Noisy Flow Research Articles

A general framework for robust control in fluid mechanics

The application of optimal control theory to complex problems in fluid mechanics has proven to be quite effective when complete state information from high-resolution numerical simulations is available [P. Moin, T.R. Bewley, Appl. Mech. Rev., Part 2 47 (6) (1994) S3–S13; T.R. Bewley, P. Moin, R. Temam, J. Fluid Mech. (1999), submitted for publication]. In this approach, an iterative optimization algorithm based on the repeated computation of an adjoint field is used to optimize the controls for finite-horizon nonlinear flow problems [F. Abergel, R. Temam, Theoret. Comput. Fluid Dyn. 1 (1990) 303–325]. In order to extend this infinite-dimensional optimization approach to control externally disturbed flows in which the controls must be determined based on limited noisy flow measurements alone, it is necessary that the controls computed be insensitive to both state disturbances and measurement noise. For this reason, robust control theory, a generalization of optimal control theory, has been examined as a technique by which effective control algorithms which are insensitive to a broad class of external disturbances may be developed for a wide variety of infinite-dimensional linear and nonlinear problems in fluid mechanics. An aim of the present paper is to put such algorithms into a rigorous mathematical framework, for it cannot be assumed at the outset that a solution to the infinite-dimensional robust control problem even exists. In this paper, conditions on the initial data, the parameters in the cost functional, and the regularity of the problem are established such that existence and uniqueness of the solution to the robust control problem can be proven. Both linear and nonlinear problems are treated, and the 2D and 3D nonlinear cases are treated separately in order to get the best possible estimates. Several generalizations are discussed and an appropriate numerical method is proposed.

A self-organizing neural network architecture for navigation using optic flow.

This article describes a self-organizing neural network architecture that transforms optic flow and eye position information into representations of heading, scene depth, and moving object locations. These representations are used to navigate reactively in simulations involving obstacle avoidance and pursuit of a moving target. The network's weights are trained during an action-perception cycle in which self-generated eye and body movements produce optic flow information, thus allowing the network to tune itself without requiring explicit knowledge of sensor geometry. The confounding effect of eye movement during translation is suppressed by learning the relationship between eye movement outflow commands and the optic flow signals that they induce. The remaining optic flow field is due to only observer translation and independent motion of objects in the scene. A self-organizing feature map categorizes normalized translational flow patterns, thereby creating a map of cells that code heading directions. Heading information is then recombined with translational flow patterns in two different ways to form maps of scene depth and moving object locations. Most of the learning processes take place concurrently and evolve through unsupervised learning. Mapping the learned heading representations onto heading labels or motor commands requires additional structure. Simulations of the network verify its performance using both noise-free and noisy optic flow information.

What can be seen in a noisy optical flow field projected by a moving planar patch in 3D space?

In this paper, we would like to propose a brand new interpretation to the so-called “structure-from-motion” (SFM) problem. The optical flow field projected by a moving rigid planar patch in 3D space is our main consideration. Instead of just obtaining an explicit 3D motion/pose solution like the old approaches did before, we focus our attention on analyzing its error sensitivity, uncertainty, and ambiguity from another point of view. Our new method can handle the above error analysis easily. As known well before, the optical flow field projected by a 3D moving planar patch can be completely expressed by eight coefficients (two for second-order, four for first-order, and two for zeroth-order). Based on these flow coefficients easily determined by a linear regression method or other similar approaches, the error sensitivity of 3D estimates can be analyzed quantitatively and qualitatively in a coarse-to-fine way. The concepts of camera fixation and singular value decomposition (SVD) play important roles in our analysis. There are three goals for our experiments: (1) To prove the correctness of the algorithms (simulated image). (2) To show the tendency of error sensitivity when the 3D poses of the target planar patch are varied in a controlled manner (simulated image). (3) To show that our analysis is workable in the real-world application (real-world image).

Acoustic analysis and parametric studies of lagged pipes

Pipelines of noisy air or steam flow systems are often lagged on the outside with an acoustically absorptive, highly porous material which in turn is covered with a thin impervious (metallic) jacket. Prediction of transverse insertion loss (reduction in break-out noise) due to this composite lagging is the subject of the present paper. A transfer matrix for the porous absorptive layer is derived for cylindrical waves in the radial direction. Making use of an impedance model, radial velocities of the bare pipe and the outer jacket for the lagged pipe are calculated. These are then combined with respective radiation impedances to calculate insertion loss due to the composite lagging as well as the bare (unconstrained) lagging. Predicted values of insertion loss are compared with the measured values from literature. Finally results of parametric studies are presented.

Statistical analysis of inherent ambiguities in recovering 3-D motion from a noisy flow field

The inherent ambiguities in recovering 3-D motion information from a single optical flow field are studied using a statistical model. The ambiguities are quantified using the Cramer-Rao lower bound. As a special case, the performance bound for the motion of 3-D rigid planar surfaces is studied in detail. The dependence of the bound on factors such as the underlying motion, surface position, surface orientation, field of view, and density of available pixels are derived as closed-form expressions. A subset of the results support S. Adiv's (1989) analysis of the inherent ambiguities of motion parameters. For the general motion of an arbitrary surface. It is shown that the aperture problem in computing the optical flow restricts the nontrivial information about the 3-D motion to a sparse set of pixels at which both components of the flow velocity are observable. Computer simulations are used to study the dependence of the inherent ambiguities on the underlying motion, the field of view, and the number of feature points for the motion in front of a nonplanar environment. >

A Lie group approach to a neural system for three-dimensional interpretation of visual motion

A novel approach is presented to neural network computation of three-dimensional rigid motion from noisy two-dimensional image flow. It is shown that the process of 3-D interpretation of image flow can be viewed as a linear signal transform. The elementary signals of this linear transform are the 2-D vector fields of the six infinitesimal generators of the 3-D Euclidean group. This transform can be performed by a neural network. Results are also reported of neural network simulations for the 3-D interpretation of image flow and a comparison of the performance of this approach with that using conventional methods. Computer simulation results verify the Lie-group-based neural network approach to three-dimensional motion perception.

