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At least 415 records · Page 23

Adaptive fuzzy system for 3-D vision

An adaptive fuzzy system using the concept of the Adaptive Resonance Theory (ART) type neural network architecture and incorporating fuzzy c-means (FCM) system equations for reclassification of cluster centers was developed. The Adaptive Fuzzy Leader Clustering (AFLC) architecture is a hybrid neural-fuzzy system which learns on-line in a stable and efficient manner. The system uses a control structure similar to that found in the Adaptive Resonance Theory (ART-1) network to identify the cluster centers initially. The initial classification of an input takes place in a two stage process; a simple competitive stage and a distance metric comparison stage. The cluster prototypes are then incrementally updated by relocating the centroid positions from Fuzzy c-Means (FCM) system equations for the centroids and the membership values. The operational characteristics of AFLC and the critical parameters involved in its operation are discussed. The performance of the AFLC algorithm is presented through application of the algorithm to the Anderson Iris data, and laser-luminescent fingerprint image data. The AFLC algorithm successfully classifies features extracted from real data, discrete or continuous, indicating the potential strength of this new clustering algorithm in analyzing complex data sets. The hybrid neuro-fuzzy AFLC algorithm will enhance analysis of a number of difficult recognition and control problems involved with Tethered Satellite Systems and on-orbit space shuttle attitude controller.

Mitra, Sunanda↗

Modeling and control of flexible space platforms with articulated payloads

The first steps in developing a methodology for spacecraft control-structure interaction (CSI) optimization are identification and classification of anticipated missions, and the development of tractable mathematical models in each mission class. A mathematical model of a generic large flexible space platform (LFSP) with multiple independently pointed rigid payloads is considered. The objective is not to develop a general purpose numerical simulation, but rather to develop an analytically tractable mathematical model of such composite systems. The equations of motion for a single payload case are derived, and are linearized about zero steady-state. The resulting model is then extended to include multiple rigid payloads, yielding the desired analytical form. The mathematical models developed clearly show the internal inertial/elastic couplings, and are therefore suitable for analytical and numerical studies. A simple decentralized control law is proposed for fine pointing the payloads and LFSP attitude control, and simulation results are presented for an example problem. The decentralized controller is shown to be adequate for the example problem chosen, but does not, in general, guarantee stability. A centralized dissipative controller is then proposed, requiring a symmetric form of the composite system equations. Such a controller guarantees robust closed loop stability despite unmodeled elastic dynamics and parameter uncertainties.

Graves, Philip C.↗

The morphology of faint galaxies in Medium Deep Survey images using WFPC2

First results from Hubble Space Telescope (HST) Medium Deep Survey images taken with Wide Field/Planetary Camera-2 (WFPC2) demonstrate that galaxy classifications can be reliably performed to magnitudes I814 approximately less than 22.0 in the F815W band. Published spectroscopic surveys to this depth indicate a mean redshift of bar-z approximately 0.5. We have classified over 200 galaxies in nine WFPC2 fields according to a basic morphological scheme. The majority of these faint galaxies appear to be similar to regular Hubble-sequence examples observed at low redshift. To the precision of our classification scheme, the relative proportion of spheroidal and disk systems of normal appearance is as expected from nearby samples, indicating that the bulk of the local galaxy population was in place at half the Hubble time. However, the most intriguing result is the relatively high proportion (approximately 40%) of objects which are in some way anomalous, and which may be of relevance in understanding the origin of the familiar excess population of faint galaxies established by others. These diverse objects include apparently interacting pairs whose multiple structure is only revealed with HST's angular resolution, galaxies with superluminous star-forming regions, diffuse low surface brightness galaxies of various forms, and compact galaxies. These anomalous galaxies contribute a substantial fraction of the excess counts at our limiting magnitude, and may provide insights into the 'faint blue galaxy' problem.

