Application of a first-order method to estimate the failure probability of component subjected to thermal transients for optimization of design parameters

Abstract

The Japan Atomic Energy Agency has been developing "Advanced Reactor Knowledge-and AI-aided Design Integration Approach through the whole plant lifecycle (ARKADIA)" to offer the best solutions for challenges in the design and operation of nuclear plants. A part of ARKADIA for design study, which included design optimization of components, is named as ARKADIA-Design. In the development of ARKADIA-Design, we have been developing a process to automatically optimize design parameters of structural components subjected to various kinds of loads, including thermal transients. In this paper, we propose a simplified procedure to estimate the failure probability of components subjected to thermal transients for design optimization. An objective function of this optimization is defined on the basis of failure probability of the components, because failure probability can be commonly used as an indicator of component integrity for various mechanisms, and it helps future introductions of a risk-informed performance-based approach to component design. To enable the necessary number of estimations for design optimization with practical calculation time, we aimed to reduce the number of analyses required for one estimation. For this purpose, we adopted the first-order second-moment (FOSM) method as the estimation method for failure probability in the process of optimization. An orthogonal table in the experiment design method is utilized to define the conditions of the analyses for evaluation of the mean and variance of thermal transient stress, which are used as inputs in the FOSM method. The superposition of ramp responses is also utilized to evaluate the time history of thermal transient stress instead of finite element analysis. The proposed procedure was applied in a demonstration study to optimize the thickness of a cylindrical vessel subjected to thermal transients derived from shutdown. We confirmed that the procedure can evaluate the failure probability depending on the cylinder thickness with practical calculation time.

Development of element functions and design optimization procedures for knowledge- and AI-aided advanced reactor lifecycle optimization method, ARKADIA

“…As the first step of the development, a representative problem was defined to optimize the thickness of the reactor vessel against the thermal transient under a manual plant trip event under normal operating conditions and seismic motion using the plant conditions of an experienced SFR in Japan (Mori et al, 2022;Okajima et al, 2023;Kikuchi et al, 2023). Assessment of the structural integrity of components during their lifetime under various operating conditions is essential for achieving safe plant design.…”

“…Although the estimation of the effect of design parameters in the plant thermal-hydraulic analysis on the thermal stress is based on first-order approximation because of the orthogonal table without considering mutual interactions of parameters, the applicability of this approach in practice is confirmed by comparing it with the evaluation results using the detailed response surface methodology (Okajima, 2023). To evaluate the thermal stress using the results of the analyses, a simplified method based on the principle of superposition method for thermal stress evaluation is used to prevent a large calculation cost for finite element analysis (Okajima, 2023). Thus, the time history of the thermal transient as a result of the PDA is divided into sections in a short period to demonstrate the specific shape of the profiles, namely step-and ramp-shaped profiles.…”

“…Thus, the time history of thermal stress can be evaluated by superimposing the results in each section to reproduce it for the duration of the analysis. Using the results of the thermal stress, a reliability index is calculated using the first-order second-moment method with values of average and variance on the resistance of materials and is translated into failure probability (Okajima, 2023). Currently, an evaluation methodology for the failure probability of the seismic loads is being developed and calculated using a tentative equation.…”

“…A demonstration of the representative problem was performed to confirm the validity of the design process as shown in Fig. 5 and developed methodologies to evaluate the failure probability (Kikuchi et al, 2023). The sodium temperature profiles at the outlet piping of the reactor vessel were obtained by plant dynamic analyses, in which the major components of the plant, assuming a small-scale SFR were modeled.…”

“…To implement design optimization based on the RIPB approach, methods to evaluate the likelihood and consequence of component failure are required. Therefore, the combinational utilization of ARKADIA-Design (e.g., design optimization tools based on failure probability) (Okajima et al, 2023) and ARKADIA-Safety (e.g., dynamic PRA methodology based on severe accident numerical simulation code (Uchibori et al, 2023) with the application of the CMMC method (Li et al, 2023) and reliability database of SFRs and related facilities (Kurisaka, 1995, Naruto andKurisaka, 2012) will help to develop a design process using the RIPB approach. This development will improve the regulatory and industrial compatibility of advanced reactors, such as SFRs, as well as their social acceptance.…”