Uncertainty quantification methodology for model parameters in sub-channel codes using MCMC sampling

Xin HE; Meiqi SONG; Xiaojing LIU

doi:10.11889/j.0253-3219.2023.hjs.46.120602

NUCLEAR TECHNIQUES, Volume. 46, Issue 12, 120602(2023)

Uncertainty quantification methodology for model parameters in sub-channel codes using MCMC sampling

Xin HE¹, Meiqi SONG^1、**, and Xiaojing LIU^1,2、*

Author Affiliations

¹College of Smart Energy, Shanghai Jiao Tong University, Shanghai 200240, China

²School of Nuclear Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

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Figures & Tables(11)

Fig. 1. Flowchart of uncertainty analysis

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$Comparison between the experimental and calculated void fraction values$

Fig. 2. Comparison between the experimental and calculated void fraction values

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Fig. 3. Error decline curve when establishing the BPNN surrogate model

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Fig. 4. Sample path of the adaptive Metropolis algorithm (a) Random-walk samples from s, (b) Random-walk samples from β

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Fig. 5. Frequency histogram of 20 000 iteration samples (a) Frequency histogram of s, (b) Frequency histogram of β

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$Envelop test for 95% confidence interval (a) Void fraction at 2 669 mm, (b) Void fraction at 3 177 mm$

Fig. 6. Envelop test for 95% confidence interval (a) Void fraction at 2 669 mm, (b) Void fraction at 3 177 mm

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$Calibration resultsof the two modified model parameters (a) Void fraction at 2 669 mm, (b) Void fraction at 3 177 mm$

Fig. 7. Calibration resultsof the two modified model parameters (a) Void fraction at 2 669 mm, (b) Void fraction at 3 177 mm

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Table 1. Proposed parameters for adaptive encryption

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Table 1. Proposed parameters for adaptive encryption

迭代次数Iteration times	$μ_{x_{1}}^{p r o}$	$μ_{x_{2}}^{p r o}$	$σ_{x_{1}}^{p r o}$	$σ_{x_{2}}^{p r o}$	$g ({μ_{x_{1}}}^{p r o}, {μ_{x_{2}}}^{p r o})$
0	2	2	0.1	0.1	43.061 8
1	2.060 339 78	2.161 652 62	0.194 794 50	0.183 065 97	24.478 4
2	2.293 104 12	2.613 720 11	0.290 378 64	0.175 015 99	10.389 2
3	2.533 876 10	3.096 206 72	0.443 189 61	0.162 979 61	2.439 26
4	2.913 810 26	3.537 998 59	0.340 335 16	0.132 918 88	0.587 00
5	3.076 087 01	3.778 482 20	0.515 250 26	0.180 676 64	0.002 125
6	3.019 567 73	4.001 705 07	0.404 149 85	0.285 124 67	8.715 76

Table 2. Uncertainty distribution of boundary condition parameters

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Table 2. Uncertainty distribution of boundary condition parameters

编号No.	相关参数Related parameter	标准差Standard deviation / %
1	压力Pressure	0.333
2	入口温度Inlet temperature	0.133
3	质量流量Mass flow	0.5
4	热流密度Heat flux	0.333
5	功率分布Power distribution	1

Table 3. Parameters proposed by adaptive algorithm iterations

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Table 3. Parameters proposed by adaptive algorithm iterations

迭代次数Iteration times	$μ_{s}^{p r o}$	$μ_{β}^{p r o}$	$σ_{s}^{p r o}$	$σ_{β}^{p r o}$	$g ({μ_{x_{1}}}^{p r o}, {μ_{x_{2}}}^{p r o})$
0	0	0	0.1	0.1	267.606
1	0.326 361 55	-0.121 673 84	0.101 055 54	0.146 140 04	230.899
2	0.540 180 39	0.001 248 39	0.153 653 07	0.267 939 87	241.762

Table 4. Uncertainty distribution of the mean and standard variance for the model parameters
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Table 4. Uncertainty distribution of the mean and standard variance for the model parameters
模型参数Model parameter 均值Mean value 标准差Standard deviation
滑速比Slip ratio 0.498 850 36 0.187 062 32
湍流交混系数Turbulent mixing parameter 0.041 123 49 0.500 499 95

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Xin HE, Meiqi SONG, Xiaojing LIU. Uncertainty quantification methodology for model parameters in sub-channel codes using MCMC sampling[J]. NUCLEAR TECHNIQUES, 2023, 46(12): 120602

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