Development of a Projection‐Based Advanced Deterministic Uncertainty Analysis in Low Dimensions

ABSTRACT This paper provides an in‐depth exploration of reduced order modeling and uncertainty quantification relevant to engineering disciplines. The objective of this study is to develop an innovative uncertainty quantification algorithm incorporating a reduced order model suitable for complex system calculations, with the goal of maintaining an appropriate level of computational accuracy while reducing overall computational costs. To achieve this, a comprehensive review of reduced order modeling and uncertainty quantification was conducted, leading to the development of a projection‐based advanced Deterministic Uncertainty Analysis algorithm in Low dimension (DUAL). DUAL introduces two effective methods for engineering calculations and analysis: data‐driven sparse sensor placement and high‐order deterministic uncertainty quantification. Data‐driven sparse sensor placement enables the identification of a small, optimal dataset from the full data by computing the rank of the basis matrix. High‐order deterministic uncertainty quantification computes the parameter and response distributions by numerically quantifying the first to fourth moments of the target distributions. DUAL utilizes both sparse sensor placement and high‐order deterministic uncertainty quantification to more accurately and cost‐effectively determine system uncertainties. The proposed numerical algorithms were applied to the FLECHT‐SEASET boil‐off and ATLAS A4.1 tests, estimating parameter and response distributions while leveraging dimension reduction in thermal hydraulic system calculations. The data‐driven sparse sensor placement module of DUAL effectively identified optimized datasets for the two benchmark problems, while the high‐order deterministic uncertainty quantification module efficiently estimated parameter and response distributions based on the first to fourth moments of the probability density function. DUAL demonstrated cost savings in overall computational expenses while maintaining appropriate accuracy levels by optimally selecting the number of basis modes in the reduced order model.