scholarly journals An Efficient Polynomial Chaos Method for Stiffness Analysis of Air Spring Considering Uncertainties

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Feng Kong ◽  
Penghao Si ◽  
Shengwen Yin
Keyword(s):  
Orthogonal Polynomial ◽  
Polynomial Chaos ◽  
Random Variables ◽  
Expansion Method ◽  
Polynomial Expansion ◽  
Response Analysis ◽  
Air Spring ◽  
Stiffness Analysis ◽  
Orthogonal Polynomial Expansion ◽  
Sparse Quadrature

Traditional methods for stiffness analysis of the air spring are based on deterministic assumption that the parameters are fixed. However, uncertainties have widely existed, and the mechanic property of the air spring is very sensitive to these uncertainties. To model the uncertainties in the air spring, the interval/random variables models are introduced. For response analysis of the interval/random variables models of the air spring system, a new unified orthogonal polynomial expansion method, named as sparse quadrature-based interval and random moment arbitrary polynomial chaos method (SQ-IRMAPC), is proposed. In SQ-IRMAPC, the response of the acoustic system related to both interval and random variables is approximated by the moment-based arbitrary orthogonal polynomial expansion. To efficiently calculate the coefficient of the interval and random orthogonal polynomial expansion, the sparse quadrature is introduced. The proposed SQ-IRMAPC was employed to analyze the mechanic performance of an air spring with interval and/or random variables, and its effectiveness has been demonstrated by fully comparing it with the most recently proposed orthogonal polynomial-based interval and random analysis method.

Seismic Response Analysis of Reinforced Concrete Frame Structures Considering the Variation of Parameters

2013 ◽  
Vol 639-640 ◽  
pp. 859-865
Author(s):  
Qiao Yun Wu ◽  
Hong Ping Zhu
Keyword(s):  
Dynamic Response ◽  
Orthogonal Polynomial ◽  
Expansion Method ◽  
Polynomial Expansion ◽  
Reinforced Concrete Frame ◽  
Structural Dynamic ◽  
Concrete Frame ◽  
Orthogonal Polynomial Expansion ◽  
Polynomial Expansion Method ◽  
The Impact

The orthogonal polynomial expansion method expression of stochastic structure was deduced. Then, based on orthogonal polynomial expansion method, taking a 20-storey reinforced concrete frame structure as an example, the impact of the randomness of structural parameters on time history response was researched. Meanwhile, in order to verify the correctness of analysis program, the calculation results of orthogonal polynomial expansion method were compared with the Monte-Carlo method which based on Newmark integral. The results show that it can get relatively accurate results when the number of terms of the orthogonal polynomial is 5. Structural mass and stiffness have a greater impact on the structural dynamic response. And the greater number of random parameters, the greater the impact on structural dynamic response.

scholarly journals A Flexible Polynomial Expansion Method for Response Analysis with Random Parameters

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Rugao Gao ◽  
Keping Zhou ◽  
Yun Lin
Keyword(s):  
Weight Function ◽  
Polynomial Chaos ◽  
Probability Distributions ◽  
Random Variables ◽  
Expansion Method ◽  
Response Analysis ◽  
Chaos Expansion ◽  
Generalized Polynomial Chaos ◽  
Generalized Polynomial ◽  
Polynomial Expansion Method

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.

Stochastic Finite Element Method Using Polynomial Chaos Expansion

2011 ◽  
Vol 199-200 ◽  
pp. 500-504 ◽  
Author(s):  
Wei Zhao ◽  
Ji Ke Liu
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Polynomial Chaos ◽  
Expansion Method ◽  
Polynomial Chaos Expansion ◽  
Polynomial Expansion ◽  
Stochastic Finite Element Method ◽  
Chaos Expansion ◽  
Stochastic Finite Element ◽  
Element Method

We present a new response surface based stochastic finite element method to obtain solutions for general random uncertainty problems using the polynomial chaos expansion. The approach is general but here a typical elastostatics example only with the random field of Young's modulus is presented to illustrate the stress analysis, and computational comparison with the traditional polynomial expansion approach is also performed. It shows that the results of the polynomial chaos expansion are improved compared with that of the second polynomial expansion method.

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