A Bi-fidelity DeepONet Approach for Modeling Uncertain and Degrading Hysteretic Systems
This addresses modeling challenges for engineering systems with uncertainty and degradation, though it appears incremental as an application of DeepONet to a specific domain.
The paper tackles modeling uncertain degrading hysteretic systems by using low-fidelity data from pristine models to train a DeepONet that captures discrepancies with the true system, resulting in significant improvements in prediction error across three numerical examples.
Nonlinear systems, such as with degrading hysteretic behavior, are often encountered in engineering applications. In addition, due to the ubiquitous presence of uncertainty and the modeling of such systems becomes increasingly difficult. On the other hand, datasets from pristine models developed without knowing the nature of the degrading effects can be easily obtained. In this paper, we use datasets from pristine models without considering the degrading effects of hysteretic systems as low-fidelity representations that capture many of the important characteristics of the true system's behavior to train a deep operator network (DeepONet). Three numerical examples are used to show that the proposed use of the DeepONets to model the discrepancies between the low-fidelity model and the true system's response leads to significant improvements in the prediction error in the presence of uncertainty in the model parameters for degrading hysteretic systems.