Application of quasi-Monte Carlo and importance sampling to Monte Carlo-based fault tree quantification for seismic probabilistic risk assessment of nuclear power plants

Kubo, Kotaro; Tanaka, Yoichi; Hakuta, Yuto*; Arake, Daisuke*; Uchiyama, Tomoaki*; Muramatsu, Ken

Mechanical Engineering Journal (Internet), 10(4), p.23-00051_1 - 23-00051_17, 2023/08

https://doi.org/10.1299/mej.23-00051

The significance of probabilistic risk assessments (PRAs) of nuclear power plants against external events was re-recognized after the Fukushima Daiichi Nuclear Power Plant accident. Regarding the seismic PRA, handling correlated failures of systems, components, and structures (SSCs) is very important because this type of failure negatively affects the redundancy of accident mitigation systems. The Japan Atomic Energy Research Institute initially developed a fault tree quantification methodology named the direct quantification of fault tree using Monte Carlo simulation (DQFM) to handle SSCs' correlated failures in detail and realistically. This methodology allows quantifying the top event occurrence probability by considering correlated uncertainties related to seismic responses and capacities with Monte Carlo sampling. The usefulness of DQFM has already been demonstrated. However, improving its computational efficiency would allow risk analysts to perform several analyses. Therefore, we applied quasi-Monte Carlo and importance sampling to the DQFM calculation of simplified seismic PRA and examined their effects. Specifically, the conditional core damage probability of a hypothetical pressurized water reactor was analyzed with some assumptions. Applying the quasi-Monte Carlo sampling accelerates the convergence of results at intermediate and high ground motion levels by an order of magnitude over Monte Carlo sampling. The application of importance sampling allows us to obtain a statistically significant result at a low ground motion level, which cannot be obtained through Monte Carlo and quasi-Monte Carlo sampling. These results indicate that these applications provide a notable acceleration of computation and raise the potential for the practical use of DQFM in risk-informed decision-making.

Sensitivity coefficient evaluation of an accelerator-driven system using ROM-Lasso method

Katano, Ryota; Yamamoto, Akio*; Endo, Tomohiro*

Nuclear Science and Engineering, 196(10), p.1194 - 1208, 2022/10

https://doi.org/10.1080/00295639.2022.2067447

In this study, we propose the ROM-Lasso method that enables efficient evaluation of sensitivity coefficients of neutronics parameters to cross-sections. In the proposed method, a vector of sensitivity coefficients is expanded by subspace bases, so-called Active Subspace (AS) based on the idea of Reduced Order Modeling (ROM). Then, the expansion coefficients are evaluated by the Lasso linear regression between cross-sections and neutronics parameters obtained by the random sampling. The proposed method can be applied in the case where the adjoint method is difficult to be applied since the proposed method uses only forward calculations. In addition, AS is an effective subspace that can expand the vector of sensitivity coefficients with the lower number of dimension. Thus, the number of unknows is reduced from the original number of input parameters and the calculation cost is dramatically improved compared to the Lasso regression without AS. In this paper, we conducted ADS burnup calculations as a verification. We have shown how AS bases are obtained and the applicability of the proposed method.

Dynamic probabilistic risk assessment of nuclear power plants using multi-fidelity simulations

Zheng, X.; Tamaki, Hitoshi; Sugiyama, Tomoyuki; Maruyama, Yu

Reliability Engineering & System Safety, 223, p.108503_1 - 108503_12, 2022/07

https://doi.org/10.1016/j.ress.2022.108503

Proposal and application of ROM-Lasso method for sensitivity coefficient evaluation

Katano, Ryota; Yamamoto, Akio*; Endo, Tomohiro*

Proceedings of International Conference on Physics of Reactors 2022 (PHYSOR 2022) (Internet), p.2032 - 2041, 2022/05

https://doi.org/10.13182/PHYSOR22-37557

We have proposed the ROM-Lasso method to perform an efficient evaluation of the sensitivity coefficients of ADS core parameters to cross sections without major modification of the core analysis system. In the ROM-Lasso method, the sensitivity coefficient vector is expanded via the subspace bases so-called Active Subspace (AS), and the effective number of unknowns is reduced. Then, the expansion coefficients are determined via the penalized linear regression with the core parameters obtained by the random sampling, and the sensitivity coefficient vector is estimated. Owing to the AS, the required number of the core calculations is dramatically reduced in the ROM-Lasso method. In this work, we take the sensitivity coefficient evaluation of the coolant void reactivity at the end of the cycle for example and demonstrate how estimation accuracy depends on the number of samples and the AS.

