Overview of Inverse Problems

Introduction - Definitions Areas of Use - Historical Development Different Approaches to Solving Inverse Problems Functional analysis Regularization of Ill-Posed Problems Stochastic or Bayesian Inversion . . . . . . . . . . . . . . . . . ConclusionDE

Modal identification of linear non-proportionally damped systems by wavelet transform

International audienceA time-frequency identification technique based on wavelet transform is formulated and applied to free-decay responses of linear systems with non-proportional viscous damping. The Cauchy mother wavelet is used. Frequencies, modal damping ratios and complex mode shapes are identified from output-only free vibration signals. This identification technique has also shown to be effective when the (non-proportional) damping is significant

Nonlinear argumental oscillators: Stability criterion and attractor's capture probability

The behaviour of a space-modulated, so-called " argumental " oscillator is studied, which is represented by a model having an even-parity space-modulating function. Analytic expressions of a stability criterion and of discrete energy levels are given. Using an integrating factor and a Van der Pol representation in the (amplitude, phase) space, an approximate implicit closed-form of the solution is given. The probability to enter a stable-oscillation regime from given initial conditions is calculated in symbolic form. These results allow an analytic approach to stability and bifurcations of the system. They also allow an assessment of the risk of occurrence of sustained large-amplitude oscillations, when the phenomenon is to be avoided, and an assessment of the conditions to apply to obtain oscillations whenever the phenomenon is desired

On the use of continuous wavelet analysis for modal identification

This paper reviews two different uses of the continuous wavelet transform for modal identification purposes. The properties of the wavelet transform, mainly energetic, allow to emphasize or filter the main information within measured signals and thus facilitate the modal parameter identification especially when mechanical systems exhibit modal coupling and/or relatively strong damping

Optimisation des amortisseurs à masse accordée placés en parallèle

Les amortisseurs à masse accordée (AMA), (" Tuned Mass Dampers " en anglais) sont de nos jours très souvent utilisés pour le contrôle passif des vibrations de bâtiments et d'ouvrages d'art comme par exemple, le gratte-ciel du centre mondial des finances de Shanghai (492 m) ou la passerelle du Millenium à Londres. Un AMA consiste en une masse liée à un niveau de la structure par l'intermédiaire d'un ressort et d'un d'amortisseur linéaires

Lateral vibration of footbridges under crowd-loading: Continuous crowd modeling approach

International audienceIn this paper, a simple 1D crowd model is proposed, which aim is to properly describe the crowd-flow phenomena occurring when pedestrians walk on a flexible footbridge. The crowd is assumed to behave like a continuous compressible fluid and the pedestrian flow is modeled in a 1-D framework using the (total) mass (of pedestrians) conservation equation. This crowd model is then coupled with a simple model for the dynamical behavior of the footbridge and an optimized modeling of synchronization effects is performed. Numerical simulations are presented to show some preliminary results

Continuous Cauchy wavelet transform of XAFS spectra.

The continuous Cauchy wavelet transform (CCWT) is applied to the analysis of XAFS spectra. Thanks to that method, XANES and EXAFS signals can be visualized in threedimension: the wavevector (k), the interatomic distance uncorrected for phase-shifts (R') and the CCWT modulus (corresponding to the continuous decomposition of the amplitude terms). Applied to EXAFS spectra, the CCWT analysis provides straightforward qualitative information related to the k-range of each “R'-EXAFS” contribution. Such information is particularly useful to perform next nearest-neighbors identification, despite the presence of spectral artifacts such as multiple-scattering features, multi-electronic excitations or noise. When applied to XANES spectra, the CCWT analysis helps highly to measure the “spectral limit” between XANES and EXAFS regions, as well as the energy range required to model properly next-nearest neighbors. To further illustrate the potential of CCWT analyses applied to XAFS spectra, we present examples related to: (1) a XANES spectrum collected at the Ti K-edge for titanite (CaTiSiO5); (2) an experimental Au LIII-edge EXAFS spectrum for gold sorbed on goethite (FeO(OH))