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Publication# Model-Based Estimation of Three-Dimensional Stiffness Parameters in Photonic-Force Microscopy

Elena Bertseva, Andrzej Kulik, Amardeep Singh, Philippe Thévenaz, Michaël Unser

*Institute of Electrical and Electronics Engineers, *2010

Article

Article

Résumé

We propose a system to characterize the 3-D diffusion properties of the probing bead trapped by a photonic-force microscope. We follow a model-based approach, where the model of the dynamics of the bead is given by the Langevin equation. Our procedure combines software and analog hardware to measure the corresponding stiffness matrix. We are able to estimate all its elements in real time, including off-diagonal terms. To achieve our goal, we have built a simple analog computer that performs a continuous preprocessing of the data, which can be subsequently digitized at a much lower rate than is otherwise required. We also provide an effective numerical algorithm for compensating the correlation bias introduced by a quadrant photodiode detector in the microscope. We validate our approach using simulated data and show that our bias-compensation scheme effectively improves the accuracy of the system. Moreover, we perform experiments with the real system and demonstrate real-time capabilities. Finally, we suggest a simple adjunction that would allow one to determine the mass matrix as well.

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Donnée

Une donnée est ce qui est connu et qui sert de point de départ à un raisonnement ayant pour objet la détermination d'une solution à un problème en relation avec cette donnée. Cela peut être une descr

Système

Un système est un ensemble d' interagissant entre eux selon certains principes ou règles. Par exemple une molécule, le système solaire, une ruche, une société humaine, un parti, une armée etc.
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We discuss in this thesis the numerical approximation of fluid-structure interaction (FSI) problems with a particular concern (albeit not exclusive) on hemodynamics applications. Firstly, we model the blood as an incompressible fluid and the artery wall as an elastic structure. To solve the coupled problem, we propose new semi-implicit algorithms based on inexact block-LU factorization of the linear system obtained after the space-time discretization and linearization of the FSI problem. As a result, the fluid velocity is computed separately from the coupled pressure-structure velocity system at each iteration, hence reducing the computational cost. This approach leads to two different families of methods which extend to FSI problems schemes that were previously adopted for pure fluid problems. The algorithms derived from inexact factorization methods are compared with other schemes based on two preconditioners for the FSI system. The first one is the classical Dirichlet-Neumann preconditioner, which has the advantage of modularity (i.e. it allows to reuse existing fluid and structure codes with minimum effort). Unfortunately, its performance is very poor in case of large added-mass effect, as it happens in hemodynamics. Alternatively, we consider a non-modular approach which consists in preconditioning the coupled system with a suitable diagonal scaling combined with an ILUT preconditioner. The system is then solved by a Krylov method. The drawback of this procedure is the loss of modularity. Independently of the preconditioner, the efficiency of semi-implicit algorithms is highlighted. All the methods are tested on two and three-dimensional blood-vessel systems. The algorithm combining the non-modular ILUT preconditioner with Krylov methods proved to be the fastest. However, modular and inexact factorization based methods should not be disregarded because they can considerably benefit from code parallelization, unlike the ILUT-Krylov approach. Finally, we improve the structure model by representing the vessel wall as a linear poroelastic medium. Our non-modular approach and the partitioned procedures arising from a domain decomposition viewpoint are extended to fluid-poroelastic structure interactions. Their numerical performance are analyzed and compared on simplified blood-vessel systems.

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The determination of instantaneous positions with high accuracy using differential GPS techniques is of great importance for several applications, like airborne topographic mapping, airborne gravimetry and altimetry. In some of these applications long baselines are involved creating additional problems in the correct determination of the position of the sensors. The determination of the attitude of the aircraft is also of great importance in this context. This paper presents a technique that, taking advantage of the integration of GPS and inertial measurements, produces real time positions. The demand for real time positioning introduces some more constraints, which must be taken into account from the start of the algorithm development to the end of its implementation. A methodology for processing GPS and raw data from an inertial measurement unit (IMU) was implemented in a feedback integrated structure. The position determination is based on real time DGPS with L1 and L2 carrier phase ambiguity fixing, using on-line IMU processed data to validate and increase the positions reliability, especially during GPS outages and when the aircraft is far away from the nearest GPS reference station. By processing L1 and L2 carrier phase measurements in differential mode between a pair of the aircraft GPS antennas (without resorting to ground reference station data), a partial estimate of the aircraft attitude is obtained. This is critical to align the low cost inertial platform in heading either when the aircraft is stopped or in flight. In addition, the DGPS absolute positions are used to update the IMU data in real time. By using the proposed methodology it was possible to explore the entire potential of a low cost IMU/GPS system. The position and attitude values are obtained from all the measurements through an extended Kalman filter. Decimeter accuracy was achieved for the positions. For the orientation of the aircraft an accuracy of 0.01º (1) for roll and pitch and 0.1º (1 sigma) for heading was achieved. The performance and the results obtained with this system using data from an airborne campaign that took place in Portugal are discussed.

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2005