Estimation of parameters in multi-mode heat transfer problems using Bayesian inference – Effect of noise and a priori

Parthasarathy, Siddharth; Balaji, C.

doi:10.1016/j.ijheatmasstransfer.2007.08.031

Cited by 62 publications

(18 citation statements)

References 6 publications

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“…In general, prior information in the form of Gaussian distribution is commonly employed in inverse heat transfer literatures. Parathasarathy and Balaji [1] studied the different forms of prior model and its effects in the estimation of single and multiple parameters. In their work, they demonstrated that in multi-parameter estimation, Bayesian inference tends to point to alternate feasible solutions when highly correlated parameters are retrieved using non-informative prior models.…”

Section: Introductionmentioning

confidence: 99%

Updating Prior Parameters Based on Likelihood Function-Bayesian Method for Parameter Estimation at High Measurement Uncertainty

Somasundharam¹,

Reddy²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. One approach in statistical analysis that distinguishes between frequentist and Bayesian is the inclusion of available prior information about the data even before measuring/ surveying the data. Many researchers argued that the inclusion of prior information resulted in a better model prediction/parameter estimation. Bayesian inference is repeatedly used in inverse problems to retrieve parameters due to the development of high efficient sampling algorithms such as Markov Chain Monte-Carlo (MCMC). Inverse problems are generally ill-posed in nature. Nevertheless, the inclusion of prior information reduces the ill-posedness of the problem to an extent. Any inverse problem relies on measured data by physical sensors, therefore induced random errors greatly affects the quality of estimation. When the uncertainty of the measured data is high, the inferences made from the resulting sampling distributions are nearly the same as the supplied prior information. The reason is that, probability of samples nearer to prior information is more at higher uncertainties of measurement and has more chance to get repeatedly accepted than the samples that are close to actual value. Therefore, in this work an effort is made to update the prior hyper parameters in each iterations of the MCMC algorithm based on the history of the likelihood function. The applicability of method is demonstrated by retrieving parameters from 1-D fin experiment. Three thermal properties such as thermal conductivity, heat transfer coefficient and emissivity are retrieved simultaneously. The estimation is carried out for both error and errorless temperature measurements and the results show that, the estimated parameters with the proposed method are in excellent agreement with the true parameter value and a maximum of 7% deviation occurs in estimating heat transfer coefficient at a measurement error of ±0.3K 4073

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Section: Introductionmentioning

confidence: 99%

Updating Prior Parameters Based on Likelihood Function-Bayesian Method for Parameter Estimation at High Measurement Uncertainty

Somasundharam¹,

Reddy²

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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“…The premise is that the prior noise statistics should be known accurately. In order to solve this problem, several adaptive algorithms have been proposed to estimate the noise information online, such as Bayesian algorithm [5][6], maximum likelihood algorithm [7][8], correlation algorithm [9][10] and covariance matching algorithm [11][12], etc.…”

Section: Introductionmentioning

confidence: 99%

Maximum Likelihood Principle Based Adaptive UKF Algorithm

Guo¹,

Huang²

2016

IJSIP

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“…It is also interesting to note that this technique has been used to estimate a variety of unknown parameters namely thermal conductivity and convective heat transfer co-efficient at the surface [9,10], time dependent heat flux [11], temperature dependent thermophysical properties and transient boundary heat flux [12], transient heat source in a radiatively participating medium [13] etc. Wang and Zabaras [13] considered a 3D combined conduction radiation problem in a participating medium with an aim to reconstruct an unknown transient heat source.…”

Section: Introductionmentioning

confidence: 99%

Application of Bayesian Inference Technique for the reconstruction of an isothermal hot spot inside a circular disc from peripheral temperature measurement – A critical assessment

Chakraborty

2015

International Journal of Heat and Mass Transfer

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Estimation of parameters in multi-mode heat transfer problems using Bayesian inference – Effect of noise and a priori

Cited by 62 publications

References 6 publications

Updating Prior Parameters Based on Likelihood Function-Bayesian Method for Parameter Estimation at High Measurement Uncertainty

Updating Prior Parameters Based on Likelihood Function-Bayesian Method for Parameter Estimation at High Measurement Uncertainty

Maximum Likelihood Principle Based Adaptive UKF Algorithm

Application of Bayesian Inference Technique for the reconstruction of an isothermal hot spot inside a circular disc from peripheral temperature measurement – A critical assessment

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