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The Extended Kalman Filter (EKF ... [more ▼]The work concerns the observability problem” --- the reconstruction of a dynamic process's full state from a partially measured state--- for nonlinear dynamic systems. The Extended Kalman Filter (EKF) is a widely-used observer for such nonlinear systems. However it suffers from a lack of theoretical justifications and displays poor performance when the estimated state is far from the real state, e.g. due to large perturbations, a poor initial state estimate, etc… We propose a solution to these problems, the Adaptive High-Gain (EKF). Observability theory reveals the existence of special representations characterizing nonlinear systems having the observability property. Such representations are called observability normal forms. A EKF variant based on the usage of a single scalar parameter, combined with an observability normal form, leads to an observer, the High-Gain EKF, with improved performance when the estimated state is far from the actual state. Its convergence for any initial estimated state is proven. Unfortunately, and contrary to the EKF, this latter observer is very sensitive to measurement noise. Our observer combines the behaviors of the EKF and of the high-gain EKF. Our aim is to take advantage of both efficiency with respect to noise smoothing and reactivity to large estimation errors. In order to achieve this, the parameter that is the heart of the high-gain technique is made adaptive. \textit{Voila}, the Adaptive High-Gain EKF. A measure of the quality of the estimation is needed in order to drive the adaptation. We propose such an index and prove the relevance of its usage. We provide a proof of convergence for the resulting observer, and the final algorithm is demonstrated via both simulations and a real-time implementation. Finally, extensions to multiple output and to continuous-discrete systems are given. [less ▲]Detailed reference viewed: 120 (9 UL) An adaptive high-gain observer for nonlinear systemsBoizot, Nicolas ; Busvelle, Eric; Gauthier, Jean-Paulin Automatica (2010), 46(9), 1483-1488In this paper the authors provide a solution to the noise sensitivity of high-gain observers. The resulting nonlinear observer possesses simultaneously 1) extended Kalman filter's good noise filtering ... [more ▼]In this paper the authors provide a solution to the noise sensitivity of high-gain observers. The resulting nonlinear observer possesses simultaneously 1) extended Kalman filter's good noise filtering properties, and 2) the reactivity of the high-gain extended Kalman filter with respect to large perturbations. The authors introduce innovation as the quantity that drives the gain adaptation. They prove a general convergence result, propose guidelines to practical implementation and show simulation results for an example. [less ▲]Detailed reference viewed: 221 (1 UL) Adaptive Isogeometric analysis for plate vibrations: An efficient approach of local refinement based on hierarchical a posteriori error estimationYu, Peng; Anitescu, Cosmin; Tomar, Satyendra et alin Computer Methods in Applied Mechanics and Engineering (2018), 342This paper presents a novel methodology of local adaptivity for the frequency-domain analysis of the vibrations of Reissner–Mindlin plates. The adaptive discretization is based on the recently developed ... [more ▼]This paper presents a novel methodology of local adaptivity for the frequency-domain analysis of the vibrations of Reissner–Mindlin plates. The adaptive discretization is based on the recently developed Geometry Independent Field approximaTion (GIFT) framework, which may be seen as a generalization of the Iso-Geometric Analysis (IGA).Within the GIFT framework, we describe the geometry of the structure exactly with NURBS (Non-Uniform Rational B-Splines), whilst independently employing Polynomial splines over Hierarchical T-meshes (PHT)-splines to represent the solution field. The proposed strategy of local adaptivity, wherein a posteriori error estimators are computed based on inexpensive hierarchical h-refinement, aims to control the discretization error within a frequency band. The approach sweeps from lower to higher frequencies, refining the mesh appropriately so that each of the free vibration mode within the targeted frequency band is sufficiently resolved. Through several numerical examples, we show that the GIFT framework is a powerful and versatile tool to perform local adaptivity in structural dynamics. We also show that the proposed adaptive local h-refinement scheme allows us to achieve significantly faster convergence rates than a uniform h-refinement. [less ▲]Detailed reference viewed: 165 (5 UL) Adaptive multiscale simulation of material failure: applications to molecular-dynamics/continuum coupling, polycrystalline materials and Hydrogen cutting of Silicon wafersBordas, Stéphane ; Kerfriden, PierreSpeeches/Talks (2014)Detailed reference viewed: 387 (3 UL) Eine adaptive Produktentwicklungsmethodik als Beitrag zur Prozessgestaltung in der ProduktentwicklungMeißner, Moritz; Gericke, Kilian ; Gries, Bruno et alin Proceedings of 16th