Time-series forecasting of a typical PWR system response under Control Element Assembly withdrawal at full power

Abstract

To expedite the decision-making process under Nuclear Power Plant (NPP) accident conditions, at a reduced computational cost, a Machine Learning (ML) time-series meta-model is proposed to map the relationships between the NPP's real-time parameters to its transient response and hence forecast its future response. To this end, three variations of Recurrent Neural Networks (RNNs), namely: the Long-Short-Term-Memory (LSTM), Gated Recurrent Unit (GRU) and a series combination of a convolutional neural network (CNN) with LSTM were developed. The NPP response was simulated using the thermal hydraulics best estimate code, MARS-KS, and cross-validated against the Design Control Document (DCD) of APR1400. The time-series database required to train, test, and validate the time-series Machine Learning (ML) expert algorithm was acquired by coupling DAKOTA software with the best estimate thermal hydraulics system code, MARS-KS to conduct a Best Estimate Plus Uncertainty (BEPU) analysis. The Monte-Carlo random propagation approach and the Latin Hypercube Sampling technique were used to sample and propagate key uncertain parameters until a statistically significant sample of the NPP transient responses was achieved. All three RNN models were developed and optimized with the help of the Talos tool, and were found to exhibit reasonable performance in forecasting the key most probable NPP transient responses, Furthermore, the uncertainty of the ML predictions was assessed by integrating a Bayesian Neural Network (BNN) with the LSTM model. The prediction accuracy ranged from 86% to 96%, when evaluated on an unseen test dataset. Based on a voting system with five performance metrics (MAE, MSE, RMSE, R2 and Accuracy) the LSTM model and its derivative CNN+LSTM outperformed the GRU model; while the CNN +LSTM is found to be the most computationally efficient.