Relevant bibliographies by topics / Dynamical Inverse Problem

Academic literature on the topic 'Dynamical Inverse Problem'

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Published: 11 March 2023

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Journal articles on the topic "Dynamical Inverse Problem"

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Khan, B. A., S. Chatterjee, S. G. Ali, and B. Talukdar. "Inverse Variational Problem for Nonlinear Dynamical Systems." Acta Physica Polonica A 141, no. 1 (January 2022): 64–73. http://dx.doi.org/10.12693/aphyspola.141.64.

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MORASSI, A., G. NAKAMURA, and M. SINI. "An inverse dynamical problem for connected beams." European Journal of Applied Mathematics 16, no. 1 (March 23, 2005): 83–109. http://dx.doi.org/10.1017/s0956792505005826.

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Avdonin, S. A., B. P. Belinskiy, and J. V. Matthews. "Dynamical inverse problem on a metric tree." Inverse Problems 27, no. 7 (June 14, 2011): 075011. http://dx.doi.org/10.1088/0266-5611/27/7/075011.

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Merritt, David. "The Dynamical Inverse Problem for Axisymmetric Stellar Systems." Astronomical Journal 112 (September 1996): 1085. http://dx.doi.org/10.1086/118080.

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Belishev, M. I. "Dynamical inverse problem for a Lamé type system." Journal of Inverse and Ill-posed Problems 14, no. 8 (December 2006): 751–66. http://dx.doi.org/10.1515/156939406779768300.

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Kharchenko, N. V. "Inverse problem of spectral analysis of conflict dynamical systems." Ukrainian Mathematical Journal 62, no. 1 (August 2010): 123–35. http://dx.doi.org/10.1007/s11253-010-0337-3.

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Baev, A. V. "Solution of the inverse dynamical seismic problem with absorption." Computational Mathematics and Modeling 4, no. 2 (1993): 122–24. http://dx.doi.org/10.1007/bf01131204.

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Federico, Salvatore, and Mawafag Alhasadi. "Inverse dynamics in rigid body mechanics." Theoretical and Applied Mechanics, no. 00 (2022): 11. http://dx.doi.org/10.2298/tam221109011f.

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Inverse Dynamics is used to calculate the forces and moments in the joints of multibody systems investigated in fields such as Biomechanics or Robotics. In a didactic spirit, this paper begins with an overview of the derivations of the kinematical and dynamical equations of rigid bodies from the point of view of modern Continuum Mechanics. Then, it introduces a matrix formulation for the solution of Inverse Dynamics problems and, finally, reports a simple two-dimensional example of application to a problem in Biomechanics.
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Chu, Moody T., and Gene H. Golub. "Structured inverse eigenvalue problems." Acta Numerica 11 (January 2002): 1–71. http://dx.doi.org/10.1017/s0962492902000016.

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An inverse eigenvalue problem concerns the reconstruction of a structured matrix from prescribed spectral data. Such an inverse problem arises in many applications where parameters of a certain physical system are to be determined from the knowledge or expectation of its dynamical behaviour. Spectral information is entailed because the dynamical behaviour is often governed by the underlying natural frequencies and normal modes. Structural stipulation is designated because the physical system is often subject to some feasibility constraints. The spectral data involved may consist of complete or only partial information on eigenvalues or eigenvectors. The structure embodied by the matrices can take many forms. The objective of an inverse eigenvalue problem is to construct a matrix that maintains both the specific structure as well as the given spectral property. In this expository paper the emphasis is to provide an overview of the vast scope of this intriguing problem, treating some of its many applications, its mathematical properties, and a variety of numerical techniques.
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Mikhaylov, Alexander, and Victor Mikhaylov. "Inverse problem for dynamical system associated with Jacobi matrices and classical moment problems." Journal of Mathematical Analysis and Applications 487, no. 1 (July 2020): 123970. http://dx.doi.org/10.1016/j.jmaa.2020.123970.

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Dissertations / Theses on the topic "Dynamical Inverse Problem"

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Rachele, Lizabeth. "An inverse problem in elastodynamics /." Thesis, Connect to this title online; UW restricted, 1996. http://hdl.handle.net/1773/5735.

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Tregidgo, Henry. "Inverse problems and control for lung dynamics." Thesis, University of Manchester, 2018. https://www.research.manchester.ac.uk/portal/en/theses/inverse-problems-and-control-for-lung-dynamics(0f3224e6-7449-4417-bd2b-8e48ec88e2bf).html.

