Article
Automation & Control Systems
Weixin Han, Zhenhua Wang, Yi Shen, Bin Xu
Summary: This article proposes a two-step interval estimation method for linear systems with time-invariant probabilistic uncertainty, utilizing PCE and zonotopic technique. By approximating error dynamics via PCE and analyzing intervals of the expanded system with zonotopic technique, the interval estimation is achieved by combining nominal observer state and estimated error interval. Experimental and simulation examples in a case study demonstrate the effectiveness of the proposed method.
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
(2021)
Article
Engineering, Civil
Zhanlin Liu, Youngjun Choe
Summary: This paper proposes a data-driven sensitivity indices method for analyzing models with dependent inputs. By constructing orthogonal polynomials, this method is able to provide intuitive interpretations of how the dependent inputs affect the variance of the output without relying on prior knowledge of the input dependence structure.
Article
Engineering, Aerospace
Brandon A. Jones, Trevor N. Wolf
Summary: This paper presents a method to generate an orthogonal basis on the n-dimensional sphere by combining hyperspherical harmonics with an orthogonalization procedure based on the raw moments of the harmonic functions. This method extends the use of Polynomial Chaos Expansions (PCEs) to problems involving probability densities on the n-sphere, such as spacecraft attitude uncertainty.
JOURNAL OF THE ASTRONAUTICAL SCIENCES
(2023)
Article
Mathematics, Applied
Maxime Breden
Summary: Generalized polynomial chaos (gPC) expansions are a powerful tool for efficiently approximating random invariant sets associated with differential equations with random coefficients. This work introduces a new framework for conducting validated continuation in parameter-dependent systems, allowing for rigorous computation of isolated branches of solutions. The proposed methodology is applied to compute random invariant periodic orbits in the Lorenz system and steady states of the Swift-Hohenberg equation.
SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
(2023)
Article
Computer Science, Interdisciplinary Applications
Mohammad Jamous, Reza Marsooli, Mahmoud Ayyad
Summary: Predicting coastal erosion requires an accurate morphodynamic model, such as XBeach. Sensitivity analysis is conducted using a computationally cost-effective approach based on the Non-Intrusive Polynomial Chaos Expansion method. Applied to Hurricane Sandy-induced coastal erosion in New Jersey, the results demonstrate the spatial variation of model sensitivity and the reduction of parameter interaction with increasing boundary conditions, leading to a reduction in uncertainty of model output.
ENVIRONMENTAL MODELLING & SOFTWARE
(2023)
Article
Engineering, Aerospace
Bin Jia, Ming Xin
Summary: This paper proposes a method based on polynomial chaos expansion and Bayesian optimization to calculate the collision probability and conjunction time of space objects. By establishing a continuous PCE model to describe the uncertainty of space objects, and using machine learning and Gaussian process regression model to determine the conjunction time and calculate the collision probability. Experimental results show that this method is close to the traditional Monte Carlo sampling method in terms of calculation performance.
JOURNAL OF SPACECRAFT AND ROCKETS
(2022)
Article
Construction & Building Technology
Deepthi Mary Dilip, G. L. Sivakumar Babu
Summary: Recognizing the importance of sustainable and durable structures, reliability-based designs are increasingly being adopted in pavement engineering. This study proposes the Reliability Based Design Optimization (RBDO) to create cost-effective flexible pavements considering uncertainties. Two meta-modelling techniques, second-order adaptive Response Surface Model (RSM) and adaptive Polynomial-Chaos based Kriging (PC-Kriging), are considered. The study highlights the need for adaptive meta-modelling approaches to address epistemic uncertainties. The proposed System Reliability Based Design Optimization (SRBDO) method integrates economic analysis and the Mechanistic-Empirical procedure to optimize pavement layer thicknesses and moduli.
CONSTRUCTION AND BUILDING MATERIALS
(2023)
Article
Mechanics
Haohao Wang, Limin Gao, Guang Yang, Baohai Wu
Summary: This study proposes a data-driven robust optimization framework that uses a novel uncertainty quantification method to quantify uncertainty based on statistical moments of scarce input data. The computational robustness and accuracy of the developed method are validated. It is applied to improve the mean performance and aerodynamic robustness of a two-dimensional compressor blade with real stagger angle errors.
Article
Engineering, Aerospace
Xun Peng, Hao Zhu, Dajun Xu, Mingyang Xiao, Weizong Wang, Guobiao Cai
Summary: This study investigated the aerodynamic uncertainty analysis and optimization of a conventional axisymmetric vehicle with an aerodynamic configuration. The prediction precision of engineering estimation and numerical simulation methods were compared, and a high-efficiency and high-precision method was developed using modified DATCOM software. An uncertainty-based design optimization framework was established to enhance the robustness and reliability of aerodynamic performance.