Symposium Design for X (2005)In den letzen Jahrzehnten ist eine Vielzahl von Modellen zur methodischen Unterstützung des Produktentwicklungsprozesses (PEP) entstanden. Diese präskriptiven Modelle beinhalten oft den impliziten ... [more ▼]In den letzen Jahrzehnten ist eine Vielzahl von Modellen zur methodischen Unterstützung des Produktentwicklungsprozesses (PEP) entstanden. Diese präskriptiven Modelle beinhalten oft den impliziten Anspruch, in jeder Branche und auf die Entwicklung jeder Art von Produkten anwendbar zu sein. Um dem gerecht zu werden, beschreiben die Modelle den PEP auf einem relativ abstrakten Niveau. Eine Anpassung an den Kontext der Produktentwicklung erfolgt in der Regel nicht. Existierende Ansätze ermöglichen eine Analyse des Kontexts aus verschiedenen Blickwinkeln, bieten jedoch keine konkreten Vorschläge, wie diese Analyse in den Prozess der Produktentwicklung einfließen kann. Welche Auswirkungen ausgewählte Kontextfaktoren auf tatsächliche PEP haben, geht aus einer schriftlichen Befragung von 1000 deutschen Unternehmen des produzierenden Gewerbes hervor. Es werden die Grundlagen einer Vorgehensweise beschrieben, welche basierend auf dem Kontext der Produktentwicklung die Gestaltung effektiver, effizienter, transparenter und methodisch unterstützter Produktentwicklungsprozesse ermöglichen soll. [less ▲]Detailed reference viewed: 141 (0 UL) An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary orderNguyen-Xuan, H.; Liu, G. R.; Bordas, Stéphane et alin Computer Methods in Applied Mechanics and Engineering (2013), 253This paper presents a singular edge-based smoothed finite element method (sES-FEM) for mechanics problems with singular stress fields of arbitrary order. The sES-FEM uses a basic mesh of three-noded ... [more ▼]This paper presents a singular edge-based smoothed finite element method (sES-FEM) for mechanics problems with singular stress fields of arbitrary order. The sES-FEM uses a basic mesh of three-noded linear triangular (T3) elements and a special layer of five-noded singular triangular elements (sT5) connected to the singular-point of the stress field. The sT5 element has an additional node on each of the two edges connected to the singular-point. It allows us to represent simple and efficient enrichment with desired terms for the displacement field near the singular-point with the satisfaction of partition-of-unity property. The stiffness matrix of the discretized system is then obtained using the assumed displacement values (not the derivatives) over smoothing domains associated with the edges of elements. An adaptive procedure for the sES-FEM is proposed to enhance the quality of the solution with minimized number of nodes. Several numerical examples are provided to validate the reliability of the present sES-FEM method. © 2012 Elsevier B.V. [less ▲]Detailed reference viewed: 395 (8 UL) Adaptive smoothed stable extended finite element method for weak discontinuities for finite elasticityJansari, Chintan; Natarajan, Sundararajan; Beex, Lars et alin European Journal of Mechanics. A, Solids (2019), 78In this paper, we propose a smoothed stable extended finite element method (S2XFEM) by combining the strain smoothing with the stable extended finite element method (SXFEM) to efficiently treat inclusions ... [more ▼]In this paper, we propose a smoothed stable extended finite element method (S2XFEM) by combining the strain smoothing with the stable extended finite element method (SXFEM) to efficiently treat inclusions and/or voids in hyperelastic matrix materials. The interface geometries are implicitly represented through level sets and a geometry based error indicator is used to resolve the geometry. For the unknown fields, the mesh is refined based on a recovery based error indicator combined with a quadtree decomposition guarantee the method’s accuracy with respect to the computational costs. Elements with hanging nodes (due to the quadtree meshes) are treated as polygonal elements with mean value coordinates as the basis functions. The accuracy and the convergence properties are compared to similar approaches for several numerical examples. The examples indicate that S2XFEM is computationally the most efficient without compromising the accuracy. [less ▲]Detailed reference viewed: 75 (0 UL) Adaptive support domain implementation on the Moving Least Squares approximation for Mfree methods applied on elliptic and parabolic PDE problems using strong-form descriptionBourantas, Georgios ; Skouras, Eugene; Nikiforidis, Georgein Computer Modeling in Engineering and Sciences (2009), 43The extent of application of meshfree methods based on point collocation (PC) techniques with adaptive support domain for strong form Partial Differential Equations (PDE) is investigated. The basis ... [more ▼]The extent of application of meshfree methods based on point collocation (PC) techniques with adaptive support domain for strong form Partial Differential Equations (PDE) is investigated. The basis functions are constructed using the Moving Least Square (MLS) approximation. The weak-form description of PDEs is used in most MLS methods to circumvent problems related