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In this work, a novel Fréchet-derivative-based global sensitivity analysis is incorporated into the probability density evolution method for the simultaneous reliability and sensitivity analysis of structures. The two methods are synthesized and realized under a two-stage uncertainty quantification framework. Fundamental and numerical algorithms of the method are described, which is validated by a benchmark problem with theoretical solutions. Then it is applied on studying stochastic seismic responses of a real-world reinforced concrete structure of 288 m high. Results demonstrate that the response characteristics of the structure will be greatly changed when both uncertainties from the ground motions and structural parameters are considered, e.g., the failure probability will be enlarged by 1 ∼ 2 orders of magnitude. Besides, contrary to the popular opinion that the uncertainty of structural parameters is trivial compared to that of parameters in the ground-motion model, the importance measures of the structural parameters can be greater than those of the parameters in the ground-motion model by a factor of 2. when the coupling effect of randomness and nonlinearity of structural materials becomes dramatic. Some issues to be further outlined are also discussed. • A two-stage UQ framework for reliability and sensitivity analysis of complex structures is proposed. • Fréchet-derivative-based global sensitivity analysis for detecting importance measures of basic input random variables. • Efficient propagation of uncertainty by synthesizing the probability density evolution method and the change of probability measure. • Simultaneous reliability and sensitivity analysis of a real-world RC structure of 288 m high. [ABSTRACT FROM AUTHOR]

The probability density evolution method (PDEM) synthesizing the change of probability measure (COM) provides a compatible framework for quantifying simultaneous aleatory and epistemic uncertainties. Nonetheless, when the effective support for the change of measure becomes narrow, the quantification error of the PDEM-COM may increase, and the PDEM-COM may even be invalid if the effective support is an empty set. To address this issue, in the present paper, the error analysis of the PDEM-COM is firstly explored, and the generalized F-discrepancy via the COM is utilized to measure the similarity of two different distributions. Then, an augmenting approach is proposed to improve the performance of the PDEM-COM by adding a number of computational simulations. The results indicate that, the PDEM-COM can still be relatively accurate as long as the effective support is sufficiently large, even when there is a significant shift in the probability measure. However, if the effective support turns to be extremely narrow, the error of hybrid uncertainty quantification via the PDEM-COM may be unsatisfied, but it can be significantly reduced by the suggested augmenting approach. Numerical examples are investigated to demonstrate the accuracy and efficiency of the proposed method. Some issues to be further studied are also outlined. • Error analysis of the PDEM-COM is studied. • Numerical illustration of the PDEM-COM for different changes of probability measure. • An augmenting approach is proposed to improve the PDEM-COM. • The accuracy and efficiency of the proposed method is validated by three engineering applications. [ABSTRACT FROM AUTHOR]