Article
Automation & Control Systems
Mohammad Amin Hariri-Ardebili, Golsa Mahdavi
Summary: This paper proposes three surrogate modeling techniques (polynomial chaos expansion, Kriging, and canonical low-rank approximation) for concrete compressive strength regression analysis. With a benchmark database of high-performance concrete, various sources of uncertainties in surrogate modeling are quantified. The Kriging-based surrogate models outperform the existing predictive models and show more stable results. The selection of a proper optimization algorithm is the most important factor in surrogate modeling.
ENGINEERING APPLICATIONS OF ARTIFICIAL INTELLIGENCE
(2023)
Article
Mathematics, Applied
Yanyan He, M. Yousuff Hussaini
Summary: In this paper, the authors propose a method to deal with epistemic uncertainty using Dempster-Shafer theory and basic belief assignments. They introduce the theoretical basics of DS theory, present a numerical approach combining DS theory with generalized polynomial chaos expansion, and conduct an error analysis for the numerical approach. The convergence of the numerical approximation is demonstrated with simple examples, and the method is applied to quantify uncertainty in quasi-one-dimensional flow.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2023)
Article
Engineering, Aerospace
Wei Zhang, Qiang Wang, Fanzhi Zeng, Chao Yan
Summary: Uncertainty is important in aircraft design, and this study proposes a new robust aerodynamic optimization technique called R-Opt. By coupling with Polynomial Chaos Expansion (PCE), R-Opt efficiently quantifies uncertainty in target responses and improves aircraft performance.
CHINESE JOURNAL OF AERONAUTICS
(2022)
Article
Engineering, Mechanical
Liqun Wang, Guolai Yang
Summary: This paper introduces a novel approach for nonintrusive interval uncertainty propagation in multibody systems using Legendre polynomials, addressing issues of wrapping effect and suitability encountered in traditional methods. Mathematical examples and benchmark tests demonstrate the effectiveness of the proposed method in dealing with large, complicated multibody dynamic systems.
NONLINEAR DYNAMICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Gael Poette
Summary: This paper investigates propagating uncertainties through the linear Boltzmann equation using Monte-Carlo (MC) schemes. Generalized Polynomial Chaos (gPC) reduced models are used to alleviate cost, but they have limitations in terms of dimensionality and noise. The paper presents new MC schemes based on multigroup-like resolution methods to improve the runtime of MC-gPC and discusses the integration of uncertainties in simulation code development.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Editorial Material
Mechanics
J. C. Garcia-Merino, C. Calvo-Jurado, E. Garcia-Macias
Summary: This paper proposes the use of adaptive polynomial chaos expansion for uncertainty propagation analysis in the numerical homogenization of polymer composites. The developed method acts as a surrogate model, saving computational effort. Numerical results and discussion evaluate the accuracy and efficiency of the method for different filler contents. The main contribution is the ability to perform uncertainty propagation analysis with minimum computational effort, which has great potential for stochastic design.
COMPOSITE STRUCTURES
(2022)
Article
Engineering, Civil
Maliki Moustapha, Stefano Marelli, Bruno Sudret
Summary: Active learning methods have gained popularity in solving complex structural reliability problems by building inexpensive surrogate models. This paper surveys recent literature and proposes a generalized modular framework for building efficient active learning strategies. The extensive benchmark results provide recommendations for practitioners and highlight the importance of combining surrogates with sophisticated reliability estimation algorithms.
Article
Energy & Fuels
Alina Galimshina, Maliki Moustapha, Alexander Hollberg, Pierryves Padey, Sebastien Lasvaux, Bruno Sudret, Guillaume Habert
Summary: Boosting building renovation is crucial for achieving carbon neutrality by 2050. Bio-based materials offer a promising alternative for energy-efficient building retrofit while temporarily storing carbon. Uncertainty quantification and robust optimization are applied to find the most cost-effective and climate-friendly solution for building renovation.
Article
Endocrinology & Metabolism
John P. H. Wilding, Rachel L. Batterham, Melanie Davies, Luc F. Van Gaal, Kristian Kandler, Katerina Konakli, Ildiko Lingvay, Barbara M. McGowan, Tugce Kalayci Oral, Julio Rosenstock, Thomas A. Wadden, Sean Wharton, Koutaro Yokote, Robert F. Kushner
Summary: One year after withdrawal of once-weekly subcutaneous semaglutide 2.4 mg and lifestyle intervention, participants regained two-thirds of their prior weight loss, with similar changes in cardiometabolic variables. Findings confirm the chronicity of obesity and suggest ongoing treatment is required to maintain improvements in weight and health.
