Startseite Technik Reliability assessment of equal height difference passive containment cooling system based on the adaptive metamodel-based subset importance sampling method in inverse uncertainty quantification framework
Artikel
Lizenziert
Nicht lizenziert Erfordert eine Authentifizierung

Reliability assessment of equal height difference passive containment cooling system based on the adaptive metamodel-based subset importance sampling method in inverse uncertainty quantification framework

  • Hong Jiang und Changhong Peng EMAIL logo
Veröffentlicht/Copyright: 3. November 2025
Veröffentlichen auch Sie bei De Gruyter Brill

Abstract

To enhance computational efficiency in estimating the posterior failure probability of passive systems, this study proposes an innovative framework integrating inverse uncertainty quantification (IUQ) with adaptive metamodel-based subset importance sampling (AM-SIS). This approach leverages updated input parameter distributions for precise posterior failure probability assessment. Within the IUQ framework, Bayesian neural networks is employed to assist established Markov Chain Monte Carlo methods for posterior sampling, significantly reducing computational costs. The coupled IUQ-AM-SIS framework is validated on polynomial benchmark cases and the equal height difference passive containment cooling system (EHDPCCS), examining scenarios with single and double calibration parameters. Results demonstrate that integrating the AM-SIS method significantly improves computational efficiency for posterior failure probability estimation, particularly in low failure probability regimes.


Corresponding Author: Changhong Peng, School of Nuclear Science and Technology, University of Science and Technology of China, No. 96, Jinzhai Road, Baohe District 230026, Hefei, China, E-mail:

  1. Research ethics: Not applicable.

  2. Informed consent: Not applicable.

  3. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  4. Use of Large Language Models, AI and Machine Learning Tools: None declared.

  5. Conflict of interest: We declare that we have no financial or personal relationships with other people or organizations that can inappropriately influence our work. There is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled “Reliability assessment of equal height difference passive containment cooling system based on the adaptive metamodel-based subset importance sampling method in inverse uncertainty quantification framework”.

  6. Research funding: None declared.

  7. Data availability: Not applicable.

References

Apostolakis, G.E. (1994). A commentary on model uncertainty. Proc. Workshop I Adv. Topics Risk Reliab. Anal-Model Uncertainty: Its Character Quantification, Annapolis, MD, pp. 973–980.Suche in Google Scholar

Barbano, R., Zhang, C., Arridge, S., Jin, B. (2021). Quantifying model uncertainty in inverse problems via Bayesian deep gradient descent. In: Proceedings of 25th International Conference on Pattern Recognition (ICPR). IEEE, Milan, Italy, pp. 1392–1399.10.1109/ICPR48806.2021.9412521Suche in Google Scholar

Buhmann, M.D. (2000). Radial basis functions. Acta Numerica. 9: 1–38, https://doi.org/10.1007/978-3-642-18754-4_3.Suche in Google Scholar

Burgazzi, L. (2004). Evaluation of uncertainties related to passive systems performance. Nucl. Eng. Des. 230: 93–106, https://doi.org/10.1016/j.nucengdes.2003.10.011 Suche in Google Scholar

Burgazzi, L. (2007). Addressing the uncertainties related to passive system reliability. Prog. Nucl. Energy. 49: 93–102, https://doi.org/10.1016/j.pnucene.2006.10.003.Suche in Google Scholar

Ferson, S., and Ginzburg, L.R. (1996). Different methods are needed to propagate ignorance and variability. Reliab. Eng Syst. Safety 54: 133–144, https://doi.org/10.1016/S0951-8320(96)00071-3.Suche in Google Scholar

Ghahramani, Z. (2016). A history of Bayesian neural networks. In: NIPS Workshop on Bayesian Deep Learning. Cambridge, UK. https://www.youtube.com/watch?v=FD8l2vPU5FY.Suche in Google Scholar

Goan, E. and Fookes, C. (2020). In: Mengersen, K., Pudlo, P., and Robert, C. (Eds.), Case studies in applied Bayesian data science. Lecture notes in mathematics, 2259. Springer International Publishing, Cham, pp. 45–87.10.1007/978-3-030-42553-1_3Suche in Google Scholar

Guo, H., Zhao, X., Cai, Q., Huang, L. (2018). Iterative method on recognition of sensitive parameter for nuclear reactor passive system physical progress. J. Natl. Univ. Defense Technol. 40: 168–174, https://doi.org/10.11887/j.cn.201802027.Suche in Google Scholar

Hoffman, F.O. and Hammonds, J.S. (1994). Propagation of uncertainty in risk assessments: the need to distinguish between uncertainty due to lack of knowledge and uncertainty due to variability. Risk Anal. 14: 707–712, https://doi.org/10.1111/j.1539-6924.1994.tb00281.x.Suche in Google Scholar PubMed

Huang, M., Peng, C., and Liu, Z. (2023). Analysis of depressurization ability for IRIS containment during SBLOCAs using RELAP5 and CONTEMPT. Ann. Nucl. Energy. 180: 109466, https://doi.org/10.1016/j.anucene.2022.109466.Suche in Google Scholar

