A novel optimization framework using frequency-based substructuring for estimation of linear bolted joint stiffness and damping

Estimating the stiffness and damping coming from a joint is a major challenge. This work proposes a novel framework to estimate the unknown parameters using frequency-based substructuring and a maximum a posteriori optimization approach. The idea is to minimize the discrepancy between the measured responses of an assembled system and the responses obtained by coupling the measured responses of the individual substructures with a joint model. The system's dynamics are assumed to be linear. However, the FRFs of the coupled system (which drive the objective function) change nonlinearly with the linear joint parameters, making it a nonlinear optimization problem. Therefore, the joint parameters are estimated iteratively using the Gauss minimization method, a well-established linearization scheme. The framework is numerically validated on simple mdof systems, and the method's effectiveness is tested by adding noise to the generated data. To demonstrate the framework's applicability on real structures, joint stiffness and damping of a known benchmark structure are estimated based on real measurements. Two different underlying joint models are applied. The first assumes just flexibility at the connection. The second assumes the joint is a separate substructure. The algorithm can find realistic stiffness parameters and a range for the damping parameters providing a good compromise between the measurements in both cases.