DIABETES OBESITY & METABOLISM
(2022)
Article
Mathematics, Applied
Max Ehre, Iason Papaioannou, Bruno Sudret, Daniel Straub
Summary: This study addresses the challenge of analyzing high-dimensional, computationally expensive engineering models in risk and reliability engineering using a combination of dimensionality reduction and surrogate modeling. The approach is extended with an active learning procedure to improve error control. The performance of this approach is demonstrated with various example problems featuring well-known caveats for reliability methods.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2022)
Article
Engineering, Civil
P-R Wagner, S. Marelli, I Papaioannou, D. Straub, B. Sudret
Summary: Estimating the probability of rare failure events is crucial for reliability assessment of engineering systems. The stochastic spectral embedding (SSER) method improves the local approximation accuracy of global, spectral surrogate modelling techniques by sequentially embedding local residual expansions in subdomains of the input space. It decomposes the failure probability into a set of easy-to-compute conditional failure probabilities. The proposed modifications to the algorithm enhance its efficiency in solving rare event estimation problems.
Editorial Material
Engineering, Industrial
B. Iooss, B. Sudret, Lo Piano, C. Prieur
RELIABILITY ENGINEERING & SYSTEM SAFETY
(2022)
Article
Engineering, Mechanical
Tong Zhou, Stefano Marelli, Bruno Sudret, Yongbo Peng
Summary: A failure-informed enrichment algorithm, named AK-PDEMi, is proposed to improve the performance of the existing AK-PDEM method for reliability analysis. The algorithm enriches the representative point set sequentially by generating new sets of representative points, which contribute to fine partitions of key sub-regions. Through comprehensive comparisons, the AK-PDEMi shows remarkable advantages over other conventional reliability algorithms.
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
(2022)
Article
Engineering, Mechanical
Pablo Wilson, Nicolas Saintier, Thierry Palin-Luc, Bruno Sudret, Sebastien Bergamo
Summary: This study investigates the characteristics of defects in cast materials and their impact on material fatigue performance using statistical tools. The results demonstrate that the defects are clustered and there is no significant link between the size of the defect and its location.
INTERNATIONAL JOURNAL OF FATIGUE
(2023)
Article
Computer Science, Interdisciplinary Applications
Maliki Moustapha, Alina Galimshina, Guillaume Habert, Bruno Sudret
Summary: Accounting for uncertainties is crucial for the safety of engineering structures. This study proposes a method for robust design optimization by considering quantiles of objective functions. By introducing the concept of common random numbers and using a surrogate-assisted approach, the computational cost of the optimization problem is reduced.
STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION
(2022)
Article
Engineering, Multidisciplinary
Nora Luthen, Stefano Marelli, Bruno Sudret
Summary: Stochastic simulators are computer models that produce varying responses with fixed input parameters. Uncertainty analysis of these simulators often requires repeated evaluations under different input values and stochastic realizations. To reduce computational costs, a surrogate model based on spectral expansions is proposed. This surrogate model approximates the marginals and covariance functions, allowing for low-cost generation of new realizations. Furthermore, the importance of the first mode of the Karhunen-Loeve expansion (KLE) is investigated.
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
(2023)
Article
Engineering, Mechanical
Xujia Zhu, Marco Broccardo, Bruno Sudret
Summary: The fragility model plays a key role in the performance-based earthquake engineering (PBEE) framework. The computation of such models is a challenge, and there is still a research gap in this domain. This study proposes a new method using stochastic polynomial chaos expansions to estimate the conditional distribution and fragility functions, and compares it with state-of-the-art methods in two case studies.
PROBABILISTIC ENGINEERING MECHANICS
(2023)
Article
Engineering, Manufacturing
Lorenzo Del Giudice, Stefano Marelli, Bruno Sudret, Michalis F. Vassiliou
Summary: This paper focuses on the influence of printing parameters on the mechanical properties of 3D printed materials produced with Binder Jet technology. By using a Design of Experiments approach, optimal points in the parameter space were selected and Sobol' sensitivity indices were calculated. The study found that the mechanical properties are primarily controlled by the binder content, and the printing speed does not affect them significantly. Curing at elevated temperatures also improves the strength of the specimens.
