Polynomial Chaos Expansion for Probabilistic Uncertainty Propagation

Yang, Shuxing; Xiong, Fenfen; Wang, Fenggang

doi:10.5772/intechopen.68484

Cited by 14 publications

(11 citation statements)

References 31 publications

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“…Recently, alternative approaches, such as the use of surrogate models 37 to mimic the behavior of the full model while being inexpensive to evaluate, have been of particular interest. One such technique is the polynomial chaos expansion method (PCE), 38,39 which has previously been used in UQ analysis of cardiac mechanics and electrophysiology. 29,40 The purpose of the present work is to present a PCE-based method for UQ in cardiac mechanics models and to perform an initial UQ and SA study including both global myocardial material properties and local variability of the microstructure orientation.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, alternative approaches, such as the use of surrogate models [37] to mimic the behaviour of the full model while being inexpensive to evaluate, have been of particular interest. One such technique is the polynomial chaos expansion method (PCE) [38,39], which has previously been used in UQ analysis of cardiac mechanics and electrophysiology [29,40].…”

Section: Introductionmentioning

confidence: 99%

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Uncertainty in cardiac myofiber orientation and stiffnesses dominate the variability of left ventricle deformation response

Rodríguez‐Cantano

Sundnes

Rognes

2019

Numer Methods Biomed Eng

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Computational cardiac modelling is a mature area of biomedical computing and is currently evolving from a pure research tool to aiding in clinical decision making. Assessing the reliability of computational model predictions is a key factor for clinical use, and uncertainty quantification (UQ) and sensitivity analysis are important parts of such an assessment. In this study, we apply UQ in computational heart mechanics to study uncertainty both in material parameters characterizing global myocardial stiffness and in the local muscle fiber orientation that governs tissue anisotropy. The uncertainty analysis is performed using the polynomial chaos expansion (PCE) method, which is a nonintrusive meta‐modeling technique that surrogates the original computational model with a series of orthonormal polynomials over the random input parameter space. In addition, in order to study variability in the muscle fiber architecture, we model the uncertainty in orientation of the fiber field as an approximated random field using a truncated Karhunen‐Loéve expansion. The results from the UQ and sensitivity analysis identify clear differences in the impact of various material parameters on global output quantities. Furthermore, our analysis of random field variations in the fiber architecture demonstrate a substantial impact of fiber angle variations on the selected outputs, highlighting the need for accurate assignment of fiber orientation in computational heart mechanics models.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Uncertainty in cardiac myofiber orientation and stiffnesses dominate the variability of left ventricle deformation response

Rodríguez‐Cantano

Sundnes

Rognes

2019

Numer Methods Biomed Eng

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“…The Wiener-Askey scheme [37] lists some commonly used probability distributions that are associated with certain univariate orthogonal polynomials. Other approaches based on statistical moments [38,39] or the Gram-Schmidt orthogonalisation [40,41] are available to generate the monovariate polynomials when the parameters are correlated or do not follow a distribution in the Wiener-Askey scheme.…”

Section: Uncertainty Propagation Techniquesmentioning

confidence: 99%

Dynamic Optimisation of Beer Fermentation under Parametric Uncertainty

Bhonsale

Impe

2021

Fermentation

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Fermentation is one of the most important stages in the entire brewing process. In fermentation, the sugars are converted by the brewing yeast into alcohol, carbon dioxide, and a variety of by-products which affect the flavour of the beer. Fermentation temperature profile plays an essential role in the progression of fermentation and heavily influences the flavour. In this paper, the fermentation temperature profile is optimised. As every process model contains experimentally determined parameters, uncertainty on these parameters is unavoidable. This paper presents approaches to consider the effect of uncertain parameters in optimisation. Three methods for uncertainty propagation (linearisation, sigma points, and polynomial chaos expansion) are used to determine the influence of parametric uncertainty on the process model. Using these methods, an optimisation formulation considering parametric uncertainty is presented. It is shown that for the non-linear beer fermentation model, the linearisation approach performed worst amongst the three methods, while second-order polynomial chaos worked the best. Using the techniques described below, a fermentation process can be optimised for ensuring high alcohol content or low fermentation time while ensuring the quality constraints. As we explicitly consider uncertainty in the process, the solution, even though conservative, will be more robust to parametric uncertainties in the model.

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“…A one-dimensional polynomial of order p can be generated iff 0 to 2p − 1 order statistical moments exist and are finite. Additionally, to normalize the polynomials, the existence of a finite 2p th moment is necessary [32,33].…”

Section: Computation Of Sensitivity Indices Using Arbitrary Polynomiamentioning

confidence: 99%

Global Sensitivity Analysis of a Spray Drying Process

2019

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Spray drying is a key unit operation used to achieve particulate products of required properties. Despite its widespread use, the product and process design, as well as the process control remain highly empirical and depend on trial and error experiments. Studying the effect of operational parameters experimentally is tedious, time consuming, and expensive. In this paper, we carry out a model-based global sensitivity analysis (GSA) of the process. Such an exercise allows us to quantify the impact of different process parameters, many of which interact with each other, on the product properties and conditions that have an impact on the functionality of the final drug product. Moreover, classical sensitivity analysis using the Sobol-based sensitivity indices was supplemented by a polynomial chaos-based sensitivity analysis, which proved to be an efficient method to reduce the computational cost of the GSA. The results obtained demonstrate the different response dependencies of the studied variables, which helps to identify possible control strategies that can result in major robustness for the spray drying process.

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Polynomial Chaos Expansion for Probabilistic Uncertainty Propagation

Cited by 14 publications

References 31 publications

Uncertainty in cardiac myofiber orientation and stiffnesses dominate the variability of left ventricle deformation response

Uncertainty in cardiac myofiber orientation and stiffnesses dominate the variability of left ventricle deformation response

Dynamic Optimisation of Beer Fermentation under Parametric Uncertainty

Global Sensitivity Analysis of a Spray Drying Process

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