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Mechanical ventilation is vital for the treatment of patients in respiratory intensive care and can be life saving. However, the risks of regional pressure gradients and over-distension must be balanced with the need to maintain function. For these reasons mechanical ventilation can benefit from the regional information provided by bedside imaging such as electrical impedance tomography (EIT). In this thesis we develop and test methods to retrieve clinically meaningful measures of lung function from EIT and examine the feasibility of closing the feedback loop to enable EIT-guided control of mechanical ventilation. Working towards this goal we develop a reconstruction algorithm capable of providing fast absolute values of conductivity from EIT measurements. We couple the resulting conductivity time series to a compartmental ordinary differential equation (ODE) model of lung function in order to recover regional parameters of elastance and airway resistance. We then demonstrate how these parameters may be used to generate optimised pressure controls for mechanical ventilation that expose the lungs to minimal gradients of pressure and are stable with respect to EIT measurement errors. The EIT reconstruction algorithm we develop is capable of producing low dimensional absolute values of conductivity in real time after a limited additional setup time. We show that this algorithm retains the ability to give fast feedback on regional lung changes. We also describe methods of improving computational efficiency for general Gauss-Newton type EIT algorithms. In order to couple reconstructed conductivity time series to our ODE model we describe and test the recovery of regional ventilation distributions through a process of regularised differentiation. We prove that the parameters of our ODE model are recoverable from these ventilation distributions apart from the degenerate case where all compartments have the same parameters. We then test this recovery process under varying levels of simulated EIT measurement and modelling errors. Finally we examine the ODE lung model using control theory. We prove that the ODE model is controllable for a wide range of parameter values and link controllability to observable ventilation patterns in the lungs. We demonstrate the generation and optimisation of pressure controls with minimal time gradients and provide a bound on the resulting magnitudes of these pressures. We then test the control generation process using ODE parameter values recovered through EIT simulations at varying levels of measurement noise. Through this work we have demonstrated that EIT reconstructions can be of benefit to the control of mechanical ventilation.
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Hellio, Gabrielle. "Modèles stochastiques de mesures archéomagnétiques." Thesis, Université Grenoble Alpes (ComUE), 2015. http://www.theses.fr/2015GREAU004/document.

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Cette thèse porte sur la construction de modèles stochastiques, régionaux et globaux du champ magnétique sur les quatre derniers millénaires à l'aide de mesures archéomagnétiques. Ces données présentent une répartition spatiale et temporelle très inhomogène, et sont caractérisées par de fortes incertitudes sur la mesure et sur la date. La reconstruction du champ constitue alors un problème inverse mal posé. Afin de déterminer la solution la plus adaptée, une information a priori sur le modèle doit être choisie. Elle consiste généralement en une régularisation arbitraire du champ magnétique (lissage en temps et en espace). Contrairement aux études précédentes, nous utilisons les statistiques temporelles du champ magnétique, dérivées des données d'observatoires, satellitaires et paléomagnétiques pour définir l'information a priori via des fonctions d'auto-covariances. Ces statistiques sont confirmées par des résultats issus de simulations numériques. Cette méthode bayésienne permet de s'affranchir de l'utilisation de fonctions supports arbitraires comme les splines pour l'interpolation temporelle. Le résultat final consiste en un ensemble de réalisations possibles du champ magnétique dont la dispersion caractérise l'incertitude sur le modèle. Afin de prendre en compte les erreurs de datation, nous développons par ailleurs une méthode basée sur l'utilisation de Markov Chain Monte Carlo (MCMC). Elle nous permet d'explorer de manière efficace l'espace des dates possibles et ainsi de sélectionner les modèles les plus probables. Cette méthode est une amélioration de la méthode de bootstrap classique, qui donne le même poids à des tirages aléatoires de dates présentant des probabilités très variables. Les ensembles de réalisations sélectionnés par la méthode MCMC aboutissent à la construction d'une densité de probabilités en lieu et place d'une courbe unique. La méthode bayésienne combinée à la méthode Markov Chain Monte Carlo nous a permis de construire des courbes régionales présentant des variations plus rapides que celles obtenues par d'autres études. Les courbes représentées sous forme de densités de probabilités ne sont pas nécessairement gaussiennes, et la méthode permet d'affiner l'estimation de l'âge de chacune des observations. La méthode bayésienne a été utilisée pour la construction de modèles globaux pour lesquels le dipôle axial présente des variations plus rapides que celui obtenu par de précédentes études. D'autre part, le champ magnétique obtenu pour les époques les plus récentes est raisonnablement similaire à celui construit à partir de mesures directes (satellites, observatoires, historiques) malgré des données beaucoup moins nombreuses et une répartition beaucoup moins homogène. Les modèles issus de cette étude offrent une alternative aux modèles existants régularisés, et pourront servir dans un objectif d'assimilation de données avec des modèles de la dynamique dans le noyau terrestre
The aim of this thesis is to build stochastic models of the magnetic field for the last four millenia from archeomagnetic measurements. The sparse repartition of these data in space and time, and their associated large measurement and dating errors lead to an ill-posed problem. To determine the best solution, one needs to choose some prior information which consists usually on arbitrary regularizations in space and time. Instead, we use the temporal statistics of the geomagnetic field available from satellites, observatories and paleomagnetic measurements, and validated by numerical simulations, to define our prior information via auto-covariance functions. This bayesian method allows to get rid of arbitrary support functions, like splines, usually necessary to interpolate the model in time. The result consists in an ensemble of several possible realizations of the magnetic field. The ensemble dispersion represents the model uncertainties. We find that the methodology can be adapted to account for the age uncertainties and we use Markov Chain Monte Carlo to explore the possible dates of observations. This method improves the bootstrap method which gives the same weight to every draws of dates presenting very disparate probabilities. Each ensemble of realizations is then constructed from each selected model and the result is presented as a probability density function. The bayesian method together with the Markov Chain Monte Carlo provides regional time series with rapid variations compared to previous studies. We find that the possible values of geomagnetic field elements are not necessarily normally distributed. Another output of the model is better age estimates of archeological artefacts. The bayesian method has been used to build global models for which the axial dipole presents more rapid variations than for previous studies. Moreover, the obtained magnetic field displays reasonably similar behavior than models obtained from direct measurements (satellites, observatories, historical), despite very few data and sparser repartition. Models obtained from this study offer an alternative to published regularized models and can be used in a purpose of data assimilation together with dynamical models in the Earth's core
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Lebel, David. "Statistical inverse problem in nonlinear high-speed train dynamics." Thesis, Paris Est, 2018. http://www.theses.fr/2018PESC2189/document.

