Interval and random analysis for structure–acoustic systems with large uncertain-but-bounded parameters

Yin, Shengwen; Yu, Dejie; Yin, Hui; Xia, Baizhan

doi:10.1016/j.cma.2016.03.034

Cited by 41 publications

(13 citation statements)

References 41 publications

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“…The discrete system equation of the acoustic domain can be written in the following matrix form [41]:…”

Section: Mathematical Model Of Asimentioning

confidence: 99%

A non-contact acoustic pressure-based method for load identification in acoustic-structural interaction system with non-probabilistic uncertainty

Lin

2019

Applied Acoustics

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A non-contact acoustic pressure-based method is proposed for load identification in the acoustic structure interaction system involving non-probabilistic uncertainty. The forward problem for load identification is established through the discretized convolution integral relationship of the dynamic loads and the Green's kernel function matrix of the system. The inverse process is constructed by using truncated single value decomposition approach in order to overcome the ill-posedness of the global kernel function matrix. In this work, two non-probabilistic models including ellipsoid model and interval model are proposed to quantify the effects of the system uncertainty. Several numerical examples are investigated to verify the effectiveness of the present methods. The results show that the non-contact acoustic pressure-based method with great convenience for dynamic load identification is accurate and effective. For the system with non-probabilistic uncertainty, the ellipsoid model and interval model are the proper choices to identify the bounds with knowing only the extreme values of the parameters. Moreover, the load bounds derived from the ellipsoid model are more reliable than those derived from the interval model.

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“…The discrete system equation of the acoustic domain can be written in the following matrix form [41]:…”

Section: Mathematical Model Of Asimentioning

confidence: 99%

A non-contact acoustic pressure-based method for load identification in acoustic-structural interaction system with non-probabilistic uncertainty

Lin

2019

Applied Acoustics

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“…For the type of tensor product expansion, the Gaussian integral method is very suitable to estimate the expansion characteristics [51]. Generally, the Gauss-Jacobi integration method is able to realize a reliable precision for the estimation of the expansion coefficient of Jacobi expansion When the Gauss-Jacobi integration point is equal to the expansion amount [35].…”

Section: Invert Response Law By Establishing Jacobian Extensionmentioning

confidence: 99%

“…Jacobi expansion for , , and V can be obtained, namely: = = 4.5, = = 3.7, and V = V = 7.2. A relative improvement criterion will be introduced for random uncertainty analysis with IJCEM [51]. For multivariate random problems, the relative improvement of responses is given by [51] Ir (k, ) = (k + e ) − (k)…”

Section: Procedures Of Ijcem For Random Analysis Of Soundmentioning

confidence: 99%

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A Flexible Polynomial Expansion Method for Response Analysis with Random Parameters

2018

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The generalized Polynomial Chaos Expansion Method (gPCEM), which is a random uncertainty analysis method by employing the orthogonal polynomial bases from the Askey scheme to represent the random space, has been widely used in engineering applications due to its good performance in both computational efficiency and accuracy. But in gPCEM, a nonlinear transformation of random variables should always be used to adapt the generalized Polynomial Chaos theory for the analysis of random problems with complicated probability distributions, which may introduce nonlinearity in the procedure of random uncertainty propagation as well as leading to approximation errors on the probability distribution function (PDF) of random variables. This paper aims to develop a flexible polynomial expansion method for response analysis of the finite element system with bounded random variables following arbitrary probability distributions. Based on the large family of Jacobi polynomials, an Improved Jacobi Chaos Expansion Method (IJCEM) is proposed. In IJCEM, the response of random system is approximated by the Jacobi expansion with the Jacobi polynomial basis whose weight function is the closest to the probability density distribution (PDF) of the random variable. Subsequently, the moments of the response can be efficiently calculated though the Jacobi expansion. As the IJCEM avoids the necessity that the PDF should be represented in terms of the weight function of polynomial basis by using the variant transformation, neither the nonlinearity nor the errors on random models will be introduced in IJCEM. Numerical examples on two random problems show that compared with gPCEM, the IJCEM can achieve better efficiency and accuracy for random problems with complex probability distributions.

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“…Recently, Wu et al have proposed a Polynomial Chaos–Chebyshev Interval (PCCI) method to determine the intervals of mean value and variance of the system response with hybrid uncertainties. Yin et al also used orthogonal polynomials and developed a unified interval and random Gegenbauer series expansion method to evaluate the uncertain response of acoustic fields with both random and interval parameters. However, the computational cost in calculating the coefficients will increase exponentially with the increase in uncertain variables.…”

Section: Introductionmentioning

confidence: 99%

Level‐set topology optimization for robust design of structures under hybrid uncertainties

Zheng

Luo

Jiang

et al. 2018

Numerical Meth Engineering

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This paper will develop a new robust topology optimization (RTO) method based on level sets for structures subject to hybrid uncertainties, with a more efficient Karhunen-Loève hyperbolic Polynomial Chaos-Chebyshev Interval method to conduct the hybrid uncertain analysis. The loadings and material properties are considered hybrid uncertainties in structures. The parameters with sufficient information are regarded as random fields, while the parameters without sufficient information are treated as intervals. The Karhunen-Loève expansion is applied to discretize random fields into a finite number of random variables, and then, the original hybrid uncertainty analysis is transformed into a new process with random and interval parameters, to which the hyperbolic Polynomial Chaos-Chebyshev Interval is employed for the uncertainty analysis. RTO is formulated to minimize a weighted sum of the mean and standard variance of the structural objective function under the worst-case scenario. Several numerical examples are employed to demonstrate the effectiveness of the proposed RTO, and Monte Carlo simulation is used to validate the numerical accuracy of our proposed method. KEYWORDS hybrid uncertainties, hyperbolic Polynomial Chaos-Chebyshev Interval method, robust design, topology optimization Int J Numer Methods Eng. 2019;117:523-542.wileyonlinelibrary.com/journal/nme

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Interval and random analysis for structure–acoustic systems with large uncertain-but-bounded parameters

Cited by 41 publications

References 41 publications

A non-contact acoustic pressure-based method for load identification in acoustic-structural interaction system with non-probabilistic uncertainty

A non-contact acoustic pressure-based method for load identification in acoustic-structural interaction system with non-probabilistic uncertainty

A Flexible Polynomial Expansion Method for Response Analysis with Random Parameters

Level‐set topology optimization for robust design of structures under hybrid uncertainties

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