantola, S., Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index. Comput Phys Commun, 181, 2010, 10.1016/j.cpc.2009.09.018.
Criales, L.E., Arısoy, Y.M., Özel, T., Sensitivity analysis of material and process parameters in finite element modeling of selective laser melting of Inconel 625. Int J Adv Manuf Technol, 86, 2016, 10.1007/s00170-015-8329-y.
