Computation of High-Order Moments of Structural Dynamic Characteristics Based on Polynomial Chaos Expansion

WAN Huaping; TAI Yonggan; ZHONG Jian; REN Weixin

doi:10.21656/1000-0887.390165

Volume 39 Issue 12

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Article Navigation > Applied Mathematics and Mechanics > 2018 > 39(12): 1331-1342

WAN Huaping, TAI Yonggan, ZHONG Jian, REN Weixin. Computation of High-Order Moments of Structural Dynamic Characteristics Based on Polynomial Chaos Expansion[J]. Applied Mathematics and Mechanics, 2018, 39(12): 1331-1342. doi: 10.21656/1000-0887.390165

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Computation of High-Order Moments of Structural Dynamic Characteristics Based on Polynomial Chaos Expansion

doi: 10.21656/1000-0887.390165

¹Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University,Shanghai 200072, P.R.China;²Department of Mechanics, Shanghai University, Shanghai 200444, P.R.China

Funds: The National Natural Science Foundation of China(51878235； 51508144)；China Postdoctoral Science Foundation(2015M581981)

Received Date: 2018-06-13
Rev Recd Date: 2018-10-16
Publish Date: 2018-12-01

Abstract

Abstract

Uncertainty of structural parameters leads to uncertainty of structural dynamic characteristics. Quantification of uncertainty of dynamic characteristics provides accurate dynamic information for structural dynamic analysis. Statistical moments (e.g., mean and variance) mainly represent the uncertainty of structural dynamic properties. The MonteCarlo simulation (MCS) requires a large number of model evaluations to ensure the convergence of the results, which hinders its application to the largescale, complex engineering structures. The polynomial chaos expansion (PCE) surrogate model was used to replace the computationally expensive finite element model (FEM), and then the statistical moments of structural dynamic characteristics were efficiently calculated. The presented PCEbased method only needs a small set of model runs before the model formulation and subsequently does not require the FEM for calculations of the statistical moments. Therefore, the issue of the high computational cost associated with the computations of dynamic characteristic statistical moments was solved. The method is suitable for parameters with arbitrary probability distribution and has high computational efficiency in calculating the highorder statistical moments. Finally, the effectiveness of the developed method was verified through an example of an aluminum plate.
- uncertainty,
- dynamic characteristic,
- highorder statistical moment,
- polynomial chaos expansion

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References(15)

References

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