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Ce travail de thèse traite du développement d'une méthode de télédiagnostique de l'état de santé des suspensions des trains à grande vitesse à partir de mesures de la réponse dynamique du train en circulation par des accéléromètres embarqués. Un train en circulation est un système dynamique dont l'excitation provient des irrégularités de la géométrie de la voie ferrée. Ses éléments de suspension jouent un rôle fondamental de sécurité et de confort. La réponse dynamique du train étant dépendante des caractéristiques mécaniques des éléments de suspension, il est possible d'obtenir en inverse des informations sur l'état de ces éléments à partir de mesures accélérométriques embarquées. Connaître l'état de santé réel des suspensions permettrait d'améliorer la maintenance des trains. D’un point de vue mathématique, la méthode de télédiagnostique proposée consiste à résoudre un problème statistique inverse. Elle s'appuie sur un modèle numérique de dynamique ferroviaire et prend en compte l'incertitude de modèle ainsi que les erreurs de mesures. Les paramètres mécaniques associés aux éléments de suspension sont identifiés par calibration Bayésienne à partir de mesures simultanées des entrées (les irrégularités de la géométrie de la voie) et sorties (la réponse dynamique du train) du système. La calibration Bayésienne classique implique le calcul de la fonction de vraisemblance à partir du modèle stochastique de réponse et des données expérimentales. Le modèle numérique étant numériquement coûteux d'une part, ses entrées et sorties étant fonctionnelles d'autre part, une méthode de calibration Bayésienne originale est proposée. Elle utilise un métamodèle par processus Gaussien de la fonction de vraisemblance. Cette thèse présente comment un métamodèle aléatoire peut être utilisé pour estimer la loi de probabilité des paramètres du modèle. La méthode proposée permet la prise en compte du nouveau type d'incertitude induit par l'utilisation d'un métamodèle. Cette prise en compte est nécessaire pour une estimation correcte de la précision de la calibration. La nouvelle méthode de calibration Bayésienne a été testée sur le cas applicatif ferroviaire, et a produit des résultats concluants. La validation a été faite par expériences numériques. Par ailleurs, l'évolution à long terme des paramètres mécaniques de suspensions a été étudiée à partir de mesures réelles de la réponse dynamique du train
The work presented here deals with the development of a health-state monitoring method for high-speed train suspensions using in-service measurements of the train dynamical response by embedded acceleration sensors. A rolling train is a dynamical system excited by the track-geometry irregularities. The suspension elements play a key role for the ride safety and comfort. The train dynamical response being dependent on the suspensions mechanical characteristics, information about the suspensions state can be inferred from acceleration measurements in the train by embedded sensors. This information about the actual suspensions state would allow for providing a more efficient train maintenance. Mathematically, the proposed monitoring solution consists in solving a statistical inverse problem. It is based on a train-dynamics computational model, and takes into account the model uncertainty and the measurement errors. A Bayesian calibration approach is adopted to identify the probability distribution of the mechanical parameters of the suspension elements from joint measurements of the system input (the track-geometry irregularities) and output (the train dynamical response).Classical Bayesian calibration implies the computation of the likelihood function using the stochastic model of the system output and experimental data. To cope with the fact that each run of the computational model is numerically expensive, and because of the functional nature of the system input and output, a novel Bayesian calibration method using a Gaussian-process surrogate model of the likelihood function is proposed. This thesis presents how such a random surrogate model can be used to estimate the probability distribution of the model parameters. The proposed method allows for taking into account the new type of uncertainty induced by the use of a surrogate model, which is necessary to correctly assess the calibration accuracy. The novel Bayesian calibration method has been tested on the railway application and has achieved conclusive results. Numerical experiments were used for validation. The long-term evolution of the suspension mechanical parameters has been studied using actual measurements of the train dynamical response
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Lyubchyk, Leonid, and Galina Grinberg. "Inverse Dynamic Models in Chaotic Systems Identification and Control Problems." Thesis, Ternopil National Economic University, 2018. http://repository.kpi.kharkov.ua/handle/KhPI-Press/36824.

