Global sensitivity analysis for dynamic systems with stochastic input processes

Dynamic systems with stochastic input processes are general engineering models. In order to apply the global sensitivity analysis on these systems to aid safety design, variance based sensitivity indices are extended to stochastic processes in this paper. Factor sensitivity indices and time sensitivity indices are defined to describe the contributions of the input factor variances of the whole time and a specific time to the output variance at the current time, respectively. Analytical expressions of sensitivity indices for linear time-invariant systems with Gaussian processes are derived due to the extensive use of them, including continuous-time systems and discrete-time systems. Monte Carlo simulation is used to verify the derived analytical expressions. The derived expressions could be used directly in practical applications to reduce computation cost. The applications of the sensitivity indices have been discussed with engineering examples, which include transient temperature measurements and a forced vibration system. Some safety design measures aided by the sensitivity indices are also discussed in these two examples.