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Algorithms
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Methods and Applications of Uncertainty Quantification in Engineering and Science
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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 "Algorithms for Multidisciplinary Applications".

Deadline for manuscript submissions: closed (31 July 2020) | Viewed by 41389

Special Issue Editors

Dr. Matteo Diez

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Guest Editor
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

E-Mail Website
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

E-Mail Website
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 submissions that pass pre-check are 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 1600 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 (11 papers)

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Research

25 pages, 1478 KiB  
Article
Multi-Fidelity Gradient-Based Strategy for Robust Optimization in Computational Fluid Dynamics
by Aldo Serafino, Benoit Obert and Paola Cinnella
Algorithms 2020, 13(10), 248; https://0-doi-org.brum.beds.ac.uk/10.3390/a13100248 - 30 Sep 2020
Cited by 5 | Viewed by 2766
Abstract
Efficient Robust Design Optimization (RDO) strategies coupling a parsimonious uncertainty quantification (UQ) method with a surrogate-based multi-objective genetic algorithm (SMOGA) are investigated for a test problem in computational fluid dynamics (CFD), namely the inverse robust design of an expansion nozzle. The low-order statistics [...] Read more.
Efficient Robust Design Optimization (RDO) strategies coupling a parsimonious uncertainty quantification (UQ) method with a surrogate-based multi-objective genetic algorithm (SMOGA) are investigated for a test problem in computational fluid dynamics (CFD), namely the inverse robust design of an expansion nozzle. The low-order statistics (mean and variance) of the stochastic cost function are computed through either a gradient-enhanced kriging (GEK) surrogate or through the less expensive, lower fidelity, first-order method of moments (MoM). Both the continuous (non-intrusive) and discrete (intrusive) adjoint methods are evaluated for computing the gradients required for GEK and MoM. In all cases, the results are assessed against a reference kriging UQ surrogate not using gradient information. Subsequently, the GEK and MoM UQ solvers are fused together to build a multi-fidelity surrogate with adaptive infill enrichment for the SMOGA optimizer. The resulting hybrid multi-fidelity SMOGA RDO strategy ensures a good tradeoff between cost and accuracy, thus representing an efficient approach for complex RDO problems. Full article
(This article belongs to the Special Issue Methods and Applications of Uncertainty Quantification in Engineering and Science)
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21 pages, 1475 KiB  
Article
Adaptive Reconstruction of Imperfectly Observed Monotone Functions, with Applications to Uncertainty Quantification
by Luc Bonnet, Jean-Luc Akian, Éric Savin and T. J. Sullivan
Algorithms 2020, 13(8), 196; https://0-doi-org.brum.beds.ac.uk/10.3390/a13080196 - 13 Aug 2020
Viewed by 3189
Abstract
Motivated by the desire to numerically calculate rigorous upper and lower bounds on deviation probabilities over large classes of probability distributions, we present an adaptive algorithm for the reconstruction of increasing real-valued functions. While this problem is similar to the classical statistical problem [...] Read more.
Motivated by the desire to numerically calculate rigorous upper and lower bounds on deviation probabilities over large classes of probability distributions, we present an adaptive algorithm for the reconstruction of increasing real-valued functions. While this problem is similar to the classical statistical problem of isotonic regression, the optimisation setting alters several characteristics of the problem and opens natural algorithmic possibilities. We present our algorithm, establish sufficient conditions for convergence of the reconstruction to the ground truth, and apply the method to synthetic test cases and a real-world example of uncertainty quantification for aerodynamic design. Full article
(This article belongs to the Special Issue Methods and Applications of Uncertainty Quantification in Engineering and Science)
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26 pages, 5131 KiB  
Article
Sensitivity Analysis for Microscopic Crowd Simulation
by Marion Gödel, Rainer Fischer and Gerta Köster
Algorithms 2020, 13(7), 162; https://0-doi-org.brum.beds.ac.uk/10.3390/a13070162 - 05 Jul 2020
Cited by 10 | Viewed by 3987
Abstract
