Performing uncertainty analysis of a nonlinear Point-Kinetics/Lumped Parameters problem using Polynomial Chaos techniques

Gilli, L.; Lathouwers, D.; Kloosterman, J.L.; Hagen, T.H.J.J. van der

doi:10.1016/j.anucene.2011.09.016

Cited by 20 publications

(4 citation statements)

References 15 publications

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“…As section 2.3 of the SM shows PCE drastically surpasses statistical methods even for calculating the (relatively simple) expected dose distribution: in the example HN patient PCE provided the same accuracy with 217 calculations as Monte Carlo sampling with almost 12 000 dose calculations. In our experience this is true in general, PC methods systematically and decisively outperform statistical methods (Gilli et al 2012, Perkó et al 2014a, Perkó et al 2014b (unless dealing with a large-higher than 50-number of input variables). As a result, given a certain computational cost, PC allows far more accurate estimates than statistical methods.…”

Section: Comparison With Statistical Methodsmentioning

confidence: 61%

Fast and accurate sensitivity analysis of IMPT treatment plans using Polynomial Chaos Expansion

et al. 2016

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The highly conformal planned dose distribution achievable in intensity modulated proton therapy (IMPT) can severely be compromised by uncertainties in patient setup and proton range. While several robust optimization approaches have been presented to address this issue, appropriate methods to accurately estimate the robustness of treatment plans are still lacking. To fill this gap we present Polynomial Chaos Expansion (PCE) techniques which are easily applicable and create a meta-model of the dose engine by approximating the dose in every voxel with multidimensional polynomials. This Polynomial Chaos (PC) model can be built in an automated fashion relatively cheaply and subsequently it can be used to perform comprehensive robustness analysis. We adapted PC to provide among others the expected dose, the dose variance, accurate probability distribution of dose-volume histogram (DVH) metrics (e.g. minimum tumor or maximum organ dose), exact bandwidths of DVHs, and to separate the effects of random and systematic errors. We present the outcome of our verification experiments based on 6 head-and-neck (HN) patients, and exemplify the usefulness of PCE by comparing a robust and a non-robust treatment plan for a selected HN case. The results suggest that PCE is highly valuable for both research and clinical applications.

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Section: Comparison With Statistical Methodsmentioning

confidence: 61%

Fast and accurate sensitivity analysis of IMPT treatment plans using Polynomial Chaos Expansion

et al. 2016

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“…Uncertainty analysis is used to capture the effect of uncertainty in parameters or inputs on the outputs of the system (typically, species composition in these cases); while sensitivity analysis has been used for this purpose , and Monte Carlo simulation , offers a straightforward but computationally expensive approach, approaches based on polynomial chaos expansion (PCE) − and probabilistic approaches − have shown much promise. Other approaches include the use of power series expansions. , Polynomial chaos expansion quantifies the effect of uncertain (kinetic) parameters on the outputs (usually the rates of reactions or product yields/composition) using orthogonal stochastic polynomial expansions.…”

Section: Model Development and Analysismentioning

confidence: 99%

A Perspective on the Impact of Process Systems Engineering on Reaction Engineering

Sivaramakrishnan

Puliyanda

Tefera

et al. 2019

Ind. Eng. Chem. Res.

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Process systems engineering (PSE), as the name suggests, emphasizes an approach to understanding the behavior of systems as a whole with a view to improving decision-making for optimization and control of processes. The discipline emphasizes the application of mathematical techniques in this effort, and a plausible claim has been made that is at the very core of the discipline of chemical engineering. Being a generalized approach to process systems in general, it finds wide application to many areas in chemical engineering. This work reviews the application of PSE to the area of reaction engineering, which is also at the core of chemical engineering. We highlight the impactful applications of PSE in reaction engineering and discuss aspects of model building and analysis, reactor control, optimization, chemometrics, and chemoinformatics.

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“…In particular, PCEs construct an approximation of the outputs, or their distribution, via a reduced number of properly selected samples. Since 1991, PCEs have been applied to a number of problems in different fields, among which nuclear reactors design (Gilli et al 2012 Evans and Swartz (1992). In space flight, the method was applied to uncertainty propagation in the 2-body problem by Cheng et al (2011) and more recently used by Jones and Alireza (2013) to estimate the collision probability between two satellites.…”

Section: Introductionmentioning

confidence: 99%

Analysis of spacecraft disposal solutions from LPO to the Moon with high order polynomial expansions

Vetrisano

Vasile

2017

Advances in Space Research

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This paper presents the analysis of disposal trajectories from libration point orbits to the Moon under uncertainty. The paper proposes the use of polynomial chaos expansions to quantify the uncertainty in the final conditions given an uncertainty in initial conditions and disposal manoeuvre. The paper will compare the use of polynomial chaos expansions against high order Taylor expansions computed with point-wise integration of the partials of the dynamics, the use of the covariance matrix propagated using a unscented transformation and a standard Monte Carlo simulation. It will be shown that the use of the ellipsoid of uncertainty, that corresponds to the propagation of the covariance matrix with a first order Taylor expansions, is not adequate to correctly capture the dispersion of the trajectories that can intersect the Moon. Furthermore, it will be shown that polynomial chaos expansions better represent the distribution of the final states compared to Taylor expansions of equal order and are comparable to a full scale Monte Carlo simulations but at a fraction of the computational cost

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Performing uncertainty analysis of a nonlinear Point-Kinetics/Lumped Parameters problem using Polynomial Chaos techniques

Cited by 20 publications

References 15 publications

Fast and accurate sensitivity analysis of IMPT treatment plans using Polynomial Chaos Expansion

Fast and accurate sensitivity analysis of IMPT treatment plans using Polynomial Chaos Expansion

A Perspective on the Impact of Process Systems Engineering on Reaction Engineering

Analysis of spacecraft disposal solutions from LPO to the Moon with high order polynomial expansions

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