Shufang Song

Subset simulation for structural reliability sensitivity analysis

Based on two procedures for efficiently generating conditional samples, i.e. Markov chain Monte Carlo (MCMC) simulation and importance sampling (IS), two reliability sensitivity (RS) algorithms are presented. On the basis of reliability analysis of Subset simulation (Subsim), the RS of the failure probability with respect to the distribution parameter of the basic variable is transformed as a set of RS of conditional failure probabilities with respect to the distribution parameter of the basic variable. By use of the conditional samples generated by MCMC simulation and IS, procedures are established to estimate the RS of the conditional failure probabilities. The formulae of the RS estimator, its variance and its coefficient of variation are derived in detail. The results of the illustrations show high efficiency and high precision of the presented algorithms, and it is suitable for highly nonlinear limit state equation and structural system with single and multiple failure modes.

A generalized Borgonovo's importance measure for fuzzy input uncertainty

In this work, the way in which fuzzy uncertainty in a models output is apportioned to fuzzy uncertainty in model inputs is studied through a sensitivity analysis. Here, an optimization technique is employed to obtain the membership functions of the fuzzy structural response, for which a global sensitivity indicator is introduced to measure the influence of fuzzy input uncertainty on fuzzy output uncertainty. The global sensitivity indicator is the important measure of the fuzzy input uncertainty, which extends Borgonovos measure. In this study, the mathematical properties of the important measure of the fuzzy input uncertainty are discussed and proved. The results of numerical examples and engineering examples show that the proposed importance measure can effectively describe the effect of fuzzy input uncertainty on fuzzy structural response. When the sensitivity indicator is larger, the basic fuzzy-valued variable becomes more important. The sensitivity indicators of the fuzzy structural response can give an essential importance sequence of all the basic fuzzy-valued variables and identify key contributing fuzzy-valued variables. The sensitivity indicators can provide the availability guidance to reduce the number of basic variables and optimize the fuzzy response model.

The uncertainty importance measures of the structural system in view of mixed uncertain variables

Abstract The uncertainty importance measure, i.e. global sensitivity analysis, of the basic variable is used for investigating the influence of model input uncertainty on model output uncertainty. There are two kinds of uncertainty importance measures of the structural reliability and response with respect to both random and fuzzy-valued input variables are investigated for problems with aleatory uncertainty and epistemic uncertainty. First, the structural reliability and probability distribution of the response at each membership level are analyzed. Then, the differences between the unconditional and conditional membership functions (MFs) of reliability and the unconditional and conditional probability density functions (PDFs) of response at all membership levels are measured for the presented uncertainty importance measures. The mathematical properties of the presented importance measures are discussed and proven in this study. The defined uncertainty importance measures are easy to apprehend and are not restricted to the distribution form of random variables or to the membership function of fuzzy-valued variables. All evaluations are based on the PDF of random variables and the MF of fuzzy-valued variables, and thus, the established importance measures are global sensitivity indicators that consider the influence of random and fuzzy-valued input uncertainty on the structural reliability and response. The results of the examples show that the proposed sensitivity indicators of uncertainty importance measure can intuitively describe the effects of random and fuzzy-valued input variables on the reliability and the probability distribution of response for single and multiple failure modes.

Uncertainty Importance Measure by Fast Fourier Transform for Wing Transonic Flutter

importance measure of basic random variable on the probability distribution of response and the importance measure of basic random variable on the failure probability) are solved by use of the fast Fourier transform technique. For the two-dimensional aircraft wing transonic flutter problem, reduced order modeling method on computational fluid dynamics is used to construct the aerodynamic state equations. Coupling structural state equations with aerodynamic state equations, the state equations of aeroelasticity system can be obtained, on which thelimitstatefunctionof flutterisfoundedbyconsideringthecriticalvelocity,whichissolvedbytheeigenvalueofthe state matrix, satisfying the requirement. For the aeroelastic flutter response models of a two-dimensional wing without flap and with a flap, two importance measure indexes can quantificationally reflect the influence of the random variables on the structural response. Comparing with the importance measure results of Monte–Carlo simulation, those of fast Fourier transform are higher in efficiency with acceptable precision.

Modified GMDH-NN algorithm and its application for global sensitivity analysis☆

Abstract Global sensitivity analysis (GSA) is a very useful tool to evaluate the influence of input variables in the whole distribution range. Sobol method is the most commonly used among variance-based methods, which are efficient and popular GSA techniques. High dimensional model representation (HDMR) is a popular way to compute Sobol indices, however, its drawbacks cannot be ignored. We show that modified GMDH-NN algorithm can calculate coefficients of metamodel efficiently, so this paper aims at combining it with HDMR and proposes GMDH-HDMR method. The new method shows higher precision and faster convergent rate. Several numerical and engineering examples are used to confirm its advantages.

Uncertainty Quantification and Sensitivity Analysis of Transonic Aerodynamics with Geometric Uncertainty

Airfoil geometric uncertainty can generate aerodynamic characteristics fluctuations. Uncertainty quantification is applied to compute its impact on the aerodynamic characteristics. In addition, the contribution of each uncertainty variable to aerodynamic characteristics should be computed by the uncertainty sensitivity analysis. In the paper, Sobol’s analysis is used for uncertainty sensitivity analysis and a nonintrusive polynomial chaos method is used for uncertainty quantification and Sobol’s analysis. It is difficult to describe geometric uncertainty because it needs a lot of input parameters. In order to alleviate the contradiction between the variable dimension and computational cost, a principal component analysis is introduced to describe geometric uncertainty of airfoil. Through this technique, the number of input uncertainty variables can be reduced and typical global deformation modes can be obtained. By uncertainty quantification, we can learn that the flow characteristics of shock wave and boundary layer separation are sensitive to the geometric uncertainty in transonic region, which is the main reason that transonic drag is sensitive to the geometric uncertainty. The sensitivity analysis shows that the model can be simplified by eliminating unimportant geometric modes. Moreover, which are the most important geometric modes to transonic aerodynamics can be learnt. This is very helpful for airfoil design.