Interval analysis for uncertain aerodynamic loads with uncertain-but-bounded parameters

Zhu, Jingjing; Qiu, Zhiping

doi:10.1016/j.jfluidstructs.2018.05.009

Cited by 20 publications

(7 citation statements)

References 30 publications

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“…Interval analysis was introduced in numerical analysis by Moore in the celebrated book [1]. Over the past 50 years, it has attracted considerable interest and has been applied in various fields, such as interval differential equations [2], aeroelasticity [3], aerodynamic load analysis [4], and so on. For more profound results and applications, see [5][6][7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Hermite-Hadamard Type Inequalities for Interval (h1, h2)-Convex Functions

Zhao

et al. 2019

Mathematics

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Section: Introductionmentioning

confidence: 99%

Hermite-Hadamard Type Inequalities for Interval (h1, h2)-Convex Functions

Zhao

et al. 2019

Mathematics

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“…Wu et al (2016) proposed a new hybrid probabilistic and interval computational scheme, which can investigate the effects of random and interval variables acting upon the overall structural stability. Zhu and Qiu (2018) quantified the uncertain parameters with insufficient information into interval variables, and extended the interval and subinterval perturbation method to evaluate the uncertain aerodynamic loads region with uncertain-but-bounded parameters. However, the uncertain parameters with insufficient information tend to be generalized, so the method is not universal.…”

Section: Introductionmentioning

confidence: 99%

Based-restraining interval extension improved truncation algorithm for response analysis of uncertain mechanical systems

Liu

Wang

et al. 2021

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Purpose This study aims to propose an improved affine interval truncation algorithm to restrain interval extension for interval function. Design/methodology/approach To reduce the occurrence times of related variables in interval function, the processing method of interval operation sequence is proposed. Findings The interval variable is evenly divided into several subintervals based on correlation analysis of interval variables. The interval function value is modified by the interval truncation method to restrain larger estimation of interval operation results. Originality/value Through several uncertain displacement response engineering examples, the effectiveness and applicability of the proposed algorithm are verified by comparing with interval method and optimization algorithm.

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“…The Taylor expansion based method (TEBM) performs the first-or second-order Taylor series expansions at the midpoint of uncertain parameters and obtains the dynamic response interval [2,[25][26][27][28][29]. The advantage of TEBM is high computational efficiency, and the calculation consumption is raised linearly as the number of interval parameters rises.…”

Section: Introductionmentioning

confidence: 99%

A Bivariate Chebyshev Polynomials Method for Nonlinear Dynamic Systems With Interval Uncertainties

Wei

Feng

Meng

2021

Preprint

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A bivariate Chebyshev polynomials approach is proposed to estimate the dynamic response bounds of nonlinear systems with interval uncertainties. The existing collocation method directly searches the maximum and minimum values of the surrogate model in the entire interval space by the scanning method (SM). The presence of too many uncertain parameters will lead to expansive computational cost. To overcome this shortcoming, the dynamic response is decomposed by a bivariate function decomposition (BFD), established based on high-order Taylor expansion, into the sum of multiple univariate and bivariate response functions. The above univariate and bivariate functions are fitted using Chebyshev polynomials, and polynomial coefficients are obtained through one-dimensional (1D) and two-dimensional (2D) interpolation points. Thus, the solution of the nonlinear dynamic systems with uncertain parameters can be transformed into that of univariate and bivariate Chebyshev interval functions. The extremum values of the low-dimensional Chebyshev interval functions can be found by SM, and then the bounds of dynamic response are acquired by interval arithmetic. Since SM searches for extreme values only in 1D and 2D uncertain domains, the amount of calculation is reduced compared to searching the whole uncertain space. The efficiency, practicability and effectiveness of the proposed interval uncertainty analysis method are proved by three dynamic examples.

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Interval analysis for uncertain aerodynamic loads with uncertain-but-bounded parameters

Cited by 20 publications

References 30 publications

Hermite-Hadamard Type Inequalities for Interval (h1, h2)-Convex Functions

Hermite-Hadamard Type Inequalities for Interval (h1, h2)-Convex Functions

Based-restraining interval extension improved truncation algorithm for response analysis of uncertain mechanical systems

A Bivariate Chebyshev Polynomials Method for Nonlinear Dynamic Systems With Interval Uncertainties

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