A polynomial chaos approach to the analysis of vehicle dynamics under uncertainty

Kewlani, Gaurav; Crawford, Justin; Iagnemma, Karl

doi:10.1080/00423114.2011.639897

Cited by 78 publications

(34 citation statements)

References 17 publications

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“…Therefore the level of accuracy depends on the capability of the basis to capture the nonlinearity of the forward model rather than on the capacity of the sample generation algorithm to properly represent the input uncertainty by the spatial distribution of the sample points. It has been documented frequently that an equivalent level of accuracy can be achieved with only a fraction of the input points of any MC approach [17]- [19].…”

Section: B Coefficient Determinationmentioning

confidence: 99%

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Polynomial Chaos reformulation in Nonlinear Stochastic Optimal Control with application on a drivetrain subject to bifurcation phenomena

Lefebvre

Belie

Crevecoeur

2018

2018 22nd International Conference on System Theory, Control and Computing (ICSTCC)

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This paper discusses a method enabling optimal control of nonlinear systems that are subject to parametric uncertainty. A stochastic optimal tracking problem is formulated that can be expressed in function of the first two stochastic moments of the state. The proposed formulation allows to penalize system performance and system robustness independently. The use of polynomial chaos expansions is investigated to arrive at a computationally tractable formulation expressing the stochastic moments in function of the polynomial expansion coefficients rigorously. It is then demonstrated how the stochastic optimal control problem can be reformulated as a deterministic optimal control problem in function of these coefficients. The proposed method is applied to find a robust control input for the start-up of an eccentrically loaded drive train that is inherently prone to bifurcation behaviour. A reference trajectory is chosen to deliberately provoke a bifurcation. The proposed framework is able to avoid the bifurcation behaviour regardlessly.Index Terms-nonlinear model based control, optimal feedback, polynomial chaos expansion, real-time calculations arXiv:1808.06785v1 [math.OC]

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Section: B Coefficient Determinationmentioning

confidence: 99%

“…Considering, (15) and (17), either (19), and the approximation of K in (25), problem (1) can be reformulated as The former is a deterministic optimal control problem in function of the coefficients and can be solved accordingly.…”

Section: Stochastic Optimal Control With Gpcmentioning

confidence: 99%

Polynomial Chaos reformulation in Nonlinear Stochastic Optimal Control with application on a drivetrain subject to bifurcation phenomena

Lefebvre

Belie

Crevecoeur

2018

2018 22nd International Conference on System Theory, Control and Computing (ICSTCC)

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“…The polynomial chaos method offered an efficient computational approach for the large nonlinear system with small number of uncertain parameters but large magnitude of uncertainties [4] [5]. While the gPC approach has been successfully applied to various problems, including prediction of vehicle dynamics [6] [7]. In this paper, these polynomial chaos-based approaches are presented with a four-degree-of-freedom vehicle model.…”

Section: Introductionmentioning

confidence: 98%

Uncertainty Analysis of Vehicle Suspension Systems Based on Polynomial Chaos Methods

Feng

Tang

et al. 2013

2013 Fourth International Conference on Intelligent Systems Design and Engineering Applications

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In this paper, a parametrical uncertainty analysis of vehicle suspension system was presented. Four degree-of-freedom(DOF) mathematical model of vehicle passive suspension has been set up and uncertainty of the model has been studied using polynomial chaos methods. By comparing with Monte Carlo simulation method, the results show that polynomial chaos methods are more efficient than Monte Carlo method and are a relatively powerful approach for the simulation of multibody dynamic system with uncertainties.

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“…More structured sampling techniques, such as Latin hypercube sampling [3], adaptive sampling [3], and importance sampling [4], have been proposed with modest computational speed improvements for complex systems. More recent works have shown that functional expansions such as polynomial chaos expansions (PCEs) [5]- [7] can lead to significant gains in terms of computational costs [6]. When dealing with complex models, the use of PCEs can be facilitated by nonintrusive PCEs [7], by allowing performing the propagation without the need to modify the model itself.…”

Section: Introductionmentioning

confidence: 99%

Parametric Uncertainty Quantification Using Polynomial Chaos Expansions Applied to a Wet Friction Clutch Model

Tod¹,

Groote²,

Lefebvre³

et al. 2019

IJMO

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Recently, designing mechatronic systems has become more and more dependent on models that are used to predict performance in a virtual environment, and the models involved are becoming increasingly more complex multiphysical systems. Instead of spending much time modeling increasingly detailed physical models, uncertainties can be explicitly considered to model the lack of knowledge. The mismatch between real-life experiments and model simulations due to parametric uncertainties can be quantified using likelihood estimation and Monte Carlo sampling techniques for propagation. In this paper, we attempt to significantly accelerate the process using polynomial chaos expansions for propagation and a genetic algorithm to maximize likelihood. The soundness of this approach is demonstrated on a wet friction clutch system. The results show that the method has a strong potential for scalability with respect to the number of uncertain parameters.

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A polynomial chaos approach to the analysis of vehicle dynamics under uncertainty

Cited by 78 publications

References 17 publications

Polynomial Chaos reformulation in Nonlinear Stochastic Optimal Control with application on a drivetrain subject to bifurcation phenomena

Polynomial Chaos reformulation in Nonlinear Stochastic Optimal Control with application on a drivetrain subject to bifurcation phenomena

Uncertainty Analysis of Vehicle Suspension Systems Based on Polynomial Chaos Methods

Parametric Uncertainty Quantification Using Polynomial Chaos Expansions Applied to a Wet Friction Clutch Model

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