Showing papers by "Gilead Tadmor published in 2006"

Wavefront-based models for inverse electrocardiography

Abstract: We introduce two wavefront-based methods for the inverse problem of electrocardiography, which we term wavefront-based curve reconstruction (WBCR) and wavefront-based potential reconstruction (WBPR). In the WBCR approach, the epicardial activation wavefront is modeled as a curve evolving on the heart surface, with the evolution governed by factors derived phenomenologically from prior measured data. The body surface potential/wavefront relationship is modeled via an intermediate mapping of wavefront to epicardial potentials, again derived phenomenologically. In the WBPR approach, we iteratively construct an estimate of epicardial potentials from an estimated wavefront curve according to a simplified model and use it as an initial solution in a Tikhonov regularization scheme. Initial simulation results using measured canine epicardial data show considerable improvement in reconstructing activation wavefronts and epicardial potentials with respect to standard Tikhonov solutions. In particular the WBCR method accurately finds the anisotropic propagation early after epicardial pacing, and the WBPR method finds the wavefront (regions of sharp gradient of the potential) both accurately and with minimal smoothing

Real-Time Particle Image Velocimetry for Feedback Loops Using FPGA Implementation

Abstract: Digital Particle Image Velocimetry (PIV) is well established as a ∞uid dynamics measurement tool, being capable of non-intrusively and concurrently measuring a distributed velocity flled. Yet the intensive computational requirements of PIV limit its usage almost exclusively to ofi-line processing, analysis and modelling. This paper proposes hardware implementation of the cross-correlation algorithm as a means to make real-time PIV available for closed-loop control. This paper introduces a real-time PIV system which exploits the low-level parallelism of the cross-correlation computation by implementing it with reconflgurable hardware. The system processes 15 complete image pairs per second, which is more than 70 times speedup over a sequential software implementation. Moreover, our hardware structure can be easily expanded to a more parallel design for faster processing given su‐cient hardware resources. This design can be reused with only minor modiflcations for difierent image sizes and interrogation areas.

Tuned POD Galerkin models for transient feedback regulation of the cylinder wake

Abstract: Proper orthogonal decomposition (POD) Galerkin models are typically obtained from a single reference, such as an attractor. The POD model provides a very efficient representation of the reference but is often incapable to handle transient dynamics and other changes in flow conditions. These shortcomings are detrimental in feedback flow control applications. A novel concept of tuned Galerkin models is suggested, by which the global model interpolates a succession of similar-structure local models. The tuned model covers a controlled transient manifold, compensating for the gradual deformation of dominant flow structures, along such transients. The model is an enabler for both improved tracking performance, as well as for optimized control hardware placement, taking into account the entire dynamic range of interest. These concepts are demonstrated in the benchmark of stabilization of the wake flow behind a circular cylinder.

Generalized Mean-Field Model for Flow Control Using a Continuous Mode Interpolation

Abstract: In the current study, a generalization of POD Galerkin models is proposed targeting strategies for experimental feedback flow control. For practical reasons, that model should incorporate a range of flow operating conditions with small number of degrees of freedom. Standard POD Galerkin models are challenged by the over-optimization at one operating condition (Deane et al. 1991). Recent successful developments to extend the dynamic range require additional modes. This leads to a control design which is less online-capable and less robust. These side constraints for control-oriented ROMs are taken into account by a ’least-dimensional’ Galerkin approximation based on a novel technique for continuous

Spatiotemporal Waveform Observers and Feedback in Shear Layer Control

Abstract: Active control enhances shear layer mixing by exciting natural instabilities. Harmonizing the periodic actuation with vortex release can be used to manipulate and improve the mixing effect. This type of feedback requires tracking large shear layer vortices. We propose an observer structure based on a very simple model, representing the collective signal of a set of sensors as a spatiotemporal waveform. The observer tracks the slow drift and abrupt changes in the spatiotemporal phasors (local Fourier coefficients). Benefiting from a much longer time constant than the period of vortex release, it naturally filters spatial and temporal high frequency noise. The discussion is illustrated by simulations and wind tunnel experiments for the flow over a backward facing step, where the design objective is shortening the recirculation bubble. Simulations of the free shear layer are used to illustrate means to track asynchronous vortex merging events.

