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.

翻译：逆不确定性量化是根据实验数据逆向量化模型输入不确定性的过程。本研究聚焦于开发针对时间依赖响应的逆不确定性量化方法，采用功能主成分分析进行降维并构建基于深度神经网络的代理模型。案例验证基于FEBA瞬态实验数据对TRACE物理模型参数进行逆不确定性量化。测量数据为时间依赖的峰值包壳温度。由于关注量具有时间依赖性，对应无限维响应，因此采用主成分分析降低关注量维度，同时保留PCT的瞬态轮廓特征，以提高逆不确定性量化效率。然而，直接对PCT时间序列剖面应用传统主成分分析难以精确表征数据，原因在于骤冷时刻的温度骤降。为此，在降维前采用功能对齐方法分离瞬态PCT剖面的相位与幅值信息。随后，利用功能主成分分析得到的主成分得分训练深度神经网络，构建TRACE的代理模型，以降低马尔可夫链蒙特卡洛采样的计算成本。采用贝叶斯神经网络估计深度神经网络代理模型预测的不确定性。本研究对比了四种采用不同降维方法与代理模型的逆不确定性量化流程。结果表明，所提方法在降低TRACE瞬态仿真维度方面具有优势，且逆不确定性量化结果的正向传播与实验数据具有更好的一致性。