Special Issue "Methods and Applications of Uncertainty Quantification in Engineering and Science"

A special issue of Algorithms (ISSN 1999-4893). This special issue belongs to the section "Evolutionary Algorithms and Machine Learning".

Deadline for manuscript submissions: 31 July 2020.

Special Issue Editors

Dr. Matteo Diez
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Guest Editor
Research Scientist, National Research Council-Institute of Marine Engineering (CNR-INM), Via di Vallerano 139, 00128 Rome, Italy
Interests: simulation-based design optimization in ship hydrodynamics; fluid-structure interaction and multidisciplinary design optimization; uncertainty quantification and reliability-based robust design optimization; design space dimensionality reduction in shape optimization; dynamic metamodeling and machine learning methods; global derivative-free bio-inspired optimization algorithms
Dr. Lorenzo Tamellini
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Guest Editor
Institute of Applied Mathematics and Information Technologies, National Research Council, 27100 Pavia, Italy
Interests: uncertainty quantification; isogeometric analysis
Prof. Dr. Maria Vittoria Salvetti
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Guest Editor
Department of Civil and Industrial Engineering, University of Pisa, 56126 Pisa, Italy
Interests: simulation and modeling of complex flows; low-order models for fluid dynamics; uncertainty quantification in CFD
Dr. Alessandro Mariotti
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Guest Editor
Department of Civil and Industrial Engineering, University of Pisa, 56126 Pisa, Italy
Interests: experimental and numerical analysis and control of bluff-body flows; drag reduction; experimental and numerical study of the flow in micro-reactors; uncertainty quantification; simulation of hemodynamic problems; numerical evaluation of coastal erosion; wind-tunnel aerodynamic experiments

Special Issue Information

Dear Colleagues,

In the last two decades, uncertainty quantification (UQ) methods have received increasing attention, as real-world problems in most science, technology, and engineering areas are affected significantly by uncertainty. When dealing with simulations of complex physical phenomena, uncertainty generally stems from physical modelling, environmental/operating conditions, and to some extent numerical discretization. In the case of problems modeled and solved by partial differential equations (PDEs), this is reflected in the choice of the modeling equations and of the corresponding terms/coefficients, and in the definition of proper initial and boundary conditions, as well as of the computational-domain shape and discretization. While the uncertainty associated with modeling and discretization can be reduced in principle, the uncertainty propagating from environmental and operating conditions is often aleatoric and intrinsic to the problem. Within this framework, solutions to PDEs are no longer sought deterministically, as statistical estimators and/or distributions of relevant simulation outputs are deemed to be a more accurate representation of the real problem under investigation. UQ represents a grand challenge for most problems and users: indeed, it generally requires repeatedly solving the PDE at hand for different values of the random parameters, which might be a very demanding computational task despite the significant development of high-performance computing systems. To overcome the limitations due to the computational cost associated with UQ, several approaches have been investigated by researchers in different areas. The aim of this Special Issue is to collect state-of-the-art research on the topic of computationally-efficient UQ methods and on their applications to complex problems. The Special Issue is organized in collaboration with the Workshop on Frontiers of Uncertainty Quantification in Fluid Dynamics (FrontUQ 2019, https://frontuq19.com/). Contributions from FrontUQ are welcome, as well as papers from other fields of application of UQ and researchers outside the workshop. Relevant topics, methods, and applications are included in (but not limited to) the list below.

Dr. Matteo Diez
Dr. Lorenzo Tamellini
Prof. Dr. Maria Vittoria Salvetti
Dr. Alessandro Mariotti
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Algorithms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1000 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • forward propagation of uncertainties
  • sensitivity analysis
  • inverse problems
  • data fusion, data assimilation, and integration with artificial intelligence or machine learning
  • metamodeling and machine learning in UQ problems
  • adaptive methods
  • multi-fidelity and multi-level methods
  • dimensionality reduction
  • intrusive and non-intrusive methods
  • UQ in complex physical and engineering problems
  • optimization under uncertainty

Published Papers (6 papers)

