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

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

Applied Mechanics ◽

10.3390/applmech2040056 ◽

2021 ◽

Vol 2 (4) ◽

pp. 956-975

Author(s):

Marcel S. Prem ◽

Michael Klanner ◽

Katrin Ellermann

Keyword(s):

Polynomial Chaos ◽

Constitutive Relations ◽

Computational Cost ◽

Material Model ◽

Polynomial Chaos Expansion ◽

Computational Technique ◽

Chaos Expansion ◽

Material Damping ◽

Fractional Damping ◽

Assembly Technique

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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Polynomial-Chaos-Expansion Based Integrated Dynamic Modelling Workflow for Computationally Efficient Reservoir Characterization: A Field Case Study

10.2118/185847-ms ◽

2017 ◽

Cited By ~ 2

Author(s):

Rajan G. Patel ◽

Tarang Jain ◽

Japan J. Trivedi

Keyword(s):

Reservoir Characterization ◽

Polynomial Chaos ◽

Dynamic Modelling ◽

Polynomial Chaos Expansion ◽

Chaos Expansion ◽

Computationally Efficient ◽

Field Case

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An Efficient Sampling Method for Regression-Based Polynomial Chaos Expansion

Communications in Computational Physics ◽

10.4208/cicp.020911.200412a ◽

2013 ◽

Vol 13 (4) ◽

pp. 1173-1188 ◽

Cited By ~ 15

Author(s):

Samih Zein ◽

Benoît Colson ◽

François Glineur

Keyword(s):

Finite Element ◽

Design Of Experiments ◽

Polynomial Chaos ◽

Polynomial Chaos Expansion ◽

Computational Time ◽

Chaos Expansion ◽

Analysis Model ◽

Element Analysis ◽

Analytical Functions ◽

The Cost

AbstractThe polynomial chaos expansion (PCE) is an efficient numerical method for performing a reliability analysis. It relates the output of a nonlinear system with the uncertainty in its input parameters using a multidimensional polynomial approximation (the so-called PCE). Numerically, such an approximation can be obtained by using a regression method with a suitable design of experiments. The cost of this approximation depends on the size of the design of experiments. If the design of experiments is large and the system is modeled with a computationally expensive FEA (Finite Element Analysis) model, the PCE approximation becomes unfeasible. The aim of this work is to propose an algorithm that generates efficiently a design of experiments of a size defined by the user, in order to make the PCE approximation computationally feasible. It is an optimization algorithm that seeks to find the best design of experiments in the D-optimal sense for the PCE. This algorithm is a coupling between genetic algorithms and the Fedorov exchange algorithm. The efficiency of our approach in terms of accuracy and computational time reduction is compared with other existing methods in the case of analytical functions and finite element based functions.

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Modified Dimension Reduction-Based Polynomial Chaos Expansion for Nonstandard Uncertainty Propagation and Its Application in Reliability Analysis

Processes ◽

10.3390/pr9101856 ◽

2021 ◽

Vol 9 (10) ◽

pp. 1856

Author(s):

Jeongeun Son ◽

Yuncheng Du

Keyword(s):

Dimension Reduction ◽

Reliability Analysis ◽

Structural Reliability ◽

Polynomial Chaos ◽

Uncertainty Propagation ◽

Surrogate Models ◽

Polynomial Chaos Expansion ◽

Chaos Expansion ◽

Computationally Efficient ◽

Standard Distribution

This paper presents an algorithm for efficient uncertainty quantification (UQ) in the presence of many uncertainties that follow a nonstandard distribution (e.g., lognormal). Using the polynomial chaos expansion (PCE), the algorithm builds surrogate models of uncertainty as functions of a standard distribution (e.g., Gaussian variables). The key to build these surrogate models is to calculate PCE coefficients of model outputs, which is computationally challenging, especially when dealing with models defined by complex functions (e.g., nonpolynomial terms) under many uncertainties. To address this issue, an algorithm that integrates the PCE with the generalized dimension reduction method (gDRM) is utilized to convert the high-dimensional integrals, required to calculate the PCE coefficients of model predictions, into several lower-dimensional ones that can be rapidly solved with quadrature rules. The accuracy of the algorithm is validated with four examples in structural reliability analysis and compared to other existing techniques, such as Monte Carlo simulations and the least angle regression-based PCE. Our results show our algorithm provides accurate UQ results and is computationally efficient when dealing with many uncertainties, thus laying the foundation to address UQ in complex control systems.

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