On the use of the GP-NARX model for predicting hysteresis effects of bolted joint structures
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Structures joined by lap-joints can present complex nonlinear dynamic behavior as a function of the stress to which the lap-joint is subjected, including contact stiffness variations and softening, along with hysteresis effects related to frictional dissipation at the contact interface. Considering applications where the use of non-parametric models that depend only on input and output data is required, this work proposes and details the GP-NARX model's use to approximate systems’ dynamics with hysteresis. Initially, the proposed model's predictive applicability is evaluated on a numerical application involving the Bouc-Wen oscillator with hysteretic damping. Then, this work proposes a GP-NARX model to describe the dynamics of the BERT benchmark, an experimental system that contains a symmetric double bolted joint that is nonlinearly dependent upon the applied excitation amplitudes, presenting as a friction joint's well-known softening effect. The structure also presents data variation related to the presence of uncertainties in the measurement process. Thus, to accommodate the experimental variability, the training step of the GP-NARX model considers several experimental realizations. The results indicate that GP-NARX can make accurate predictions of the response of both investigated applications, emphasizing its practical ability, where the confidence intervals of the proposed model were able to accommodate the noisy experimental data, learning the nonlinear relation between the input and output data points.