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Research

Open AccessArticle
Uncertainty Quantification Approach on Numerical Simulation for Supersonic Jets Performance
Algorithms 2020, 13(5), 130; https://doi.org/10.3390/a13050130 - 22 May 2020
Abstract
One of the main issues addressed in any engineering design problem is to predict the performance of the component or system as accurately and realistically as possible, taking into account the variability of operating conditions or the uncertainty on input data (boundary conditions [...] Read more.
One of the main issues addressed in any engineering design problem is to predict the performance of the component or system as accurately and realistically as possible, taking into account the variability of operating conditions or the uncertainty on input data (boundary conditions or geometry tolerance). In this paper, the propagation of uncertainty on boundary conditions through a numerical model of supersonic nozzle is investigated. The evaluation of the statistics of the problem response functions is performed following ‘Surrogate-Based Uncertainty Quantification’. The approach involves: (a) the generation of a response surface starting from a DoE in order to approximate the convergent–divergent ‘physical’ model (expensive to simulate), (b) the application of the UQ technique based on the LHS to the meta-model. Probability Density Functions are introduced for the inlet boundary conditions in order to quantify their effects on the output nozzle performance. The physical problem considered is very relevant for the experimental tests on the UQ approach because of its high non-linearity. A small perturbation to the input data can drive the solution to a completely different output condition. The CFD simulations and the Uncertainty Quantification were performed by coupling the open source Dakota platform with the ANSYS Fluent® CFD commercial software: the process is automated through scripting. The procedure adopted in this work demonstrate the applicability of advanced simulation techniques (such as UQ analysis) to industrial technical problems. Moreover, the analysis highlights the practical use of the uncertainty quantification techniques in predicting the performance of a nozzle design affected by off-design conditions with fluid-dynamic complexity due to strong nonlinearity. Full article
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Open AccessArticle
p-Refined Multilevel Quasi-Monte Carlo for Galerkin Finite Element Methods with Applications in Civil Engineering
Algorithms 2020, 13(5), 110; https://doi.org/10.3390/a13050110 - 28 Apr 2020
Abstract
Civil engineering applications are often characterized by a large uncertainty on the material parameters. Discretization of the underlying equations is typically done by means of the Galerkin Finite Element method. The uncertain material parameter can be expressed as a random field represented by, [...] Read more.
Civil engineering applications are often characterized by a large uncertainty on the material parameters. Discretization of the underlying equations is typically done by means of the Galerkin Finite Element method. The uncertain material parameter can be expressed as a random field represented by, for example, a Karhunen–Loève expansion. Computation of the stochastic responses, i.e., the expected value and variance of a chosen quantity of interest, remains very costly, even when state-of-the-art Multilevel Monte Carlo (MLMC) is used. A significant cost reduction can be achieved by using a recently developed multilevel method: p-refined Multilevel Quasi-Monte Carlo (p-MLQMC). This method is based on the idea of variance reduction by employing a hierarchical discretization of the problem based on a p-refinement scheme. It is combined with a rank-1 Quasi-Monte Carlo (QMC) lattice rule, which yields faster convergence compared to the use of random Monte Carlo points. In this work, we developed algorithms for the p-MLQMC method for two dimensional problems. The p-MLQMC method is first benchmarked on an academic beam problem. Finally, we use our algorithm for the assessment of the stability of slopes, a problem that arises in geotechnical engineering, and typically suffers from large parameter uncertainty. For both considered problems, we observe a very significant reduction in the amount of computational work with respect to MLMC. Full article
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Open AccessFeature PaperArticle
Application of Generalized Polynomial Chaos for Quantification of Uncertainties of Time Averages and Their Sensitivities in Chaotic Systems
Algorithms 2020, 13(4), 90; https://doi.org/10.3390/a13040090 - 13 Apr 2020
Abstract
In this paper, we consider the effect of stochastic uncertainties on non-linear systems with chaotic behavior. More specifically, we quantify the effect of parametric uncertainties to time-averaged quantities and their sensitivities. Sampling methods for Uncertainty Quantification (UQ), such as the Monte–Carlo (MC), are [...] Read more.
In this paper, we consider the effect of stochastic uncertainties on non-linear systems with chaotic behavior. More specifically, we quantify the effect of parametric uncertainties to time-averaged quantities and their sensitivities. Sampling methods for Uncertainty Quantification (UQ), such as the Monte–Carlo (MC), are very costly, while traditional methods for sensitivity analysis, such as the adjoint, fail in chaotic systems. In this work, we employ the non-intrusive generalized Polynomial Chaos (gPC) for UQ, coupled with the Multiple-Shooting Shadowing (MSS) algorithm for sensitivity analysis of chaotic systems. It is shown that the gPC, coupled with MSS, is an appropriate method for conducting UQ in chaotic systems and produces results that match well with those from MC and Finite-Differences (FD). Full article
