skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Uncertainty Propagation Analysis of Computational Models in Laser Powder Bed Fusion Additive Manufacturing Using Polynomial Chaos Expansions

Abstract

Computational models for simulating physical phenomena during laser-based powder bed fusion additive manufacturing (L-PBF AM) processes are critical for enhancing our understanding of these phenomena, enable process optimization, and accelerate qualification and certification of AM materials and parts. It is a well-known fact that such models typically involve multiple sources of uncertainty that originate from different sources such as model parameters uncertainty, or model/code inadequacy, among many others. Uncertainty quantification (UQ) is a broad field that focuses on characterizing such uncertainties in order to maximize the benefit of these models. Although UQ has been a center theme in computational models associated with diverse fields such as computational fluid dynamics and macro-economics, it has not yet been fully exploited with computational models for advanced manufacturing. The current study introduces one among the first efforts to conduct uncertainty propagation (UP) analysis in the context of L-PBF AM. More specifically, we present a generalized polynomial chaos expansions (gPCE) framework to assess the distributions of melt pool dimensions due to uncertainty in input model parameters. We develop the methodology and then employ it to validate model predictions, both through benchmarking them against Monte Carlo (MC) methods and against experimental data acquired from an experimentalmore » testbed.« less

Authors:
 [1];  [2];  [1];  [1];  [1];  [1]
  1. Texas A & M Univ., College Station, TX (United States)
  2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1527295
Report Number(s):
LLNL-JRNL-769893
Journal ID: ISSN 1087-1357; 961399
Grant/Contract Number:  
AC52-07NA27344; NNX15AD71G
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Manufacturing Science and Engineering
Additional Journal Information:
Journal Volume: 140; Journal Issue: 12; Journal ID: ISSN 1087-1357
Publisher:
ASME
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE

Citation Formats

Tapia, Gustavo, King, Wayne, Johnson, Luke, Arroyave, Raymundo, Karaman, Ibrahim, and Elwany, Alaa. Uncertainty Propagation Analysis of Computational Models in Laser Powder Bed Fusion Additive Manufacturing Using Polynomial Chaos Expansions. United States: N. p., 2018. Web. doi:10.1115/1.4041179.
Tapia, Gustavo, King, Wayne, Johnson, Luke, Arroyave, Raymundo, Karaman, Ibrahim, & Elwany, Alaa. Uncertainty Propagation Analysis of Computational Models in Laser Powder Bed Fusion Additive Manufacturing Using Polynomial Chaos Expansions. United States. doi:10.1115/1.4041179.
Tapia, Gustavo, King, Wayne, Johnson, Luke, Arroyave, Raymundo, Karaman, Ibrahim, and Elwany, Alaa. Fri . "Uncertainty Propagation Analysis of Computational Models in Laser Powder Bed Fusion Additive Manufacturing Using Polynomial Chaos Expansions". United States. doi:10.1115/1.4041179. https://www.osti.gov/servlets/purl/1527295.
@article{osti_1527295,
title = {Uncertainty Propagation Analysis of Computational Models in Laser Powder Bed Fusion Additive Manufacturing Using Polynomial Chaos Expansions},
author = {Tapia, Gustavo and King, Wayne and Johnson, Luke and Arroyave, Raymundo and Karaman, Ibrahim and Elwany, Alaa},
abstractNote = {Computational models for simulating physical phenomena during laser-based powder bed fusion additive manufacturing (L-PBF AM) processes are critical for enhancing our understanding of these phenomena, enable process optimization, and accelerate qualification and certification of AM materials and parts. It is a well-known fact that such models typically involve multiple sources of uncertainty that originate from different sources such as model parameters uncertainty, or model/code inadequacy, among many others. Uncertainty quantification (UQ) is a broad field that focuses on characterizing such uncertainties in order to maximize the benefit of these models. Although UQ has been a center theme in computational models associated with diverse fields such as computational fluid dynamics and macro-economics, it has not yet been fully exploited with computational models for advanced manufacturing. The current study introduces one among the first efforts to conduct uncertainty propagation (UP) analysis in the context of L-PBF AM. More specifically, we present a generalized polynomial chaos expansions (gPCE) framework to assess the distributions of melt pool dimensions due to uncertainty in input model parameters. We develop the methodology and then employ it to validate model predictions, both through benchmarking them against Monte Carlo (MC) methods and against experimental data acquired from an experimental testbed.},
doi = {10.1115/1.4041179},
journal = {Journal of Manufacturing Science and Engineering},
number = 12,
volume = 140,
place = {United States},
year = {2018},
month = {10}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 11 works
Citation information provided by
Web of Science

Figures / Tables:

Figure 1 Figure 1: Computational complexity of the gPCE model based on values for t and q.

