Functional PCA and deep neural networks-based Bayesian inverse uncertainty quantification with transient experimental data

Abstract

This work focuses on developing an inverse uncertainty quantification (IUQ) process for time-dependent responses, using dimensionality reduction by functional principal component analysis (PCA) and deep neural network (DNN)-based surrogate models. The demonstration is based on the IUQ of TRACE physical model parameters using the FEBA benchmark transient experimental data on peak cladding temperatures during reflooding. The quantity-of-interest (QoI) is time-dependent peak cladding temperature (PCT) profiles. Conventional PCA can hardly represent the data precisely due to the sudden temperature drop at the time of quenching. As a result, a functional alignment method is used to separate the phase and amplitude information in the PCT profiles before conventional PCA is applied for dimensionality reduction. The resulting PC scores are then used to build DNN-based surrogate models to significantly reduce the computational cost in Markov Chain Monte Carlo sampling, while the code/interpolation uncertainty is accounted for using Bayesian neural networks. We compared four IUQ processes with different dimensionality reduction methods and surrogate models. The proposed approach has demonstrated the best performance in reducing the dimensionality of the transient PCT profiles. This approach also produces the posterior distributions of the physical model parameters with which the model predictions have the best agreement with the experimental data.