A bi-fidelity DeepONet approach for modeling hysteretic systems under uncertainty

This study proposes a multi-fidelity paradigm for developing surrogates of degrading hysteretic systems under uncertainty through the use of deep operator networks (DeepONets). Instead of attempting to directly train a DeepONet on the original response, this study adopts a residual modeling approach wherein the DeepONet is trained on the discrepancy between the original (high-fidelity) data source and a relatively simpler (low-fidelity) representation of the system. Within these examples, a conventional Bouc-Wen model is treated as a “low-fidelity” representation given that it is free of any further assumptions about the nonlinear behavior, while the “high-fidelity” data is generated from different structures with various forms of complex hysteretic behavior. The results of this study show that the proposed multi-fidelity approach consistently outperforms standard surrogates trained on only the original datasets considering a variety of systems with unknown parameters. The results also show that the difference in performance grows as training data becomes more scarce, a critical consideration for many real-world engineering systems, and that the proposed multi-fidelity approach maintains its performance edge even when controlling for training time and noise in the training data.