Functional PCA and Deep Neural Networks-based Bayesian Inverse
  Uncertainty Quantification with Transient Experimental Data
Ziyu Xie Mahmoud Yaseen Xu Wu
Inverse UQ is the process to inversely quantify the model input uncertainties
based on experimental data. This work focuses on developing an inverse UQ
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 inverse UQ of
TRACE physical model parameters using the FEBA transient experimental data. The
measurement data is time-dependent peak cladding temperature (PCT). Since the
quantity-of-interest (QoI) is time-dependent that corresponds to
infinite-dimensional responses, PCA is used to reduce the QoI dimension while
preserving the transient profile of the PCT, in order to make the inverse UQ
process more efficient. However, conventional PCA applied directly to the PCT
time series profiles 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 of the transient
PCT profiles before dimensionality reduction. DNNs are then trained using PC
scores from functional PCA to build surrogate models of TRACE in order to
reduce the computational cost in Markov Chain Monte Carlo sampling. Bayesian
neural networks are used to estimate the uncertainties of DNN surrogate model
predictions. In this study, we compared four different inverse UQ processes
with different dimensionality reduction methods and surrogate models. The
proposed approach shows an improvement in reducing the dimension of the TRACE
transient simulations, and the forward propagation of inverse UQ results has a
better agreement with the experimental data.