Solving uncertain differential equations using interval legendre polynomials based collocation method

Rao, Tharasi Dilleswar; Chakraverty, Snehashish

doi:10.1080/09720502.2019.1638614

Cited by 6 publications

(1 citation statement)

References 14 publications

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“…The input parameters of the interval model are defined as interval variables, as well the responses of the interval model include the upper and lower bounds and the uncertainty level of the model. For complex interval models, orthogonal polynomials can be used to establish the proxy models (Wu et al 2014;Wang et al 2020;Rao and Chakraverty 2019), as well Monte Carlo method can be used to solve the responses of the interval models (Hurtado and Alvarez 2012;Cai et al 2020). The calculation efficiency of the Monte Carlo method, however, is very low since it requires a large amount of sampling (Cai et al 2020).…”

Section: Introductionmentioning

confidence: 99%

Interval analysis and optimization of axial friction force of drive-shaft systems considering rough surface characteristics

Feng

Shangguan

2021

Struct Multidisc Optim

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The axial friction force (AFF) of drive-shaft systems is mainly caused by friction inside tripod joints. In order to study the influence of the friction on the AFF more deeply, a novel deterministic model for calculating the AFF considering rough surface characteristics (RSC) is established based on the fractal theory. Through measuring the AFF of a drive-shaft system, the deterministic model is verified. After considering RSC, the AFF has considerable uncertainty. Based on Legendre polynomials and the deterministic model of the AFF, an interval model for calculating the AFF considering RSC is proposed to study the AFF more efficiently. In the interval model, the factors affecting the AFF are considered as interval variables. Combining Legendre polynomials and the vertex method, a novel method called Legendre-vertex method is proposed to solve the responses of the interval model in an efficient manner. Multi-objective interval uncertainty optimization of the AFF is subsequently carried out to obtain the optimal design parameters of the drive-shaft system. In the optimization, both the upper bound and the uncertainty level of the AFF are regarded as optimization objectives. The results suggest that the Legendrevertex method can solve responses of an interval model in an efficient manner, which is suitable for the interval analysis and optimization of the AFF considering RSC, as well the multi-objective interval uncertainty optimization of the AFF not only ensures that the upper bound of the AFF meets the design requirement but also improves the robustness of the AFF.

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