References of "Arnst, Maarten"
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See detailAn overview of nonintrusive characterization, propagation, and sensitivity analysis of uncertainties in computational mechanics
Arnst, Maarten ULg; Ponthot, Jean-Philippe ULg

in International Journal for Uncertainty Quantification (in press)

In this paper, we offer a short overview of a number of methods that have been reported in the computational-mechanics literature for quantifying uncertainties in engineering applications. Within a ... [more ▼]

In this paper, we offer a short overview of a number of methods that have been reported in the computational-mechanics literature for quantifying uncertainties in engineering applications. Within a probabilistic framework, we describe the characterization of uncertainties using mathematical statistics methods, the propagation of uncertainties through computational models using either Monte Carlo sampling or stochastic expansion methods, and the sensitivity analysis of uncertainties using variance- and differentiation-based methods. We restrict our attention to nonintrusive methods that can be implemented as wrappers around existing computer programs, thus requiring no modification of the source code. We include some recent advances in the propagation and sensitivity analysis of uncertainties that are characterized by arbitrary probability distributions that may exhibit statistical dependence. Finally, we demonstrate the methods integrated in the proposed overview through a nonlinear engineering application relevant to metal forming. [less ▲]

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See detailA probabilistic model of the adhesive contact forces between rough surfaces in the MEMS stiction context
Hoang Truong, Vinh ULg; Wu, Ling ULg; Arnst, Maarten ULg et al

Conference (2014, June 26)

Stiction is a common failure mechanism in microelectromechanical systems (MEMS) in which two interacting bodies permanently adhere together. This problem is due to the comparability of adhesive surface ... [more ▼]

Stiction is a common failure mechanism in microelectromechanical systems (MEMS) in which two interacting bodies permanently adhere together. This problem is due to the comparability of adhesive surface forces (e.g. Van der Waals forces, capillary forces) and body forces in the MEMS context. To predict the adhesive contact forces coupled with stiction phenomenon, the combination of the Nayak statistical approach with the asperity-based theories is a common solution. However, this method contains some limitations due to the underlying assumptions: infinite size of the interacting rough surfaces and negligibility of asperity interactions. Furthermore, the Nayak solution suffers from a considerable dependency on the choice of the minimum wave length considered in the surface representation, which remains diXcult to select. The main goal of our research is to propose an improved method (i) which accounts for the Vnite size of the interacting surfaces, (ii) accounts for the uncertainties related to these surface topologies, (iii) in which the minimum wave length selection is physically based, and (iv) in which the validity of the asperity-based theories is demonstrated. From the topology measurements of MEMS samples, an analysis of the power spectral density function is carried out to determine the minimum relevant wave length for the problem of interest (here capillary stiction). We also show that at this scale of interest the asperity-based theories remain valid for polysilicon materials. Moreover, instead of considering inVnite surfaces as in the Nayak approach, a set of surfaces, whose sizes are representative of the MEMS structure, is generated based on the approximated power spectral density analysis and using the Monte Carlo method. From this description of the contacting surfaces, the adhesive contact forces can be evaluated by applying the asperity contact theories, leading to a probabilistic distribution of the adhesive contact forces. In addition, as the contact forces are rooted from the micro-scale adhesive forces, while their consequence, stiction, happens at the macro-scale of the considered device, the multi-scale nature of the phenomenon is accounted for. To predict this macro-scale behavior in a probabilistic form, the uncertainty quantiVcation process is coupled with a multiscale analysis. [less ▲]

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See detailProbabilistic Assessment of the Lifetime of Low-Earth-Orbit Spacecraft: Uncertainty Characterization
Dell'Elce, Lamberto ULg; Arnst, Maarten ULg; Kerschen, Gaëtan ULg

in Journal of Guidance Control & Dynamics (2014)

Orbital lifetime estimation is a problem of great timeliness and importance in astrodynamics. In view of the stochastic nature of the thermosphere and of the complexity of drag modeling, any deterministic ... [more ▼]

Orbital lifetime estimation is a problem of great timeliness and importance in astrodynamics. In view of the stochastic nature of the thermosphere and of the complexity of drag modeling, any deterministic assessment of orbital lifetime is likely to be bound to failure. This is why the present paper performs uncertainty quantification of satellite orbital lifetime estimation. Specifically, this paper focuses on the probabilistic characterization of the dominant sources of uncertainty inherent to low-altitude satellites. Uncertainties in the initial state of the satellite and in the atmospheric drag force, as well as uncertainties introduced by modeling limitations associated with atmospheric density models, are considered. Mathematical statistics methods, in conjunction with mechanical modeling considerations, are used to infer the probabilistic characterization of these uncertainties from experimental data and atmospheric density models. This characterization step facilitates the application of uncertainty propagation and sensitivity analysis methods, which in turn allows gaining insight into the impact that these uncertainties have on the orbital lifetime. The proposed developments are illustrated using one CubeSat of the QB50 constellation. [less ▲]

