Uncertainty quantification in simulations of power systems: Multi-element polynomial chaos methods

Prempraneerach, Pradya; Hover, Franz S.; Triantafyllou, Michael S.; Karniadakis, George

doi:10.1016/j.ress.2010.01.012

Cited by 43 publications

(27 citation statements)

References 26 publications

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“…(16), that the number of coefficients in expansion (15) grows rapidly with the number of variables n and the polynomial degree p. Therefore, in order to reduce the computational burden and to improve the approximation quality of the method, Blatman and Sudret proposed in [13] an adaptive sparse polynomial chaos expansion (SPCE). In their approach the iterative algorithm allows to eliminate these of the expansion coefficients which are not significant in approximating the function h(X) leading to the optimal polynomial representation.…”

Section: Sampling Methodsmentioning

confidence: 99%

“…The method has been further modified to the so-called multi-element generalized polynomial chaos, see e.g. [15], where the random space is decomposed into local elements and the generalised polynomial chaos method is subsequently implemented within individual elements. Usage of PCE for statistics of the rotor system responses under uncertainties modeled by Gaussian random variables is considered in [16], where PCE is using at the stage of solving the equations of motion.…”

Section: Introductionmentioning

confidence: 99%

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Polynomial chaos expansion method in estimating probability distribution of rotor-shaft dynamic responses

Lasota¹,

Stocki²,

Tauzowski³

et al. 2015

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. The main purpose of the study is an assessment of computational efficiency of selected numerical methods for estimation of vibrational response statistics of a large multi-bearing turbo-generator rotor-shaft system. The effective estimation of the probability distribution of structural responses is essential for robust design optimization and reliability analysis of such systems. The analyzed scatter of responses is caused by random residual unbalances as well as random stiffness and damping parameters of the journal bearings. A proper representation of these uncertain parameters leads to multidimensional stochastic models. Three estimation techniques are compared: Monte Carlo sampling, Latin hypercube sampling and the sparse polynomial chaos expansion method. Based on the estimated values of the first four statistical moments the probability density function of the maximal vibration amplitude is evaluated by the maximal entropy principle method. The method is inherently suited for an accurate representation of the probability density functions with an exponential behavior, which appears to be characteristic for the investigated rotor-shaft responses. Performing multiple numerical tests for a range of sample sizes it was found that the sparse polynomial chaos method provides the best balance between the accuracy and computational effectiveness in estimating the unknown probability distribution of the maximal vibration amplitude.

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Section: Sampling Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Polynomial chaos expansion method in estimating probability distribution of rotor-shaft dynamic responses

Lasota¹,

Stocki²,

Tauzowski³

et al. 2015

Bulletin of the Polish Academy of Sciences Technical Sciences

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“…Relatively recent work has applied gPC to both classical and optimal control system design [63,85,86]. Also, MEgPC has been used applied to uncertainty quantification in power systems [87] and mobile robots [88].…”

Section: 27mentioning

confidence: 99%

Motion Planning of Uncertain Ordinary Differential Equation Systems

Hays

Sandu

Sandu³

et al. 2014

Journal of Computational and Nonlinear Dynamics

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“…Relatively recent work has applied gPC to both classical and optimal control system design [41,63,64]. Also, MEgPC has been used applied to uncertainty quantification in power systems [65] and mobile robots [66].…”

Section: 25mentioning

confidence: 99%

Parametric Design Optimization of Uncertain Ordinary Differential Equation Systems

Hays

Sandu

et al. 2011

Volume 9: Transportation Systems; Safety Engineering, Risk Analysis and Reliability Methods; Applied Stochastic Optimization, U

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Uncertainty quantification in simulations of power systems: Multi-element polynomial chaos methods

Cited by 43 publications

References 26 publications

Polynomial chaos expansion method in estimating probability distribution of rotor-shaft dynamic responses

Polynomial chaos expansion method in estimating probability distribution of rotor-shaft dynamic responses

Motion Planning of Uncertain Ordinary Differential Equation Systems

Parametric Design Optimization of Uncertain Ordinary Differential Equation Systems

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