Toward Affordable Uncertainty Quantification for Industrial Problems: Part I — Theory and Validation

Volume 2C: Turbomachinery ◽

10.1115/gt2017-64842 ◽

2017 ◽

Cited By ~ 2

Author(s):

Tiziano Ghisu ◽

Shahrokh Shahpar

Keyword(s):

Uncertainty Quantification ◽

Polynomial Chaos ◽

Computational Cost ◽

Black Box ◽

Sparse Grid ◽

Test Functions ◽

Uncertainty Distribution ◽

Analytical Test ◽

Column Pivoting ◽

The Given

Non-intrusive Polynomial Chaos (NIPC) methods have become popular for uncertainty quantification, as they have the potential to achieve a significant reduction in computational cost (number of evaluations) with respect to traditional techniques such as the Monte Carlo approach, while allowing the model to be still treated as a black box. This work makes use of Least Squares Approximations (LSA) in the context of appropriately selected PC bases. An efficient technique based on QR column pivoting has been employed to reduce the number of evaluations required to construct the approximation, demonstrating the superiority of the method with respect to sparse grid quadratures and to LSA with randomly selected quadrature points. Orthogonal (or orthonormal) polynomials used for the PC expansion are calculated numerically based on the given uncertainty distribution, making the approach optimal for any type of input uncertainty. The benefits of the proposed techniques are verified on a number of analytical test functions of increasing complexity and on two engineering test problem (uncertainty quantification of the deflection of a 3- and a 10-bar structure with up to 15 uncertain parameters). The results demonstrate how an LSA approach within a PC framework can be an effective method for UQ, with a significant reduction in computational cost with respect to full tensor and sparse grid quadratures.

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Affordable Uncertainty Quantification for Industrial Problems: Application to Aero-Engine Fans

Journal of Turbomachinery ◽

10.1115/1.4038982 ◽

2018 ◽

Vol 140 (6) ◽

Cited By ~ 5

Author(s):

Tiziano Ghisu ◽

Shahrokh Shahpar

Keyword(s):

Uncertainty Quantification ◽

Uncertainty Distribution ◽

Blade Shape ◽

Shape Uncertainty ◽

Column Pivoting ◽

The Cost ◽

Sparse Grid Quadrature ◽

The Impact ◽

The Given ◽

Bypass Ratio

Uncertainty quantification (UQ) is an increasingly important area of research. As components and systems become more efficient and optimized, the impact of uncertain parameters is likely to become critical. It is fundamental to consider the impact of these uncertainties as early as possible during the design process, with the aim of producing more robust designs (less sensitive to the presence of uncertainties). The cost of UQ with high-fidelity simulations becomes therefore of fundamental importance. This work makes use of least-squares approximations in the context of appropriately selected polynomial chaos (PC) bases. An efficient technique based on QR column pivoting has been employed to reduce the number of evaluations required to construct the approximation, demonstrating the superiority of the method with respect to full-tensor quadrature (FTQ) and sparse-grid quadrature (SGQ). Orthonormal polynomials used for the PC expansion are calculated numerically based on the given uncertainty distribution, making the approach optimal for any type of input uncertainty. The approach is used to quantify the variability in the performance of two large bypass-ratio jet engine fans in the presence of shape uncertainty due to possible manufacturing processes. The impacts of shape uncertainty on the two geometries are compared, and sensitivities to the location of the blade shape variability are extracted. The mechanisms at the origin of the change in performance are analyzed in detail, as well as the differences between the two configurations.

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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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Multifidelity Uncertainty Quantification for Online Simulations of Automotive Propulsion Systems

10.1115/detc2021-67585 ◽

2021 ◽

Author(s):

Hang Yang ◽

Alex Gorodetsky ◽

Yuji Fujii ◽

Kon-Well Wang

Keyword(s):

Monte Carlo ◽

Uncertainty Quantification ◽

Polynomial Chaos ◽

Computational Cost ◽

Decomposition Methods ◽

Computationally Efficient ◽

Generalized Polynomial Chaos ◽

Propulsion Systems ◽

Generalized Polynomial ◽

Low Order

Abstract The increasing complexity and demanding performance requirement of modern automotive propulsion systems necessitate more intelligent and robust predictive controls. Due to the significant uncertainties from both unavoidable modeling errors and probabilistic environmental disturbances, the ability to quantify the effect of these uncertainties to the system behaviors is of crucial importance to enable advanced control designs for automotive propulsion systems. Furthermore, the quantification of uncertainty must be computationally efficient such that it can be conducted on board a vehicle in real-time. However, traditional uncertainty quantification methods for complicated nonlinear systems, such as Monte Carlo, often rely on sampling — a computationally prohibitive process for many applications. Previous research has shown promises of using spectral decomposition methods such as generalized Polynomial Chaos to reduce the online computational cost of uncertainty quantification. However, such method suffers from scalability and bias issues. This paper seeks to alleviate these computational bottlenecks by developing a multifidelity uncertainty quantification method that combines low-order generalized Polynomial Chaos with Monte Carlo estimation via Control Variates. Results on the mean and variance estimates of the axle shaft torque show that the proposed method can correct the bias of low-order Polynomial Chaos expansions while significantly reducing variance compared to the conventional Monte Carlo.

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