to the increased level of resolution necessary near natural (Neumann) boundary conditions (BCs), dislocations, or regions of steep gradients. Alternatively, one can adopt Radial Basis Function (RBF) approximation on the strong-form of PDEs using meshless PC methods, due to the delta function behavior (exact solution on nodes). The present approach is one of the few successful attempts of using MLS approximation [Atluri, Liu, and Han (2006), Han, Liu, Rajendran and Atluri (2006), Atluri and Liu (2006)] instead of RBF approximation for the meshless PC method using strong-form description. To increase the accuracy of the MLS interpolation method and its robustness in problems with natural BCs, a suitable support domain should be chosen in order to ensure an optimized area of coverage for interpolation. To this end, the basis functions are constructed using two different approaches, pertinent to the dimension of the support domain. On one hand, a compact form for the support domain is retained by keeping its radius constant. On the other hand, one can control the number of neighboring nodes as the support domain of each point. The results show that some inaccuracies are present near the boundaries using the first approach, due to the limited number of nodes belonging to the support domain, which results in failed matrix inversion. Instead, the second approach offers capability for fully matrix inversion under many (if not all) circumstances, resulting in basis functions of increased accuracy and robustness. This PC method, applied along with an intelligent adaptive refinement, is demonstrated for elliptic and for parabolic PDEs, related to many flow and mass transfer problems. [less ▲]Detailed reference viewed: 180 (5 UL) An adaptive variational Quasicontinuum methodology for lattice networks with localized damageRokos, Ondrej; Peerlings, Ron; Zeman, Jan et alin International Journal for Numerical Methods in Engineering (2017), 112(2), Lattice networks with dissipative interactions can be used to describe the mechanics of discrete meso‐structures of materials such as 3D‐printed structures and foams. This contribution deals with the ... [more ▼]Lattice networks with dissipative interactions can be used to describe the mechanics of discrete meso‐structures of materials such as 3D‐printed structures and foams. This contribution deals with the crack initiation and propagation in such materials and focuses on an adaptive multiscale approach that captures the spatially evolving fracture. Lattice networks naturally incorporate non‐locality, large deformations and dissipative mechanisms taking place inside fracture zones. Because the physically relevant length scales are significantly larger than those of individual interactions, discrete models are computationally expensive. The Quasicontinuum (QC) method is a multiscale approach specifically constructed for discrete models. This method reduces the computational cost by fully resolving the underlying lattice only in regions of interest, while coarsening elsewhere. In this contribution, the (variational) QC is applied to damageable lattices for engineering‐scale predictions. To deal with the spatially evolving fracture zone, an adaptive scheme is proposed. Implications induced by the adaptive procedure are discussed from the energy‐consistency point of view, and theoretical considerations are demonstrated on two examples. The first one serves as a proof of concept, illustrates the consistency of the adaptive schemes and presents errors in energies. The second one demonstrates the performance of the adaptive QC scheme for a more complex problem. [less ▲]Detailed reference viewed: 146 (3 UL) Adaptive-gain Extended Kalman Filter: Extension to the Continuous-discrete CaseBoizot, Nicolas ; Busvelle, Eric; Gauthier, Jean-PaulScientific Conference (2009)In the present article we propose a nonlinear observer that merges the behaviors 1) of an extended Kalman filter, mainly designed to smooth off noise , and 2) of high-gain observers devoted to handle ... [more ▼]In the present article we propose a nonlinear observer that merges the behaviors 1) of an extended Kalman filter, mainly designed to smooth off noise , and 2) of high-gain observers devoted to handle large perturbations in the state estimation. We specifically aim at continuous-discrete systems. The strategy consists in letting the high-gain self adapt according to the innovation. We define innovation computed over a time window and justify its usage via an important lemma. We prove the general convergence of the resulting observer. [less ▲]Detailed reference viewed: 134 (0 UL) Addressing volumetric locking and instabilities by selective integration in smoothed finite elementsHung, Nguyen-Xuan; Bordas, Stéphane ; Hung, Nguyen-Dangin Communications in Numerical Methods in Engineering (2009), 25(1), 19-34This paper promotes the development of a novel family of finite elements with smoothed strains, offering remarkable properties. In the smoothed finite element method (FEM), elements are divided into ... [more ▼]This paper promotes the development of a novel family of finite elements with smoothed