The Analysis for Ex-Vessel debris coolability of BWR

Matsumoto, Toshinori; Iwasawa, Yuzuru; Ajima, Kohei*; Sugiyama, Tomoyuki

Proceedings of Asian Symposium on Risk Assessment and Management 2020 (ASRAM 2020) (Internet), 10 Pages, 2020/11

The probability of ex-vessel debris coolability under the wet cavity strategy is analyzed. The first step is the uncertainty analyses by severe accident analysis code MELCOR to obtain the melt condition. Five uncertain parameters which are relating with the core degradation and transfer process were chosen. Input parameter sets were generated by LHS. The analyses were conducted and the conditions of the melt were obtained. The second step is the analyses for the behavior of melt under the water by JASMINE code. The probabilistic distribution of parameters are determined from the results of MELCOR analyses. Fifty-nine parameter sets were generated by LHS. The depth of water pool is set to be 0.5, 1.0 and 2.0 m. Debris height were compared with the criterion to judge the debris coolability. As the result, the success probability of debris cooling was obtained through the sequence of calculations. The technical difficulties of this evaluation method are also discussed.

Estimation of sensitivity coefficient based on lasso-type penalized linear regression

Katano, Ryota; Endo, Tomohiro*; Yamamoto, Akio*; Tsujimoto, Kazufumi

Journal of Nuclear Science and Technology, 55(10), p.1099 - 1109, 2018/10

https://doi.org/10.1080/00223131.2018.1479988

In this study, we propose the penalized regression "adaptive smooth-lasso" for the estimation of sensitivity coefficients of the neutronics parameters. The proposed method estimates the sensitivity coefficients of the neutronics parameters using the variation of the microscopic cross sections and the neutronics parameter obtained by random sampling. The proposed method utilizes only the forward calculations. Thus, the proposed method can be applied for the complex reactor analysis for which the application of the adjoint method is difficult. In this study, we proposed a penalty term considering the characteristics of the sensitivity coefficients of the neutronics parameter to the microscopic multi-group cross sections. Through verification calculation, we show that the proposed method achieves high accuracy with less computational cost compared to the method based on random sampling proposed in the previous studies.

Bayesian optimization analysis of containment-venting operation in a Boiling Water Reactor severe accident

Zheng, X.; Ishikawa, Jun; Sugiyama, Tomoyuki; Maruyama, Yu

Nuclear Engineering and Technology, 49(2), p.434 - 441, 2017/03

https://doi.org/10.1016/j.net.2016.12.011

Calculation of prompt neutron decay constant with Monte Carlo differential operator sampling

Nagaya, Yasunobu

Proceedings of Joint International Conference on Mathematics and Computation, Supercomputing in Nuclear Applications and the Monte Carlo Method (M&C + SNA + MC 2015) (CD-ROM), 9 Pages, 2015/04

A new method to calculate the prompt neutron decay constant () with the Monte Carlo method is proposed. It is based on the conventional - search algorithm but no iteration is required for the value search. The eigenvalue is expressed in the truncated Taylor series with regard to ; the differential coefficients are calculated with the differential operator sampling, which is one of the Monte Carlo perturbation techniques. In order to examine the applicability of the proposed method, verification has been performed for simple geometries of a bare fast system (Godiva) and an unreflected thermal system (STACY). Comparisons has been done with the pulsed neutron source (PNS) simulation and the direct calculation from the definition of the value. The results with the proposed method show good agreement with the reference PNS simulation.

Uncertainty and sensitivity studies with the probabilistic accident consequence assessment code OSCAAR

Homma, Toshimitsu; Tomita, Kenichi*; Hato, Shinji*

Nuclear Engineering and Technology, 37(3), p.245 - 258, 2005/06

This paper addresses two types of uncertainty: stochastic uncertainty and subjective uncertainty in probabilistic accident consequence assessments. The off-site consequence assessment code OSCAAR has been applied to uncertainty and sensitivity analyses on the individual risks of early fatality and latent cancer fatality in the population due to a severe accident. A new stratified meteorological sampling scheme was successfully implemented into the trajectory model for atmospheric dispersion and the statistical variability of the probability distributions of the consequence was examined. A total of 65 uncertain input parameters was considered and 128 runs of OSCAAR were performed in the parameter uncertainty analysis. The study provided the range of uncertainty for the expected values of individual risks of early and latent cancer fatality close to the site. In the sensitivity analyses, the correlation/regression measures were useful for identifying those input parameters whose uncertainty makes an important contribution to the overall uncertainty for the consequence.

Short design descriptions of other systems of the HTTR

Sakaba, Nariaki; Furusawa, Takayuki; Kawamoto, Taiki; Ishii, Yoshiki; Ota, Yukimaru

Nuclear Engineering and Design, 233(1-3), p.147 - 154, 2004/10

https://doi.org/10.1016/j.nucengdes.2004.08.024

The HTTR mainly consists of the core components, reactor pressure vessel, cooling systems, instrumentation and control systems, and containment structures. The design of remaining utility systems is described in this paper. They are: auxiliary helium systems which include the helium purification system, the helium sampling system, and the helium storage and supply system; fuel handling and storage system. The helium purification systems are installed in the primary and secondary helium cooling systems in order to reduce the quantity of chemical impurities. The helium sampling systems monitor the concentration of impurities. The helium storage and supply systems keep the steady pressure of the helium system during the normal operation. The fuel handling and storage system is utilised to handle the new and spent fuels safely and reliably.