Interval and subinterval perturbation methods for a structural-acoustic system with interval parameters

Change-of-variable interval stochastic perturbation method for hybrid uncertain structural-acoustic systems with random and interval variables

“…By introducing the subinterval technique into the CVISPM, an improved CVISPM can be developed based on the numerical procedure of the subinterval perturbation method discussed by Xia et al (2013a). The subinterval technique is used to reduce the actual uncertainty levels of the interval variables, whereas the acceptable uncertainty levels are not improved.…”

“…Considering that the CVISPM is based on a first-order perturbation technique, the IPM is also based on a first-order perturbation technique for the response analysis of the ISAS. A detailed discussion on using the IPM for the response analysis of the ISAS can be found in (Xia et al, 2013a). The response confidence intervals along the top boundary line of the ISAS yielded by IMCSM and IPM are plotted in Fig.…”

“…Recently, an interval perturbation method, based on perturbation theory and interval operations, was proposed. By combining this method with the finite element method, the interval perturbation method has been applied in a wide variety of engineering uncertainty problems (Qiu and Elishakoff, 1998;Zhang et al, 2007;Impollonia and Muscolino, 2011;Fujita and Takewaki, 2011;Chen et al, 2003;Yu, 2012, 2013;Xia et al, 2013a). A common shortcoming of the interval methods is that the probability density functions within the response confidence intervals are missing.…”

Hybrid uncertainty propagation of coupled structural–acoustic system with large fuzzy and interval parameters

“…However, due to the unpredictable effect of neglecting high-order terms in Neumann series, the traditional perturbation method will not be effective for the cases with large uncertainty level. By employing the subinterval theory and SMW formula, Xia et al [13,14] extended the perturbation method to the problem with large interval parameters, and obtained acceptable computational accuracy. Fuzzy set theory is another efficient category to model the system uncertainties based on the subjective opinions.…”

Hybrid finite element/statistical energy method for mid-frequency analysis of structure−acoustic systems with interval parameters

“…In the last two decades, the vibro-acoustic response of a system with uncertain properties caused by manufacturing imperfections, aggressive environmental factors and unpredictable external loads has been an important issue in engineering design [1][2][3]. Before performing an uncertain analysis, there are two main steps to make: firstly, an approach should be selected to model the system; secondly, choose a way in which the system uncertainties will be described.…”