Solution of inverse heat conduction problem for determining heat input, weld shape, and grain structure during laser welding

Karkhin, Victor A.; Plochikhine, V. V.; Bergmann, H. W.

doi:10.1179/136217102225004202

Cited by 37 publications

(21 citation statements)

References 6 publications

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“…Though convective transport can play a role in many practical source inversion problems, we will limit our attention here to a purely diffusion-driven inverse problem in order to focus on the demonstration and analysis of the new formulation. Diffusive source inversion problems themselves arise in the context of porous media flows [85] and heat conduction [9,4,57,54,96]. …”

Section: Resultsmentioning

confidence: 99%

“…Truncating the K-L expansion in this context amounts to using a "modified" prior covariance kernel given by (54). Since the eigenvalues λ k decay-exponentially fast for a smooth covariance kernel [28], algebraically fast in other cases-a small number of terms may be sufficient to capture almost all of the prior covariance.…”

Section: Dimensionality Reduction In Inverse Problemsmentioning

confidence: 99%

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Computationally efficient Bayesian inference for inverse problems.

Marzouk¹,

Najm²,

Rahn³

2007

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Bayesian statistics provides a foundation for inference from noisy and incomplete data, a natural mechanism for regularization in the form of prior information, and a quantitative assessment of uncertainty in the inferred results. Inverse problemsrepresenting indirect estimation of model parameters, inputs, or structural componentscan be fruitfully cast in this framework. Complex and computationally intensive forward models arising in physical applications, however, can render a Bayesian approach prohibitive. This difficulty is compounded by high-dimensional model spaces, as when the unknown is a spatiotemporal field.We present new algorithmic developments for Bayesian inference in this context, showing strong connections with the forward propagation of uncertainty. In particular, we introduce a stochastic spectral formulation that dramatically accelerates the Bayesian solution of inverse problems via rapid evaluation of a surrogate posterior. We also explore dimensionality reduction for the inference of spatiotemporal fields, using truncated spectral representations of Gaussian process priors. These new approaches are demonstrated on scalar transport problems arising in contaminant source inversion and in the inference of inhomogeneous material or transport properties.We also present a Bayesian framework for parameter estimation in stochastic models, where intrinsic stochasticity may be intermingled with observational noise. Evaluation of a likelihood function may not be analytically tractable in these cases, and thus several alternative Markov chain Monte Carlo (MCMC) schemes, operating on the product space of the observations and the parameters, are introduced.3 xxxx Acknowledgements

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Section: Resultsmentioning

confidence: 99%

Section: Dimensionality Reduction In Inverse Problemsmentioning

confidence: 99%

Computationally efficient Bayesian inference for inverse problems.

Marzouk¹,

Najm²,

Rahn³

2007

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“…Finally, mixed approaches in which an apparent source term is determined in the liquid and vapour zones representing the different phenomena were utilized in Ref. [12].…”

Section: Introductionmentioning

confidence: 99%

Estimation of a source term in a quasi steady two-dimensional heat transfer problem: application to an electron beam welding

et al. 2011

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In previous work, we have analyzed the feasibility of the estimation for a source term S(x, y, z) in a transversal section. The present study is concerned with a twodimensional inverse phase change problem. The goal is the estimation of the dissipated heat flux in the liquid zone (reconstruction of a source term in the energy equation) from experimentally measured temperatures in the solid zone. This work has an application in the electron beam welding of steels of thickness about 8 cm. The direct thermometallurgical problem is treated in a quasi steady two-dimensional longitudinal section (x, y). The beam displacement is normally in the y direction. But in the quasi steady simulation, the beam is steady in the study section. The sample is divided in the axial direction z in few sections. At each section, a source term is defined with a part of the beam and creates a vaporized zone and a fused zone. The goal of this work is the rebuilding of the complete source term with the estimations at each section. In this paper, we analyze the feasibility of the estimation. For this work, we use only the simulated measurements without noise.

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“…[25][26][27][28][29] First, unlike the previous efforts, a finite element based numerical heat transfer model considering non-linear material properties and effect of phase change is used to compute the weld pool geometry. Secondly, two well-tested nonlinear multivariate optimization techniques have been used for the estimation of the optimum value of absorptivity.…”

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confidence: 99%