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Inverse dynamic models approach for chaotic system synchronization in the presence of uncertain parameters is considered. The problem is identifying and compensating unknown state-dependent parametric disturbance describing an unmodelled dynamics that generates chaotic motion. Based on the method of inverse model control, disturbance observers and compensators are synthesized. A control law is proposed that ensures the stabilization of chaotic system movement along master reference trajectory. The results of computational simulation of controlled Rösller attractor synchronization are also presented.
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Sehlstedt, Niklas. "Hybrid methods for inverse force estimation in structural dynamics." Doctoral thesis, KTH, Vehicle Engineering, 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3528.

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Herman, Michael [Verfasser], and Wolfram [Akademischer Betreuer] Burgard. "Simultaneous estimation of rewards and dynamics in inverse reinforcement learning problems." Freiburg : Universität, 2020. http://d-nb.info/1204003297/34.

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Lefeuvre, Thibault. "Sur la rigidité des variétés riemanniennes." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLS562/document.

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Une variété riemannienne est dite rigide lorsque la longueur des géodésiques périodiques (cas des variétés fermées) ou des géodésiques diffusées (cas des variétés ouvertes) permet de reconstruire globalement la géométrie de la variété. Cette notion trouve naturellement son origine dans des dispositifs d’imagerie numérique tels que la tomographie par rayons X. Grâce une approche résolument analytique initiée par Guillarmou et fondée sur de l’analyse microlocale (plus particulièrement sur certaines techniques récentes dues à Faure-Sjostrand et Dyatlov-Zworski permettant une étude analytique fine des flots Anosov), nous montrons que le spectre marqué des longueurs, c’est-à-dire la donnée des longueurs des géodésiques périodiques marquées par l’homotopie, d’une variété fermée Anosov ou Anosov à pointes hyperboliques détermine localement la métrique de la variété. Dans le cas d’une variété ouverte avec ensemble capté hyperbolique, nous montrons que la distance marquée au bord, c’est-à-dire la donnée de la longueur des géodésiques diffusées marquées par l’homotopie, détermine localement la métrique. Enfin, dans le cas d’une surface asymptotiquement hyperbolique, nous montrons qu’une notion de distance renormalisée entre paire de points au bord à l’infini permet de reconstruire globalement la géométrie de la surface
A Riemannian manifold is said to be rigid if the length of periodic geodesics (in the case of a closed manifold) or scattered geodesics (in the case of an open manifold) allows to recover the full geometry of the manifold. This notion naturally arises in imaging devices such as X-ray tomography. Thanks to a analytic framework introduced by Guillarmou and based on microlocal analysis (and more precisely on the analytic study of hyperbolic flows of Faure-Sjostrand and Dyatlov-Zworski), we show that the marked length spectrum, that is the lengths of the periodic geodesics marked by homotopy, of a closed Anosov manifold or of an Anosov manifold with hyperbolic cusps locally determines its metric. In the case of an open manifold with hyperbolic trapped set, we show that the length of the scattered geodesics marked by homotopy locally determines the metric. Eventually, in the case of an asymptotically hyperbolic surface, we show that a suitable notion of renormalized distance between pair of points on the boundary at infinity allows to globally reconstruct the geometry of the surface
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Simon, Guillaume. "Endogeneity and instrumental variables in dynamic processes : inverse problems in finance." Thesis, Toulouse 1, 2011. http://www.theses.fr/2011TOU10061.

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L’objectif de ma thèse est de fournir un environnement théorique pour la définition de l’endogénéité dans les processus en temps continu. La définition de l’endogénéité dans le cas statique est difficile, l’enjeu de ce travail est donc de voir quelles sont les implications et le cadre mathématique nécessaire pour définir l’endogénéité pour les processus. C’est l’objet du premier chapitre. On donne d’abord une extension des modèles séparables en termes de décomposition en semi-martingale. Pour les modèles non-séparables, on définit alors notre fonction d’intérêt comme un temps d’arrêt pour un processus de bruit additionnel, dont le rôle est joué par un mouvement Brownien pour les diffusions, et un processus de Poisson pour les processus de comptage. Ce travail a été mené dans le cadre d’un thèse CIFRE avec Société Générale Asset Management (devenue désormais Lyxor AM). SGAM était un fonds spéculatif (Hedge Fund) pour lequel le traitement de l’information présente dans les bases de données est un problème constant et difficile. De fait, comprendre la nature des processus sous-jacents aux durées de vie des Hedge Funds dans les bases de données est essentiel, c’est ce à quoi s’attache le second chapitre. Le troisième chapitre apporte une réponse claire à une problématique peu ou pas traitée (l’effet causal de certaines variables endogènes sur la durée de vie des fonds) à l’aide des conclusions du deuxième chapitre et des résultats du premier. Enfin, comme la résolution de tels problèmes nécessite de faire appel à la théorie des problèmes inverses, une application originale de cette théorie est aussi considérée pour l’allocation de portefeuille dans le dernier chapitre
The objective of this thesis is to draw the theory of endogeneity in dynamic models in continuous time. Defining endogeneity in the static case is difficult, the aim of this work is to understand what are the implications and what is the mathematical framework to define endogeneity for dynamic processes. This is the subject of the first chapter. We first provide an extension of the separable set-up to a separate dynamic framework given in term of semi-martingale decomposition. Then we define our function of interest as a stopping time for an additional noise process, whose role is played by a Brownian motion for diffusions, and a Poisson process for counting processes. Société Générale Asset Management (now Lyxor AM) has supporter this thesis. SGAM was a financial investment company (Hedge Fund) for statistical study of which Hedge Fund databases was a constant and hard problem. Consequently, understanding the nature of the underlying duration processes of Hedge Funds in databases was a crucial problem. This is the aim of the second chapter. The third chapter brings a clear answer to a rarely tackled question (the casual effect of some precise, endogeneous variables on the funds' lifetimes) thanks to the empirical findings of the second chapter and the results of the first. Finally, as the resolution of such problems needs the inverse problem theory, an original application of this theory is also considered in the last chapter for portfolio allocation
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Rivers, Derick Lorenzo. "Dynamic Bayesian Approaches to the Statistical Calibration Problem." VCU Scholars Compass, 2014. http://scholarscompass.vcu.edu/etd/3599.

