Machine Learning Applications and Uncertainty Quantification Analysis for Reflood Tests
Abstract
:Featured Application
Abstract
1. Introduction
2. Methods and Data Preparation
2.1. FLECHT SEASET Reflood Tests
2.2. UQ Analysis
2.3. Machine Learning Model
2.3.1. Linear Regression
2.3.2. Random Forest
2.3.3. Deep Neural Networks
2.4. Dataset
2.5. Standard Deviation Method
3. Results and Discussions
3.1. Uncertainty Quantification Results
3.2. Machine Learning Predictions and Comparisons
3.3. Sensitive Physical Model Investigation Results
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
ARD | Absolute Relative Difference |
BEPU | Best Estimate Plus Uncertainty |
COBRA-TF | Coolant-Boiling in Rod Arrays—Two Fluid |
DA | Data Assimilation |
DFFB | Dispersed Flow Film Boiling |
DNN | Deep Neural Network |
ECCS | Emergency Core Cooling System |
FEBA | Flooding Experiment with Blocked Arrays |
FLECHT SEASET | Full-Length Emergency Core Cooling Heat Transfer-Separate Effects Tests and System-Effects Tests |
IAFB | Inverted Annular Film Boiling |
LOCA | Loss Of Coolant Accident |
LR | Linear Regression |
MARS | Multidimensional Analysis of Reactor Safety |
MSE | Mean Squared Error |
PAPIRUS | Parallel Computing Platform Integrated for Uncertainty and Sensitivity Analysis |
PWR | Pressurized Water Reactor |
RBHT | Rod Bundle Heat Transfer |
RELAP | Reactor Excursion and Leak Analysis Program |
RF | Random Forest |
SFB | Saturated Film Boiling |
SPACE | Safety and Performance Analysis Code for Nuclear Power Plants |
STARU | Sampling Method for Highly Nonlinear System Uncertainty Analysis |
STD | Standard Deviation |
SVM | Support Vector Machine |
TRACE | TRAC/RELAP Advanced Computational Engine |
UQ | Uncertainty Quantification |
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Test No. | Flooding Rate (m/s) | Power (W/m) | Initial Clad Temperature at 1.83 m (K) | Pressure (MPa) |
---|---|---|---|---|
31021 | 0.0386 | 1300 | 1153 | 0.28 |
31302 | 0.0765 | 2300 | 1142 | 0.28 |
31504 | 0.0240 | 2300 | 1136 | 0.28 |
33849 | 0.0259 | 1900 | 1018 | 0.28 |
34103 | 0.0381 | 2400 | 1158 | 0.28 |
34316 | 0.0250 | 2400 | 1162 | 0.28 |
34420 | 0.0389 | 2400 | 1392 | 0.27 |
34711 | 0.0170 | 1400 | 1161 | 0.13 |
35050 | 0.0259 | 1600 | 1031 | 0.14 |
C | Type | Parameter Descriptions | Uncertainty Band (Min to Max) |
---|---|---|---|
1 | Form loss | Form loss coefficient for forward flow corresponding to elevation | 0.01–0.24 |
2 | Form loss coefficient for reverse flow corresponding to elevation | 0.98–1.55 | |
3 | Interfacial friction factors | Interfacial friction coefficient between vapor-droplet | 0.99–1.80 |
4 | Continuous liquid–vapor interfacial friction factor for bubbly flow | 1.43–2.04 | |
5 | Continuous liquid–vapor interfacial friction factor for slug flow | 0.35–1.07 | |
6 | Continuous liquid–vapor interfacial friction factor for annular flow | 0.46–1.05 | |
7 | Continuous liquid–vapor interfacial friction factor for horizontally stratified flow | 0.08–0.48 | |
8 | Continuous liquid–vapor interfacial friction factor for inverted annular flow | 0.82–1.41 | |
9 | Continuous liquid–vapor interfacial friction factor for inverted slug flow | 0.72–1.04 | |
10 | Entrainment | Droplet entrainment factor | 0.15–0.40 |
11 | Droplet de-entrainment factor | 0.22–1.20 | |
12 | Interphase heat transfer coefficients | Single-phase liquid flow regime | 1.45–2.08 |
13 | Bubbly flow regime | 0.01–0.52 | |
