Functional PCA and Deep Neural Networks-based Bayesian Inverse Uncertainty Quantification with Transient Experimental Data

TL;DR

The paper develops a Bayesian inverse UQ framework for time-dependent QoIs by integrating functional PCA with DNN/BNN surrogates, enabling efficient inference of TRACE calibration parameters from FEBA FEBA transient data. Functional alignment separates phase and amplitude in PCT time series, allowing compact PC representations that retain waveform features. Four IUQ variants compare conventional PCA and functional PCA with GP, DNN, and BNN surrogates, demonstrating that fPCA plus DNN/BNN yields better forward predictions and uncertainty quantification for transient PCT, with code uncertainty accounted in posterior intervals. This approach accelerates IUQ for nuclear thermal-hydraulics while improving agreement with experiments and providing a pathway to include discrepancy and hierarchical modeling in future work.

Abstract

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.

Figures (21)

• Figure 1: (a) TRACE simulation model and its related axial power profile for FEBA test 216; (b) A typical PCT profile from TRACE simulation.
• Figure 2: PCA of a multivariate Gaussian distribution centered at (3,1.5). The vector shows the new base based on the PCA result.
• Figure 3: Illustration of the inaccuracies in the reconstructed PCT profiles using conventional PCA for 2 simulation tests with different physical model parameters.
• Figure 4: Illustration of functional alignment with some simple test functions: left: curves with different phases and amplitudes; middle: warped data that have curves aligned at the crest and trough points; right: warping functions.
• Figure 5: Procedure for fPCA and its inverse process. It includes the following major steps: (1) run TRACE at different samples of $\bm{\theta}$ to generate the PCT profiles, (2) apply functional alignment of the PCT profiles to obtain the warped data (aligned at $t_{\text{max}}$ and $t_{\text{quench}}$) and warping functions, (3) apply PCA for dimensionality reduction of the warped data and warping functions, (4) build and validate the surrogate models based on the resulting PC scores (samples of the transformed new variables), (5) at a new sample $\bm{\theta}^{*}$, run the surrogate models to get the estimated PC scores, (6) use reverse PCA to obtain the corresponding warped data and warping function, (7) use reverse functional alignment to obtain the original PCT profile.