Cross-covariance based global dynamic sensitivity analysis

For identifying the cross-covariance source of dynamic output at each time instant for structural system involving both input random variables and stochastic processes, a global dynamic sensitivity (GDS) technique is proposed. The GDS considers the effect of time history inputs on the dynamic output. In the GDS, the cross-covariance decomposition is firstly developed to measure the contribution of the inputs to the output at different time instant, and an integration of the cross-covariance change over the specific time interval is employed to measure the whole contribution of the input to the cross-covariance of output. Then, the GDS main effect indices and the GDS total effect indices can be easily defined after the integration, and they are effective in identifying the important inputs and the non-influential inputs on the cross-covariance of output at each time instant, respectively. The established GDS analysis model has the same form with the classical ANOVA when it degenerates to the static case. After degeneration, the first order partial effect can reflect the individual effects of inputs to the output variance, and the second order partial effect can reflect the interaction effects to the output variance, which illustrates the consistency of the proposed GDS indices and the classical variance-based sensitivity indices. The MCS procedure and the Kriging surrogate method are developed to solve the proposed GDS indices. Several examples are introduced to illustrate the significance of the proposed GDS analysis technique and the effectiveness of the proposed solution.