Bayesian model identification through harmonic balance method for hysteresis prediction in bolted joints

Hysteresis is a nonlinear phenomenon present in many structures, such as those assembled by bolted joints. Despite a large number of recent findings related to identification techniques for these systems, the problem is still challenging and open to contributions. To fill the gap concerning the proposition of identification algorithms based on closed-form solutions, this work introduces the use of the harmonic balance method to identify a stochastic Bouc–Wen model for predicting the nonlinear behavior of bolted structures. A piecewise smooth procedure is applied on the hysteretic restoring force to become possible to derive an analytical approximation of the response based on the Fourier series. Firstly, the analytical approximation is used to calibrate deterministic Bouc–Wen parameters by minimizing the error between the Fourier amplitudes of the numerical model and those extracted from experimental data using the cross-entropy optimization method. Since the experimental data investigated here contain variability due to the measurement process (aleatoric uncertainties), the deterministic parameters are then used as a priori conditions to update their probability density functions via the Bayesian inference. Having the model parameters as random variables, the stochastic Bouc–Wen model is obtained. This methodology was illustrated in a bolted structure benchmark. The results indicate that the method proposed can identify an accurate stochastic Bouc–Wen model for predicting the dynamics of bolted structures, even taking into account data variability.