scholarly journals Stability analysis of a clutch system with uncertain parameters using sparse polynomial chaos expansions

2019 ◽  
Vol 20 (1) ◽  
pp. 104
Author(s):  
Duc Thinh Kieu ◽  
Baptiste Bergeot ◽  
Marie-Laure Gobert ◽  
Sébastien Berger
Keyword(s):  
Stability Analysis ◽  
Polynomial Chaos ◽  
Deterministic Model ◽  
Computational Cost ◽  
Uncertain Parameters ◽  
Sparse Polynomial ◽  
Clutch System ◽  
Frictional Forces ◽  
The Stability ◽  
Polynomial Chaos Expansions

In vehicle transmission systems, frictional forces acting during the sliding phase of the clutch engagement may produce unwanted vibrations. The prediction of the stability of a clutch system remains however a laborious task, as the parameters which have the highest impact on the stability, such as the friction law or the damping, lead to significant dispersions and must be considered as uncertain in such studies. Non-intrusive generalized polynomial chaos (gPC) expansions have already been used in this context. However, the number of deterministic model evaluations (i.e. the computational cost) required to compute the PC coefficients becomes prohibitive for large numbers of uncertain parameters. The sparse polynomial chaos, recently developed by Blatman and Sudret, may overcome this issue. In this paper, the method has been applied to the stability analysis of a clutch system owning up to eight uncertain parameters. Comparisons with the reference Monte Carlo method and classic full PC expansions show that sparse PC expansions allow substantial computational cost reductions while ensuring a high accuracy of the results.

Uncertainty Study of Periodic-Grating Wideband Filters With Sparse Polynomial-Chaos Expansions

2019 ◽  
Vol 31 (18) ◽  
pp. 1499-1502
Author(s):  
A. D. Papadopoulos ◽  
T. T. Zygiridis ◽  
E. N. Glytsis ◽  
N. V. Kantartzis ◽  
C. S. Antonopoulos
Keyword(s):  
Polynomial Chaos ◽  
Sparse Polynomial ◽  
Periodic Grating ◽  
Polynomial Chaos Expansions ◽  
Wideband Filters

An adaptive sparse polynomial-chaos technique based on anisotropic indices

2020 ◽  
Vol 39 (3) ◽  
pp. 691-707
Author(s):  
Christos Salis ◽  
Nikolaos V. Kantartzis ◽  
Theodoros Zygiridis
Keyword(s):  
Polynomial Chaos ◽  
Computational Cost ◽  
Uncertainty Assessment ◽  
Design Parameters ◽  
Test Problems ◽  
Content Type ◽  
Sparse Polynomial ◽  
Index Sets ◽  
The Mean ◽  
Expansion Coefficients

Purpose The fabrication of electromagnetic (EM) components may induce randomness in several design parameters. In such cases, an uncertainty assessment is of high importance, as simulating the performance of those devices via deterministic approaches may lead to a misinterpretation of the extracted outcomes. This paper aims to present a novel heuristic for the sparse representation of the polynomial chaos (PC) expansion of the output of interest, aiming at calculating the involved coefficients with a small computational cost. Design/methodology/approach This paper presents a novel heuristic that aims to develop a sparse PC technique based on anisotropic index sets. Specifically, this study’s approach generates those indices by using the mean elementary effect of each input. Accurate outcomes are extracted in low computational times, by constructing design of experiments (DoE) which satisfy the D-optimality criterion. Findings The method proposed in this study is tested on three test problems; the first one involves a transmission line that exhibits several random dielectrics, while the second and the third cases examine the effects of various random design parameters to the transmission coefficient of microwave filters. Comparisons with the Monte Carlo technique and other PC approaches prove that accurate outcomes are obtained in a smaller computational cost, thus the efficiency of the PC scheme is enhanced. Originality/value This paper introduces a new sparse PC technique based on anisotropic indices. The proposed method manages to accurately extract the expansion coefficients by locating D-optimal DoE.

scholarly journals A Polynomial Chaos-Based Kalman Filter Approach for Parameter Estimation of Mechanical Systems

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
Emmanuel D. Blanchard ◽  
Adrian Sandu ◽  
Corina Sandu
Keyword(s):  
Parameter Estimation ◽  
Kalman Filter ◽  
Polynomial Chaos ◽  
Sampling Rate ◽  
Mechanical Systems ◽  
Posteriori Probability ◽  
Uncertain Parameters ◽  
A Posteriori ◽  
A Posteriori Probability ◽  
Polynomial Chaos Expansions

Mechanical systems operate under parametric and external excitation uncertainties. The polynomial chaos approach has been shown to be more efficient than Monte Carlo for quantifying the effects of such uncertainties on the system response. Many uncertain parameters cannot be measured accurately, especially in real time applications. Information about them is obtained via parameter estimation techniques. Parameter estimation for large systems is a difficult problem, and the solution approaches are computationally expensive. This paper proposes a new computational approach for parameter estimation based on the extended Kalman filter (EKF) and the polynomial chaos theory for parameter estimation. The error covariances needed by EKF are computed from polynomial chaos expansions, and the EKF is used to update the polynomial chaos representation of the uncertain states and the uncertain parameters. The proposed method is applied to a nonlinear four degree of freedom roll plane model of a vehicle, in which an uncertain mass with an uncertain position is added on the roll bar. The main advantages of this method are an accurate representation of uncertainties via polynomial chaos, a computationally efficient update formula based on EKF, and the ability to provide a posteriori probability densities of the estimated parameters. The method is able to deal with non-Gaussian parametric uncertainties. The paper identifies and theoretically explains a possible weakness of the EKF with approximate covariances: numerical errors due to the truncation in the polynomial chaos expansions can accumulate quickly when measurements are taken at a fast sampling rate. To prevent filter divergence, we propose to lower the sampling rate and to take a smoother approach where time-distributed observations are all processed at once. We propose a parameter estimation approach that uses polynomial chaos to propagate uncertainties and estimate error covariances in the EKF framework. Parameter estimates are obtained in the form of polynomial chaos expansion, which carries information about the a posteriori probability density function. The method is illustrated on a roll plane vehicle model.

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