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Fuzzy Logic Particle Tracking

A new all-electronic Particle Image Velocimetry technique that can efficiently map high speed gas flows has been developed in-house at the NASA Lewis Research Center. Particle Image Velocimetry is an optical technique for measuring the instantaneous two component velocity field across a planar region of a seeded flow field. A pulsed laser light sheet is used to illuminate the seed particles entrained in the flow field at two instances in time. One or more charged coupled device (CCD) cameras can be used to record the instantaneous positions of particles. Using the time between light sheet pulses and determining either the individual particle displacements or the average displacement of particles over a small subregion of the recorded image enables the calculation of the fluid velocity. Fuzzy logic minimizes the required operator intervention in identifying particles and computing velocity. Using two cameras that have the same view of the illumination plane yields two single exposure image frames. Two competing techniques that yield unambiguous velocity vector direction information have been widely used for reducing the single-exposure, multiple image frame data: (1) cross-correlation and (2) particle tracking. Correlation techniques yield averaged velocity estimates over subregions of the flow, whereas particle tracking techniques give individual particle velocity estimates. For the correlation technique, the correlation peak corresponding to the average displacement of particles across the subregion must be identified. Noise on the images and particle dropout result in misidentification of the true correlation peak. The subsequent velocity vector maps contain spurious vectors where the displacement peaks have been improperly identified. Typically these spurious vectors are replaced by a weighted average of the neighboring vectors, thereby decreasing the independence of the measurements. In this work, fuzzy logic techniques are used to determine the true correlation displacement peak even when it is not the maximum peak, hence maximizing the information recovery from the correlation operation, maintaining the number of independent measurements, and minimizing the number of spurious velocity vectors. Correlation peaks are correctly identified in both high and low seed density cases. The correlation velocity vector map can then be used as a guide for the particle-tracking operation. Again fuzzy logic techniques are used, this time to identify the correct particle image pairings between exposures to determine particle displacements, and thus the velocity. Combining these two techniques makes use of the higher spatial resolution available from the particle tracking. Particle tracking alone may not be possible in the high seed density images typically required for achieving good results from the correlation technique. This two-staged velocimetric technique can measure particle velocities with high spatial resolution over a broad range of seeding densities.

Source record↗

Fuzzy inference enhanced information recovery from digital PIV using cross-correlation combined with particle tracking

Particle Image Velocimetry provides a means of measuring the instantaneous 2-component velocity field across a planar region of a seeded flowfield. In this work only two camera, single exposure images are considered where both cameras have the same view of the illumination plane. Two competing techniques which yield unambiguous velocity vector direction information have been widely used for reducing the single exposure, multiple image data: cross-correlation and particle tracking. Correlation techniques yield averaged velocity estimates over subregions of the flow, whereas particle tracking techniques give individual particle velocity estimates. The correlation technique requires identification of the correlation peak on the correlation plane corresponding to the average displacement of particles across the subregion. Noise on the images and particle dropout contribute to spurious peaks on the correlation plane, leading to misidentification of the true correlation peak. The subsequent velocity vector maps contain spurious vectors where the displacement peaks have been improperly identified. Typically these spurious vectors are replaced by a weighted average of the neighboring vectors, thereby decreasing the independence of the measurements. In this work fuzzy logic techniques are used to determine the true correlation displacement peak even when it is not the maximum peak on the correlation plane, hence maximizing the information recovery from the correlation operation, maintaining the number of independent measurements and minimizing the number of spurious velocity vectors. Correlation peaks are correctly identified in both high and low seed density cases. The correlation velocity vector map can then be used as a guide for the particle tracking operation. Again fuzzy logic techniques are used, this time to identify the correct particle image pairings between exposures to determine particle displacements, and thus velocity. The advantage of this technique is the improved spatial resolution which is available from the particle tracking operation. Particle tracking alone may not be possible in the high seed density images typically required for achieving good results from the correlation technique. This two staged approach offers a velocimetric technique capable of measuring particle velocities with high spatial resolution over a broad range of seeding densities.

