Transmissibility Physics-Guided Deep Learning Network for Seismic Response Prediction Under Limited Domain Knowledge, Sparse Measurements, and Unknown Excitations

Abstract

Swift seismic inspections are crucial for assessing structural safety before reoccupation. The prediction of seismic responses at unmeasured locations in scenarios with sparse response measurements, aided by physical models, has garnered significant attention to expedite inspection processes and safety assessments. However, existing techniques encounter challenges such as low efficiency due to costly seismic excitation measurement setups, limited scalability from incomplete sensor deployment, and substantial discrepancies stemming from insufficient knowledge, including the failure to address nonlinear effects adequately. To tackle these obstacles, a novel Transmissibility Physics-guided Deep Learning (TPDL) framework is introduced for predictions at arbitrary locations under unknown excitations, sparse measurements, and limited knowledge. Leveraging the governing equation of nonlinear structural dynamics in the frequency domain, the nonlinear Transmissibility Function (TF), defined as the ratio of two nonlinear frequency domain responses, is analytically derived by decomposing it into a linear-fidelity term associated with linear transmissibility information and a compensation term linked to unidentified nonlinearities. Guided by this formulation, a physics-guided deep network comprising two modules has been devised, simplifying the learning task from full structural dynamics to nonlinear behavior. The first module directly embeds known linear structural parameters to establish a training-free mapping to linear responses at unmeasured locations, thereby eliminating the need for explicit seismic excitation and facilitating rapid framework deployment. In parallel, the second module encodes the nonlinear compensation term by identifying unknown nonlinearities to correct the linear responses. Given the ill-posed nature of the nonlinear compensation term due to sparse measurements, a channel-sparse regularization technique incorporated into the loss function is employed to promote sparse outputs, mitigating the ill-posed dilemma and enhancing the model's generalization capabilities for unmeasured locations. Numerical studies and shaking table experiments validate TPDL's effectiveness in scenarios with uncalibrated numerical models, demonstrating its advantages of requiring fewer training samples and achieving superior accuracy at unmeasured locations compared to conventional approaches.