Hybrid uncertain analysis for structural–acoustic problem with random and interval parameters

Xia, Baizhan; Yu, Dejie; Liu, Jian

doi:10.1016/j.jsv.2012.12.028

Cited by 56 publications

(17 citation statements)

References 37 publications

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“…where j = √ −1 is an imaginary unitary, = / is the wave number, is the angular frequency, is the acoustic speed of fluid, and K is the acoustic system stiffness matrix; M is the acoustic system mass matrix; C is the acoustic system damping matrix; p stands for the sound pressure vector; F stands for the acoustic system load vector. Equation (1) can be queried in [47]. There are many inherent uncertainties in the engineering sound field, such as uncertain physical property of acoustic medium caused by the variation of temperature and the uncertain velocity exciting produced by unpredictable environment.…”

Section: Random Model Of Uncertain Acoustic Problemsmentioning

confidence: 99%

“…The analysis of the effects of vibration and noise is one of the key points for the design of engineering systems with high level NVH performance. During the last decades, lots of uncertainty analysis methods based on the perturbation theory have been proposed for random response analysis of acoustic problem [46][47][48][49][50]. However, the perturbation based method can only solve random problems with small uncertainty level [50].…”

Section: Introductionmentioning

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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Section: Random Model Of Uncertain Acoustic Problemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Flexible Polynomial Expansion Method for Response Analysis with Random Parameters

2018

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“…Vibration reduction is a vital issue in structural engineering, and the related theoretical development and technological innovation are always highly concerned by researchers and engineers . Traditional passive vibration control techniques by virtue of vibration isolation materials will obviously increase structural weight so that they are no longer suitable for fine designs.…”

Section: Introductionmentioning

confidence: 99%

A nonprobabilistic time-variant reliability-based optimization approach to the reliable active controller design of structural vibration considering convex uncertainties

Wang

Liu

Yang

2018

Struct Control Health Monit

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It is observed that the controller, as the "brain" of the active control system, plays a vital role in the vibration-rejecting aspect, and thereby, techniques of the optimal controller design are attracting increasing attention in dynamical engineering recently. However, due to the existence of uncertainty effects originating from modeling parameters and environmental conditions, current design means based on the classical optimal control theory are no longer feasible. In view of this, a new nonprobabilistic time-variant reliability-based optimization (NTRBO) strategy considering convex uncertainties is presented in this study for the reliable controller design of structural vibration. Boundary rules and autocorrelation characteristics of dynamical responses under the linear quadratic regulator control are first determined using the state-space transformation and the convex process theory. Inspired by the out-crossing idea and the safety factor notation, a new piecewise function of the time-variant reliability index is defined, and the nonprobabilistic reliability constraint is then established. Weighing matrices in the Riccati equation, as the keys to construct the controller, are indeed optimized by solving the developed NTRBO model.The usage, validity, and efficiency of the presented reliable control methodology are eventually demonstrated by several example applications. KEYWORDSactive control of vibration, nonprobabilistic time-variant reliability-based optimization (NTRBO) strategy, the convex process theory, the linear quadratic regulator (LQR) control, uncertainty

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“…Based on the probabilistic reliability model and interval arithmetic, the interval of the probabilistic reliability index of structural systems was presented by Qiu and Wang. 15 Xia et al 16 performed hybrid uncertain analysis in a structuralacoustic problem using random and interval parameters. Chen et al 17 presented a hybrid perturbation method (HPM) for the prediction of the exterior acoustic field with interval variables and random variables.…”

Section: Introductionmentioning

confidence: 99%

Structural hybrid reliability index and its convergent solving method based on random–fuzzy–interval reliability model

Zhou

Sun

2016

Advances in Mechanical Engineering

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Aiming to resolve the problems of a variety of uncertainty variables that coexist in the engineering structure reliability analysis, a new hybrid reliability index to evaluate structural hybrid reliability, based on the random-fuzzy-interval model, is proposed in this article. The convergent solving method is also presented. First, the truncated probability reliability model, the fuzzy random reliability model, and the non-probabilistic interval reliability model are introduced. Then, the new hybrid reliability index definition is presented based on the random-fuzzy-interval model. Furthermore, the calculation flowchart of the hybrid reliability index is presented and it is solved using the modified limit-step length iterative algorithm, which ensures convergence. And the validity of convergent algorithm for the hybrid reliability model is verified through the calculation examples in literature. In the end, a numerical example is demonstrated to show that the hybrid reliability index is applicable for the wear reliability assessment of mechanisms, where truncated random variables, fuzzy random variables, and interval variables coexist. The demonstration also shows the good convergence of the iterative algorithm proposed in this article.

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Hybrid uncertain analysis for structural–acoustic problem with random and interval parameters

Cited by 56 publications

References 37 publications

A Flexible Polynomial Expansion Method for Response Analysis with Random Parameters

A Flexible Polynomial Expansion Method for Response Analysis with Random Parameters

A nonprobabilistic time-variant reliability-based optimization approach to the reliable active controller design of structural vibration considering convex uncertainties

Structural hybrid reliability index and its convergent solving method based on random–fuzzy–interval reliability model

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