Wernet, Mark P.↗

Black light - How sensors filter spectral variation of the illuminant

Visual sensor responses may be used to classify objects on the basis of their surface reflectance functions. In a color image, the image data are represented as a vector of sensor responses at each point in the image. This vector depends both on the surface reflectance functions and on the spectral power distribution of the ambient illumination. Algorithms designed to classify objects on the basis of their surface reflectance functions typically attempt to overcome the dependence of the sensor responses on the illuminant by integrating sensor data collected from multiple surfaces. In machine vision applications, it is shown that it is often possible to design the sensor spectral responsivities so that the vector direction of the sensor responses does not depend upon the illuminant. The conditions under which this is possible are given and an illustrative calculation is performed. In biological systems, where the sensor responsivities are fixed, it is shown that some changes in the illumination cause no change in the sensor responses. Such changes in illuminant are called black illuminants. It is possible to express any illuminant as the sum of two unique components. One component is a black illuminant. The second component is called the visible component. The visible component of an illuminant completely characterizes the effect of the illuminant on the vector of sensor responses.

Brainard, David H.↗

Radio-planetary from tie from Phobos-2 VLBI data

In an ongoing effort to improve the knowledge of the relative orientation (the 'frame tie') of the planetary ephemeris reference frame used in deep navigation and a second reference frame that is defined by the coordinates of a set of extragalactic radio sources, VLBI observations of the Soviet Phobos-2 spacecraft and nearby (in angle) radio sources were obtained at two epochs in 1989, shortly after the spacecraft entered orbit about Mars. The frame tie is an important systematic error source affecting both interplanetary navigation and the process of improving the theory of the Earth's orientation. The data from a single Phobos-2 VLBI session measure one component of the direction vector from Earth to Mars in the frame of the extragalactic radio sources (the 'radio frame'). The radio frame has been shown to be stable and internally consistent with an accuracy of 5 nrad. The planetary ephemeris reference frame has an internal consistency of approximately 15 nrad. The planetary and radio source reference frames were aligned prior to 1989 and measurements of occulations of the radio source 3C273 by the Moon. The Phobos-2 VLBI measurements provide improvement in the accuracy of two of the three angles describing a general rotation between the planetary and radio reference frames. A complete set of measurements is not available because data acquisition was terminated prematurely by loss of spacecraft. The analysis of the two Phobos-2 VLBI data sets indicates that, in the directions of the two rotation components determined by these data, the JPL planetary ephemeris DE200 is aligned with the radio frame as adopted by the International Earth Rotation Service within an accuracy of 20-40 nrad, depending on direction. The limiting errors in the solutions for these offsets are spacecraft trajectory (20 nrad), instrumental biases (19 nrad), and dependence of quasar coordinates on observing frequency (24 nrad).

Hildebrand, C. E.↗

Lunar Reconnaissance Orbiter (LRO) Guidance, Navigation and Control (GN&C) Overview

The National Aeronautics and Space Administration s (NASA) Lunar Reconnaissance Orbiter (LRO) launched on June 18, 2009 from the Cape Canaveral Air Force Station aboard an Atlas V launch vehicle and into a direct insertion trajectory to the oon. LRO, which was designed, built, and operated by the NASA Goddard Space Flight Center in Greenbelt, MD, is gathering crucial data on the lunar environment that will help astronauts prepare for long-duration lunar expeditions. The mission has a nominal life of 1 year as its seven instruments find safe landing sites, locate potential resources, characterize the radiation environment, and test new technology. To date, LRO has been operating well within the bounds of its requirements and has been collecting excellent science data images taken from the LRO Camera Narrow Angle Camera of the Apollo landing sites appeared on cable news networks. A significant amount of information on LRO s science instruments is provided at the LRO mission webpage. LRO s Guidance, Navigation and Control (GN&C) subsystem is made up of an onboard attitude control system (ACS) and a hardware suite of sensors and actuators. The LRO onboard ACS is a collection of algorithms based on high level and derived requirements, and reflect the science and operational events throughout the mission lifetime. The primary control mode is the Observing mode, which maintains the lunar pointing orientation and any offset pointing from this baseline. It is within this mode that all science instrument calibrations, slews and science data is collected. Because of a high accuracy requirement for knowledge and pointing, the Observing mode makes use of star tracker (ST) measurement data to determine an instantaneous attitude pointing. But even the star trackers alone do not meet the tight requirements, so a six-state Kalman Filter is employed to improve the noisy measurement data. The Observing mode obtains its rate information from an inertial reference unit (IRU) and in the event of an IRU failure, the rate data is be derived from the star tracker, but with degraded pointing performance. The Delta-V control mode responsibility is to maintain attitude pointing during the cruise trajectory, insertion burns and lunar orbit maintenance by adjustments made to the spacecraft s velocity magnitude and vector direction. The ACS also provides for a thruster based system momentum management algorithm (known as Delta-H) to maintain the system and wheel momentum to within acceptable levels. In the event an anomaly causes the LRO spacecraft to lose the ability to maintain its current attitude pointing, a Sun Safe mode is included in the ACS for the purpose of providing a known power and thermally safe coarse inertial sun attitude for an indefinite period of time, within the manageable limits of the reaction wheels. The Sun Safe mode is also the initial spacecraft control mode off of the launch vehicle and provides for a means to null tip-off rates immediately after separation. The nominal configuration is to use the IRU for rate information in the controller. In the event of a gyro failure a gyroless control mode was developed that computes rate information from the CSS data.