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See detailReduced chaos expansions with random coefficients in reduced-dimensional stochastic modeling of coupled problems
Arnst, Maarten ULg; Ghanem, Roger; Phipps, Eric et al

in International Journal for Numerical Methods in Engineering (2014), 97

We address the curse of dimensionality in methods for solving stochastic coupled problems with an emphasis on stochastic expansion methods such as those involving polynomial chaos expansions. The proposed ... [more ▼]

We address the curse of dimensionality in methods for solving stochastic coupled problems with an emphasis on stochastic expansion methods such as those involving polynomial chaos expansions. The proposed method entails a partitioned iterative solution algorithm that relies on a reduced-dimensional representation of information exchanged between subproblems to allow each subproblem to be solved within its own stochastic dimension while interacting with a reduced projection of the other subproblems. The proposed method extends previous work by the authors by introducing a reduced chaos expansion with random coefficients. The representation of the exchanged information by using this reduced chaos expansion with random coefficients enables an expeditious construction of doubly stochastic polynomial chaos expansions that separate the effect of uncertainty local to a subproblem from the effect of statistically independent uncertainty coming from other subproblems through the coupling. After laying out the theoretical framework, we apply the proposed method to a multiphysics problem from nuclear engineering. [less ▲]

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See detailProbabilistic model for MEMS micro-beam resonance frequency made of polycrystalline linear anisotropic material
Lucas, Vincent ULg; Wu, Ling ULg; Arnst, Maarten ULg et al

Conference (2013, December)

In order to ensure the accuracy of MEMS vibrometers, the first resonance frequency should be predicted at the design phase. However, this prediction cannot be deterministic: there is a scatter in the ... [more ▼]

In order to ensure the accuracy of MEMS vibrometers, the first resonance frequency should be predicted at the design phase. However, this prediction cannot be deterministic: there is a scatter in the reached value resulting from the uncertainties involved in the manufacturing process. The purpose of this work is to take into account these uncertainties of the microstructure and to propagate them up to the micro-beam resonance frequency. The objective is a non-deterministic model that can be used since the design stage. Towards this end a 3-scales stochastic model predicting the resonance frequency of a micro-beam made of a polycrystalline linear anisotropic material is described. Uncertainties are related to the sizes and orientations of the grains. The first part of the problem is a homogenization procedure performed on a volume which is not representative, due to the small scale of the problem inherent in MEMS. The method is thus non-deterministic and a meso-scale probabilistic elasticity tensor is predicted. This stage is followed by a perturbation stochastic finite element procedure to propagate the meso-scale uncertainties to the macro-scale, leading to a probabilistic model of the resonance frequency of the MEMS. [less ▲]

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See detailA probabilistic characterization, propagation, and sensitivity analysis of uncertainties in a metal forming application
Arnst, Maarten ULg; Ponthot, Jean-Philippe ULg

Conference (2013, September 05)

In metal forming processes, after leaving the tooling, formed pieces of metal have a tendency to partially return to their original shape because of their elastic recovery. This phenomenon, referred to as ... [more ▼]

In metal forming processes, after leaving the tooling, formed pieces of metal have a tendency to partially return to their original shape because of their elastic recovery. This phenomenon, referred to as the springback, is quite complex and depends not only on material properties such as Young's modulus and yield stress but also on many process parameters such as sheet thickness and bending angles. The springback is difficult to predict and is a major quality concern in forming processes because when the springback is smaller or larger than expected, it can cause serious problems to subsequent assembly processes due to geometry mismatches. In this communication, we present a probabilistic analysis of a metal forming application. We consider the bending of a metal sheet with uncertain elastoplastic material properties. First, we use methods from mathematical statistics to obtain a probabilistic characterization of the elastoplastic material properties from data. Next, we map this probabilistic representation of the elastoplastic material properties into a probabilistic representation of the deformed shape of the metal sheet through a mechanical model implemented using the Metafor software. Finally, we conduct a stochastic sensitivity analysis to determine which elastoplastic material properties are most influential in driving uncertainty in the deformed shape after the springback. Our probabilistic analysis involves so called nonintrusive methods, that is, methods that can be implemented as wrappers around the Metafor software without requiring modification of its source code. Further, it includes recent methods for the propagation and sensitivity analysis of uncertainties characterized by arbitrary probability distributions that may exhibit statistical dependence. [less ▲]