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The problem of statistical calibration of a measuring instrument can be framed both in a statistical context as well as in an engineering context. In the first, the problem is dealt with by distinguishing between the "classical" approach and the "inverse" regression approach. Both of these models are static models and are used to estimate "exact" measurements from measurements that are affected by error. In the engineering context, the variables of interest are considered to be taken at the time at which you observe the measurement. The Bayesian time series analysis method of Dynamic Linear Models (DLM) can be used to monitor the evolution of the measures, thus introducing a dynamic approach to statistical calibration. The research presented employs the use of Bayesian methodology to perform statistical calibration. The DLM framework is used to capture the time-varying parameters that may be changing or drifting over time. Dynamic based approaches to the linear, nonlinear, and multivariate calibration problem are presented in this dissertation. Simulation studies are conducted where the dynamic models are compared to some well known "static'" calibration approaches in the literature from both the frequentist and Bayesian perspectives. Applications to microwave radiometry are given.
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Books on the topic "Dynamical Inverse Problem"

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Gladwell, Graham M. L., and Antonino Morassi, eds. Dynamical Inverse Problems: Theory and Application. Vienna: Springer Vienna, 2011. http://dx.doi.org/10.1007/978-3-7091-0696-9.

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Morassi, Antonino, and G. M. L. Gladwell. Dynamical inverse problems: Theory and application. Wien: Springer, 2011.

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Maksimov, V. I. Dynamical inverse problems of distributed systems. Utrecht: VSP, 2002.

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Takewaki, Izuru. Dynamic structural design: Inverse problem approach. Southampton: WIT Press, 2000.

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S, Osipov I͡U. Inverse problems for ordinary differential equations: Dynamical solutions. Basel, Switzerland: Gordon and Breach, 1995.

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El Hami, Abdelkhalak, and Bouchaib Radi. Dynamics of Large Structures and Inverse Problems. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2017. http://dx.doi.org/10.1002/9781119332275.

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Digas, B. V., and S. I. Tarasova. Control, stability, and inverse problems of dynamics. Moscow: Maik Nauka/Interperiodica Pub., 2006.

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Pelant, Jaroslav. Inverse problem for two-dimensional flow through cascades. Letnany, Czech Republic: Information Centre for Aeronautics, 1998.

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Moreau, Madylam R., and SpringerLink (Online service), eds. Turbulence Nature and the Inverse Problem. Dordrecht: Springer Netherlands, 2009.

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Pelant, Jaroslav. Inverse problem for two-dimensional flow around a profile. Letnany, Czech Republic: Information Centre for Aeronautics, 1998.

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Book chapters on the topic "Dynamical Inverse Problem"

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Hartenstein, Hannes, Matthias Ruhl, Dietmar Saupe, and Edward R. Vrscay. "On the Inverse Problem of Fractal Compression." In Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems, 617–47. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-56589-2_26.

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Gibbons, John. "The Zabolotskaya-Khokhlov Equation and the Inverse Scattering Problem of Classical Mechanics." In Dynamical Problems in Soliton Systems, 36–41. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-662-02449-2_6.

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Puel, François. "Three Dimensional Equations of Szebehely of the Inverse Problem and Frenet Reference Frame." In Long-Term Dynamical Behaviour of Natural and Artificial N-Body Systems, 471–75. Dordrecht: Springer Netherlands, 1988. http://dx.doi.org/10.1007/978-94-009-3053-7_43.

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Evensen, Geir, Femke C. Vossepoel, and Peter Jan van Leeuwen. "Weak Constraint 4DVar." In Springer Textbooks in Earth Sciences, Geography and Environment, 49–61. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-96709-3_5.

