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

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Conference Proceeding
Advances in Applied Mechanics Research, Conference Proceedings - 7th Australasian Congress on Applied Mechanics, ACAM 2012, 2012, pp. 306 - 314
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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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