Save / Share:

Works referenced in this record:

An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis
journal, April 2010


Variance Components and Generalized Sobol' Indices
journal, January 2013

  • Owen, Art B.
  • SIAM/ASA Journal on Uncertainty Quantification, Vol. 1, Issue 1
  • DOI: 10.1137/120876782

Mesoscale modelling of selective laser melting: Thermal fluid dynamics and microstructural evolution
journal, January 2017


Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics
journal, January 2009


Polynomial Chaos-Based Analysis of Probabilistic Uncertainty in Hypersonic Flight Dynamics
journal, January 2010

  • Prabhakar, Avinash; Fisher, James; Bhattacharya, Raktim
  • Journal of Guidance, Control, and Dynamics, Vol. 33, Issue 1
  • DOI: 10.2514/1.41551

Uncertainty propagation in CFD using polynomial chaos decomposition
journal, September 2006


ALGORITHM 659: implementing Sobol's quasirandom sequence generator
journal, March 1988

  • Bratley, Paul; Fox, Bennett L.
  • ACM Transactions on Mathematical Software, Vol. 14, Issue 1
  • DOI: 10.1145/42288.214372

Uncertainty quantification and validation of 3D lattice scaffolds for computer-aided biomedical applications
journal, July 2017

  • Gorguluarslan, Recep M.; Choi, Seung-Kyum; Saldana, Christopher J.
  • Journal of the Mechanical Behavior of Biomedical Materials, Vol. 71
  • DOI: 10.1016/j.jmbbm.2017.04.011

Modeling metal deposition in heat transfer analyses of additive manufacturing processes
journal, September 2014


The Homogeneous Chaos
journal, October 1938

  • Wiener, Norbert
  • American Journal of Mathematics, Vol. 60, Issue 4
  • DOI: 10.2307/2371268

The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
journal, January 2002


Integration of Design for Manufacturing Methods With Topology Optimization in Additive Manufacturing
journal, January 2017

  • Ranjan, Rajit; Samant, Rutuja; Anand, Sam
  • Journal of Manufacturing Science and Engineering, Vol. 139, Issue 6
  • DOI: 10.1115/1.4035216

Model Validation via Uncertainty Propagation and Data Transformations
journal, July 2004

  • Chen, Wei; Baghdasaryan, Lusine; Buranathiti, Thaweepat
  • AIAA Journal, Vol. 42, Issue 7
  • DOI: 10.2514/1.491

Accelerated process optimization for laser-based additive manufacturing by leveraging similar prior studies
journal, May 2016


Overview of modelling and simulation of metal powder bed fusion process at Lawrence Livermore National Laboratory
journal, November 2014


Laser powder-bed fusion additive manufacturing: Physics of complex melt flow and formation mechanisms of pores, spatter, and denudation zones
journal, April 2016


Global sensitivity analysis using polynomial chaos expansions
journal, July 2008


In situ absorptivity measurements of metallic powders during laser powder-bed fusion additive manufacturing
journal, December 2017


Density of additively-manufactured, 316L SS parts using laser powder-bed fusion at powers up to 400 W
journal, May 2014

  • Kamath, Chandrika; El-dasher, Bassem; Gallegos, Gilbert F.
  • The International Journal of Advanced Manufacturing Technology, Vol. 74, Issue 1-4
  • DOI: 10.1007/s00170-014-5954-9

Finite Element Simulation of Selective Laser Melting process considering Optical Penetration Depth of laser in powder bed
journal, January 2016


Prediction of porosity in metal-based additive manufacturing using spatial Gaussian process models
journal, October 2016


Simulation of Laser Beam Melting of Steel Powders using the Three-Dimensional Volume of Fluid Method
journal, January 2013


Solutions for modelling moving heat sources in a semi-infinite medium and applications to laser material processing
journal, November 2007


Numerical Modeling of Metal-Based Additive Manufacturing Using Level Set Methods
journal, April 2017

  • Ye, Qian; Chen, Shikui
  • Journal of Manufacturing Science and Engineering, Vol. 139, Issue 7
  • DOI: 10.1115/1.4036290

Investigations on Temperature Fields during Laser Beam Melting by Means of Process Monitoring and Multiscale Process Modelling
journal, January 2014

  • Schilp, J.; Seidel, C.; Krauss, H.
  • Advances in Mechanical Engineering, Vol. 6
  • DOI: 10.1155/2014/217584

Laser Transformation Hardening
journal, February 2002


Multiscale Modeling of Powder Bed–Based Additive Manufacturing
journal, July 2016