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AbstractIt is also possible to formulate the 4DVar problem with the model acting as a weak constraint. We then search for a model solution close to the measurements that “almost” satisfies the dynamical model and its initial and boundary conditions. The concept of the model being a “weak constraint” as opposed to “strong constraint” was introduced by Sasaki (1970b). An early weak-constraint assimilation study is the one byBennett and McIntosh (1982 who solved the weak-constraint variational inverse problem for an ocean tidal model.
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Wadati, Miki. "Quantum Inverse Scattering Method." In Dynamical Problems in Soliton Systems, 68–80. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-662-02449-2_11.

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Gladwell, Graham M. L. "Matrix Inverse Eigenvalue Problems." In Dynamical Inverse Problems: Theory and Application, 1–28. Vienna: Springer Vienna, 2011. http://dx.doi.org/10.1007/978-3-7091-0696-9_1.

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Wunsch, Carl. "Tracer Inverse Problems." In Oceanic Circulation Models: Combining Data and Dynamics, 1–77. Dordrecht: Springer Netherlands, 1989. http://dx.doi.org/10.1007/978-94-009-1013-3_1.

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Kaup, D. J. "Approximations for the Inverse Scattering Transform." In Dynamical Problems in Soliton Systems, 12–22. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/978-3-662-02449-2_3.

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Pilant, M., and W. Rundell. "Age Structured Population Dynamics." In Inverse Problems and Theoretical Imaging, 122–29. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-75298-8_16.

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Arneodo, A., G. Grasseau, and M. Holschneider. "Wavelet Transform Analysis of Invariant Measures of Some Dynamical Systems." In inverse problems and theoretical imaging, 182–96. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/978-3-642-75988-8_15.

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Conference papers on the topic "Dynamical Inverse Problem"

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Avdonin, Sergei A., Alexander S. Blagoveshchensky, Abdon E. Choque-Rivero, and Victor S. Mikhaylov. "Dynamical inverse problem for two-velocity systems on finite trees." In 2016 Days on Diffraction (DD). IEEE, 2016. http://dx.doi.org/10.1109/dd.2016.7756807.

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Pàmies-Vilà, Rosa, and Josep M. Font-Llagunes. "Validation of the Inverse Dynamic Analysis of Human Gait Using a Forward Dynamics Approach." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-13023.

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One of the aims of the dynamic analysis of human gait is to know the joint forces and torques that the musculoskeletal system produces during the motion. For this purpose, an 18 segment 3D model with 57 degrees of freedom is implemented. The analysis of a captured motion can be addressed by means of forward or inverse dynamic analyses. In this work, both analyses are computed using multibody dynamics techniques. The forward dynamic analysis is carried out with the aim of simulating the movement of the multibody system using the results of the inverse problem as input data. Since the inverse analysis is solved using a dynamically consistent methodology, the forward dynamic analysis allows us to simulate up to the 90% of the gait cycle without any controller. After that, a proportional derivative (PD) controller is implemented to stabilize the system, which gets to simulate the complete captured motion. Moreover, the dynamic contribution of the controller is really low and the simulated motion is extremely close to the original one. The methodology presented allows us to validate the correctness of the inverse dynamics analysis and it is an intermediate step towards the prediction problem: it requires dynamical consistency too, but the uncertainties involved in the problem are lower than in a predictive approach.
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Bottasso, Carlo L., and Alessandro Croce. "Multibody Inverse Dynamics Using an Energy Preserving Direct Transcription Process." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48331.

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We propose a procedure for the solution of inverse multibody dynamic problems, here intended as optimal control problems for dynamical systems governed by differential-algebraic equations. The numerical solution is obtained by a direct transcription process based on an energy preserving scheme that ensures nonlinear unconditional stability. The resulting finite-dimensional problem is solved by sequential quadratic programming. We test the proposed methodology with the help of representative examples.
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Mandali, Priyanka, and Qiao Sun. "Stable Inversion Using the Assumed-Modes Rayleigh-Ritz Approximation for Tip Tracking of an Elastic Beam." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87794.

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Inversion control has been very successful in the control of nonlinear dynamical systems. However, when applied to flexible manipulators, inverse dynamics through direct integration in temporal space causes unbounded controller command. For nearly three decades, researchers have exhausted all possible solutions. Still, a perfect solution does not exist that would yield a perfect tip tracking. It has been suggested that seeking an inverse dynamics solution for a given tip trajectory is an ill-posed problem. It has also been suggested that increasing model accuracy by including more terms in a truncated beam model worsens the controller’s ability of stability. In this paper, we seek to understand the nature of the inverse dynamics instability. We use one assumed mode to approximate the beam deflection in a single link manipulator. The mode shape is chosen to ensure a boundedness of the inverse dynamics solution. Such solution is then applied in an inversion controller. Numerical simulations and experiments have both been conducted to show its performance.
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Coutel, S., C. H. Lamarque, and S. Pernot. "Identification Method for Both Linear and Piecewise Linear Dynamical Systems." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48625.