Huang, X., Zong, W., Wang, T., Lin, Z., Ren, Z., Lin, C. and Yin, Y. (2020). Study on typical design basis conditions of HPR1000 with nuclear safety analysis code ATHLET. Front. Energy Res. 8: 127, https://doi.org/10.3389/fenrg.2020.00127.Suche in Google Scholar

Hui, K., Chen, W., Zhao, Q., Li, S., and Yan, J. (2023). Experimental study on transient heat transfer characteristics during the dropping of containment pressure. Int. J. Ther. Sci. 185: 108093, https://doi.org/10.1016/j.ijthermalsci.2022.108093.Suche in Google Scholar

IAEA (2014). Progress in methodologies for the assessment of passive safety system reliability in advanced reactors. IAEA-TECDOC-1752, International Atomic Energy Agency, https://www.iaea.org/publications/10783/progress-in-methodologies-for-the-assessment-of-passive-safety-system-reliability-in-advanced-reactors.Suche in Google Scholar

Jiang, H., Li, H., Yu, S., and Peng, C. (2025). Reliability assessment of passive EHRS of IRIS based on the AM-SIS-ANN method. Ann. Nucl. Energy 224: 111707, https://doi.org/10.1016/j.anucene.2025.111707.Suche in Google Scholar

Lancaster, P. and Salkauskas, K. (1981). Surfaces generated by moving least squares methods. Math. Comput. 37: 141–158, https://doi.org/10.1090/S0025-5718-1981-0616367-1.Suche in Google Scholar

Ma, X., and Zabaras, N. (2009). An efficient Bayesian inference approach to inverse problems based on an adaptive sparse grid collocation method. Inverse Problems. 25: 035013, https://doi.org/10.1088/0266-5611/25/3/035013.Suche in Google Scholar

Marques, M., Pignatel, J., Saignes, P., D’auria, F., Burgazzi, L., Müller, C., Bolado-Lavin, R., Kirchsteiger, C., La Lumia, V. and Ivanov, I. (2005). Methodology for the reliability evaluation of a passive system and its integration into a probabilistic safety assessment. Nucl. Eng. Des. 235: 2612–2631, https://doi.org/10.1016/j.nucengdes.2005.06.008.Suche in Google Scholar

Marzouk, Y.M., and Najm, H.N. (2009). Dimensionality reduction and polynomial chaos acceleration of Bayesian inference in inverse problems. J. Comput. Phys. 228: 1862-1902, https://doi.org/10.1016/j.jcp.2008.11.024.Suche in Google Scholar

Marzouk, Y.M., Najm, H.N., and Rahn, L.A. (2007). Stochastic spectral methods for efficient Bayesian solution of inverse problems. J. Comput. Phys. 224: 560–586, https://doi.org/10.1016/j.jcp.2006.10.010.Suche in Google Scholar

Nagel, J.B. (2019). Bayesian techniques for inverse uncertainty quantification. IBK Bericht 504, ETH Zürich.Suche in Google Scholar

O’Hagan, A. (2006). Bayesian analysis of computer code outputs: a tutorial. Reliab. Eng. Syst. Safety 91: 1290–1300, https://doi.org/10.1016/j.ress.2005.11.025.Suche in Google Scholar

Oberkampf, W.L., Helton, J.C., Joslyn, C.A., Wojtkiewicz, S.F., Ferson, S. (2004). Challenge problems: uncertainty in system response given uncertain parameters. Reliab. Eng. Syst. Safety 85: 11–19, https://doi.org/10.1016/j.ress.2004.03.002.Suche in Google Scholar

Olivier, A., Shields, M.D., and Graham-Brady, L. (2021). Bayesian neural networks for uncertainty quantification in data-driven materials modeling. Comput. Methods Appl. Mech. Eng. 386: 114079, https://doi.org/10.1016/j.cma.2021.114079.Suche in Google Scholar

Pagani, L.P., Apostolakis, G.E., and Hejzlar, P. (2005). The impact of uncertainties on the performance of passive systems. Nucl. Technol. 149: 129–140, https://doi.org/10.13182/NT149-129.Suche in Google Scholar

Rao, K.D., Kushwaha, H., Verma, A.K., Srividya, A. (2007). Quantification of epistemic and aleatory uncertainties in level-1 probabilistic safety assessment studies. Reliab. Eng. Syst. Safety 92: 947–956, https://doi.org/10.1016/j.ress.2006.07.002.Suche in Google Scholar

Santner, T.J., Williams, B.J., Notz, W.I. (2003). The design and analysis of computer experiments. Springer, 1st ed.10.1007/978-1-4757-3799-8_1Suche in Google Scholar

Schueller, G.I. (2009). Efficient Monte Carlo simulation procedures in structural uncertainty and reliability analysis-recent advances. Struct. Eng. Mech. 32: 1–20, https://doi.org/10.12989/sem.2009.32.1.001.Suche in Google Scholar