In-Process Monitoring of Selective Laser Melting: Spatial Detection of Defects Via Image Data Analysis
journal, November 2016

  • Grasso, Marco; Laguzza, Vittorio; Semeraro, Quirico
  • Journal of Manufacturing Science and Engineering, Vol. 139, Issue 5
  • DOI: 10.1115/1.4034715

A three-dimensional finite element analysis of the temperature field during laser melting of metal powders in additive layer manufacturing
journal, October 2009


Predicting Microstructure From Thermal History During Additive Manufacturing for Ti-6Al-4V
journal, June 2016

  • Irwin, Jeff; Reutzel, Edward W.; Michaleris, Pan
  • Journal of Manufacturing Science and Engineering, Vol. 138, Issue 11
  • DOI: 10.1115/1.4033525

A Review on Process Monitoring and Control in Metal-Based Additive Manufacturing
journal, October 2014

  • Tapia, Gustavo; Elwany, Alaa
  • Journal of Manufacturing Science and Engineering, Vol. 136, Issue 6
  • DOI: 10.1115/1.4028540

Data mining and statistical inference in selective laser melting
journal, January 2016

  • Kamath, Chandrika
  • The International Journal of Advanced Manufacturing Technology, Vol. 86, Issue 5-8
  • DOI: 10.1007/s00170-015-8289-2

Finite element analysis of single layer forming on metallic powder bed in rapid prototyping by selective laser processing
journal, January 2002

  • Matsumoto, M.; Shiomi, M.; Osakada, K.
  • International Journal of Machine Tools and Manufacture, Vol. 42, Issue 1
  • DOI: 10.1016/S0890-6955(01)00093-1

Laser powder bed fusion additive manufacturing of metals; physics, computational, and materials challenges
journal, December 2015

  • King, W. E.; Anderson, A. T.; Ferencz, R. M.
  • Applied Physics Reviews, Vol. 2, Issue 4
  • DOI: 10.1063/1.4937809

An Integrated Approach to Additive Manufacturing Simulations Using Physics Based, Coupled Multiscale Process Modeling
journal, October 2014

  • Pal, Deepankar; Patil, Nachiket; Zeng, Kai
  • Journal of Manufacturing Science and Engineering, Vol. 136, Issue 6
  • DOI: 10.1115/1.4028580

Gaussian process-based surrogate modeling framework for process planning in laser powder-bed fusion additive manufacturing of 316L stainless steel
journal, September 2017

  • Tapia, Gustavo; Khairallah, Saad; Matthews, Manyalibo
  • The International Journal of Advanced Manufacturing Technology, Vol. 94, Issue 9-12
  • DOI: 10.1007/s00170-017-1045-z

Numerical and experimental analysis of heat distribution in the laser powder bed fusion of Ti-6Al-4V
journal, June 2018


3D FE simulation for temperature evolution in the selective laser sintering process
journal, February 2004


Bayesian calibration of computer models
journal, August 2001

  • Kennedy, Marc C.; O'Hagan, Anthony
  • Journal of the Royal Statistical Society: Series B (Statistical Methodology), Vol. 63, Issue 3
  • DOI: 10.1111/1467-9868.00294

Regularization and variable selection via the elastic net
journal, April 2005


    Works referencing / citing this record:

    Uncertainty analysis of microsegregation during laser powder bed fusion
    journal, February 2019

    • Ghosh, Supriyo; Mahmoudi, Mohamad; Johnson, Luke
    • Modelling and Simulation in Materials Science and Engineering, Vol. 27, Issue 3
    • DOI: 10.1088/1361-651x/ab01bf

    Uncertainty quantification of grain morphology in laser direct metal deposition
    journal, April 2019

    • Nath, Paromita; Hu, Zhen; Mahadevan, Sankaran
    • Modelling and Simulation in Materials Science and Engineering, Vol. 27, Issue 4
    • DOI: 10.1088/1361-651x/ab1676

    A Review of Model Inaccuracy and Parameter Uncertainty in Laser Powder Bed Fusion Models and Simulations
    journal, February 2019

    • Moges, Tesfaye; Ameta, Gaurav; Witherell, Paul
    • Journal of Manufacturing Science and Engineering, Vol. 141, Issue 4
    • DOI: 10.1115/1.4042789

    Chaotic Signatures Exhibited by Plasmonic Effects in Au Nanoparticles with Cells
    journal, October 2019

    • Martines-Arano, Hilario; García-Pérez, Blanca Estela; Vidales-Hurtado, Mónica Araceli
    • Sensors, Vol. 19, Issue 21
    • DOI: 10.3390/s19214728