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See detailUQ benchmark problems for multiphysics modeling
Arnst, Maarten ULg

Conference (2013, July 23)

Multiphysics problems are found in numerous areas of science and engineering. They can take the form of a single equation that tightly couples different types of physical behavior or the form of a system ... [more ▼]

Multiphysics problems are found in numerous areas of science and engineering. They can take the form of a single equation that tightly couples different types of physical behavior or the form of a system of equations wherein the solution to certain equations is passed to other equations to determine physical properties or loadings or both. Further, there are multiphysics problems that couple different types of physical behavior with fundamentally different descriptions at different scales, as well as multiphysics problems that couple physical behavior in different regions of space through a shared interface. Uncertainty quantification for multiphysics problems raises various conceptual, mathematical, and numerical challenges. Modeling challenges arise in the characterization of parametric uncertainties and modeling errors that may exist either within subsidiary components or at their interfaces. Further, once these parametric uncertainties and modeling errors are modeled, mathematical challenges arise in the analysis of the local and global existence, uniqueness, regularity, and stability of solutions. Finally, both the use of monolithic solution methods and the use of partitioned solution methods raise numerical challenges relevant to error analysis, stability, convergence, and computational efficiency. This presentation will report on interactions with the USACM community to set up one or more benchmark problems for multiphysics modeling. The ultimate goal of uncertainty quantification in these benchmark problems will be discussed, and the conceptual, mathematical, and numerical challenges in addressing these benchmark problems will be described. [less ▲]

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See detailStochastic Dimension Reduction of Multi Physics Systems through Measure Transformation
Phipps, Eric; Constantine, Paul; Red-Horse, John et al

Conference (2013, February 26)

Uncertainty quantification of multiphysics systems represents numerous mathematical and computational challenges. Indeed, uncertainties that arise in each physics in a fully coupled system must be ... [more ▼]

Uncertainty quantification of multiphysics systems represents numerous mathematical and computational challenges. Indeed, uncertainties that arise in each physics in a fully coupled system must be captured throughout the whole system, the so-called curse of dimensionality. We present techniques for mitigating the curse of dimensionality in network-coupled multiphysics systems by using the structure of the network to transform uncertainty representations as they pass between components. Examples from the simulation of nuclear power plants will be discussed. [less ▲]

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See detailElements of stochastic processes 2012--2013: course material
Arnst, Maarten ULg; Dell'Elce, Lamberto ULg

Learning material (2013)

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See detailStochastic modeling in mechanics 2012--2013: course material
Arnst, Maarten ULg; Dell'Elce, Lamberto ULg

Learning material (2013)

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See detailHybrid Sampling/Spectral Method for Solving Stochastic Coupled Problems
Arnst, Maarten ULg; Soize, Christian; Ghanem, Roger

in SIAM/ASA Journal on Uncertainty Quantification (2013), 1(1), 218-243

In this paper, we present a hybrid method that combines Monte Carlo sampling and spectral methods for solving stochastic coupled problems. After partitioning the stochastic coupled problem into subsidiary ... [more ▼]

In this paper, we present a hybrid method that combines Monte Carlo sampling and spectral methods for solving stochastic coupled problems. After partitioning the stochastic coupled problem into subsidiary subproblems, the proposed hybrid method entails iterating between these subproblems in a way that enables the use of the Monte Carlo sampling method for subproblems that depend on a very large number of uncertain parameters and the use of spectral methods for subproblems that depend on only a small or moderate number of uncertain parameters. To facilitate communication between the subproblems, the proposed hybrid method shares between the subproblems a reference representation of all the solution random variables in the form of an ensemble of samples; for each subproblem solved by a spectral method, it uses a dimension-reduction technique to transform this reference representation into a subproblem-specific reduced-dimensional representation to facilitate a computationally efficient solution in a reduced-dimensional space. After laying out the theoretical framework, we provide an example relevant to microelectomechanical systems. [less ▲]

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See detailMeasure transformation and efficient quadrature in reduced-dimensional stochastic modeling of coupled problems
Arnst, Maarten ULg; Ghanem, Roger; Phipps, Eric et al

in International Journal for Numerical Methods in Engineering (2012), 92

Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of ... [more ▼]

Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled numerical models is to facilitate the communication of information across physics, scale, and domain interfaces, as well as between the iterations of solvers used for response computations. In a probabilistic context, any information that is to be communicated between subproblems or iterations should be characterized by an appropriate probabilistic representation. Although the number of sources of uncertainty can be expected to be large in most coupled problems, our contention is that exchanged probabilistic information often resides in a considerably lower-dimensional space than the sources themselves. In this work, we thus propose to use a dimension reduction technique for obtaining the representation of the exchanged information, and we propose a measure transformation technique that allows subproblem implementations to exploit this dimension reduction to achieve computational gains. The effectiveness of the proposed dimension reduction and measure transformation methodology is demonstrated through a multiphysics problem relevant to nuclear engineering. [less ▲]

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See detailDimension reduction in stochastic modeling of coupled problems
Arnst, Maarten ULg; Ghanem, Roger; Phipps, Eric et al

in International Journal for Numerical Methods in Engineering (2012), 92

Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of ... [more ▼]

Coupled problems with various combinations of multiple physics, scales, and domains are found in numerous areas of science and engineering. A key challenge in the formulation and implementation of corresponding coupled numerical models is to facilitate the communication of information across physics, scale, and domain interfaces, as well as between the iterations of solvers used for response computations. In a probabilistic context, any information that is to be communicated between subproblems or iterations should be characterized by an appropriate probabilistic representation. Although the number of sources of uncertainty can be expected to be large in most coupled problems, our contention is that exchanged probabilistic information often resides in a considerably lower dimensional space than the sources themselves. This work thus presents an investigation into the characterization of the exchanged information by a reduced-dimensional representation and in particular by an adaptation of the Karhunen-Loève decomposition. The effectiveness of the proposed dimension–reduction methodology is analyzed and demonstrated through a multiphysics problem relevant to nuclear engineering. [less ▲]

Detailed reference viewed: 36 (13 ULg)
See detailStochastic Dimension Reduction Techniques for Uncertainty Quantification of Multiphysics Systems
Phipps, Eric; Arnst, Maarten ULg; Constantine, Paul et al

Conference (2012, April 02)

Uncertainty quantification of multiphysics systems represents numerous mathematical and computational challenges. Indeed, uncertainties that arise in each physics in a fully coupled system must be ... [more ▼]

Uncertainty quantification of multiphysics systems represents numerous mathematical and computational challenges. Indeed, uncertainties that arise in each physics in a fully coupled system must be captured throughout the whole system, the so-called curse of dimensionality. We present techniques for mitigating the curse of dimensionality in network-coupled multiphysics systems by using the structure of the network to transform uncertainty representations as they pass between components. Examples from the simulation of nuclear power plants will be discussed. [less ▲]

Detailed reference viewed: 42 (7 ULg)
See detailDimension Reduction and Measure Transformation in Stochastic Multiphysics Modeling
Arnst, Maarten ULg; Ghanem, Roger; Phipps, Eric et al

Conference (2012, April 02)

We present a computational framework based on stochastic expansion methods for the efficient propagation of uncertainties through multiphysics models. The framework leverages an adaptation of the Karhunen ... [more ▼]

We present a computational framework based on stochastic expansion methods for the efficient propagation of uncertainties through multiphysics models. The framework leverages an adaptation of the Karhunen-Loeve decomposition to extract a low-dimensional representation of information passed from component to component in a stochastic coupled model. After a measure transformation, the reduced-dimensional interface thus created enables a more efficient solution in a reduced-dimensional space. We demonstrate the proposed approach on an illustration problem from nuclear engineering [less ▲]

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See detailDimension Reduction and Measure Transformation in Stochastic Analysis of Coupled Systems
Arnst, Maarten ULg; Ghanem, Roger; Phipps, Eric et al

Scientific conference (2011, September 29)

Detailed reference viewed: 36 (9 ULg)
See detailDimension Reduction and Measure Transformation in Stochastic Simulations of Coupled Systems
Arnst, Maarten ULg; Ghanem, Roger; Phipps, Eric et al

Conference (2011, July 25)

Detailed reference viewed: 19 (1 ULg)
See detailUncertain Handshaking for Coupled Physics
Phipps, Eric; Arnst, Maarten ULg; Red-Horse, John et al

Conference (2011, July 18)

Detailed reference viewed: 26 (3 ULg)