Deep Transfer Learning for Efficient Performance-based Assessment of Stochastic Nonlinear Dynamic Systems through Metamodeling

Abstract

Performance-based engineering (PBE) has gained significant interest over the past decade for enabling more economic and innovative designs. Nonetheless, the vast computational demand required in propagating general uncertainty through nonlinear structural systems for providing a probabilistic assessment of performance can represent a significant barrier to implementation. To address this issue, transfer learning is coupled with a state-of-the-art deep learning metamodeling scheme and stratified sampling for enabling rapid performance-based assessments. In particular, the metamodeling scheme adopted in this work combines proper orthogonal decomposition-based model order reduction with long short-term memory (LSTM) neural networks. This approach has recently been shown to be capable of efficiently reproducing both global displacement and local hysteretic responses of nonlinear structural systems subject to general stochastic excitation with remarkable accuracy. The transfer learning approach is introduced to advance this metamodeling scheme for the rapid estimation of nonlinear time history responses at multiple hazard intensity levels, therefore, enabling probabilistic performance assessments through generalized stratified stochastic simulation. Specifically, transfer learning is embedded within stratified sampling by first calibrating the metamodel for a stratum associated with extreme responses. The information gathered in this strata is subsequently used to inform the training for all remaining strata therefore significantly diminishing the overall training effort. To illustrate the scheme, a case study consisting of a 37-story fiber-discretized nonlinear steel moment-resisting frame subject to extreme winds is considered. The loads are modeled through a wind tunnel-informed stochastic model that is calibrated to a site-specific wind hazard curve. Uncertainty is propagated through stratifying with respect to wind speed. The LSTM metamodel is first calibrated to a high-fidelity dataset generated in the strata associated with the highest hazard intensities. Once calibrated, the LSTM metamodel is shown to be capable of simulating a full range of stochastic nonlinear responses with a four-order-of-magnitude speedup as compared to state-of-the-art direct integration. This enables the estimation of the conditional strata failure probability through direct stochastic simulation. Transfer learning is then implemented for extending, with only trivial additional training, the LSTM metamodel to the simulation of stochastic dynamic responses for all remaining strata, therefore, enabling the estimation of the unconditional failure probability. From the case study, the remarkable efficiency and accuracy of the scheme are seen illustrating the potential of the proposed framework for estimating the failure probability of nonlinear structural systems within the setting of PBE.