Uncertainty Propagation in a Hybrid Data-Driven and Physics-Based Submodeling Method for Refined Response Estimation

Higher accuracy in estimation of stress distribution, especially in the critical locations with stress variation, is important for a more reliable prediction of possible damage or prognosis of the structure. A structure can have several such locations and it is not economically feasible to monitor all of them with traditional sensing methods. Moreover, these methods often provide response measurements at a few localized points and demand deployment in large numbers to get a distributed response. Hybrid submodeling is a data-driven physics-based submodeling method to achieve a refined estimate of distributed structural response in and around the critical locations or other locations of interest. This method uses measured response on the pre-meditated boundaries around the location of interest to drive the corresponding submodel of the structural component or connection to achieve a more spatially refined response. The method accumulates and propagates uncertainty in different stages of response estimation such as uncertainty in sensor location, measurement noise, uncertainty in submodel geometry, material properties, and boundary condition uncertainty at submodel boundaries. This article demonstrates uncertainty propagation in the hybrid-submodeling method, considering uncertainty in the submodel boundary conditions as the only source of uncertainty. This is demonstrated by using DIC digital image correlation (DIC) to measurements to drive the submodel region around a critical location on a structural component. Monte-Carlo simulation (MCS) is used to study the uncertainty propagated to the response in the hybrid-submodeling method. The study observed lower variability in the distribution of response in each location obtained through hybrid submodeling compared to its corresponding distribution from DIC measurements on the plate under the same loading conditions.