Comparison of POD-UDEIM and POD-ECSW model order reduction in the case of damaging RC structures subjected to earthquakes

This paper uses Hyper-Reduced Order Models (HROMs) to accelerate parametric and sensitivity analyses on reinforced concrete structures subjected to earthquakes. The number of Degrees Of Freedom (DOFs) is reduced using a Proper Orthogonal Decomposition (POD) reduced basis. The nonlinear terms of the matrix system are approximated using an Unassembled Discrete Empirical Interpolation Method (UDEIM) or an Energy Conserving with Sampling and Weighting procedure (ECSW). Both strategies are compared regarding accuracy and time-savings on a L-shaped three-story building modeled by damaging multifibre beam elements. The efficiency of the HROMs is assessed in the case of parametric analyses about the external loading (e.g., ground motions) or mechanical properties (e.g., elastic modulus, or tensile strength). Results (1) show that both methods correctly model the nonlinear response of the structure with a strain energy error of less than 0.5 % and a speed-up factor between 20 and 32 during the online phases, and (2) prove that the POD-ECSW is more accurate than the POD-UDEIM despite an offline phase that requires more CPU time.