Adaptive Sampling of Dynamic Scenarios close to the Limit Surface using Deep Neural Network and Monte Carlo Dropout

Probabilistic safety assessment (PSA) is widely used to evaluate and investigate the risk of a nuclear power plant (NPPs). This methodology combines event tree and fault tree models to efficiently identify the event sequences that fail in the ultimate safety goal and assumes a static probability of failure. However, this static PRA can be limited. For instance, there is only a Boolean representation of system success/failure while the partial operation of components can induce a different consequence. Also, the timing of events is rigidly preset by the analyst, therefore, not considerably modeled. Dynamic PSA has been suggested to supplement these flaws. In general, dynamic PSA takes count into t partial operations of components and systems, and timedependencies between events to realistically model target system response. Therefore, Dynamic PSA generates numerous sequences which are originally represented by the few sequences in classical PSA. It implies that expensive deterministic analysis including thermal-hydraulic (TH) code runs should be iteratively executed to analyze the scenarios of Dynamic PRA. To overcome this computational challenge, research has been conducted to replace the expensive code runs with a simplified surrogate model. A data-driven model has been widely studied as a surrogate model of the expensive TH code. Radaideh et al. predicted the sequences of important parameters, such as cold-leg temperature and peak cladding temperature (PCT), using deep neural networks under small break loss of coolant accident (LOCA) [1]. Deep learning-based accident trend estimation (DeBATE) has been developed by the Korea Atomic Energy Research Institute, which can estimate the trends of important parameters using a quantile recurrent neural network [2]. The feasibility of the simplified DeBATE models was validated by training 8,000 input-output data sets calculated by MARS-KS (Multi-dimensional Analysis of Reactor Safety KINS Standard, i.e., the Korean regulatory safety analysis code) [3, 4]. However, a datadriven model can generate strange predictions when untrained scenarios are given. Since a data-driven approach does not model thermal-hydraulic phenomena, the strange predictions are unreliable. Nonetheless, a data-driven approach can focus computational resources on the region of interest. A limit surface/state (LS) is a practical concept for system reliability assessment. In the scenario consequence space spanned by scenario configuring parameters, the LS discriminates the system failure and success regions. Therefore, if the LS can be identified, the result of notsimulated scenarios can be conservatively assumed. Therefore, an algorithm finding the LS with a minimized number of simulations can save computation resources while retaining risk-sensitiveness and informativeness. A data-driven model can be a metamodel for this algorithm. The Idaho National Laboratory developed a limit surface searching algorithm with adaptive sampling and an active learning method. This algorithm samples notsimulated scenarios based on the predictions of the metamodel, which trains the record of previous simulations [5]. They tested various kinds of metamodels such as support vector machines (SVMs) [6], k-nearest neighborhood [7], and Gaussian process [5]. Similarly, adaptive kriging Monte Carlo simulation (AK-MCS) has been applied to identify operational conditions that lead to failure of a passive safety system and a lead fast reactor, respectively [8, 9]. AK-MCS embeds kriging, i.e., Gaussian process modeling, as a metamodel to estimate the consequence of notsimulated scenarios [10]. This research suggests an adaptive sampling method to identify LS with a minimized number of simulations using deep learning and Monte Carlo dropout (MCDO). The suggested method is analogous to AK-MCS; however, we embed a different metamodel (i.e., deep neural network) and tailored it to be specialized in finding the LS. Retained advantaged is that the suggested method and AK-MCS consider not only closeness to the LS but also the uncertainty of consequence predictions. To investigate the prediction uncertainty, we employed the MCDO method introduced by Gal and Ghahramani in 2016 [11]. The case study result shows that the suggested sampling method can efficiently find out the LS with a minimized number of simulations.