Uncertainty Quantification in Vibroacoustic Analysis of a Vehicle Body Using Generalized Polynomial Chaos Expansion

2020 ◽  
Author(s):  
J.D. Schmid ◽  
M. Luegmair ◽  
K. Sepahvand ◽  
S. Marburg
Keyword(s):  
Uncertainty Quantification ◽  
Polynomial Chaos ◽  
Polynomial Chaos Expansion ◽  
Vehicle Body ◽  
Chaos Expansion ◽  
Generalized Polynomial Chaos ◽  
Generalized Polynomial

A Metamodeling Approach for Instant Severity Assessment and Uncertainty Quantification of Iliac Artery Stenoses

2019 ◽  
Vol 142 (1) ◽  
Author(s):  
S. G. H. Heinen ◽  
K. Gashi ◽  
D. A. F van den Heuvel ◽  
J. P. P. M. de Vries ◽  
F. N. van de Vosse ◽  
...  
Keyword(s):  
Uncertainty Quantification ◽  
Iliac Artery ◽  
Polynomial Chaos ◽  
Polynomial Chaos Expansion ◽  
Chaos Expansion ◽  
Generalized Polynomial Chaos ◽  
Pressure Drops ◽  
Output Uncertainty ◽  
Generalized Polynomial ◽  
2D Model

Abstract Two-dimensional (2D) or three-dimensional (3D) models of blood flow in stenosed arteries can be used to patient-specifically predict outcome metrics, thereby supporting the physicians in decision making processes. However, these models are time consuming which limits the feasibility of output uncertainty quantification (UQ). Accurate surrogates (metamodels) might be the solution. In this study, we aim to demonstrate the feasibility of a generalized polynomial chaos expansion-based metamodel to predict a clinically relevant output metric and to quantify the output uncertainty. As an example, a metamodel was constructed from a recently developed 2D model that was shown to be able to estimate translesional pressure drops in iliac artery stenoses (−0.9 ± 12.7 mmHg, R2 = 0.81). The metamodel was constructed from a virtual database using the adaptive generalized polynomial chaos expansion (agPCE) method. The constructed metamodel was then applied to 25 stenosed iliac arteries to predict the patient-specific pressure drop and to perform UQ. Comparing predicted pressure drops of the metamodel and in vivo measured pressure drops, the mean bias (−0.2 ± 13.7 mmHg) and the coefficient of determination (R2 = 0.80) were as good as of the original 2D computational fluid dynamics (CFD) model. UQ results of the 2D and metamodel were comparable. Estimation of the uncertainty interval using the original 2D model took 14 days, whereas the result of the metamodel was instantly available. In conclusion, it is feasible to quantify the uncertainty of the output metric and perform sensitivity analysis (SA) instantly using a metamodel. Future studies should investigate the possibility to construct a metamodel of more complex problems.

STOCHASTIC STRUCTURAL MODAL ANALYSIS INVOLVING UNCERTAIN PARAMETERS USING GENERALIZED POLYNOMIAL CHAOS EXPANSION

2011 ◽  
Vol 03 (03) ◽  
pp. 587-606 ◽  
Author(s):  
K. SEPAHVAND ◽  
S. MARBURG ◽  
H.-J. HARDTKE
Keyword(s):  
Modal Analysis ◽  
Polynomial Chaos ◽  
Continuous Model ◽  
Polynomial Chaos Expansion ◽  
Uncertain Parameters ◽  
Chaos Expansion ◽  
Parameter Uncertainties ◽  
Generalized Polynomial Chaos ◽  
Generalized Polynomial ◽  
Key Issues

In this paper, the application of generalized polynomial chaos expansion in stochastic structural modal analysis including uncertain parameters is investigated. We review the theory of polynomial chaos and relating error analysis. A general formulation for the representation of modal problems by the polynomial chaos expansion is derived. It shows how the modal frequencies and modal shapes are influenced by the parameter uncertainties. The key issues that arise in the polynomial chaos simulation of modal analysis are discussed for two examples: a discrete 2-DOF system and continuous model of a microsensor. In both cases, the polynomial chaos expansion is used for the approximation of uncertain parameters, eigenfrequencies and eigenvectors. We emphasize the accuracy and time efficiency of the method in estimation of the stochastic modal responses in comparison with the sampling techniques, such as the Monte Carlo simulation.

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