Dynamic computation for rigid–flexible multibody systems with hybrid uncertainty of randomness and interval

Wu, Jinglai; Luo, Liang; Zhu, Bin; Zhang, Nong; Xie, Maoqing

doi:10.1007/s11044-019-09677-1

Cited by 16 publications

(4 citation statements)

References 38 publications

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“…Therefore, another objective of the UP is to calculate the lower and upper bounds of the mean and variance of the concerned responses [33]. In some hybrid-uncertainty problems, the error bars [34] are used to evaluate the overall uncertain extent of the response, which is defined as follows:…”

Section: Uncertainty Propagation Problemsmentioning

confidence: 99%

“…Wu et al [33] developed the Polynomial-Chaos-Chebyshev-Interval (PCCI) method, where the PCE theory that accounts for the random variables is integrated with the Chebyshev method that handles the interval uncertainty. Then Wu et al [34] improved the method and applied it to rigid-flexible multibody systems. Fu et al [35] also proposed a UP method for accelerating unbalanced rotating systems with both random and interval variables, which is also based on PEC theory and the Chebyshev method.…”

Section: Introductionmentioning

confidence: 99%

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A random-bound Chebyshev method for uncertainty propagation of nonlinear dynamics under imprecise probabilities

Zhang,

Li,

et al. 2024

Preprint

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The distribution-free P-box is an effective quantification model for uncertainties with only imprecise probabilistic information. However, its application to nonlinear dynamical systems is limited due to a lack of efficient uncertainty propagation (UP) methods. To end this, this work develops a random-bound Chebyshev (RBC) UP method based on the framework of the interval Monte Carlo (IMC) method. First, the Chebyshev method is applied to solve the interval analysis in the IMC simulations. Here, the bounds of intervals can be regarded as random variables whose cumulative density functions (CDFs) are the CDF bounds of the P-box. Since the CDF bounds of distribution-free P-boxes are always arbitrary and non-parameterized, the data-driven polynomial chaos expansion (DD-PCE), which only requires the information of statistical moments, is introduced to solve the problem of random bounds. Then a sparse-regression strategy is utilized to deal with the ‘curse of dimensionality’ of the DD-PCE for high-dimensional problems. As a result, the RBC method efficiently achieves a non-intrusive UP of nonlinear dynamics with distribution-free P-boxes. The method is also effective for hybrid UP problems with random, interval, and P-box variables. Then the RBC method is validated based on test cases, including a duffing oscillator, a vehicle ride, and an engineering application of launch-vehicle trajectory. The results verify the ability of the method to deal with complex black-box problems. In comparison with the reference solutions based on the IMC simulations, with relative errors of less than 1%, the proposed method requires less than 0.0004% sample size and 0.015% calculation time.

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Section: Uncertainty Propagation Problemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A random-bound Chebyshev method for uncertainty propagation of nonlinear dynamics under imprecise probabilities

Zhang,

Li,

et al. 2024

Preprint

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“…Then, the auxiliary algorithms are applied to find the extreme values of the surrogate model, and obtain the interval results of the dynamic response. The common auxiliary algorithms include IA [35,42,43], genetic algorithm (GA) [40,44,45] and SM [46][47][48]39]. IA has the fastest computing velocity, but often yields calculation errors due to the wrapping effect, especially when the dynamic response is largely uncertain and nonlinear.…”

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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“…In the second model, uncertain parameters are quantified as random interval variables, where the bounds of interval variables are expressed as random variables instead of deterministic values. Wu et al 40 proposed a new hybrid uncertain computational method, two evaluation indices namely interval mean and interval error bar, are presented to quantify the system response, and an orthogonal series expansion method, termed as improved Polynomial‐Chaos‐Chebyshev‐Interval (PCCI) method, which solves the random and interval uncertainty under one integral framework. Zheng et al 41 develop a new robust topology optimization method based on level sets for structures subject to hybrid uncertainties, with a more efficient Karhunen‐Loève hyperbolic PCCI method to conduct the hybrid uncertain analysis.…”

Section: Introductionmentioning

confidence: 99%

New reliability modeling methods for structural systems with hybrid uncertainty

Zhao

Yang

Liu

et al. 2020

Quality & Reliability Eng

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The present study investigates the hybrid reliability modeling of structures in which the inputs contain both random variables and interval variables. Hybrid uncertainty is divided into three categories, including random variables mixed with random variables, interval variables mixed with interval variable, and random variables mixed with interval variables. In order to perform the reliability analysis of structural systems, first, the Bayes method is proposed in the present study to obtain distribution parameters of random variables. Moreover, the self-sample method is introduced to obtain the interval boundaries based on the least available measuring data. Then, the reliability models are established for three situations and the reliability indices are defined and derived accordingly. The abovementioned three types of reliability indices outline the general situation of structural systems. Finally, the specific calculation process is described in details through different examples. Furthermore, the accuracy and efficiency of the proposed method is discussed by comparing the results obtained from the Monte Carlo simulation and those of other methods. The obtained results indicate that the performance of the proposed model in solving reliability modeling problems is better.

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Dynamic computation for rigid–flexible multibody systems with hybrid uncertainty of randomness and interval

Cited by 16 publications

References 38 publications

A random-bound Chebyshev method for uncertainty propagation of nonlinear dynamics under imprecise probabilities

A random-bound Chebyshev method for uncertainty propagation of nonlinear dynamics under imprecise probabilities

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

New reliability modeling methods for structural systems with hybrid uncertainty

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