Stochastic Model Updating with Analytical Probabilistic Characterization of Transmissibility Estimates

This chapter presents a Bayesian framework for input-measurement-free stochastic model updating by integrating transmissibility functions under single excitation with computational acceleration strategies. The methodology employs a multivariate complex Gaussian ratio distribution to statistically characterize raw transmissibility estimates, coupled with a likelihood function that incorporates theoretical transmissibility predictions parameterized by updatable model variables. To address the high-dimensional sampling challenges in transitional Markov Chain Monte Carlo inference, a vectorized likelihood formulation eliminates computational bottlenecks through analytically loop-free operations. This is further enhanced by a distributed parallel computing scheme that leverages multi-core CPUs across networked nodes for scalable stochastic simulations. Numerical and experimental validations demonstrate that the raw transmissibility function-based approach achieves accuracy comparable to conventional frequency–response–function-based methods while eliminating the need for input measurements. Parametric studies quantify uncertainty propagation mechanisms with respect to sampling duration, reference point selection, and frequency bandwidth. Through vectorized algorithms and distributed parallelism, the proposed method enables efficient model updating of dynamic systems, establishing a paradigm for input-measurement-free scenarios in structural stochastic model updating under multiple sources of uncertainty.