Publications

Efficient random vibration analysis of nonlinear systems with long short-term memory networks for uncertainty quantification

Najera-Flores, David A.; Brink, Adam R.

Complex mechanical structures are often subjected to random vibration environments. One strategy to analyze these nonlinear structures numerically is to use finite element analysis with an explicit solver to resolve interactions in the time domain. However, this approach is impractical because the solver is conditionally stable and requires thousands of iterations to resolve the contact algorithms. As a result, only short runs can be performed practically because of the extremely long runtime needed to obtain sufficient sampling for long-time statistics. The proposed approach uses a machine learning algorithm known as the Long Short-Term Memory (LSTM) network to model the response of the nonlinear system to random input. The LSTM extends the capability of the explicit solver approach by taking short samples and extending them to arbitrarily long signals. The efficient LSTM algorithm enables the capability to perform Monte Carlo simulations to quantify model-form and aleatoric uncertainty due to the random input.