Griffiths, R. E.↗

NASA's Marshall Space Flight Center Recent Studies and Technology Developments in the Area of SSA/Orbital Debris

NASA/MSFC has been investigating the various aspects of the growing orbital debris problem since early 2009. Data shows that debris ranging in size from 5 mm to 10 cm presents the greatest threat to operational spacecraft today. Therefore, MSFC has focused its efforts on small orbital debris. Using off-the-shelf analysis packages, like the ESA MASTER software, analysts at MSFC have begun to characterize the small debris environment in LEO to support several spacecraft concept studies and hardware test programs addressing the characterization, mitigation, and ultimate removal, if necessary, of small debris. The Small Orbital Debris Active Removal (SODAR) architectural study investigated the overall effectiveness of removing small orbital debris from LEO using a low power, space-based laser. The Small Orbital Debris Detection, Acquisition, and Tracking (SODDAT) conceptual technology demonstration spacecraft was developed to address the challenges of in-situ small orbital debris environment classification including debris observability and instrument requirements for small debris observation. Work is underway at MSFC in the areas of hardware and testing. By combining off the shelf digital video technology, telescope lenses, and advanced video image FPGA processing, MSFC is building a breadboard of a space based, passive orbital tracking camera that can detect and track faint objects (including small debris, satellites, rocket bodies, and NEOs) at ranges of tens to hundreds of kilometers and speeds in excess of 15 km/sec,. MSFC is also sponsoring the development of a one-of-a-kind Dynamic Star Field Simulator with a high resolution large monochrome display and a custom collimator capable of projecting realistic star images with simple orbital debris spots (down to star magnitude 11-12) into a passive orbital detection and tracking system with simulated real-time angular motions of the vehicle mounted sensor. The dynamic star field simulator can be expanded for multiple sensors (including advanced star trackers), real-time vehicle pointing inputs, and more complex orbital debris images. This system is also adaptable to other sensor optics, missions, and installed sensor testing.

Wiegmann, Bruce M.↗

The effects of seasonal differences in climatic conditions on Landsat spectral signatures and associated land cover classification

Unsupervised classification algorithms are used to analyze Landsat computer-compatible tape data for an area of approximately 840 sq km in central Oklahoma, over the period from June 12 to August 4, 1979. The results obtained show that changes in remotely sensed spectral signatures and land cover classes are associated with a period of transition from moisture availability in late spring to moisture deficit in midsummer, with the latter being marked by greater visible spectrum reflectance and greater near-IR absorption, although each surface cover type has responded differently to the seasonal change in water availability. Consideration of these results has led to the identification of important factors in the use of multidate satellite data in environmental change monitoring. Naturally induced trends in surface albedo introduce noise into studies aimed at identifying anthropogenic land cover change. Specific problems associated with prairie-forest ecotonal areas in the southern Great Plains involve the seasonally induced differences in separability of forest, bush, and grassland cover types.

Harrington, J. A., Jr.↗

Metabrain for Embedded Cognition (MBEC)

This study presents the application of Hidden Markov Models (HMM) to determine specialized features without expert input. Specifically, the application of such a method for classification of high multi-path fading is targeted, for demonstrating the feasibility of such an approach. This is the first step in the development of a meta-brain for embedded cognition (M-BEC) suite that can be used to apply machine learning to various communication systems at NASA GRC. The project explores the concept of fading and how it affects communication systems in a negative way. Currently, supervised learning methods are used to study the effects of fading on space links. However, such models rely on expert features to make predictions as to the state of a link and whether fading is present. This project offers the possibility of having the HMM learn what characteristics are important and make predictions based on those characteristics. This project explores Hidden Markov Models, their theory and applications to various problems, as well as the underlying equations and assumptions. A preliminary result is presented and recommendations are made as to the use of such an approach for communications systems.

Propagation↗

Gravitation

Investigations of several problems of gravitation are discussed. The question of the existence of black holes is considered. While black holes like those in Einstein's theory may not exist in other gravity theories, trapped surfaces implying such black holes certainly do. The theories include those of Brans-Dicke, Lightman-Lee, Rosen, and Yang. A similar two-tensor theory of Yilmaz is investigated and found inconsistent and nonviable. The Newman-Penrose formalism for Riemannian geometries is adapted to general gravity theories and used to implement a search for twisting solutions of the gravity theories for empty and nonempty spaces. The method can be used to find the gravitational fields for all viable gravity theories. The rotating solutions are of particular importance for strong field interpretation of the Stanford/Marshall gyroscope experiment. Inhomogeneous cosmologies are examined in Einstein's theory as generalizations of homogeneous ones by raising the dimension of the invariance groups by one more parameter. The nine Bianchi classifications are extended to Rosen's theory of gravity for homogeneous cosmological models.

