Identification of Fractional Damping Parameters in Structural Dynamics Using Polynomial Chaos Expansion

In order to analyze the dynamics of a structural problem accurately, a precise model of the structure, including an appropriate material description, is required. An important step within the modeling process is the correct determination of the model input parameters, e.g., loading conditions or material parameters. An accurate description of the damping characteristics is a complicated task, since many different effects have to be considered. An efficient approach to model the material damping is the introduction of fractional derivatives in the constitutive relations of the material, since only a small number of parameters is required to represent the real damping behavior. In this paper, a novel method to determine the damping parameters of viscoelastic materials described by the so-called fractional Zener material model is proposed. The damping parameters are estimated by matching the Frequency Response Functions (FRF) of a virtual model, describing a beam-like structure, with experimental vibration data. Since this process is generally time-consuming, a surrogate modeling technique, named Polynomial Chaos Expansion (PCE), is combined with a semi-analytical computational technique, called the Numerical Assembly Technique (NAT), to reduce the computational cost. The presented approach is applied to an artificial material with well defined parameters to show the accuracy and efficiency of the method. Additionally, vibration measurements are used to estimate the damping parameters of an aluminium rotor with low material damping, which can also be described by the fractional damping model.

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Propagation of Modeling Uncertainty by Polynomial Chaos Expansion in Multidisciplinary Analysis

Journal of Mechanical Design ◽

10.1115/1.4034110 ◽

2016 ◽

Vol 138 (11) ◽

Cited By ~ 6

Author(s):

S. Dubreuil ◽

N. Bartoli ◽

C. Gogu ◽

T. Lefebvre

Keyword(s):

Polynomial Chaos ◽

Computational Cost ◽

Polynomial Chaos Expansion ◽

Feedback Loops ◽

Nonlinear Stochastic System ◽

Chaos Expansion ◽

Multidisciplinary Analysis ◽

Modeling Uncertainties ◽

Coupling Variables ◽

Non Gaussian

Multidisciplinary analysis (MDA) is nowadays a powerful tool for analysis and optimization of complex systems. The present study is interested in the case where MDA involves feedback loops between disciplines (i.e., the output of a discipline is the input of another and vice versa). When the models for each discipline involve non-negligible modeling uncertainties, it is important to be able to efficiently propagate these uncertainties to the outputs of the MDA. The present study introduces a polynomial chaos expansion (PCE)-based approach to propagate modeling uncertainties in MDA. It is assumed that the response of each disciplinary solver is affected by an uncertainty modeled by a random field over the design and coupling variables space. A semi-intrusive PCE formulation of the problem is proposed to solve the corresponding nonlinear stochastic system. Application of the proposed method emphasizes an important particular case in which each disciplinary solver is replaced by a surrogate model (e.g., kriging). Three application problems are treated, which show that the proposed approach can approximate arbitrary (non-Gaussian) distributions very well at significantly reduced computational cost.

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A Sparse Data-Driven Polynomial Chaos Expansion Method for Uncertainty Propagation

Volume 2A: 42nd Design Automation Conference ◽

10.1115/detc2016-59795 ◽

2016 ◽

Cited By ~ 1

Author(s):

F. Wang ◽

F. Xiong ◽

S. Yang ◽

Y. Xiong

Keyword(s):

Polynomial Chaos ◽

Uncertainty Propagation ◽

Computational Cost ◽

Expansion Method ◽

Polynomial Chaos Expansion ◽

Data Driven ◽

High Dimensional ◽

Chaos Expansion ◽

Least Angle Regression ◽

Structure Problem

The data-driven polynomial chaos expansion (DD-PCE) method is claimed to be a more general approach of uncertainty propagation (UP). However, as a common problem of all the full PCE approaches, the size of polynomial terms in the full DD-PCE model is significantly increased with the dimension of random inputs and the order of PCE model, which would greatly increase the computational cost especially for high-dimensional and highly non-linear problems. Therefore, a sparse DD-PCE is developed by employing the least angle regression technique and a stepwise regression strategy to adaptively remove some insignificant terms. Through comparative studies between sparse DD-PCE and the full DD-PCE on three mathematical examples with random input of raw data, common and nontrivial distributions, and a ten-bar structure problem for UP, it is observed that generally both methods yield comparably accurate results, while the computational cost is significantly reduced by sDD-PCE especially for high-dimensional problems, which demonstrates the effectiveness and advantage of the proposed method.

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Application of an Adaptive Polynomial Chaos Expansion on Computationally Expensive Three-Dimensional Cardiovascular Models for Uncertainty Quantification and Sensitivity Analysis

Journal of Biomechanical Engineering ◽

10.1115/1.4034709 ◽

2016 ◽

Vol 138 (12) ◽

Cited By ~ 14

Author(s):

Sjeng Quicken ◽

Wouter P. Donders ◽

Emiel M. J. van Disseldorp ◽

Kujtim Gashi ◽

Barend M. E. Mees ◽

...

