Inverse estimation of thermal properties using Bayesian inference and three different sampling techniques

Somasundharam, S.; Reddy, K. S.

doi:10.1080/17415977.2016.1138946

Cited by 11 publications

(8 citation statements)

References 14 publications

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“…The accepted realizations constitute the solution of the inverse problem in the form of a probabilistic estimate of process outcomes. MCMC is based on Bayes' theorem and is utilized in many inverse problems due to its simplicity 34–36 . According to Bayes' theorem, measurements

Y_{\exp} ((), t_{normalk}) \in ℝ^{N_{k} \times 3}

, with N k the number of experimental data, which correspond to covered lengths of the three lineal sensors at times t 1 … t k , are connected to the corresponding surrogate model responses S = ( S 1 , S 2 , S 3 )

\in ℝ^{N_{k} \times 3}

as follows:

bold-italicP (|(), S, {bold-italicY}_{boldexp}) \propto bold-italicP (|(), {bold-italicY}_{boldexp}, S) bold-italicP ((), S) .

where P ( S | Y exp ) denotes the posterior probability, P ( Y exp | S ) the likelihood distribution and P ( S ) the prior distribution.…”

Section: Methodsmentioning

confidence: 99%

“…MCMC is based on Bayes' theorem and is utilized in many inverse problems due to its simplicity. [34][35][36] According to Bayes' theorem, measurements Y exp t k ð Þℝ N k × 3 , with N k the number of experimental data, which correspond to covered lengths of the three lineal sensors at times t 1 …t k , are connected to the corresponding surrogate model responses S = (S 1 , S 2 , S 3 ) ℝ N k × 3 as follows:…”

Section: Inverse Algorithmmentioning

confidence: 99%

See 1 more Smart Citation

Real time uncertainty estimation in filling stage of resin transfer molding process

Tifkitsis

Skordos

2020

Polymer Composites

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This paper addresses the development of a digital twin, based on an inversion procedure, integrating process monitoring with simulation of composites manufacturing to provide a real time probabilistic estimation of process outcomes. A computationally efficient surrogate model was developed based on Kriging. The surrogate model reduces the computational time allowing inversion in real time. The tool was implemented in the filling stage of an resin transfer molding processing of a carbon fiber reinforced part resulting in the probabilistic prediction of unknown parameters. Flow monitoring data were acquired using dielectric sensors. The inverse scheme based on Markov Chain Monte Carlo uses input parameters, such as permeability and viscosity, as unknown stochastic variables. The scheme enhances the model by reducing model parameter uncertainty yielding an accurate on line estimation of process outcomes and critical events such as racetracking. The inverse scheme provides a prediction of filling duration with an error of about 5% using information obtained within the first 30% of the process.

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Y_{\exp} ((), t_{normalk}) \in ℝ^{N_{k} \times 3}

\in ℝ^{N_{k} \times 3}

as follows:

bold-italicP (|(), S, {bold-italicY}_{boldexp}) \propto bold-italicP (|(), {bold-italicY}_{boldexp}, S) bold-italicP ((), S) .

where P ( S | Y exp ) denotes the posterior probability, P ( Y exp | S ) the likelihood distribution and P ( S ) the prior distribution.…”

Section: Methodsmentioning

confidence: 99%

Section: Inverse Algorithmmentioning

confidence: 99%

Real time uncertainty estimation in filling stage of resin transfer molding process

Tifkitsis

Skordos

2020

Polymer Composites

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“…The results from the Bayesian framework in conjunction with Markov random field (MRF)-MCMC showed the ability in providing solutions with the uncertainties quantified. Different sampling techniques for the use of Bayesian framework prove the efficiency in retrieving the thermophysical properties using inverse method [38]. The results from the work of Deng and Hwang [39] give evidence that the Bayesian method delivers the best training method with the back propagation algorithm.…”