Fennelly, A. J.↗

Membership generation using multilayer neural network

There has been intensive research in neural network applications to pattern recognition problems. Particularly, the back-propagation network has attracted many researchers because of its outstanding performance in pattern recognition applications. In this section, we describe a new method to generate membership functions from training data using a multilayer neural network. The basic idea behind the approach is as follows. The output values of a sigmoid activation function of a neuron bear remarkable resemblance to membership values. Therefore, we can regard the sigmoid activation values as the membership values in fuzzy set theory. Thus, in order to generate class membership values, we first train a suitable multilayer network using a training algorithm such as the back-propagation algorithm. After the training procedure converges, the resulting network can be treated as a membership generation network, where the inputs are feature values and the outputs are membership values in the different classes. This method allows fairly complex membership functions to be generated because the network is highly nonlinear in general. Also, it is to be noted that the membership functions are generated from a classification point of view. For pattern recognition applications, this is highly desirable, although the membership values may not be indicative of the degree of typicality of a feature value in a particular class.

Kim, Jaeseok↗

Utilization of Machine Learning Techniques for Managing the Tracking and Data Relay Satellite Constellation

National Aeronautics and Space Administration’s (NASA) Goddard Space Flight Center (GSFC) operates a constellation of ten geosynchronous Tracking and Data Relay Satellites (TDRS). The TDRS constellation consists of multiple geosynchronous communication relay satellites located around the equator so they can provide continual coverage of any mission in low earth orbit. The TDRS are located primarily in three oceanic regions around the earth. NASA’s White Sands Complex provides the ground communication support for TDRS located over the Atlantic and Pacific Oceans. Another TDRS ground station in Guam supports the TDRS over the Indian Ocean. With these satellites the TDRS network can provide continuous coverage of satellites in low-earth orbit. The NASA Space Network (SN) project office at GSFC manages the constellation of spacecraft. Major customers of the TDRS constellation include, but are not limited to, the International Space Station and the Hubble Space Telescope. The TDRS constellation has three generations of satellites and has been active for over 30 years providing reliable communication links between customer satellites and corresponding ground stations. However, one of the major concerns for TDRS, and in any space mission, is to ensure the health and safety of the spacecraft. Generally, engineers use telemetry data to monitor and analyze the performance and state of health of the spacecraft. Telemetry data contains hundreds of parameters that monitor each important component in the spacecraft, which can be utilized to recognize and characterize the behavior of the spacecraft. Each parameter contains considerable information to represent time-dependent properties of each spacecraft subsystem and component. During the entire life of a TDRS spacecraft, thousands of gigabytes of telemetry data are transmitted in real-time from the spacecraft to the ground station at the White Sands Complex in Las Cruces, New Mexico, and recorded as historical data sets for engineers to process and analyze the events that occurred on-orbit. These parameters contain the function of multiple spacecraft subsystems, such as the attitude control system (ACS), Thermal, Electrical Power Subsystem (EPS), etc. . The first and second generations have exceeded their required lifetime and NASA is keen to manage these spacecrafts carefully in order to maximize the remaining life using the spacecraft telemetry. The challenge is to know when the risk of losing a spacecraft in geosynchronous orbit exceeds the benefit of continued operations for customer support. In the TDRS fleet, the EPS is the most critical subsystem related to spacecraft operations. Failure of the EPS would strand a spacecraft in geosynchronous orbit. Since EPS provides power to the spacecraft, component failures ultimately lead to the inability to support the spacecraft loads and the communications payload. For instance, TDRS-8 has several anomalies in EPS including the Bus Voltage Limiter (BVL) shunt current, solar array loss of circuits, and failed battery cells. Any of these anomalies can cause critical issues to the spacecraft. Therefore, developing a system to analyze and perform early detection of a potential anomaly is an important issue in telemetry data analysis. In recent years, Telemetry Mining (TM) has been proposed to process telemetry data by using Data Mining (DM) techniques such as classification, clustering, regression and anomaly detection. Anomaly detection, also known as outlier detection, has been widely used in many data mining areas such as remote sensing, medical data processing and digital image processing. The goal of anomaly detection is to detect abnormal data, which contains a relatively low probability of occurrence among the entire data set. Early detection of anomalies is one of the most significant issues in managing the spacecraft configuration. If anomalies can be detected early enough, then the redundant resources can be used to extend the life of the operational spacecraft. We present an unsupervised anomaly detection method to process the EPS data extracted from TDRS-8. This is different from traditional analytical methods, which use telemetry data to illustrate behavior and physical meaning of each spacecraft component. TM connects multiple parameters as a vector and then conducts data analysis on this high dimension telemetry vector. This method is looking at the properties of a high dimensional vector that is able to consider the relationship between different parameters in the anomaly detection problem. This kind of method performs much better than the traditional limit checking method. In addition, we propose a new approach of real-time anomaly detection to process telemetry data in real-time, which can then be applied to spacecraft monitoring with high reliability, low cost and high accuracy.

