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, Shubhankar

doi:10.1016/j.ijheatmasstransfer.2015.04.058

Cited by 6 publications

(4 citation statements)

References 26 publications

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“…In figure 9(a), the shape of the probability distribution is not similar to those obtained for schemes 1, 2, and 3. The reason for this is the application of multi-dimensional BIT, and it can also be seen in the work of Chakraborty and Das [25] and Parthasarathy and Balaji [26]. The reconstructed velocity profiles using the MAP values have been shown in figure 9(b) and velocity contour in figure 9(c).…”

Section: Calibration and Uq Of Model Coefficient C ϵ1mentioning

confidence: 87%

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Bayesian interface technique-based inverse estimation of closure coefficients of standard k − ϵ turbulence model by limiting the number of DNS data points for flow over a periodic hill

Kumar Chaurasia,

Chakraborty

2024

Inverse Problems

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Among different numerical methods for modeling turbulent flow, Reynolds-averaged Navier–Stokes (RANS) is the most commonly used and computationally reasonable. However, the accuracy of RANS is lower than that of other high-fidelity numerical methods. In this work, the uncertainties associated with the coefficients of the standard k − ϵ RANS turbulence model are estimated and calibrated to improve the accuracy. The calibration is performed by considering the coefficients individually as well as collectively. The first three coefficients of the standard k − ϵ turbulence model are calibrated among the five coefficients ( C μ , C ϵ 1 , C ϵ 2 , σ ϵ and σ k ). The Bayesian inference technique using the Metropolis–Hastings algorithm is applied to quantify uncertainties and calibration. Flow over a periodic hill is selected as a test case. The separation height of the bubble at x / h = 2 and x / h = 4 , along with the streamwise velocity at various locations, has been chosen as the quantities of interest for comparing the results with DNS. The calibration is performed using known high-fidelity data (direct numerical simulation) from the available data set. The velocity field is re-calculated from the calibrated closure coefficients and compared with the same calculated with the standard coefficients of k − ϵ turbulence model (baseline). The deviation of calibrated C µ is almost 50%–60% from baseline and for C ϵ 1 and C ϵ 2 it is 3%–12% and 6%–9% respectively. The algorithm is tested for different Reynold numbers and data points. A sensitivity analysis is also performed.

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Section: Calibration and Uq Of Model Coefficient C ϵ1mentioning

confidence: 87%

“…Xiao et al [14] emphasized the Bayesian inference technique (BIT) over the Kalman filter because BIT is more accurate and less time-consuming. BIT has been proven to be an efficient method for ill-posed heat transfer problems and other problems [25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

Bayesian interface technique-based inverse estimation of closure coefficients of standard k − ϵ turbulence model by limiting the number of DNS data points for flow over a periodic hill

Kumar Chaurasia,

Chakraborty

2024

Inverse Problems

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“…长期以来, 传热反问题求解的主要困难是其在数学上的不适定性 [32] , 即数据的微小变化会导致目作为传热反问题的一种, 热传导反问题在钢淬火 [33] 、再加热炉 [34] 、熔融物料反应器 [8] 、激光表面加热 [ 3 5~3 7 ] 、池沸腾 [ 3 8 ] 、降膜工艺 [ 3 9 ] 、盘式制动系统 [40,41] 、机械加工 [42] 、微波加热 [43] 、膨胀型涂料 [44] 等不同领域具有广泛的工业应用. Tikhonov正则化 [45,46] 、空间推进法 [47~50] 、函数规范法 [51] 、迭代正则化方法 [52] 或基于最大似然估计 [53] 的贝叶斯推理方法 [54] 等已被广泛研究并应用于求解此类问题. 其中, 由于三维瞬态热传导反问题通常存在严重的不适定性和高昂的计算成本, 在实际应用中开发快速稳定的求解策略十分重要.…”

Section: 识别传热反问题unclassified

Three-dimensional transient inverse heat conduction problems in the enhanced pool boiling heat transfer

et al. 2019

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“…To overcome the limitations of conventional deterministic estimation methods and the GUM, we propose a Bayesian inference approach to the problem of quantifying uncertainties in parameters inferred from a TRT test. There has been a recent increase in the use of Bayesian inference techniques for solutions to inverse problems in heat transfer [48][49][50][51][52][53][54]. This has been facilitated by improved computational capabilities and numerical sampling techniques, such as the Markov chain Monte Carlo (MCMC) technique [49].…”

Section: Introductionmentioning

confidence: 99%

Bayesian inference for thermal response test parameter estimation and uncertainty assessment

et al. 2018

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The effective ground thermal conductivity and borehole thermal resistance constitute information needed to design a ground-source heat pump (GSHP). In situ thermal response tests (TRTs) are considered reliable to obtain these parameters, but interpreting TRT data by a deterministic approach may result in significant uncertainties in the estimates. In light of the impact of the two parameters on GSHP applications, the quantification of uncertainties is necessary. For this purpose, in this study, we develop a stochastic method based on Bayesian inference to estimate the two parameters and associated uncertainties. Numerically generated noisy TRT data and reference sandbox TRT data were used to verify the proposed method. The posterior probability density functions obtained were used to extract the point estimates of the parameters and their credible intervals. Following its verification, the proposed method was applied to in situ TRT data, and the relationship between test time and estimation accuracy was examined. The minimum TRT time of 36 h recommended by ASHRAE produced an uncertainty of ~±21% for effective thermal conductivity. However, the uncertainty of estimation decreased exponentially with increasing TRT time, and was ±8.3% after a TRT time of 54 h, lower than the generally acceptable range of uncertainty of ±10%. Based on the obtained results, a minimum TRT time of 50 h is suggested and that of 72 h is expected to produce sufficiently accurate estimates for most cases.

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

Cited by 6 publications

References 26 publications

Bayesian interface technique-based inverse estimation of closure coefficients of standard k − ϵ turbulence model by limiting the number of DNS data points for flow over a periodic hill

Bayesian interface technique-based inverse estimation of closure coefficients of standard k − ϵ turbulence model by limiting the number of DNS data points for flow over a periodic hill

Three-dimensional transient inverse heat conduction problems in the enhanced pool boiling heat transfer

Bayesian inference for thermal response test parameter estimation and uncertainty assessment

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