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Parameter Estimation for Dynamical Systems Under Continuous and Discontinuous Gaussian Noise Using Data Assimilation Techniques

Conference Proceedings of the Society for Experimental Mechanics Series

Jacobs, Justin; Najera-Flores, David A.; Brink, Adam R.; Flanagan, Tatiana P.

Complex aerospace structures typically include unknown states, parameters, or inputs. The unknown parameters may be due to changes in the structure that are not captured by the mathematical model assumed. These models are often reduced order models (ROM) that have simplified physics or have been obtained through data-driven techniques, such as trained neural networks. In this paper, we evaluate two data assimilation techniques to perform parameter estimation of dynamical systems by leveraging measured responses to correct process model predictions. We study two different noise models: discontinuous and continuous Gaussian noises. We use ensemble Kalman filter and Kalman-Bucy filter techniques on representative structures, such as the slender flat beam with nonlinear features to illustrate how this approach could be applied to more complex structures.

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Confronting Domain Shift in Trained Neural Networks

Proceedings of Machine Learning Research

Martinez, Carianne M.; Najera-Flores, David A.; Brink, Adam R.; Quinn, D.D.; Chatzi, Eleni C.; Forrest, Stephanie F.

Neural networks (NNs) are known as universal function approximators and can interpolate nonlinear functions between observed data points. However, when the target domain for deployment shifts from the training domain and NNs must extrapolate, the results are notoriously poor. Prior work Martinez et al. (2019) has shown that NN uncertainty estimates can be used to correct binary predictions in shifted domains without retraining the model. We hypothesize that this approach can be extended to correct real-valued time series predictions. As an exemplar, we consider two mechanical systems with nonlinear dynamics. The first system consists of a spring-mass system where the stiffness changes abruptly, and the second is a real experimental system with a frictional joint that is an open challenge for structural dynamicists to model efficiently. Our experiments will test whether 1) NN uncertainty estimates can identify when the input domain has shifted from the training domain and 2) whether the information used to calculate uncertainty estimates can be used to correct the NN’s time series predictions. While the method as proposed did not significantly improve predictions, our results did show potential for modifications that could improve models’ predictions and play a role in structural health monitoring systems that directly impact public safety.

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

Proceedings of ISMA 2018 - International Conference on Noise and Vibration Engineering and USD 2018 - International Conference on Uncertainty in Structural Dynamics

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.

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27 Results
27 Results