Machine Learning (ML)↗

Global Survey and Statistics of Radio-Frequency Interference in AMSR-E Land Observations

Radio-frequency interference (RFI) is an increasingly serious problem for passive and active microwave sensing of the Earth. To satisfy their measurement objectives, many spaceborne passive sensors must operate in unprotected bands, and future sensors may also need to operate in unprotected bands. Data from these sensors are likely to be increasingly contaminated by RFI as the spectrum becomes more crowded. In a previous paper we reported on a preliminary investigation of RFI observed over the United States in the 6.9-GHz channels of the Advanced Microwave Scanning Radiometer (AMSR-E) on the Earth Observing System Aqua satellite. Here, we extend the analysis to an investigation of RFI in the 6.9- and 10.7-GHz AMSR-E channels over the global land domain and for a one-year observation period. The spatial and temporal characteristics of the RFI are examined by the use of spectral indices. The observed RFI at 6.9 GHz is most densely concentrated in the United States, Japan, and the Middle East, and is sparser in Europe, while at 10.7 GHz the RFI is concentrated mostly in England, Italy, and Japan. Classification of RFI using means and standard deviations of the spectral indices is effective in identifying strong RFI. In many cases, however, it is difficult, using these indices, to distinguish weak RFI from natural geophysical variability. Geophysical retrievals using RFI-filtered data may therefore contain residual errors due to weak RFI. More robust radiometer designs and continued efforts to protect spectrum allocations will be needed in future to ensure the viability of spaceborne passive microwave sensing.

microwave remote sensing↗

Communications and control for electric power systems

The first section of the report describes the AbNET system, a hardware and software communications system designed for distribution automation (it can also find application in substation monitoring and control). The topology of the power system fixes the topology of the communications network, which can therefore be expected to include a larger number of branch points, tap points, and interconnections. These features make this communications network unlike any other. The network operating software has to solve the problem of communicating to all the nodes of a very complex network in as reliable a way as possible even if the network is damaged, and it has to do so with minimum transmission delays and at minimum cost. The design of the operating protocols is described within the framework of the seven-layer Open System Interconnection hierarchy of the International Standards Organization. Section 2 of the report describes the development and testing of a high voltage sensor based on an electro-optic polymer. The theory of operation is reviewed. Bulk fabrication of the polymer is discussed, as well as results of testing of the electro-optic coefficient of the material. Fabrication of a complete prototype sensor suitable for use in the range 1-20 kV is described. The electro-optic polymer is shown to be an important material for fiber optic sensing applications. Appendix A is theoretical support for this work. The third section of the report presents the application of an artificial neural network, Kohonen's self-organizing feature map, for the classification of power system states. This classifier maps vectors of an N-dimensional space to a 2-dimensional neural net in a nonlinear way preserving the topological order of the input vectors. These mappings are studied using a nonlinear power system model.

Kirkham, H.↗

Using a Multiwavelength Suite of Microwave Instruments to Investigate the Microphysical Structure of Deep Convective Cores

Due to the large natural variability of its microphysical properties, the characterization of solid precipitation is a longstanding problem. Since in situ observations are unavailable in severe convective systems, innovative remote sensing retrievals are needed to extend our understanding of such systems. This study presents a novel technique able to retrieve the density, mass, and effective diameter of graupel and hail in severe convection through the combination of airborne microwave remote sensing instruments. The retrieval is applied to measure solid precipitation properties within two convective cells observed on 2324 May 2014 over North Carolina during the IPHEx campaign by the NASA ER-2 instrument suite. Between 30 and 40 degrees of freedom of signal are associated with the measurements, which is insufficient to provide full microphysics profiling. The measurements have the largest impact on the retrieval of ice particle sizes, followed by ice water contents. Ice densities are mainly driven by a priori assumptions, though low relative errors in ice densities suggest that in extensive regions of the convective system, only particles with densities larger than 0.4 gcm3 are compatible with the observations. This is in agreement with reports of large hail on the ground and with hydrometeor classification derived from ground-based polarimetric radars observations. This work confirms that multiple scattering generated by large ice hydrometeors in deep convection is relevant for airborne radar systems already at Ku band. A fortiori, multiple scattering will play a pivotal role in such conditions also for Ku band spaceborne radars (e.g., the GPM Dual Precipitation Radar).

