## 1 Introduction  
It is well known that seismic demand stands at the core of the seismic vulnerability analysis of structures [1]. There are many kinds of structural seismic demands such as pier displacement ductility and residual drift, which have been studied in seismic fragility evaluations [2]. However, due to the inherent randomness in engineering structures or a lack of knowledge, many uncertainties exist in structural seismic demands and capacities. The seismic vulnerability created by having to consider all uncertain items can lead to a computational burden. Therefore, to quantitatively model engineering structures and propagate the uncertainties, it is necessary to conduct a sensitivity analysis to the seismic requirements from a mass of uncertain parameters [3]. The sensitivity analysis of uncertain parameters in civil engineering has been developed to study the contributions of the structural input uncertain parameters or the relative conditions to the structural output variables. Generally, sensitivity analyses are divided into local sensitivity analysis and global sensitivity analysis [4]. Local sensitivity analysis is defined as the rank of the output fluctuations with respect to the input perturbation around nominal values such as the derivatives of the dynamical equation [5]. However, the local sensitivity analysis cannot reflect the effects of the uncertain parameters on the structural responses globally for the nonlinear models. Therefore, much global sensitivity analysis is applied to quantify the effects of the parameters on the uncertainties at the entire distribution ranges of those structural demands, such as the use of the information entropy importance method [6], MII method [7] and variance importance method [8]. However, the assumption of the variance importance method is not usually reasonable since taking variance as a measure of uncertainty is not sufficient to describe output variability [9]. In this regard, the former two methods have been used in the sensitivity analysis of uncertain parameters for seismic demands in recent years. [PERSON] et al. investigated the sensitivity of uncertainties, including ground motion variables and structural properties, on the demand parameters for two benchmark reinforced concrete frame buildings. The entropy-based importance indexes of uncertainties were obtained by running nonlinear time history analyses (NTHA) one thousand times in Monte Carlo (MC) simulations [10]. [PERSON] et al. applied the MII and variance importance methods to analyse the sensitivity of uncertain parameters involved in the seismic demands of bridge structures by MC simulations and kernel density estimation, respectively [11]. [PERSON] and [PERSON] applied the Sobol sequence instead of MC methods to simulate the samples of eight uncertain parameters and the orthogonal polynomial estimation method to obtain the MII measures on four seismic demands of steel-reinforced concrete frame structures [12]. The aforementioned studies on the global sensitivity analysis of uncertain parameters to seismic demands are based on sampling-based methods such as MC simulation or Sobol sequences, which require a large number of NTHA of structural models because the global sensitivity index evaluation involves a double loop simulation to propagate the uncertainties for evaluation of the unconditional and the conditional probability density function (PDF) of seismic demands. Due to the high computational cost of sampling-based MII analysis, a highly efficient uncertainty propagation technology is necessary. The uncertainty PDF propagating problem can be converted to a reconstruction PDF by the use of fractional statistical moments. The point-estimate method (PEM) has been proven to be an effective tool to estimate statistical moments of model outputs from the several moments of the input variables, which can significantly reduce the computational cost caused by MC simulations [13].