Microscopic crowd simulation can help to enhance the safety of pedestrians in situations that range from museum visits to music festivals. To obtain a useful prediction, the input parameters must be chosen carefully. In many cases, a lack of knowledge or limited measurement [...] Read more.
Microscopic crowd simulation can help to enhance the safety of pedestrians in situations that range from museum visits to music festivals. To obtain a useful prediction, the input parameters must be chosen carefully. In many cases, a lack of knowledge or limited measurement accuracy add uncertainty to the input. In addition, for meaningful parameter studies, we first need to identify the most influential parameters of our parametric computer models. The field of uncertainty quantification offers standardized and fully automatized methods that we believe to be beneficial for pedestrian dynamics. In addition, many methods come at a comparatively low cost, even for computationally expensive problems. This allows for their application to larger scenarios. We aim to identify and adapt fitting methods to microscopic crowd simulation in order to explore their potential in pedestrian dynamics. In this work, we first perform a variance-based sensitivity analysis using Sobol’ indices and then crosscheck the results by a derivative-based measure, the activity scores. We apply both methods to a typical scenario in crowd simulation, a bottleneck. Because constrictions can lead to high crowd densities and delays in evacuations, several experiments and simulation studies have been conducted for this setting. We show qualitative agreement between the results of both methods. Additionally, we identify a one-dimensional subspace in the input parameter space and discuss its impact on the simulation. Moreover, we analyze and interpret the sensitivity indices with respect to the bottleneck scenario. Full article
(This article belongs to the Special Issue Methods and Applications of Uncertainty Quantification in Engineering and Science)
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24 pages, 13780 KiB  
Article
Generalized Polynomial Chaos Expansion for Fast and Accurate Uncertainty Quantification in Geomechanical Modelling
by Claudia Zoccarato, Laura Gazzola, Massimiliano Ferronato and Pietro Teatini
Algorithms 2020, 13(7), 156; https://0-doi-org.brum.beds.ac.uk/10.3390/a13070156 - 30 Jun 2020
Cited by 7 | Viewed by 3164
Abstract
Geomechanical modelling of the processes associated to the exploitation of subsurface resources, such as land subsidence or triggered/induced seismicity, is a common practice of major interest. The prediction reliability depends on different sources of uncertainty, such as the parameterization of the constitutive model [...] Read more.
Geomechanical modelling of the processes associated to the exploitation of subsurface resources, such as land subsidence or triggered/induced seismicity, is a common practice of major interest. The prediction reliability depends on different sources of uncertainty, such as the parameterization of the constitutive model characterizing the deep rock behaviour. In this study, we focus on a Sobol’-based sensitivity analysis and uncertainty reduction via assimilation of land deformations. A synthetic test case application on a deep hydrocarbon reservoir is considered, where land settlements are predicted with the aid of a 3-D Finite Element (FE) model. Data assimilation is performed via the Ensemble Smoother (ES) technique and its variation in the form of Multiple Data Assimilation (ES-MDA). However, the ES convergence is guaranteed with a large number of Monte Carlo (MC) simulations, that may be computationally infeasible in large scale and complex systems. For this reason, a surrogate model based on the generalized Polynomial Chaos Expansion (gPCE) is proposed as an approximation of the forward problem. This approach allows to efficiently compute the Sobol’ indices for the sensitivity analysis and greatly reduce the computational cost of the original ES and MDA formulations, also enhancing the accuracy of the overall prediction process. Full article
(This article belongs to the Special Issue Methods and Applications of Uncertainty Quantification in Engineering and Science)
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24 pages, 1066 KiB  
Article
Binary Time Series Classification with Bayesian Convolutional Neural Networks When Monitoring for Marine Gas Discharges
by Kristian Gundersen, Guttorm Alendal, Anna Oleynik and Nello Blaser
Algorithms 2020, 13(6), 145; https://0-doi-org.brum.beds.ac.uk/10.3390/a13060145 - 19 Jun 2020
Cited by 12 | Viewed by 4664
Abstract
The world’s oceans are under stress from climate change, acidification and other human activities, and the UN has declared 2021–2030 as the decade for marine science. To monitor the marine waters, with the purpose of detecting discharges of tracers from unknown locations, large [...] Read more.
