Damage detection in nonlinear vibrating structures using model updating

This paper presents two distinct model updating strategies for dynamical systems with local nonlinearities based on acceleration time history responses measured spatially across the vibrating structure. Both linear and nonlinear parameters are calibrated by minimizing the selected metric based on measured and predicted response using the newly proposed variant of differential search algorithm named as multi-cluster hybrid adaptive differential search (MCHADS) algorithm. The first model updating strategy involves the decoupling of linear and nonlinear characteristics of the system. In this scheme, we first establish the dynamic stiffness matrix using input and output measurements and then the underlying linear system is alone updated using it. Later, localization of the nonlinear attachment is attempted using the inverse property of the FRF of the nonlinear system and the established dynamic stiffness matrix of the underlying linear system from the previous step. Once the linear system is updated and with the already identified location(s) of nonlinear attachment(s), the nonlinear parameters are identified by formulating it as an optimization problem using the proposed MCHADS algorithm. The major advantage of the first approach is the reduction of the complex problem of nonlinear model updating to linear model updating. The second approach involves updating both linear and nonlinear parameters simultaneously using the proposed MCHADS algorithm. Investigations have been carried out by solving several numerically simulated examples and also with the experimental data of a benchmark problem to evaluate the effectiveness of the two proposed nonlinear model updating strategies. Further, investigations are also carried out to evaluate the capability of the model updating approaches towards damage identification in initially healthy nonlinear systems. Conclusions are drawn based on these investigations, highlighting the strengths and weaknesses of the two model updating approaches