Keyword(s):

Sensitivity Analysis ◽

Uncertainty Quantification ◽

Polynomial Chaos ◽

Computational Cost ◽

Three Dimensional ◽

Polynomial Chaos Expansion ◽

Patient Specific ◽

Chaos Expansion ◽

Model Input ◽

Cardiovascular Models

When applying models to patient-specific situations, the impact of model input uncertainty on the model output uncertainty has to be assessed. Proper uncertainty quantification (UQ) and sensitivity analysis (SA) techniques are indispensable for this purpose. An efficient approach for UQ and SA is the generalized polynomial chaos expansion (gPCE) method, where model response is expanded into a finite series of polynomials that depend on the model input (i.e., a meta-model). However, because of the intrinsic high computational cost of three-dimensional (3D) cardiovascular models, performing the number of model evaluations required for the gPCE is often computationally prohibitively expensive. Recently, Blatman and Sudret (2010, “An Adaptive Algorithm to Build Up Sparse Polynomial Chaos Expansions for Stochastic Finite Element Analysis,” Probab. Eng. Mech., 25(2), pp. 183–197) introduced the adaptive sparse gPCE (agPCE) in the field of structural engineering. This approach reduces the computational cost with respect to the gPCE, by only including polynomials that significantly increase the meta-model’s quality. In this study, we demonstrate the agPCE by applying it to a 3D abdominal aortic aneurysm (AAA) wall mechanics model and a 3D model of flow through an arteriovenous fistula (AVF). The agPCE method was indeed able to perform UQ and SA at a significantly lower computational cost than the gPCE, while still retaining accurate results. Cost reductions ranged between 70–80% and 50–90% for the AAA and AVF model, respectively.

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Application of Polynomial Chaos Expansion to Optimize Injection-Production Parameters under Uncertainty

Mathematical Problems in Engineering ◽

10.1155/2020/5374523 ◽

2020 ◽

Vol 2020 ◽

pp. 1-13

Author(s):

Liang Zhang ◽

ZhiPing Li ◽

Hong Li ◽

Caspar Daniel Adenutsi ◽

FengPeng Lai ◽

...

Keyword(s):

Optimization Design ◽

Polynomial Chaos ◽

Computational Cost ◽

Integrated Approach ◽

Polynomial Chaos Expansion ◽

Oil Field ◽

Chaos Expansion ◽

Field Development ◽

Production Parameters ◽

Well Pattern

The optimization of oil field development scheme considering the uncertainty of reservoir model is a challenging and difficult problem in reservoir engineering design. The most common method used in this regard is to generate multiple models based on statistical analysis of uncertain reservoir parameters and requires a large number of simulations to efficiently handle all uncertainties, thus requiring a huge amount of computational power. In order to reduce the computational burden, a method which combines reservoir simulation, an economic model, polynomial chaos expansion with response surface methodology, and Levy flight particle swarm optimization (LFPSO) algorithm is proposed to determine the optimal injection-production parameters with reservoir uncertainties at a reasonable computational cost. This approach is applied to a five-spot well pattern optimization design for obtaining the optimal parameters, including oil-water well distance, injection rate, and bottom hole pressure, while considering the uncertainties of porosity, permeability, and relative permeability. The results of the case study indicated that the integrated approach is practical and efficient for performing reservoir optimization with uncertain reservoir parameters.

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Advanced computational technique based on kriging and Polynomial Chaos Expansion for structural stability of mechanical systems with uncertainties

Journal of Engineering Mathematics ◽

10.1007/s10665-021-10157-9 ◽

2021 ◽

Vol 130 (1) ◽

Author(s):

E. Denimal ◽

J.-J. Sinou

Keyword(s):

Material Properties ◽

Polynomial Chaos ◽

Polynomial Chaos Expansion ◽

Computational Time ◽

Computational Technique ◽

Chaos Expansion ◽

Computationally Efficient ◽

Buckling Loads ◽

Compression Load ◽

Rigid Supports

AbstractIn this paper, a numerical strategy based on the combination of the kriging approach and the Polynomial Chaos Expansion (PCE) is proposed for the prediction of buckling loads due to random geometric imperfections and fluctuations in material properties of a mechanical system. The original computational approach is applied on a beam simply supported at both ends by rigid supports and by one punctual spring whose location and stiffness vary. The beam is subjected to a deterministic axial compression load. The PCE-kriging meta-modelling approach is employed to efficiently perform a parametric analysis with random geometrical and material properties. The approach proved to be computationally efficient in terms of number of model evaluations and in terms of computational time to predict accurately the buckling loads of a beam system. It is demonstrated that the buckling loads are substantially impacted not only by both the location and the stiffness of the spring, but also by the random parameters.

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