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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. • Bi-fidelity DeepONet approach for modeling hysteretic, degrading systems is proposed. • Proposed bi-fidelity approach routinely produces lower mean validation errors. • Performance advantage of bi-fidelity network is greatest for limited training data. • Degree of "mis-match" between low- and high-fidelity models erodes performance. • Advantage of proposed network remains when controlling for computational costs. [ABSTRACT FROM AUTHOR]

The experimental dynamical response of three types of nonlinear hysteretic systems is identified employing phenomenological models togheter with the Differential Evolutionary algorithm. The mass–spring–damper system is characterized by hysteretic restoring forces provided by assemblies of shape memory and steel wire ropes subject to flexure or coupled states of tension and flexure. The energy dissipation due to phase transformations and inter-wire friction and the stretching-induced geometric nonlinearities give rise to different shapes of hysteresis cycles. The mechanical device subject to strong seismic excitations is investigated in its ultimate limit state whereby inelastic strains are induced in the steel wires together with a global nonsymmetric response of the system. The targeted dynamical characterization of the hysteretic oscillator up to its ultimate limit state has a special meaning when the device is employed in the field of vibration control. The dynamical response is identified exploiting the measurements of the oscillating mass relative displacement and inertia force that must be balanced, at each time instant, by the overall restoring forces provided by the mechanism. The restoring force is assumed to be the sum of different contributions such as a cubic nonsymmetric elastic force and a nonsymmetric hysteretic force modeled according to a modified version of the Bouc–Wen model. The parameters are identified minimizing the difference between the numerical and the experimental restoring force histories. High levels of accuracy are achieved in the identification with mean square errors lower than 2%. [ABSTRACT FROM AUTHOR]

Several different data-driven strategies for nonlinear identification are applied to experimental data exhibiting various types of hysteretic behavior. The experimental data contain displacement and restoring force information for several tests conducted using different configurations of a rheological testing device with various assemblies of nickel titanium-Naval Ordnance Laboratory (NiTiNOL) and steel wire strands. Among the different configurations, the response of the wire strands shows three distinct forms of nonlinear behavior: classical quasi-linear softening hysteresis; strongly pinched, hardening hysteresis; and slightly pinched, hardening hysteresis. The data-driven methods applied for nonlinear identification include polynomial basis functions and neural networks. The polynomial basis nonlinear identification methods are used for the construction and characterization of reduced-order models to gain insight into the physical modeling of the hysteretic phenomena. The neural network methods are found to be more useful for predictive purposes, demonstrating an ability to produce accurate results on both training and testing data. [ABSTRACT FROM AUTHOR]