SENSITIVITY ANALYSIS OF IMAGE CLASSIFICATION MODELS USING GENERALIZED POLYNOMIAL CHAOS

ADDRESSING EPISTEMIC UNCERTAINTY IN STATISTICAL TOLERANCE ANALYSIS: A NON-DETERMINISTIC APPROACH - 6th International Conference on Uncertainty Quantification in Computational Sciences and Engineering - 15-18 June 2025, Rhodes Island, Greece

FORWARD UNCERTAINTY PROPAGATION FOR FINITE ELEMENT MODELS WITH NON-GAUSSIAN PARAMETERS - 6th International Conference on Uncertainty Quantification in Computational Sciences and Engineering - 15-18 June 2025, Rhodes Island, Greece

UPDATING DIGITAL TWINS SUBJECTED TO UNCERTAIN CORROSION CONDITIONS USING THE UNSCENTED KALMAN FILTER - 6th International Conference on Uncertainty Quantification in Computational Sciences and Engineering - 15-18 June 2025, Rhodes Island, Greece

Discretization of a random field by the generalized polynomial chaos (GPC) begins with selecting a specific type of orthogonal polynomial (e.g. Legendre and Hermite polynomials) (e.g. Ghanem and Spanos, 1991). This selection of a type of orthogonal polynomial can be performed based on the reported experiences (e.g. Xiu and Karniadakis, 2003) or data revealing the distribution of a random field to be discretized. If such data or reported experiences are unavailable, a third way may be generating some pilot tests to study the performance of a specific type of orthogonal polynomial in discretizing this random field. This study tries to develop an evolutionary algorithm-based auxiliary tool for the implementation of such pilot tests. A similar tool (Allaix and Carbone, 2009), which is based on the singleobjective evolutionary algorithm, had been developed for constructing the Karhunen-Loeve (KL) representation of a random field. Both KL and GPC expansions are two of the popular random field discretization methods (Ghanem and Spanos, 1991). But, the KL expansion should be applied under a prerequisite of knowing the covariance matrix of a random field to be discretized (e.g. Ghanem and Spanos, 1991); while, the GPC expansions can be applied without similar prerequisites (e.g. Xiu and Karniadakis, 2003). Therefore, the development of an auxiliary tool for constructing a GPC representation of a random field would be necessary. The succeeding research considers the derivation of an GPC representation of a random field as a multi-objective (MO) problem having two goals: (a) limiting the computational efforts spent in applying the resulting GPC representation; and (b) keeping the resulting GPC representation satisfying all accuracy standards (e.g. getting the sufficiently accurate prediction of statistical parameters of a random field). The former goal will be attained by limiting the highest order of polynomial term and total number of uncorrelated random variables used to construct a GPC representation; while the latter goal will be attained by minimizing multiple error estimators. Since there are multiple goals to be attained, a multiple objective evolutionary algorithm (MOEA) is required. Among all available MOEAs, the strength Pareto evolutionary algorithm II (SPEA 2) (Zitzler, et al., 2001) is chosen. The highest order of polynomial term and total number of uncorrelated random variables used to construct an GPC representation are considered as two parameters to be identified. The remainder of this study is organized into four sections. In Sec. 2, the theoretical backgrounds of GPC expansions (e.g. Xiu and Karniadakis, 2003) are briefly reviewed. In Sec. 3, the SPEA 2 (Zitzler, et al., 2001) is used to construct a parameter identification procedure to identify the aforementioned highest order of orthogonal polynomial and total

RISQ: RANDOM INTERVAL SPATIAL UNCERTAINTY QUANTIFICATION SOFTWARE - 6th International Conference on Uncertainty Quantification in Computational Sciences and Engineering - 15-18 June 2025, Rhodes Island, Greece

LOW-COMPLEXITY ZONOTOPES CAN ENHANCE UNCERTAINTY QUANTIFICATION (UQ) - 4th International Conference on Uncertainty Quantification in Computational Sciences and Engineering - 28-30 June 2021, Streamed from Athens, Greece

High-dimensional uncertainty quantification for Mars atmospheric entry using adaptive generalized polynomial chaos

This work explores generalized polynomial chaos (GPC) surrogate models and their effectiveness for general acoustics and vibration applications. GPC is primarily known as an uncertainty quantification (UQ) technique and in that context the underlying polynomial-based model has been shown to be effective in mapping input probability distributions to the corresponding output probability distributions. In this study, GPC surrogate models – including those generated by both quadrature and regression methods – are evaluated for their effectiveness in non-UQ focused analyses. As points of comparison, Krylov subspace and other more traditional reduced order modeling techniques are demonstrated and compared to GPC models so that the differences may be better understood. Example problems with several different levels of complexity are used to show how the computational burden as well as the overall effectiveness of the method changes as the number of input variables that must be considered grows.

Uncertainty quantification in a resonant nonlinear MEMS structure

The goal of this book was to introduce the reader to the recent advances in the field of uncertainty quantification and error propagation for computer vision, image processing, and image analysis that are based on partial differential equations (PDEs). Our original motivation was the observation that more and more often, measured data in the form of images are being used as part of the simulation pipeline, and that error propagation and uncertainty quantification—starting from images but then moving through the pipeline—are important to understanding the ending result of this scientific or engineering process. To analyze the image processing pipeline, we have presented concepts that enable error propagation to be formulated with a set of basic operations: the idea of stochastic images and corresponding (numerical PDE) operations on those images. From this perspective, one approach commonly used within the engineering literature is to employ Monte Carlo sampling techniques to attempt to quantify the impact of errors and variability on an engineering pipeline. Within the uncertainty quantification world, alternative approaches such as the class of generalized polynomial chaos (gPC) methods, which make assumptions about the ability to approximate the process of interest through polynomial approximations, have gained traction as a way of accelerating the convergence of the error and uncertainty quantification process in a computationally tractable way. In this book, we have shown the results of our exploration of the use of the gPC methodology for image processing and computer vision problems. We have relied on the fact that all the prerequisites of the gPC framework (e.g., finite variance, smoothness in the stochastic space, etc.) are intrinsically satisfied in the image processing context. In particular, we have shown how the generalized polynomial chaos (gPC) approach and its corresponding rules for computation (e.g., sums, products, projections on the gPC space, etc.) lead to straightforward generalizations to image processing and computer vision techniques. We have shown that the gPC methodology, when combined with image processing and computer vision techniques, provides a powerful approach to error propagation and uncertainty quantification, and to accessing system sensitivity.

