Comparison of interval method and polynomial chaos method for solving dynamics problem with uncertainties

Wu, J; Luo, Z; Zhang, N; Zhang, Y; Chen, L

Comparison of interval method and polynomial chaos method for solving dynamics problem with uncertainties

Wu, J

Luo, Z

Zhang, N

Zhang, Y

Chen, L

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Publication Type:: Conference Proceeding
Citation:: Advances in Applied Mechanics Research, Conference Proceedings - 7th Australasian Congress on Applied Mechanics, ACAM 2012, 2012, pp. 306 - 314
Issue Date:: 2012-01-01

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Field	Value	Language
dc.contributor.author	Wu, J https://orcid.org/0000-0002-4925-4242	en_US
dc.contributor.author	Luo, Z https://orcid.org/0000-0002-6953-3986	en_US
dc.contributor.author	Zhang, N https://orcid.org/0000-0001-6408-0044	en_US
dc.contributor.author	Zhang, Y https://orcid.org/0000-0003-0059-5369	en_US
dc.contributor.author	Chen, L	en_US
dc.date.issued	2012-01-01	en_US
dc.identifier.citation	Advances in Applied Mechanics Research, Conference Proceedings - 7th Australasian Congress on Applied Mechanics, ACAM 2012, 2012, pp. 306 - 314	en_US
dc.identifier.isbn	9781922107619	en_US
dc.identifier.uri	http://hdl.handle.net/10453/33291
dc.description.abstract	The parameters in most engineering problems are under uncertainty due to manufacturing and assembly tolerances, deviations in loads and other environmental factors, which make the uncertainty of system response too notable to be ignored. Two methods are used to solve uncertain problems in this paper, in which the polynomial chaos method is tailored for random variables while the interval method is used to fit for interval variables. The polynomial chaos method, belonging to a kind of probabilistic methods, can be used to obtain statistic characteristics of the response but requires the statistic information of uncertain parameters. The interval method to be proposed is based on the Runge-Kutta algorithm to solve ordinary differential equations (ODEs) with interval parameters. Taylor inclusion model is included in the numerical implementation, and the Taylor coefficients are calculated through real point iterative process, which is expected to reduce the overestimation intrinsic to interval computations. The vehicle handling problem is used as an engineering application to demonstrate the effectiveness of the proposed method. In the numerical model, the uncertain parameters are modelled as interval parameters and random parameters, respectively. The results show that: (1) the polynomial chaos method makes the mean value of responses consistent with the Monte Carlo simulation, but the standard deviation of responses exhibits large error; (2) the interval method achieves the bounds of responses which contain the actual results tightly; (3) both the polynomial chaos and interval methods are more computationally effective than the Monte Carlo simulation.	en_US
dc.relation.ispartof	Advances in Applied Mechanics Research, Conference Proceedings - 7th Australasian Congress on Applied Mechanics, ACAM 2012	en_US
dc.title	Comparison of interval method and polynomial chaos method for solving dynamics problem with uncertainties	en_US
dc.type	Conference Proceeding
utslib.for	0913 Mechanical Engineering	en_US
dc.location.activity	Adelaide
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Mechanical and Mechatronic Engineering
utslib.copyright.status	closed_access
pubs.publication-status	Published	en_US

Abstract:

The parameters in most engineering problems are under uncertainty due to manufacturing and assembly tolerances, deviations in loads and other environmental factors, which make the uncertainty of system response too notable to be ignored. Two methods are used to solve uncertain problems in this paper, in which the polynomial chaos method is tailored for random variables while the interval method is used to fit for interval variables. The polynomial chaos method, belonging to a kind of probabilistic methods, can be used to obtain statistic characteristics of the response but requires the statistic information of uncertain parameters. The interval method to be proposed is based on the Runge-Kutta algorithm to solve ordinary differential equations (ODEs) with interval parameters. Taylor inclusion model is included in the numerical implementation, and the Taylor coefficients are calculated through real point iterative process, which is expected to reduce the overestimation intrinsic to interval computations. The vehicle handling problem is used as an engineering application to demonstrate the effectiveness of the proposed method. In the numerical model, the uncertain parameters are modelled as interval parameters and random parameters, respectively. The results show that: (1) the polynomial chaos method makes the mean value of responses consistent with the Monte Carlo simulation, but the standard deviation of responses exhibits large error; (2) the interval method achieves the bounds of responses which contain the actual results tightly; (3) both the polynomial chaos and interval methods are more computationally effective than the Monte Carlo simulation.

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http://hdl.handle.net/10453/33291