14 | Slug flow regime | 1.61–2.06 | |
15 | Bubbly–annular flow regime | 1.08–1.51 | |
16 | Cap/slug–annular transition flow regime | 0.59–1.09 | |
17 | Annular flow regime | 0.62–1.05 | |
18 | Stratified flow regime | 0.85–1.45 | |
19 | Stratified–bubbly transition flow regime | 0.46–0.87 | |
20 | Cap/slug–stratified transition flow regime | 0.86–1.36 | |
21 | Bubbly/annular–stratified transition flow regime | 1.43–2.33 | |
22 | Cap/slug–bubbly/annular–stratified transition flow regime | 0.54–1.09 | |
23 | Annular–stratified transition flow regime | 0.63–1.31 | |
24 | Inverted annular flow regime | 0.29–0.79 | |
25 | Hot wall interpolation regime | 0.30–0.80 | |
26 | Inverted slug flow regime | 0.65–1.02 | |
27 | Dispersed flow regime | 1.59–2.30 | |
28 | Single-phase vapor flow regime | 0.58–1.35 | |
29 | Flashing | 0.18–0.71 | |
30 | Convective heat transfer | Noncondensable gas–vapor–water mixture or stratified flow heat transfer modes | 0.99–1.60 |
31 | Natural convection heat transfer model | 0.06–0.72 | |
32 | Forced convection heat transfer model | 1.28–1.83 | |
33 | Subcooled nucleate boiling heat transfer model | 0.45–1.05 | |
34 | Saturated nucleate boiling heat transfer model | 1.25–2.21 | |
35 | Subcooled transition boiling heat transfer model | 0.35–1.08 | |
36 | Saturated transition boiling heat transfer model | 1.34–1.84 | |
37 | Subcooled film boiling heat transfer model | 0.23–0.42 | |
38 | Saturated film boiling heat transfer model | 0.77–1.13 | |
39 | Single-phase vapor heat transfer model | 0.31–0.79 | |
40 | Supercritical flow heat transfer model | 0.40–1.12 | |
41 | Condensation heat transfer model | 0.83–1.42 | |
42 | Post-CHF heat transfer model | 0.60–1.11 |
Quantity | DNN | LR | RF |
---|---|---|---|
Number of hidden layers | 2 | - | - |
Number of nodes in the hidden layer | 256, 128 | - | - |
Loss function | MSE | MSE | MSE |
Activator | ReLU | - | - |
Optimizer | Adam | - | - |
Training samples | 20,000 | 20,000 | 20,000 |
Testing samples | 4000 | 4000 | 4000 |
Number of trees | - | - | 200 |
Random seed number (random state) | - | - | 10 |
Number of epochs | 200 | - | - |
Validation split | 10% | - | - |
Quantity | LR | RF | DNN | System Code |
---|---|---|---|---|
Computation time, minutes | 0.21 | 2.74 | 2.51 | ~16,000 |
Machine used | Desktop | Desktop | Desktop | Workstation |
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Tiep, N.H.; Kim, K.-D.; Jeong, H.-Y.; Xuan-Mung, N.; Hoang, V.-K.; Ngoc Anh, N.; Vu, M.T. Machine Learning Applications and Uncertainty Quantification Analysis for Reflood Tests. Appl. Sci. 2024, 14, 324. https://doi.org/10.3390/app14010324
Tiep NH, Kim K-D, Jeong H-Y, Xuan-Mung N, Hoang V-K, Ngoc Anh N, Vu MT. Machine Learning Applications and Uncertainty Quantification Analysis for Reflood Tests. Applied Sciences. 2024; 14(1):324. https://doi.org/10.3390/app14010324
Chicago/Turabian StyleTiep, Nguyen Huu, Kyung-Doo Kim, Hae-Yong Jeong, Nguyen Xuan-Mung, Van-Khanh Hoang, Nguyen Ngoc Anh, and Mai The Vu. 2024. "Machine Learning Applications and Uncertainty Quantification Analysis for Reflood Tests" Applied Sciences 14, no. 1: 324. https://doi.org/10.3390/app14010324
APA StyleTiep, N. H., Kim, K.-D., Jeong, H.-Y., Xuan-Mung, N., Hoang, V.-K., Ngoc Anh, N., & Vu, M. T. (2024). Machine Learning Applications and Uncertainty Quantification Analysis for Reflood Tests. Applied Sciences, 14(1), 324. https://doi.org/10.3390/app14010324