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

2016 ◽  
Vol 138 (12) ◽  
Author(s):  
Sjeng Quicken ◽  
Wouter P. Donders ◽  
Emiel M. J. van Disseldorp ◽  
Kujtim Gashi ◽  
Barend M. E. Mees ◽  
...  

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.

2018 ◽  
Vol 189 ◽  
pp. 300-310 ◽  
Author(s):  
Alexander Avdonin ◽  
Stefan Jaensch ◽  
Camilo F. Silva ◽  
Matic Češnovar ◽  
Wolfgang Polifke

2009 ◽  
Vol 94 (7) ◽  
pp. 1161-1172 ◽  
Author(s):  
Thierry Crestaux ◽  
Olivier Le Maıˆtre ◽  
Jean-Marc Martinez

2021 ◽  
Author(s):  
Giuseppe Abbiati ◽  
Stefano Marelli ◽  
Nikolaos Tsokanas ◽  
Bruno Sudret ◽  
Bozidar Stojadinovic

Hybrid Simulation is a dynamic response simulation paradigm that merges physical experiments and computational models into a hybrid model. In earthquake engineering, it is used to investigate the response of structures to earthquake excitation. In the context of response to extreme loads, the structure, its boundary conditions, damping, and the ground motion excitation itself are all subjected to large parameter variability. However, in current seismic response testing practice, Hybrid Simulation campaigns rely on a few prototype structures with fixed parameters subjected to one or two ground motions of different intensity. While this approach effectively reveals structural weaknesses, it does not reveal the sensitivity of structure's response. This thus far missing information could support the planning of further experiments as well as drive modeling choices in subsequent analysis and evaluation phases of the structural design process.This paper describes a Global Sensitivity Analysis framework for Hybrid Simulation. This framework, based on Sobol' sensitivity indices, is used to quantify the sensitivity of the response of a structure tested using the Hybrid Simulation approach due to the variability of the prototype structure and the excitation parameters. Polynomial Chaos Expansion is used to surrogate the hybrid model response. Thereafter, Sobol' sensitivity indices are obtained as a by-product of polynomial coefficients, entailing a reduced number of Hybrid Simulations compared to a crude Monte Carlo approach. An experimental verification example highlights the excellent performance of Polynomial Chaos Expansion surrogates in terms of stable estimates of Sobol' sensitivity indices in the presence of noise caused by random experimental errors.


2021 ◽  
Vol 2 (4) ◽  
pp. 956-975
Author(s):  
Marcel S. Prem ◽  
Michael Klanner ◽  
Katrin Ellermann

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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