remote sensing retrievals↗

An Automatic Cloud Mask Algorithm Based on Time Series of MODIS Measurements

Quality of aerosol retrievals and atmospheric correction depends strongly on accuracy of the cloud mask (CM) algorithm. The heritage CM algorithms developed for AVHRR and MODIS use the latest sensor measurements of spectral reflectance and brightness temperature and perform processing at the pixel level. The algorithms are threshold-based and empirically tuned. They don't explicitly address the classical problem of cloud search, wherein the baseline clear-skies scene is defined for comparison. Here, we report on a new CM algorithm which explicitly builds and maintains a reference clear-skies image of the surface (refcm) using a time series of MODIS measurements. The new algorithm, developed as part of the Multi-Angle Implementation of Atmospheric Correction (MAIAC) algorithm for MODIS, relies on fact that clear-skies images of the same surface area have a common textural pattern, defined by the surface topography, boundaries of rivers and lakes, distribution of soils and vegetation etc. This pattern changes slowly given the daily rate of global Earth observations, whereas clouds introduce high-frequency random disturbances. Under clear skies, consecutive gridded images of the same surface area have a high covariance, whereas in presence of clouds covariance is usually low. This idea is central to initialization of refcm which is used to derive cloud mask in combination with spectral and brightness temperature tests. The refcm is continuously updated with the latest clear-skies MODIS measurements, thus adapting to seasonal and rapid surface changes. The algorithm is enhanced by an internal dynamic land-water-snow classification coupled with a surface change mask. An initial comparison shows that the new algorithm offers the potential to perform better than the MODIS MOD35 cloud mask in situations where the land surface is changing rapidly, and over Earth regions covered by snow and ice.

Lyapustin, Alexei↗

QuantifyML: How good is my machine learning model?

This paper presents an approach, QuantifyML, which employs model counting to assess the learnability and robustness of machine learning models. Typically the efficacy of machine learning models is determined by computing their accuracy statistically on test data sets. However, this may be misleading, if the test data is not representative of the problem that is being studied. Further, two different models may have the same accuracy on a given data set, measured statistically, but may be very different in their behavior on unseen data. Also, models with high accuracy could have poor adversarial robustness. In QuantifyML, our goal is to precisely quantify the extent to which machine learning models have learned and generalized from the given data. In QuantifyML, a trained model is translated into a C program, which is fed to the CBMC model checking tool to produce a formula in Conjunctive Normal Form (CNF), which in turn is analyzed with state-of-the-art model counters to efficiently obtain precise counts w.r.t different outputs. QuantifyML enables i) evaluating the learnability of models by comparing the counts for the outputs to ground truth, expressed as logical predicates (if available), ii) comparing the performance of different models that may be built with different machine learning algorithms (e.g., decision-trees vs. neural networks), and iii) quantifying the robustness of trained models around given inputs. Our evaluation demonstrates these applications of QuantifyML on decision trees and neural networks trained to learn relational properties of graphs, for which we know the ground truth, and to perform image classification, for which we do not have the ground truth, but we can quantify local robustness.

Deep Neural Networks↗

Tone Noise and Nearfield Pressure Produced by Jet-Cavity Interaction

Cavity flow resonance can cause numerous problems in aerospace applications. While our long-term goal is to understand cavity flows well enough to devise effective cavity resonance suppression techniques, this paper describes a fundamental study of resonant tones produced by jet-cavity interaction at subsonic and supersonic speeds. Our specific jet-cavity configuration can also be used as a test bed for evaluating active and passive flow resonance control concepts. Two significant findings emerge from this study. 1) Originally, we expected that tones produced by jet-cavity interaction would resemble cavity tones or jet tones or would involve some simple combinations of each. The experimental data do not support these expectations: instead, the jet cavity interaction produce a unique set of tones. We propose simple yet and physically insightful correlations for these tones. Although the pressure patterns on the cavity floor display very complex variations with the Mach number for a length/depth = 8 cavity, the tones correspond to the acoustic modes of the cavity-independent of flow. For a length/ depth = 3 cavity, however, a surprise emerges: the pressure patterns on the cavity floor are not so complex but the tones depend significantly on the flow. Additionally, we examine the role of external feedback unique to jet-cavity interaction. 2) Previous research led us to expect that traditional classifications (open, transitional, or closed) for cavities in an infinite flight stream would be insensitive to small changes in Mach number and would depend primarily on cavity length/depth ratios. Use of the novel high resolution photoluminescent pressure sensitive paint shows that the classifications are actually quite sensitive to jet Mach number for a length/depth = 8 cavity. However, these classifications provide no guidance whatsoever for tone amplitude or frequency. Detailed experimental data and insights presented here will assist researchers who are performing numerical simulations of jet-cavity flows as a first step toward devising resonance suppression methods.

