Data-driven modeling of bolted joints by Iwan dictionary and Laplace prior-enhanced sparse Bayesian learning

Abstract

Numerous constitutive and phenomenological models have been developed in an attempt to adequately represent the frictional hysteresis of bolted joints. However, those models do not comprehensively account for parameters of interest, such as multiscale asperities, variable normal forces, and thermal environments, limiting their applicability to certain conditions. This paper develops a data-driven modeling approach to calibrate bolted joints, enabling the simulation of their asymmetric hysteresis arising from parameters of interest. To this end, an Iwan dictionary is developed from the superposition principle of the Iwan bolted joint model, and reconstructed completely by the macro-slip physical information and the Duhem hysteresis operator. Subsequently, a Laplace prior-enhanced sparse Bayesian learning method is employed to sparsely identify Iwan dictionary’s coefficients and quantify their associated uncertainties, by minimizing the residual between measured and simulated forces. Within this Bayesian learning method, coefficients are estimated initially by an overdetermined linear formulation which is constructed using the Iwan dictionary and the derivatives of measured forces, and then are updated by implementing the sensitivity analysis to the data-driven model. Numerical and experimental studies demonstrate that the coefficients of the Iwan dictionary are identified sparsely, resulting in a data-driven model that is both concise and interpretable. The resulting model activates only a few of the most relevant basis functions of the Iwan dictionary, effectively capturing the asymmetric hysteresis of bolted joints subjected to variable torsional, thermal, and tensile conditions.