Explicit reliability sensitivities of linear structures with interval uncertainties under stationary stochastic excitation

Reliability sensitivity evaluation of randomly excited linear structures with uncertain parameters is addressed. The excitation is modeled as a stationary Gaussian random process. Uncertainty affecting structural parameters is handled within a non-probabilistic framework by applying the interval model. Under the assumption of independent up-crossings of a specified threshold, a procedure for the analytical derivation of interval reliability sensitivity is presented. The key idea is to perform stochastic analysis in the frequency domain by applying the improved interval analysis via extra unitary interval in conjunction with a novel series expansion of the inverse of an interval matrix with modifications, herein called Interval Rational Series Expansion (IRSE). This approach yields approximate explicit expressions of interval response statistics and structural reliability along with their sensitivities with respect to the uncertain parameters. Reliability sensitivities provide useful information to increase the safety level and can be also exploited in the context of first-order interval Taylor series expansion to estimate the bounds of interval reliability when slight uncertainties are involved. A wind-excited truss structure with interval stiffness properties is analyzed to show the effectiveness of the proposed procedure.