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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]

This paper deals with the issue on metamodelling (a.k.a. surrogate modelling) of nonlinear stochastic dynamical systems, which are often with multiple input uncertainties Θ ∈ R n , viz., the dimension n may range from low to high (e.g., n ≥ 10). In this paper, to circumvent the problem of "curse of dimensionality" of high-dimensional input uncertainties, the feature spaces of outputs and inputs are firstly extracted from the original output and input spaces, and thus a feature mapping strategy is proposed. To form the feature output space, the nonlinear autoregressive with exogenous inputs (NARX) and the proper orthogonal decomposition (POD) are adopted, while the feature input space is detected by the active subspace method (ASM). It is found that the dimension of feature input (output) space may be much less than the one of original input (output) space, thus the applicability of many metamodelling methods can be naturally enhanced. On the constructed input–output feature space, the procedure of metamodelling is completed by the polynomial chaos expansion (PCE) combined with Kriging, which can capture global behaviours as well as local characteristics of the computational model. Two techniques are introduced to accelerate the proposed feature mapping strategy, consisting of the GF-discrepancy minimization algorithm for the design of experiments (DoEs), and the manifold optimization technique for the parameter identification of ASM. Four benchmarks, including a mathematical function (n = 2), a dynamical quarter car model (n = 10), a Bouc–Wen nonlinear oscillator subjected to earthquake ground motions (n = 30), and the first sub-system (as a black box) of the NASA UQ Challenge 2019 (n = 100), are studied to demonstrate the accuracy and efficiency of the proposed method. Some problems to be further studied are also outlined. [ABSTRACT FROM AUTHOR]