PROGRESS IN ADDITIVE MANUFACTURING
(2023)
Article
Engineering, Multidisciplinary
Nora Luthen, Olivier Roustant, Fabrice Gamboa, Bertrand Iooss, Stefano Marelli, Bruno Sudret
Summary: Variance-based global sensitivity analysis, particularly Sobol' analysis, is widely used to determine the importance of input variables in a computational model. This paper introduces a method based on Poincare chaos expansions (PoinCE) for computing spectral expansions using Poincare basis functions or basis partial derivatives. The results from two numerical examples show that the derivative-based expansions provide more accurate estimates for Sobol' indices compared to polynomial chaos expansions (PCE), outperforming them in terms of bias and variance. Additionally, an analytical expression for the derivative-based sensitivity measure (DGSM) is derived using PoinCE coefficients and its performance as an upper bound for the corresponding total Sobol' indices is explored.
INTERNATIONAL JOURNAL FOR UNCERTAINTY QUANTIFICATION
(2023)
Article
Geosciences, Multidisciplinary
Emilie Rouzies, Claire Lauvernet, Bruno Sudret, Arthur Vidard
Summary: Pesticide transfers in agricultural catchments pose diffuse but significant risks to water quality. Spatialized pesticide transfer models are valuable for assessing the impact of landscape structure on water quality. However, before using these models in practical situations, it is crucial to quantify their uncertainties. This study used global sensitivity analysis to quantify uncertainties in the PESHMELBA pesticide transfer model and compared different methods for sensitivity analysis.
GEOSCIENTIFIC MODEL DEVELOPMENT
(2023)
Article
Engineering, Multidisciplinary
N. Luthen, S. Marelli, B. Sudret
Summary: Sparse polynomial chaos expansions (PCE) are an efficient and widely used surrogate modeling method for uncertainty quantification. This paper aims to help practitioners identify the most suitable methods for constructing a surrogate PCE for their model. Through benchmarking and investigating the synergies between sparse regression solvers and basis adaptivity schemes, the paper provides insights into the importance of choosing the proper solver and basis-adaptive scheme. Furthermore, a novel solver and basis adaptivity selection scheme guided by cross-validation error is introduced, which produces close-to-optimal results in terms of accuracy and robustness.
INTERNATIONAL JOURNAL FOR UNCERTAINTY QUANTIFICATION
(2022)
Article
Engineering, Mechanical
R. Allahvirdizadeh, A. Andersson, R. Karoumi
Summary: The operational safety of high-speed trains on ballasted bridges relies on preventing ballast destabilization. This study explores the impact of epistemic uncertainties on the system using ISRA. Neglecting these uncertainties can lead to overestimation of permissible train speeds and reduced system safety.
PROBABILISTIC ENGINEERING MECHANICS
(2024)
Article
Engineering, Mechanical
Lujie Shi, Leila Khalij, Christophe Gautrelet, Chen Shi, Denis Benasciutti
Summary: This study proposes an innovative Two-phase method based on the Langlie method and the D-optimality criterion to overcome the intrinsic shortcomings of the staircase method used in estimating the fatigue limit distribution. Through simulation-based study, it is demonstrated that the proposed method improves the estimation performance for the mean and standard deviation of the fatigue limit distribution.
PROBABILISTIC ENGINEERING MECHANICS
(2024)
Article
Engineering, Mechanical
Axay Thapa, Atin Roy, Subrata Chakraborty
Summary: This article compares different metamodeling approaches for reliability analysis of tunnels to evaluate their performance. The study found that Kriging and support vector regression models perform well in estimating the reliability of underground tunnels.
PROBABILISTIC ENGINEERING MECHANICS
(2024)
Article
Engineering, Mechanical
Jiaqi Wang, Zhenzhou Lu, Lu Wang
Summary: This paper proposes an efficient method to estimate the FP-GS using reliability updating, avoiding the time-consuming double-loop structure analysis. By utilizing the likelihood function and adaptive Kriging model, the unconditional FP and all conditional FPs can be estimated simultaneously.
PROBABILISTIC ENGINEERING MECHANICS
(2024)
Article
Engineering, Mechanical
Jiaxu Li, Ming Liu, Xu Yan, Qianting Yang
Summary: Wind pressure is essential for architectural design, and this study found that using different probabilistic distribution models can improve the accuracy of reference wind pressure calculation. In the research conducted in Liaoning Province, the extreme value type III model and moment method achieved the best fit. Additionally, probability density functions for wind speed and wind direction were established for further analysis of wind pressure.
PROBABILISTIC ENGINEERING MECHANICS
(2024)
Article
Engineering, Mechanical
Yufan Cheng, Xinchen Zhuang, Tianxiang Yu
Summary: This paper proposes a time-dependent kinematic reliability analysis method that takes into account the truncated random variables and joint clearances, effectively addressing the issues of dimension variables and correlation between joint clearance variables. The proposed method transforms time-dependent reliability into time-independent reliability, greatly reducing computational complexity and obtaining upper and lower bounds of failure probability.
PROBABILISTIC ENGINEERING MECHANICS
(2024)