Schueller, G.I., and Pradlwarter, H.J. (2007). Benchmark study on reliability estimation in higher dimensions of structural systems—an overview. Struct. Saf. 29: 167–182, https://doi.org/10.1016/j.strusafe.2006.07.010.Suche in Google Scholar

Sui, D., Lu, D., Shang, C., Wei, Y., Zhang, X. (2017). Response characteristics of HPR1000 primary circuit under different working conditions of the atmospheric relief system after SBLOCA. Nucl. Eng. Des. 314: 307–317, https://doi.org/10.1016/j.nucengdes.2017.01.027.Suche in Google Scholar

Suykens, J.A., and Vandewalle, J. (1999). Least squares support vector machine classifiers. Neural Process. Lett. 9: 293–300, https://doi.org/10.1023/A:1018628609742.10.1023/A:1018628609742Suche in Google Scholar

Van Oijen, M., Rougier, J., and Smith, R. (2005). Bayesian calibration of process-based forest models: bridging the gap between models and data. Tree Physiol. 25: 915–927, https://doi.org/10.1093/treephys/25.7.915.Suche in Google Scholar PubMed

Wang, G., Wang, Z., Hu, B., Wang, Z., Zhang, J. (2015). Sensitivity analysis on containment pressure response using coupled DAKOTA and WGOTHIC codes. Atomic Energy Scie. Technol. 49: 2176–2180, https://doi.org/10.7538/yzk.2015.49.12.2176.Suche in Google Scholar

Winkler, R.L. (1996). Uncertainty in probabilistic risk assessment. Reliab. Eng. Syst. Safety 54: 127–132, https://doi.org/10.1016/S0951-8320(96)00070-1.Suche in Google Scholar

Wu, X. and Kozlowski, T. (2017). Inverse uncertainty quantification of reactor simulations under the Bayesian framework using surrogate models constructed by polynomial chaos expansion. Nucl. Eng. Des. 313: 29–52, https://doi.org/10.1016/j.nucengdes.2016.11.032.Suche in Google Scholar

Wu, X., Kozlowski, T., and Meidani, H. (2018a). Kriging-based inverse uncertainty quantification of nuclear fuel performance code BISON fission gas release model using time series measurement data. Reliab. Eng. Syst. Safety 169: 422–436, https://doi.org/10.1016/j.ress.2017.09.029.Suche in Google Scholar

Wu, X., Kozlowski, T., Meidani, H., Shirvan, K. (2018b). Inverse uncertainty quantification using the modular Bayesian approach based on Gaussian process, Part 1: theory. Nucl. Eng. Des. 335: 339–355, https://doi.org/10.1016/j.nucengdes.2018.06.004.Suche in Google Scholar

Wu, X., Mui, T., Hu, G., Meidani, H., Kozlowski, T. (2017). Inverse uncertainty quantification of TRACE physical model parameters using sparse gird stochastic collocation surrogate model. Nucl. Eng. Des. 319: 185–200, https://doi.org/10.1016/j.nucengdes.2017.05.011.Suche in Google Scholar

Xie, Z., Yaseen, M., and Wu, X. (2024). Functional PCA and deep neural networks-based Bayesian inverse uncertainty quantification with transient experimental data. Comput. Methods Appl. Mech. Eng. 420: 116721, https://doi.org/10.1016/j.cma.2023.116721.Suche in Google Scholar

Xing, J., Liu, Z., Ma, W., Yuan, Y., Sun, Z., Li, W. and Wang, H. (2021). Scaling analysis and evaluation for the design of integral test facility of HPR1000 containment (PANGU). Nucl. Eng. Des. 373: 111035, https://doi.org/10.1016/j.nucengdes.2020.111035.Suche in Google Scholar

Xiu, D. and Karniadakis, G.E. (2002). The Wiener–Askey polynomial chaos for stochastic differential equations. SIAM J. Sci. Comput. 24: 619–644, https://doi.org/10.1137/S1064827501387826.Suche in Google Scholar

Zhao, Q., Tian, Y., Hui, K., Wang, X., Chong, D. and Wang, J. (2024). Simulation study on the transient operating characteristics of equal height difference passive containment cooling system. Ann. Nucl. Energy 209: 110808, https://doi.org/10.1016/j.anucene.2024.110808.Suche in Google Scholar

Zou, J.Han, Y. and So, S.S. (2009). Overview of artificial neural networks. Artificial Neural Netw. Methods Appl.. 485: 14–22, https://doi.org/10.1007/978-1-60327-101-1_2.Suche in Google Scholar PubMed

Received: 2025-06-23
Accepted: 2025-10-21
Published Online: 2025-11-03
Published in Print: 2025-12-17

© 2025 Walter de Gruyter GmbH, Berlin/Boston

Heruntergeladen am 13.12.2025 von https://www.degruyterbrill.com/document/doi/10.1515/kern-2025-0053/html
Button zum nach oben scrollen