Visual navigation with a neural network

A simple linear neural network modelled on areas MT and MST of primate visual cortex can determine the direction of self-motion of an observer by using the optical flow field induced by observer translation relative to a rigid planar environment. The model's input layer consists of a set of motion detectors covering a 20° × 20° portion of the visual field with a subset of eight detectors selective to four primary directions and two speeds representing the optical motion within a single receptive field. Heading is represented distributively on the output layer in terms of azimuth and elevation. The network's heading accuracy under ideal conditions is on the order of 1° of visual angle, which is in agreement with perceptual studies of heading accuracy in human observers. The network's performance under noisy optical flow conditions matches remarkably well that of human subjects. Moreover, the network's tolerance of noise makes it potentially useful in robotic vision. A subsequent problem is to extend the model to combined observer translation and rotation.

Inherent ambiguities in recovering 3-D motion and structure from a noisy flow field

One of the major areas in research on dynamic scene analysis is recovering 3-D motion and structure from optical flow information. Two problems which may arise due to the presence of noise in the flow field are examined. First, motion parameters of the sensor or a rigidly moving object may be extremely difficult to estimate because there may exist a large set of significantly incorrect solutions which induce flow fields similar to the correct one. The second problem is in the decomposition of the environment into independently moving objects. Two such objects may induce optical flows which are compatible with the same motion parameters, and hence, there is no way to refute the hypothesis that these flows are generated by one rigid object. These ambiguities are inherent in the sense that they are algorithm-independent. Using a mathematical analysis, situations where these problems are likely to arise are characterized. A few examples demonstrate the conclusions. Constraints and parameters which can be recovered even in ambiguous situations are presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Audible cerebrospinal fluid flow through a ventriculoperitoneal shunt

✓ An audible, noisy cerebrospinal fluid flow is an uncommon sequela of ventriculoperitoneal shunting. Two cases presenting this phenomenon are described.

Small-computer procedure for optimal filtering of haemodynamic data.

Most reported methods dealing with the optimal filtering of haemodynamic data are based on computationally onerous procedures and pay little attention to execution speed. In the paper the problem of filtering noisy aortic flow and pressure waveforms is considered and the possibility of applying a Kalman filter technique, which does not require a preliminary identification of the signal generation process, is discussed. The basic hypothesis is that, in a cardiac cycle, the waveforms considered can be described by functions which permit Taylor series expansion. Thus the signal model is easy to obtain and the filtering procedure is fast, even if implemented on a minicomputer. The filter was applied to flow and pressure signals simultaneously measured in the canine ascending aorta under different physiological conditions. The filter performance is described and discussed.

A model for visual flow-field cueing and self-motion estimation

A computational model for visual flow-field cueing and self-motion estimation is developed and simulated. The model is predicated on the notion that the pilot makes noisy, sampled measurements on the spatially distributed visual flow-field surrounding him and, on the basis of these measurements, generates estimates of his own linear and angular terrain-relative velocities which optimally satisfy, in a least-squares sense, the visual kinematic flow constraints. The least-squares formulation is applicable to general observer motions and viewing geometries; it is projection-plane independent and rational in its treatment of redundant and noisy flow cues. A subsidiary but significant output of the model is an `impact time' map, and observer-centered spatially scaled replica of the viewed surface. Simulations are presented to demonstrate the parametric sensitivity and ability to model relevant human visual performance data. Preliminary simulation results of human visual performance are encouraging.

Determining the instantaneous axis of translation from optic flow generated by arbitrary sensor motion (abstract only)

This paper develops a simple and robust procedure for determining the instantaneous axis of translation from image sequences induced by unconstrained sensor motion. The procedure is based upon the fact that difference vectors at discontinuities in optic flow fields generated by sensor motion relative to a stationary environment are oriented along translational field lines. This is developed into a procedure consisting of three steps: 1) locally computing difference vectors from an optic flow field; 2) thresholding the difference vectors; and 3) minimizing the angles between the difference vector field and a set of radial field lines which correspond to a particular translational axis. This method does not require a priori knowledge about sensor motion or distances in the environment. The necessary environmental constraints are rigidity and sufficient variation in depth along visual directions to endow the flow field with discontinuities. The method has been successfully applied to noisy, sparse, and low resolution flow fields generated from real world image sequences. Experiments are reviewed which indicate that the human visual system also utilizes discontinuities in optic flows in determining self-motion. In addition, due to the computational simplicity of the procedure, hardware realization for real-time implementation is possible.

Signal compression method applied for a measurement of sound attenuation by a barrier under wind effects.

Signal compression method was applied for a measurement of wind effects to a sound attenuation by a barrier. This method uses special computer generated test signal, which can be compressed to a pulse like signal by a numerical phase shift filter. External noise can be reduced and effects of reflected sounds can be eliminated by this method, so it is suitable for a measurement of sound attenuation in noisy air flow conditions. Experiments were performed in rather small test room for short propagation path length. Obtained signals and computer processed waveforms are illustrated with the results of attenuation characteristics for five wind conditions.