Uncertainty Propagation and Global Sensitivity Analysis in Hybrid Simulation using Polynomial Chaos Expansion

摘要

Hybrid simulation is a very effective testing strategy for simulating the dynamic response of structural systems whose dimensions and complexities exceed the capacity of conventional testing facilities. The hybrid model of the prototype structure, which combines numerical and physical substructures, accurately reproduces the overall dynamic response of the structure with reduced costs and effort. In current practice, the parameters that characterize the numerical subdomain are deterministic. The values of these parameters are often determined through deliberate simplifications, ignoring the associated uncertainties. However, the effect of uncertainties may be significant. The objective of the work, presented in this paper, is to use uncertainty quantification and global sensitivity analysis to evaluate the effect of uncertainties on the response of a hybrid model in simulations. Sobol indices are selected to explain the total variance of output parameters, e.g. maximum absolute displacement peaks, with respect to the variance of input parameters, e.g. viscous damping. In detail, a generalized polynomial chaos expansion of the hybrid system response is derived and Sobol indices are post-processed from the entailing polynomial coefficients. The proposed approach is illustrated using a nonlinear two-degrees-of-freedom benchmark case study that covers a class of prototype typical for hybrid simulation tests.