Section: Introductionmentioning

confidence: 99%

Simultaneous estimation of unknown parameters using a-priori knowledge for the estimation of interfacial heat transfer coefficient during solidification of Sn–5wt%Pb alloy—an ANN-driven Bayesian approach

2019

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The present methodology focuses on model reduction in which the prevalent one-dimensional transient heat conduction equation for a horizontal solidification of Sn-5wt%Pb alloy is replaced with Artificial Neural Network (ANN) in order to estimate the unknown constants present in the interfacial heat transfer coefficient correlation. As a novel approach, ANN-driven forward model is synergistically combined with Bayesian framework and Genetic algorithm to simultaneously estimate the unknown parameters and modelling error. Gaussian noise is then added to the temperature distribution obtained using the forward approach to represent real-time experiments. The hallmark of the present work is to reduce the computational time of both the forward and the inverse methods and to simultaneously estimate the unknown parameters using a-priori engineering knowledge. The results of the present methodology prove that the simultaneous estimation of unknown parameters can be effectively obtained only with the use of Bayesian framework.

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“…The threedimensional direct problem involving turbulent, unsteady and conjugate heat transfer boundary condition is numerically solved for known values of 47 different heat fluxes, and temperature histories of 18 different locations inside the brake disc were obtained. Somasundharam and Reddy [15] used MH-MCMC sampling algorithm in Bayesian inverse framework and estimated thermal conductivity, heat transfer coefficient and emissivity. They used Parallel Tempering (PT) and Evolutionary Monte Carlo (EMC) along with MH-MCMC to sample through correlated posterior probability density function (PPDF) to retrieve the three mentioned thermal properties.…”

Section: Introductionmentioning

confidence: 99%

“…They concluded that at high noise levels, Parallel Tempering (PT) and Evolutionary Monte Carlo (EMC) perform equally and estimate the parameter with the deviation of maximum 9%. Sensitivity analysis [15][16][17][18][19] is an important study that indicates the effectiveness of the change in parameter estimated on the temperature. Sensitivity analysis has control over the selection of the inverse method.…”

Section: Introductionmentioning

confidence: 99%

A Bayesian inference approach: estimation of heat flux from fin for perturbed temperature data

Kumar

Gnanasekaran

2018

Sādhanā

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This paper reports the estimation of the unknown boundary heat flux from a fin using the Bayesian inference method. The setup consists of a rectangular mild steel fin of dimensions 250915096 mm 3 and an aluminium base plate of dimensions 250915098 mm 3. The fin is subjected to constant heat flux at the base and the fin setup is modelled using ANSYS14.5. The problem considered is a conjugate heat transfer from the fin, and the Navier-Stokes equation is solved to obtain the flow parameters. Grid independence study is carried out to fix the number of grids for the study considered. To reduce the computational cost, computational fluid dynamics (CFD) is replaced with artificial neural network (ANN) as the forward model. The Markov Chain Monte Carlo (MCMC) powered by Metropolis-Hastings sampling algorithm along with the Bayesian framework is used to explore the estimation space. The sensitivity analysis of the estimated temperature with respect to the unknown parameter is discussed to know the dependency of the temperature with the parameter. This paper signifies the effect of a prior model on the execution of the inverse algorithm at different noise levels. The unknown heat flux is estimated for the surrogated temperature and the estimates are reported as mean, Maximum a Posteriori (MAP) and standard deviation. The effect of a-priori information on the estimated parameter is also addressed. The standard deviation in the estimation process is referred to as the uncertainty associated with the estimated parameters.

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Inverse estimation of thermal properties using Bayesian inference and three different sampling techniques

Cited by 11 publications

References 14 publications

Real time uncertainty estimation in filling stage of resin transfer molding process

Real time uncertainty estimation in filling stage of resin transfer molding process

Simultaneous estimation of unknown parameters using a-priori knowledge for the estimation of interfacial heat transfer coefficient during solidification of Sn–5wt%Pb alloy—an ANN-driven Bayesian approach

A Bayesian inference approach: estimation of heat flux from fin for perturbed temperature data

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