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This paper introduces a variational LSTM metamodel with augmented inputs to efficiently capture both aleatoric and epistemic uncertainties in nonlinear dynamic structural systems. The model uses random system parameters as augmented inputs, alongside excitation series, to represent aleatoric uncertainty, while epistemic uncertainty is approximated via Monte Carlo dropout. This approach achieves accurate nonlinear response predictions with confidence bounds, at a fraction of the computational cost of full Bayesian methods.
Get accurate uncertainty estimates in your dynamic system models without breaking the bank: a variational LSTM with Monte Carlo dropout offers near-free epistemic uncertainty quantification.
Uncertainty propagation in high-dimensional nonlinear dynamic structural systems is pivotal in state-of-the-art performance-based design and risk assessment, where uncertainties from both excitations and structures, i.e., the aleatoric uncertainty, must be considered. This poses a significant challenge due to heavy computational demands. Machine learning techniques are thus introduced as metamodels to alleviate this burden. However, the"black box"nature of Machine learning models underscores the necessity of avoiding overly confident predictions, particularly when data and training efforts are insufficient. This creates a need, in addition to considering the aleatoric uncertainty, of estimating the uncertainty related to the prediction confidence, i.e., epistemic uncertainty, for machine learning-based metamodels. We developed a probabilistic metamodeling technique based on a variational long short-term memory (LSTM) with augmented inputs to simultaneously capture aleatoric and epistemic uncertainties. Key random system parameters are treated as augmented inputs alongside excitation series carrying record-to-record variability to capture the full range of aleatoric uncertainty. Meanwhile, epistemic uncertainty is effectively approximated via the Monte Carlo dropout scheme. Unlike computationally expensive full Bayesian approaches, this method incurs negligible additional training costs while enabling nearly cost-free uncertainty simulation. The proposed technique is demonstrated through multiple case studies involving stochastic seismic or wind excitations. Results show that the calibrated metamodels accurately reproduce nonlinear response time histories and provide confidence bounds indicating the associated epistemic uncertainty.