Garrick, Joseph↗

Unified analysis of ducted turbomachinery noise

The methodologies of Hanson and Zorumski are combined to yield a unified analysis of ducted turbomachinery noise. It is shown that the far-field broad-band and discrete noise spectral components can be expressed in terms of modal cross-spectral matrices and directivity vectors which are derivable from the duct analysis.

Zorumski, W. E.↗

Four methods of attitude determination for spin-stabilized spacecraft with applications and comparative results

The attitude of a spacecraft is determined by specifying independent parameters which relate the spacecraft axes to an inertial coordinate system. Sensors which measure angles between spin axis and other vectors directed to objects or fields external to the spacecraft are discussed. For the spin-stabilized spacecraft considered, the spin axis is constant over at least an orbit, but separate solutions based on sensor angle measurements are different due to propagation of errors. Sensor-angle solution methods are described which minimize the propagated errors by making use of least squares techniques over many sensor angle measurements and by solving explicitly (in closed form) for the spin axis coordinates. These methods are compared with star observation solutions to determine if satisfactory accuracy is obtained by each method.

Smith, G. A.↗

Morphology of Arabidopsis grown under chronic centrifugation and on the clinostat

Morphological measurements were made on populations of Arabidopsis thaliana grown from seed for 21 days under essentially constant environmental conditions except for the influence of gravitational or centrifugal accelerations. Growth conditions were what had been proposed for experiments in an artificial satellite. Observations are reported for plants grown at normal 1-g upright or on horizontal clinostats and for plants grown on a centrifuge. Increased g-force, up to 15 times normal, was found to have significant but small effects on some morphological end points. The plants' sensitivity to the magnitude of the g-force was much less than to its vector direction. Data from centrifuge experiments were extrapolated to zero-g to predict a set of morphological characteristics of a plant developing in the satellite environment. As an alternative means of predicting properties of a zero-g plant, characteristics of plants grown on horizontal clinostats were measured. The results of these two predictive methods were not in agreement. Clinostat grown plants were morphologically distinct from upright stationary controls.

Brown, A. H.↗

Single-axis attitude determination accuracy

This paper extends the analysis of attitude determination accuracy introduced at the 1975 American Astronautical Society/American Institute of Aeronautics and Astronautics (AAS/AIAA) Astrodynamics Conference. It contains more generalized expressions, new geometrical relations, and additional applications. A complete set of attitude accuracy equations for both arc-length (portion of a great circle) and rotation-angle (dihedral angle) measurements are presented. These expressions can then be applied to determine the geometrical conditions under which a specified accuracy can be achieved by using either the attitude or a selected reference-vector direction as the independent variable. Representative applications to attitude determination accuracy studies and launch window analyses are discussed. The clear physical interpretation and straightforward graphical procedures greatly simplify mission analysis, maneuver planning, hardware configuration studies, and interpretation of results.

Chen, L. C.↗

CCD sensors for spacecraft optical navigation

The optical navigation process uses spaceborne measurements of the apparent direction vector from the spacecraft to a target body, (planet, satellite, star, etc.) to improve estimates of the spacecraft trajectory. Ground-based controllers assimilate the optical measurements, together with spacecraft radio-tracking data and target ephemeris data, to generate a best estimate of the trajectory relative to the target. The present paper deals with a development program supporting the use of (solid state) CCD (Charged Coupled Device) imagers for spacecraft navigation. It is shown that stars can be detected that are two to three magnitudes fainter than with an equivalent vidicon based instrument, that effects of global response nonuniformity and dark current spikes can be essentially eliminated from the data as a result of the reproducibility of both effects, and that charge trailing during readout of star image data can lead to position measurement errors.