strains, offering remarkable properties. In the smoothed finite element method (FEM), elements are divided into subcells. The strain at a point is defined as a weighted average of the standard strain field over a representative domain. This yields superconvergent stresses, both in regular and singular settings, as well as increased accuracy, with slightly lower computational cost than the standard FEM. The one-subcell version that does not exhibit volumetric locking yields more accurate stresses but less accurate displacements and is equivalent to a quasi-equilibrium FEM. It is also subject to instabilities. In the limit where the number of subcells goes to infinity, the standard FEM is recovered, which yields more accurate displacements and less accurate stresses. The specific contribution of this paper is to show that expressing the volumetric part of the strain field using a one-subcell formulation is sufficient to get rid of volumetric locking and increase the displacement accuracy compared with the standard FEM when the single subcell version is used to express both the volumetric and deviatoric parts of the strain. Selective integration also alleviates instabilities associated with the single subcell element, which are due to rank deficiency. Numerical examples on various compressible and incompressible linear elastic test cases show that high accuracy is retained compared with the standard FEM without increasing computational cost. [less ▲]Detailed reference viewed: 120 (0 UL) Advances in Applied MechanicsBordas, Stéphane Book published by Elsevier (2014)Advances in Applied Mechanics draws together recent significant advances in various topics in applied mechanics. Published since 1948, Advances in Applied Mechanics aims to provide authoritative review ... [more ▼]Advances in Applied Mechanics draws together recent significant advances in various topics in applied mechanics. Published since 1948, Advances in Applied Mechanics aims to provide authoritative review articles on topics in the mechanical sciences, primarily of interest to scientists and engineers working in the various branches of mechanics, but also of interest to the many who use the results of investigations in mechanics in various application areas, such as aerospace, chemical, civil, environmental, mechanical and nuclear engineering. [less ▲]Detailed reference viewed: 1118 (47 UL) Advances in enriched finite element formulations for fracture and cutting: engineering and surgical simulation applicationsBordas, Stéphane Scientific Conference (2017, June 21)Detailed reference viewed: 647 (20 UL) Advances in error estimation for homogenisationAlves Paladim, Daniel; Kerfriden, Pierre; Moitinho de Almeida, José Paulo et alin 13th U.S. National Congress on Computational Mechanics (2015, July)In this paper, the concept of modeling error is extended to the homogenisation of elliptic PDEs. The main difficulty is the lack of a full description of the diffusion coefficients. We overcome this ... [more ▼]In this paper, the concept of modeling error is extended to the homogenisation of elliptic PDEs. The main difficulty is the lack of a full description of the diffusion coefficients. We overcome this obstacle by representing them as a random a field. Under this framework, it is possible to quantify the accuracy of the surrogate model (the homogenised model) in terms of first moments of the energy norm and quantities of interest. This work builds on the seminal work of [1]. The methodology here presented rely on the Constitutive Relation Error (CRE) which states that a certain measures of the primal and dual surrogate model upper bound the exact error. The surrogate model, in agreement with homogenisation, is deterministic. This property exploited to obtain bounds whose computation is also deterministic. It is also shown that minimising the CRE in the set of homogenisation schemes leads us to an optimal surrogate that is closely related to the classical Voigt and Reuss models. Numerical examples demonstrate that the bounds are easy and affordable to compute, and useful as long as the mismatch between he diffusion coefficients of the microstructure remain small. In the case of high mismatch, extensions are proposed, through the introduction of stochastic surrogate models.. [1]Romkes, Albert, J. Tinsley Oden, and Kumar Vemaganti."Multi-scale goal-oriented adaptive modeling of random heterogeneous materials." Mechanics of materials 38.8(2006): 859-872. [less ▲]Detailed reference viewed: 122 (5 UL) ADVANCES IN GEOMETRY INDEPENDENT APPROXIMATIONSAnitescu, Cosmin; Atroshchenko, Elena; Bordas, Stéphane et alScientific Conference (2019, April 11)We present recent advances in geometry independent field approximations. The GIFT approach is a generalisation of isogeometric analysis where the approximation used to describe the field variables no ... [more ▼]We present recent advances in geometry independent field approximations. The GIFT approach is a generalisation of isogeometric analysis where the approximation used to describe the field variables no-longer has to be identical to the approximation used to describe the geometry of the