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Piecewise linear systems identification method is outlined in this article. Wavelets Analysis principles are widely used in this paper. Firstly, wavelets provide a very efficient mean to construct filters that are able to cut known degree polynomial terms in experimental signal. Secondly, wavelets are introduced to detect and to localize singularities in experimental signals that are characteristic of phase changes in a piecewise linear system. Eventually, we present a method to solve inverse problem that enables extracting instantaneous parameters from experimental data of physical studied system.
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Desaix, M., D. Anderson, M. Lisak, and M. L. Quiroga-Teixeiro. "An approximation procedure for the Zakharov-Shabat eigenvalue problem for real single-humped potentials." In Nonlinear Guided Waves and Their Applications. Washington, D.C.: Optica Publishing Group, 1996. http://dx.doi.org/10.1364/nlgw.1996.sad.13.

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The nonlinear Schrödinger equation, describing the dynamical evolution of an optical pulse under the influence of linear (anomalous) dispersion or diffraction and nonlinear self-phase modulation can be taken in the form: where q(t) represents the form of the initially launched pulse. A key role in the inverse scattering scheme for solving the nonlinear Schrödinger is played by the concomitant Zakharov-Shabat scattering problem, [1]: where v1 and v2 are the Jost functions, which satisfy the asymptotic relations: v1 → exp(–iζt) and v2 → 0 as t → –∞.
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Seifried, Robert, and Markus Burkhardt. "Servo-Constraints for Control of Flexible Multibody Systems With Contact." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-12334.

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This paper presents inversion based feedforward control design for flexible multibody systems with kinematic loops and end-effector contact. The inverse model provides for a given desired output trajectories, e.g. end-effector point and contact force, the required control inputs for exact output reproduction. A very appealing and efficient model inversion approach for such multibody systems is the use of so-called servo-constraints. These can be seen as an extension of classical mechanical constraints and yield a set of differential-algebraic equations. This allows an efficient numerical solution without burdensome symbolic manipulations. In addition, the use of servo-constraints allows the straight-forward treatment of flexible multibody systems with various topologies. The arising set of differential-algebraic equations describes the inverse model. The inverse model might be purely algebraic or include a dynamical part, which is called internal dynamics in nonlinear control theory. For its numerical solution it is advisable to transform the set of differential-algebraic equations to its underlying set of ordinary differential equations. The solution method for this internal dynamics depends then on its stability. For systems with unstable internal dynamics, as considered in this paper, a solution can be computed from a boundary-value problem. The efficiency of this approach is demonstrated for a flexible multibody system with a kinematic loop and a closed end-effector contact.
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Meghdari, A., S. H. Mahboobi, and A. L. Gaskarimahalle. "Dynamics Modeling of “CEDRA” Rescue Robot on Uneven Terrains." In ASME 2004 International Mechanical Engineering Congress and Exposition. ASMEDC, 2004. http://dx.doi.org/10.1115/imece2004-59239.

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In this paper an effective approach for kinematic and dynamic modeling of high mobility wheeled mobile robots (WMR) has been presented. As an example of these robots, the method has been applied on CEDRA rescue robot which is a complex, multibody mechanism. The model is derived for 6-DOF motions enabling movement in x, y, z directions, as well as pitch, roll and yaw rotations. Forward kinematics equations are derived using Denavit-Hartenberg method and the wheels Jacobian matrices. Moreover the inverse kinematics of the robot is obtained and solved for the wheel velocities and steering commands in terms of desired velocity, heading and measured link angles. Finally dynamical analysis of the rover has been thoroughly studied. Due to the complexity of this multi-body system especially on rough terrain, Kane’s method of dynamics has been used to model this problem. The approach has been developed in such a way that it can easily be extended to other mechanisms and rovers.
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Banerjee, Amit, and Issam Abu Mahfouz. "Comparative Study of Evolutionary Algorithms for Parameter Identification of an Impact Oscillator." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-38855.

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The use of non-classical evolutionary optimization techniques such as genetic algorithms, differential evolution, swarm optimization and genetic programming to solve the inverse problem of parameter identification of dynamical systems leading to chaotic states has been gaining popularity in recent years. In this paper, three popular evolutionary algorithms — differential evolution, particle swarm optimization and the firefly algorithm are used for parameter identification of a clearance-coupled-impact oscillator system. The behavior of impacting systems is highly nonlinear exhibiting a myriad of harmonic, low order and high order sub-harmonic resonances, as well as chaotic vibrations. The time-history simulations of the single-degree-of-freedom impact oscillator were obtained by the Neumark-β numerical integration algorithm. The results are illustrated by bifurcation graphs, state space portraits and Poincare’ maps which gives valuable insights on the dynamics of the impact system. The parameter identification problem relates to finding one set of system parameters given a chaotic or periodic system response as a set of Poincaré points and a different but known set of system parameters. The three evolutionary algorithms are compared over a set of parameter identification problems. The algorithms are compared based on solution quality to evaluate the efficacy of using one algorithm over another.
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Delaune, Xavier, Philippe Piteau, Vincent Debut, and Jose Antunes. "Experimental Validation of Inverse Techniques for the Remote Identification of Impact Forces in Gap-Supported Systems Subjected to Local and Flow Turbulence Excitations." In ASME 2010 Pressure Vessels and Piping Division/K-PVP Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/pvp2010-26133.