The world’s oceans are under stress from climate change, acidification and other human activities, and the UN has declared 2021–2030 as the decade for marine science. To monitor the marine waters, with the purpose of detecting discharges of tracers from unknown locations, large areas will need to be covered with limited resources. To increase the detectability of marine gas seepage we propose a deep probabilistic learning algorithm, a Bayesian Convolutional Neural Network (BCNN), to classify time series of measurements. The BCNN will classify time series to belong to a leak/no-leak situation, including classification uncertainty. The latter is important for decision makers who must decide to initiate costly confirmation surveys and, hence, would like to avoid false positives. Results from a transport model are used for the learning process of the BCNN and the task is to distinguish the signal from a leak hidden within the natural variability. We show that the BCNN classifies time series arising from leaks with high accuracy and estimates its associated uncertainty. We combine the output of the BCNN model, the posterior predictive distribution, with a Bayesian decision rule showcasing how the framework can be used in practice to make optimal decisions based on a given cost function. Full article
(This article belongs to the Special Issue Methods and Applications of Uncertainty Quantification in Engineering and Science)
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17 pages, 7760 KiB  
Article
Uncertainty Quantification Approach on Numerical Simulation for Supersonic Jets Performance
by Carlo Cravero, Davide De Domenico and Andrea Ottonello
Algorithms 2020, 13(5), 130; https://0-doi-org.brum.beds.ac.uk/10.3390/a13050130 - 22 May 2020
Cited by 5 | Viewed by 3413
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
(This article belongs to the Special Issue Methods and Applications of Uncertainty Quantification in Engineering and Science)
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30 pages, 1297 KiB  
Article
p-Refined Multilevel Quasi-Monte Carlo for Galerkin Finite Element Methods with Applications in Civil Engineering
by Philippe Blondeel, Pieterjan Robbe, Cédric Van hoorickx, Stijn François, Geert Lombaert and Stefan Vandewalle
Algorithms 2020, 13(5), 110; https://0-doi-org.brum.beds.ac.uk/10.3390/a13050110 - 28 Apr 2020
Cited by 5 | Viewed by 3470
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
(This article belongs to the Special Issue Methods and Applications of Uncertainty Quantification in Engineering and Science)
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16 pages, 1256 KiB  
Article
Application of Generalized Polynomial Chaos for Quantification of Uncertainties of Time Averages and Their Sensitivities in Chaotic Systems
by Kyriakos Dimitrios Kantarakias and George Papadakis
Algorithms 2020, 13(4), 90; https://0-doi-org.brum.beds.ac.uk/10.3390/a13040090 - 13 Apr 2020
Cited by 2 | Viewed by 3243
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
(This article belongs to the Special Issue Methods and Applications of Uncertainty Quantification in Engineering and Science)
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22 pages, 903 KiB  
Article
Uncertainty Propagation through a Point Model for Steady-State Two-Phase Pipe Flow
by Andreas Strand, Ivar Eskerud Smith, Tor Erling Unander, Ingelin Steinsland and Leif Rune Hellevik
Algorithms 2020, 13(3), 53; https://0-doi-org.brum.beds.ac.uk/10.3390/a13030053 - 28 Feb 2020
Cited by 4 | Viewed by 3720
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
(This article belongs to the Special Issue Methods and Applications of Uncertainty Quantification in Engineering and Science)
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20 pages, 390 KiB  
Article
Approximation and Uncertainty Quantification of Systems with Arbitrary Parameter Distributions Using Weighted Leja Interpolation
by Dimitrios Loukrezis and Herbert De Gersem
Algorithms 2020, 13(3), 51; https://0-doi-org.brum.beds.ac.uk/10.3390/a13030051 - 26 Feb 2020
Cited by 2 | Viewed by 3489
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
(This article belongs to the Special Issue Methods and Applications of Uncertainty Quantification in Engineering and Science)
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24 pages, 1502 KiB  
Article
Application and Evaluation of Surrogate Models for Radiation Source Search
by Jared A. Cook, Ralph C. Smith, Jason M. Hite, Razvan Stefanescu and John Mattingly
Algorithms 2019, 12(12), 269; https://0-doi-org.brum.beds.ac.uk/10.3390/a12120269 - 12 Dec 2019
Cited by 4 | Viewed by 4056
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
(This article belongs to the Special Issue Methods and Applications of Uncertainty Quantification in Engineering and Science)
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