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Open AccessArticle
Uncertainty Propagation through a Point Model for Steady-State Two-Phase Pipe Flow
Algorithms 2020, 13(3), 53; https://doi.org/10.3390/a13030053 - 28 Feb 2020
Abstract
Uncertainty propagation is used to quantify the uncertainty in model predictions in the presence of uncertain input variables. In this study, we analyze a steady-state point-model for two-phase gas-liquid flow. We present prediction intervals for holdup and pressure drop that are obtained from [...] Read more.
Uncertainty propagation is used to quantify the uncertainty in model predictions in the presence of uncertain input variables. In this study, we analyze a steady-state point-model for two-phase gas-liquid flow. We present prediction intervals for holdup and pressure drop that are obtained from knowledge of the measurement error in the variables provided to the model. The analysis also uncovers which variables the predictions are most sensitive to. Sensitivity indices and prediction intervals are calculated by two different methods, Monte Carlo and polynomial chaos. The methods give similar prediction intervals, and they agree that the predictions are most sensitive to the pipe diameter and the liquid viscosity. However, the Monte Carlo simulations require fewer model evaluations and less computational time. The model predictions are also compared to experiments while accounting for uncertainty, and the holdup predictions are accurate, but there is bias in the pressure drop estimates. Full article
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Open AccessArticle
Approximation and Uncertainty Quantification of Systems with Arbitrary Parameter Distributions Using Weighted Leja Interpolation
Algorithms 2020, 13(3), 51; https://doi.org/10.3390/a13030051 - 26 Feb 2020
Abstract
Approximation and uncertainty quantification methods based on Lagrange interpolation are typically abandoned in cases where the probability distributions of one or more system parameters are not normal, uniform, or closely related distributions, due to the computational issues that arise when one wishes to [...] Read more.
Approximation and uncertainty quantification methods based on Lagrange interpolation are typically abandoned in cases where the probability distributions of one or more system parameters are not normal, uniform, or closely related distributions, due to the computational issues that arise when one wishes to define interpolation nodes for general distributions. This paper examines the use of the recently introduced weighted Leja nodes for that purpose. Weighted Leja interpolation rules are presented, along with a dimension-adaptive sparse interpolation algorithm, to be employed in the case of high-dimensional input uncertainty. The performance and reliability of the suggested approach is verified by four numerical experiments, where the respective models feature extreme value and truncated normal parameter distributions. Furthermore, the suggested approach is compared with a well-established polynomial chaos method and found to be either comparable or superior in terms of approximation and statistics estimation accuracy. Full article
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Open AccessArticle
Application and Evaluation of Surrogate Models for Radiation Source Search
Algorithms 2019, 12(12), 269; https://doi.org/10.3390/a12120269 - 12 Dec 2019
Abstract
Surrogate models are increasingly required for applications in which first-principles simulation models are prohibitively expensive to employ for uncertainty analysis, design, or control. They can also be used to approximate models whose discontinuous derivatives preclude the use of gradient-based optimization or data assimilation [...] Read more.
Surrogate models are increasingly required for applications in which first-principles simulation models are prohibitively expensive to employ for uncertainty analysis, design, or control. They can also be used to approximate models whose discontinuous derivatives preclude the use of gradient-based optimization or data assimilation algorithms. We consider the problem of inferring the 2D location and intensity of a radiation source in an urban environment using a ray-tracing model based on Boltzmann transport theory. Whereas the code implementing this model is relatively efficient, extension to 3D Monte Carlo transport simulations precludes subsequent Bayesian inference to infer source locations, which typically requires thousands to millions of simulations. Additionally, the resulting likelihood exhibits discontinuous derivatives due to the presence of buildings. To address these issues, we discuss the construction of surrogate models for optimization, Bayesian inference, and uncertainty propagation. Specifically, we consider surrogate models based on Legendre polynomials, multivariate adaptive regression splines, radial basis functions, Gaussian processes, and neural networks. We detail strategies for computing training points and discuss the merits and deficits of each method. Full article
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