Adaptive high-gain extended kalman filter and applications

Doctoral thesis (2010)

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 ... [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 ▲]

Adaptive Isogeometric analysis for plate vibrations: An efficient approach of local refinement based on hierarchical a posteriori error estimation

in Computer Methods in Applied Mechanics and Engineering (2018), 342

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 ... [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 ▲]

Adaptive multiscale simulation of material failure: applications to molecular-dynamics/continuum coupling, polycrystalline materials and Hydrogen cutting of Silicon wafers

Speeches/Talks (2014)

An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order

in Computer Methods in Applied Mechanics and Engineering (2013), 253

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 ... [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 ▲]

Adaptive support domain implementation on the Moving Least Squares approximation for Mfree methods applied on elliptic and parabolic PDE problems using strong-form description

in Computer Modeling in Engineering and Sciences (2009), 43

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 ... [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 ▲]

Adaptive-gain Extended Kalman Filter: Extension to the Continuous-discrete Case

Scientific 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 ▲]

Advances in Applied Mechanics

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 ▲]

Advances in error estimation for homogenisation

in 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 ▲]

Against mass media trends: Minority growth in cultural globalization

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 ▲]

Agent-based Model of Initial Token Allocations: Evaluating Wealth Concentration in Fair Launches

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 ▲]