Eisenman, A. R.↗

An identification algorithm for linear stochastic systems with time delays

Linear discrete stochastic control systems containing unknown multiple time delays, plant parameters and noise variances are considered. An algorithm is established which uses the maximum-likelihood technique to identify the unknown parameters. An estimated likelihood function is evaluated based on the previous parameter estimates, which in turn generates a new descent direction vector to update the unknown parameters. The delays and plant parameters are identified in their respective parameter spaces. An example of a second-order stochastic system has been implemented by digital simulation to demonstrate the applicability of the algorithm.

Leondes, C. T.↗

Classification of surface units in the equatorial region of Mars based on Viking Orbiter color, albedo, and thermal data

Clusters corresponding to mappable surface units are sought in Viking Orbiter color, albedo, and thermal inertia data for the equatorial region of Mars. A principal components analysis indicated that 84% of the variance within the data for this region can be carried along two vector directions which typify the dominant trend of Martian surface materials. These dominant trends were deemphasized by stretching the data from a five-dimensional elliptical swarm into a hypersphere, through the use of principal component techniques. The decorrelated data were then plotted in a triangle diagram with red/violet, albedo and thermal inertia apices to facilitate inherent cluster discrimination. As many as eight clusters can be identified, with important mixing between them. The three major clusters consist of red and grey material extremes, along with intermediate value materials.

Arvidson, R. E.↗

Reduction of flow-measurement uncertainties in laser velocimeters with nonorthogonal channels

An analysis of certain geometrical limitations inherent in the application of laser velocimeters with nonorthogonal channels has led to the development of advanced-LDA-calibration and data-acquisition techniques that minimize systematic and statistical errors, respectively. The data-acquisition technique optimizes the number of velocity samples collected from three velocimeter channels as a function of local turbulence intensity, vector direction, and prescribed confidence interval. Linear velocity surveys and streamline traces measured in a turbulent flow field with a three-dimensional laser velocimeter are presented and the validity and accuracy of the theoretical analysis are discussed.

Snyder, P. K.↗

Simplified Decoding of Convolutional Codes

Some complicated intermediate steps shortened or eliminated. Decoding of convolutional error-correcting digital codes simplified by new errortrellis syndrome technique. In new technique, syndrome vector not computed. Instead, advantage taken of newly-derived mathematical identities simplify decision tree, folding it back on itself into form called "error trellis." This trellis graph of all path solutions of syndrome equations. Each path through trellis corresponds to specific set of decisions as to received digits. Existing decoding algorithms combined with new mathematical identities reduce number of combinations of errors considered and enable computation of correction vector directly from data and check bits as received.

Truong, T. K.↗

A zonal method for modeling powered-lift aircraft flow fields

A zonal method for modeling powered-lift aircraft flow fields is based on the coupling of a three-dimensional Navier-Stokes code to a potential flow code. By minimizing the extent of the viscous Navier-Stokes zones the zonal method can be a cost effective flow analysis tool. The successful coupling of the zonal solutions provides the viscous/inviscid interations that are necessary to achieve convergent and unique overall solutions. The feasibility of coupling the two vastly different codes is demonstrated. The interzone boundaries were overlapped to facilitate the passing of boundary condition information between the codes. Routines were developed to extract the normal velocity boundary conditions for the potential flow zone from the viscous zone solution. Similarly, the velocity vector direction along with the total conditions were obtained from the potential flow solution to provide boundary conditions for the Navier-Stokes solution. Studies were conducted to determine the influence of the overlap of the interzone boundaries and the convergence of the zonal solutions on the convergence of the overall solution. The zonal method was applied to a jet impingement problem to model the suckdown effect that results from the entrainment of the inviscid zone flow by the viscous zone jet. The resultant potential flow solution created a lower pressure on the base of the vehicle which produces the suckdown load. The feasibility of the zonal method was demonstrated. By enhancing the Navier-Stokes code for powered-lift flow fields and optimizing the convergence of the coupled analysis a practical flow analysis tool will result.

Roberts, D. W.↗