Model and analysis of single event transient sensitivity based on uncertainty quantification

The in-house Direct Simulation Monte Carlo code (DSMC-IEMC) has been used in Ariane group for more than 30 years to simulate rarefied gas dynamics in hypersonic conditions. In order to improve the accuracy of the simulations, chemical reactions have been implemented. Considering chemical reactions in the DSMC-IEMC code implies new input data taken into account. Among these parameters, the rotational and vibrational relaxation number, and the Arrhenius coefficients of chemical reactions are now needed to compute the simulation. These parameters are usually chosen to better reproduce the physics of the computation. Some comparison with experimental data can be made to define their values. However, it often remains an uncertainty in their choice. Considering the 2D Cylinder test case with chemical reactions, the aim of this work is to quantify the influence of the different models (relaxation process, chemical models) available in the DSMC-IEMC code and of their main parameters in order to analyze the changes due to the implementation of chemical models in a DSMC code. After the verification of the Total Collision Energy (TCE) chemical model and of the differently weighted molecules scheme for the 2D Cylinder test-case, a sensibility analysis is driven using a generalized Polynomial Chaos.

This article addresses the problem of quantifying the uncertainty in planning aircraft ground movement operations using towbarless robotic tractors taking into account the inherent uncertainties of the problem, specifically, the uncertainties in the weight of the aircraft and in the rolling resistance of the wheels of the main landing gear. The tractor‐aircraft system is represented as a tractor‐trailer system with random parameters characterized by means of probability density functions. The quantification of the uncertainties is conducted within an optimal control framework using the formulation of a stochastic optimal control problem, which is solved through a stochastic collocation method based on generalized polynomial chaos. Specifically, the stochastic optimal control problem is converted into a set of deterministic optimal control problems, in which a reduced number of sample values of the random parameters are employed to solve particular instances of the problem. Using these sample values, it is possible to express the obtained optimal solutions as orthogonal polynomial expansions in terms of the uncertain parameters, which allows both statistical and global sensitivity analysis of the stochastic optimal solutions to be carried out in an efficient way. The objectives of this article are to understand the effects of the uncertainties in the model parameters of the tractor‐aircraft system on the solutions of the optimal control problem and to identify which uncertain parameters have more influence on the variability of these solutions. The ultimate goal is to determine the best approach for executing aircraft ground movement operations in the presence of such uncertainties.

In the framework of process safety studies, consequence assessment of accidental scenarios is a crucial step affecting the eventual risk profile associated with the facilities under analysis. Conventional models used for consequence assessment are based on integral models, and may not be adequate to cope with the dynamic evolution of accidental scenarios and their three‐dimensional features. On the other hand, consequence assessment models based on computational fluid dynamics (CFD) approaches are promising to cope with complex scenarios and environments, but setting the simulation introduces relevant uncertainties associated with both the input data, assumptions, and with the modelling of physical effects involved. In the present study, uncertainty quantification (UQ) techniques are applied to support advanced safety studies based on CFD simulations of hazardous gas dispersion. Firstly, the accidental scenarios are characterized by defining release scenarios and conditions and quantifying source terms using integral models. At the same time, input meteorological data are gathered. This enables the development of high‐fidelity CFD simulations of gas dispersion based on different input sets and eventually the implementation of UQ techniques. The generalized polynomial chaos (gPC) expansion is employed to obtain hazardous gas concentration based on the variation of wind direction and speed. The present method is applied for the analysis of a real plant featuring a complex layout. The results show the advantages of the present approach by quantifying the influence of meteorological conditions and providing indications for supporting the development of protection systems and emergency measures.

Two squeeze‐film gas damping models are proposed to quantify uncertainties associated with the gap size and the ambient pressure. Modeling of gas damping has become a subject of increased interest in recent years due to its importance in micro‐electro‐mechanical systems (MEMS). In addition to the need for gas damping models for design of MEMS with movable micro‐structures, knowledge of parameter dependence in gas damping contributes to the understanding of device‐level reliability. In this work, two damping models quantifying the uncertainty in parameters are generated based on rarefied flow simulations. One is a generalized polynomial chaos (gPC) model, which is a general strategy for uncertainty quantification, and the other is a compact model developed specifically for this problem in an early work. Convergence and statistical analysis have been conducted to verify both models. By taking the gap size and ambient pressure as random fields with known probability distribution functions (PDF), the output PDF for the damping coefficient can be obtained. The first four central moments are used in comparisons of the resulting non‐parametric distributions. A good agreement has been found, within 1%, for the relative difference for damping coefficient mean values. In study of geometric uncertainty, it is found that the average damping coefficient can deviate up to 13% from the damping coefficient corresponding to the average gap size. The difference is significant at the nonlinear region where the flow is in slip or transitional rarefied regimes. Copyright © 2010 John Wiley & Sons, Ltd.