domain. As such, the geometry can be described using usual CAD representations, e.g. NURBS, which are the most common in the CAD area, whilst local refinement and meshes approximations can be used to describe the field variables, enabling local adaptivity. We show in which cases the approach passes the patch test and present applications to various mechanics, fracture and multi-physics problems. [less ▲]Detailed reference viewed: 333 (25 UL) Against mass media trends: Minority growth in cultural globalizationCosenza, M. G.; Gavidia, Marino ; Gonzalez-Avella, J. C.in PLoS ONE (2020)We investigate the collective behavior of a globalized society under the influence of endogenous mass media trends. The mass media trend is a global field corresponding to the statistical mode of the ... [more ▼]We investigate the collective behavior of a globalized society under the influence of endogenous mass media trends. The mass media trend is a global field corresponding to the statistical mode of the states of the agents in the system. The interaction dynamics is based on Axelrod’s rules for the dissemination of culture. We find situations where the largest minority group, possessing a cultural state different from that of the predominant trend transmitted by the mass media, can grow to almost half of the size of the population. We show that this phenomenon occurs when a critical number of long-range connections are present in the underlying network of interactions. We have numerically characterized four phases on the space of parameters of the system: an ordered phase; a semi-ordered phase where almost half of the population consists of the largest minority in a state different from that of the mass media; a disordered phase; and a chimera-like phase where one large domain coexists with many very small domains. [less ▲]Detailed reference viewed: 197 (14 UL) An agenda for establishing the Ecological Footprint as communication instrument and indicator for sustainable development in small countries: Case study LuxembourgHild, Paula ; Schmitt, Bianca; Morgane, Mey et alPoster (2010, June)The Ecological Footprint methodology proposed by the Global Footprint Network (GFN) seems to be not entirely appropriate for small countries with less than one million inhabitants [Ewing et al., 2008 ... [more ▼]The Ecological Footprint methodology proposed by the Global Footprint Network (GFN) seems to be not entirely appropriate for small countries with less than one million inhabitants [Ewing et al., 2008]. This may be a reason why e.g. results for Luxembourg, a country with 470,000 inhabitants, have never been included into official country Footprint comparisons. Therefore, the methodology needs to be adapted to be used for communication purpose in Luxembourg. This contribution presents Luxembourg’s approach for illustrating the national consumption impacts to finally discuss the integration of the Ecological Footprint as an indicator for sustainable development in the national indicator system. [less ▲]Detailed reference viewed: 103 (2 UL) Agent-based Model of Initial Token Allocations: Evaluating Wealth Concentration in Fair LaunchesDelgado Fernandez, Joaquin ; Barbereau, Tom Josua ; Papageorgiou, Orestis E-print/Working paper (2022)With advancements in distributed ledger technologies and smart contracts, tokenized voting rights gained prominence within Decentralized Finance (DeFi). Voting rights tokens (aka. governance tokens) are ... [more ▼]With advancements in distributed ledger technologies and smart contracts, tokenized voting rights gained prominence within Decentralized Finance (DeFi). Voting rights tokens (aka. governance tokens) are fungible tokens that grant individual holders the right to vote upon the fate of a project. The motivation behind these tokens is to achieve decentral control. Because the initial allocations of these tokens is often un-democratic, the DeFi project Yearn Finance experimented with a fair launch allocation where no tokens are pre-mined and all participants have an equal opportunity to receive them. Regardless, research on voting rights tokens highlights the formation of oligarchies over time. The hypothesis is that the tokens' tradability is the cause of concentration. To examine this proposition, this paper uses an Agent-based Model to simulate and analyze the concentration of voting rights tokens post fair launch under different trading modalities. It serves to examine three distinct token allocation scenarios considered as fair. The results show that regardless of the allocation, concentration persistently occurs. It confirms the hypothesis that the disease is endogenous: the cause of concentration is the tokens tradablility. The findings inform theoretical understandings and practical implications for on-chain governance mediated by tokens. [less ▲]Detailed reference viewed: 114 (13 UL) Agentenbasierte, hybride Steuerungsarchitektur für cyberphysische RefabrikationssystemeGroß, Sebastian ; Gerke, Wolfgang; Plapper, Peter in Jäkel, Jens; Thiel, Robert (Eds.) Tagungsband AALE 2020 Automatisierung und Mensch-Technik-Interaktion (2020, March 05)Detailed reference viewed: 98 (3 UL)