Author Affiliations
1College of Smart Energy, Shanghai Jiao Tong University, Shanghai 200240, China2School of Nuclear Science and Engineering, Shanghai Jiao Tong University, Shanghai 200240, Chinashow less
Fig. 1. Flowchart of uncertainty analysis
Fig. 2. Comparison between the experimental and calculated void fraction values
Fig. 3. Error decline curve when establishing the BPNN surrogate model
Fig. 4. Sample path of the adaptive Metropolis algorithm (a) Random-walk samples from s, (b) Random-walk samples from β
Fig. 5. Frequency histogram of 20 000 iteration samples (a) Frequency histogram of s, (b) Frequency histogram of β
Fig. 6. Envelop test for 95% confidence interval (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
迭代次数Iteration times | | | | | |
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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 |
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Table 1. Proposed parameters for adaptive encryption
编号No. | 相关参数Related parameter | 均值Mean value | 标准差Standard deviation / % |
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1 | 压力Pressure | 0 | 0.333 | 2 | 入口温度Inlet temperature | 0 | 0.133 | 3 | 质量流量Mass flow | 0 | 0.5 | 4 | 热流密度Heat flux | 0 | 0.333 | 5 | 功率分布Power distribution | 0 | 1 |
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Table 2. Uncertainty distribution of boundary condition parameters
迭代次数Iteration times | | | | | |
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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 |
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Table 3. Parameters proposed by adaptive algorithm iterations
模型参数Model parameter | 均值Mean value | 标准差Standard deviation |
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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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Table 4. Uncertainty distribution of the mean and standard variance for the model parameters