Abstract Summary
Model updating bridges the gap between experimentation and simulations, building trust in the model predictions. Stochastic model updating (SMU) gives a better understanding of the effect of uncertainties in the structure due to modelling errors, measurement errors and imprecise assumptions of boundary conditions, material/geometric properties, etc. SMU can identify the variability in nonlinear parameters of dynamical systems and at the same time assist in defining the parameter space. The Bayesian model updating framework of various model updating methods is used in this research to develop such stochastic models for jointed structures. Existing physical joint models such as cubic stiffness, dry friction, Iwan, Valanis, Dahl, Bouc-Wen and lumped models are used to generate samples of backbone curves. Backbone curves can aid in understanding the system's nonlinearity in the absence of any forced excitation. Researchers have used several control-based experimental methods over time to generate these backbone curves, such as phase-locked-loop (PLL) control testing, response-controlled stepped-sine testing, control-based continuation testing and resonant decay testing. This study focuses on the Resonant Decay method to generate the backbone curves where steady-state vibrations of the system are captured once the excitation is removed from the system and the free decay is achieved. Using this free decay, instantaneous frequency and amplitude are extracted to obtain the backbone curve. These backbone curves are used to develop the stochastic model of the system. The Bayesian model referred to here is the Monte Carlo Markov Chain (MCMC) with the Metropolis-Hastings algorithm as the sampler to sample from a high dimensional probability distribution. To reduce the computational time without losing the performance of the MCMC model, a machine learning (ML) model is integrated with the Bayesian model for stochastic modelling of a non-linear system. This integration is performed to make the Bayesian model less computationally exhaustive. The samples of the backbone curves are treated as a database for training, testing and validation of the machine learning (ML) model. Experimental validation of this ML-integrated Bayesian is performed using vibration testing of a non-linear system to generate backbone curves. The resonant decay method is employed by exciting the system at its first natural frequency and then removing the excitation to allow free decay. Backbone curves are extracted from this free decay. These experimentally generated backbone curves are used to validate the ML-integrated Bayesian results and finally develop the stochastic model.