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Predictive computations of the nonlinear dynamical responses of gap-supported tubes subjected to flow excitation have been the subject of active research. Nevertheless, experimental results are still necessary, for validation of the theoretical predictions as well as for asserting the integrity of field components. Because carefully instrumented test tubes and tube-supports are seldom possible, due to space limitations and to the severe environment conditions, there is a need for robust techniques capable of extracting relevant information from the actual vibratory response data. Although at the present time such analysis is over-ambitious, as far as the multi-supported tube bundles of real-life components are concerned, the same instrumentation difficulties frequently apply in the case of laboratory test rigs. Therefore, the subject of this paper is of practical significance even in the more modest realm of laboratory experiments. The knowledge of the dynamical contact/impact (vibro-impact) forces is of paramount significance, as also the tube/support gaps. Following our previous studies in this area using wave-propagation techniques [1–3], we recently applied modal methods for extracting such information. Based on numerically simulated time-domain vibro-impact responses, the dynamical support forces, as well as the vibratory responses at the support locations, were identified from one or several vibratory responses at remote locations, from which the support gaps could also be inferred [4]. Also recently, for the related problem of friction force identification on bowed strings, preliminary experiments have shown the feasibility of these identification techniques [5]. In the present paper, the modal identification techniques developed in [4,5] are tested using an experimental rig built at CEA/Saclay, consisting on a randomly excited clamped-free beam which impacts on an intermediate gap-support. Identification of the impact force, as well as of the beam motion at the gap-support, are achieved based on remote measurements of the beam response provided by two accelerometers. A significant feature of the experimental identifications presented in this paper is that, beyond the results obtained under a point-force shaker excitation, we test here an original technique to identify the gap-supported reactions in flow-excited systems, which was recently introduced in [4]. As for most inverse problems, the identification results may prove sensitive to both noise and modeling errors. Therefore, regularization techniques discussed in [4] are used to mitigate the effects of unmeasured noise perturbations. Overall, the experimentally identified results compare reasonably well with the measured contact forces and motions at the gap-supports. Actually, even if our identifications are not immaculate at the present time, they remain nevertheless quite usable.
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Reports on the topic "Dynamical Inverse Problem"

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Ablowitz, Mark J., Gregory Beylkin, and Duane P. Sather. Nonlinear Problems in Fluid Dynamics and Inverse Scattering. Fort Belvoir, VA: Defense Technical Information Center, May 1993. http://dx.doi.org/10.21236/ada266234.

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Banks, H. T. Modeling, Inverse Problems and Feedback Control for Distributed Dynamical Systems. Fort Belvoir, VA: Defense Technical Information Center, November 2000. http://dx.doi.org/10.21236/ada387505.

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Ablowitz, Mark J. Nonlinear Problems in Fluid Dynamics and Inverse Scattering: Nonlinear Waves and Inverse Scattering. Fort Belvoir, VA: Defense Technical Information Center, December 1994. http://dx.doi.org/10.21236/ada289148.

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Ablowitz, Mark J. Nonlinear Problems in Fluid Dynamics and Inverse Scattering - Inverse Scattering and Nonlinear Waves. Fort Belvoir, VA: Defense Technical Information Center, July 1994. http://dx.doi.org/10.21236/ada299054.

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Beylkin, Gregory. Nonlinear Problems in Fluid Dynamics and Inverse Scattering. Propagation and Capturing of Singularities in Problems of Fluid Dynamics and Inverse Scattering. Fort Belvoir, VA: Defense Technical Information Center, July 1994. http://dx.doi.org/10.21236/ada282873.

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Beylkin, Gregory. Nonlinear Problems in Fluid Dynamics and Inverse Scattering: Propagation and capturing of singularities in problems of fluid dynamics and inverse scattering. Fort Belvoir, VA: Defense Technical Information Center, December 1994. http://dx.doi.org/10.21236/ada289146.

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Beylkin, Gregory. Nonlinear Problems in Fluid Dynamics and Inverse Scattering: Propagation and Capturing of Singularities in Problems of Fluid Dynamics and Inverse Scattering. Fort Belvoir, VA: Defense Technical Information Center, May 1996. http://dx.doi.org/10.21236/ada327352.

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Rabitz, H. Analysis of forward and inverse problems in chemical dynamics and spectroscopy. Office of Scientific and Technical Information (OSTI), January 1991. http://dx.doi.org/10.2172/5901969.

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Rabitz, H. Analysis of forward and inverse problems in chemical dynamics and spectroscopy. Office of Scientific and Technical Information (OSTI), January 1992. http://dx.doi.org/10.2172/6956545.

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Sather, Duane P. Nonlinear Problems in Fluid Dynamics and Inverse Scattering: Langmuir Circulations and Spiral Flows. Fort Belvoir, VA: Defense Technical Information Center, November 1994. http://dx.doi.org/10.21236/ada289194.

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