A Reduced Order Galerkin Model for the Reacting Flame Holder

Abstract: Fu Li∗ and Gilead Tadmor† Communication & Digital Signal Processing Center, Northeastern University, 440 Dana Research Building, Boston, MA 02115, U.S.A. Bernd R. Noack‡ Institute of Fluid Dynamics and Technical Acoustics, Sfb 557, Berlin University of Technology, Strasse des 17. Juni, 10623 Berlin, Germany Andrzej Banaszuk§ United Technologies Research Center, MS 129-15, 411 Silver Lane, East Hartford, CT 06108, U.S.A. and Prashant G. Mehta¶ Mechanical and Industrial Engineering University of Illinois at Urbana-Champaign, Urbana, IL 61801, U.S.A.

Control Oriented Models & Feedback Design in Fluid Flow Systems: A Review

Abstract: The nonlinearity and high dimension of computational fluid dynamics (CFD) models (O(104) at the low end) reflect fluid dynamics? intrinsic complexity. It is a formidable challenge, setting fluid flow control apart from conventional applications. Its implications include restrictions on model based control design, reliable state estimation, and thus, on feedback implementation. Seeking low order, design accessible models, the issue of an ample dynamic envelope, covering targeted free and actuated transients, is in the essence. We review some enablers for very low order, Galerkin models (GMs). Those include the combination of empirical proper orthogonal decomposition (POD) and physics based modes, estimation of turbulence and pressure effects, actuation models, interpolated models that cover an enhanced dynamic range, and auxiliary, phasor models, focused on sensor readings. The dynamic manifold of model validity must be respected for a meaningful use of the model, but can also be exploited, such as by a restriction to slow drift in the system?s periodic behavior, enabling the use of simplifying dynamic phasor models. Finally, we shall highlight some intrinsic performance limitations in GM based feedback flow control.

A Reduced Order Galerkin Model for the Reacting Blufi Body Flame Holder

Abstract: A low dimensional Galerkin model is developed for the near wake ∞ow behind a ∞ame- holder. The model includes the two leading proper orthogonal decomposition (POD) modes, representing the flrst von-Karman vortex shedding harmonic, characteristic of the non-reactive ∞ow, and a shift mode, capturing energy balancing with a dynamic mean fleld correction. The model is used to demonstrate the attenuating efiect of heat release on vortex shedding. In particular, vortex shedding suppression due to combustion can be explained by the emergence and the stabilizing efiect of a hot shift mode, associated with expansion due to heat release.

A wavefront-based constraint for potential surface solutions in inverse electrocardiography.

Abstract: Inverse electrocardiography in recent years has generally been approached using one of two quite distinct source models, either a potential-based approach or an activation- based approach. Each approach has advantages and disadvan- tages relative to the other, which are inherited by all specific methods based on a given approach. Recently our group has been working to develop models which can bridge between these two approaches, hoping to capture some of the most important advantages of both. In this work we present one such effort, which we term wavefront-based potential reconstruc- tion (WBPR). It is a modification of standard regularization methods for potential-based inverse electrocardiography, into which we incorporate a constraint based on a wavefront-like approximation to the potential-based solution. Initial results indicate significant improvement with respect to localization and characterization of the wavefront in simulations using both epicardially and supra-ventricularly paced heartbeats.

Imposing FIR Structure on H2 Preview Tracking and Smoothing Solutions

Abstract: In this paper we study continuous-time H2 feedforward tracking and estimation problems with FIR (finite impulse response) solutions. Both causal and non-causal solutions are considered. It is shown that these problems can be treated as special cases of static problems in the lifted domain, which, in turn, can be solved in terms of a two-point boundary value (Hamilton-Jacobi) system. This results in fixed dimension, closed-form solutions.