A collocation interval analysis method for interval structural parameters and stochastic excitation

Abstract

Uncertainty propagation, one of the structural engineering problems, is receiving increasing attention owing to the fact that most significant loads are random in nature and structural parameters are typically subject to variation. In the study, the collocation interval analysis method based on the first class Chebyshev polynomial approximation is presented to investigate the least favorable responses and the most favorable responses of interval-parameter structures under random excitations. Compared with the interval analysis method based on the first order Taylor expansion, in which only information including the function value and derivative at midpoint is used, the collocation interval analysis method is a non-gradient algorithm using several collocation points which improve the precision of results owing to better approximation of a response function. The pseudo excitation method is introduced to the solving procedure to transform the random problem into a deterministic problem. To validate the procedure, we present numerical results concerning a building under seismic ground motion and aerofoil under continuous atmosphere turbulence to show the effectiveness of the collocation interval analysis method. uncertainty propagation, interval analysis, Taylor series expansion, Chebyshev polynomial, Pseudo excitation method PACS number(s): 02.30.Mv, 02.50Ey, 02.60Gf, 02.70.Jn Citation:Qi W C, Qiu Z P. A collocation interval analysis method for interval structural parameters and stochastic excitation.

A two-layer optimization framework for UAV path planning with interval uncertainties

“…Compared to well-adopted interval analysis methods based on the Taylor expansion, the CIAM is a good non-gradient algorithm using several collocation points to improve the approximation accuracy [17,19]. Also, we use the ABC algorithm to address the third issue.…”

“…The details of the CIAM and ABC algorithm are not included in this paper due to space constraints. Interested readers should refer to [17] and [21] for details. We will tackle the second issue in the next section.…”

“…Despite being efficient, the Taylor-based methods are limited to handling of uncertainties within small intervals because they depend on the first or second order sensitivity at the nominal points. To overcome this, an alternative called the collocation interval analysis method (CIAM) has been proposed [17]. The CIAM does not rely on sensitivity and thus works well when interval numbers are of large scale.…”

Non-probabilistic analysis of a double-disk rotor system with uncertain parameters

“…Qiu et al [20] had proposed many interval approaches including perturbation method, Taylor interval expansion method and interval collocation method to calculate static and dynamic problems in structures. Qi et al [21] further compared these interval methods with probabilistic ones in the aspects of efficiency, accuracy and overestimations. Wu et al [22] proposed a non-intrusive interval method for dynamic systems with uncertain parameters by introducing the Chebyshev inclusion function, which has been successfully applied to uncertain vehicle systems [23].…”

Uncertainty Analysis of Heat Transfer Properties of Corrugated-core Sandwich Panel

“…However, due to the complexity and severity of the service environment of ITPS, one can only obtain little information about the uncertainties. In this case, it is feasible to use interval analysis method to quantify these uncertainties [12,13].…”