Raman, Ganesh↗

A new method for recognizing quadric surfaces from range data and its application to telerobotics and automation

The problem of recognizing and positioning of objects in three-dimensional space is important for robotics and navigation applications. In recent years, digital range data, also referred to as range images or depth maps, have been available for the analysis of three-dimensional objects owing to the development of several active range finding techniques. The distinct advantage of range images is the explicitness of the surface information available. Many industrial and navigational robotics tasks will be more easily accomplished if such explicit information can be efficiently interpreted. In this research, a new technique based on analytic geometry for the recognition and description of three-dimensional quadric surfaces from range images is presented. Beginning with the explicit representation of quadrics, a set of ten coefficients are determined for various three-dimensional surfaces. For each quadric surface, a unique set of two-dimensional curves which serve as a feature set is obtained from the various angles at which the object is intersected with a plane. Based on a discriminant method, each of the curves is classified as a parabola, circle, ellipse, hyperbola, or a line. Each quadric surface is shown to be uniquely characterized by a set of these two-dimensional curves, thus allowing discrimination from the others. Before the recognition process can be implemented, the range data have to undergo a set of pre-processing operations, thereby making it more presentable to classification algorithms. One such pre-processing step is to study the effect of median filtering on raw range images. Utilizing a variety of surface curvature techniques, reliable sets of image data that approximate the shape of a quadric surface are determined. Since the initial orientation of the surfaces is unknown, a new technique is developed wherein all the rotation parameters are determined and subsequently eliminated. This approach enables us to position the quadric surfaces in a desired coordinate system. Experiments were conducted on raw range images of spheres, cylinders, and cones. Experiments were also performed on simulated data for surfaces such as hyperboloids of one and two sheets, elliptical and hyperbolic paraboloids, elliptical and hyperbolic cylinders, ellipsoids and the quadric cones. Both the real and simulated data yielded excellent results. Our approach is found to be more accurate and computationally inexpensive as compared to traditional approaches, such as the three-dimensional discriminant approach which involves evaluation of the rank of a matrix. Finally, we have proposed one other new approach, which involves the formulation of a mapping between the explicit and implicit forms of representing quadric surfaces. This approach, when fully realized, will yield a three-dimensional discriminant, which will recognize quadric surfaces based upon their component surfaces patches. This approach is faster than prior approaches and at the same time is invariant to pose and orientation of the surfaces in three-dimensional space.

Alvertos, Nicolas↗

Ground testing at MSFC

The large-scale field collection of acoustic data and their analysis are described in this review. The entire sound-field program has the purpose of solving complex problems of excessive noise propagation associated with the static test firing of large space-booster powerplants. The site of data collection has been Mississippi Test Facility (MTF), where far-field sound-propagation and correlated meteorological measurements were initiated in 1962. The statistical evaluation of sound-measurement data shows that the polar distribution of sound in the springtime (at MTF) is determined mainly by the temperature field of the atmosphere. Greater deformation of sound-intensity polar distribution occurs in the autumn as a result of the influence of the wind field. The data on sound attenuation as a function of distance from its source revealed attenuation in excess of the expected magnitude. The excess was mainly between 1 and 10 kilometers from the source, with maximum attenuation (17 to 18 decibels) near 6 kilometers. Excess sound attenuation was compared with calculated sound dispersion. For all sound frequencies in all seasons the deviation between reference and empirical attenuation values formed a bell-shaped distribution on a semilogarithmic plot. The physical causes for the sound- attenuation behavior are considered to be atmospheric diffraction and scattering effects. Statistical analysis of sod-intensity extremes indicated amplification of the sound signals by focusing which could be expected along selected azimuths. Empirical amplification values showed the maximum occurring in winter (50 decibels at 22 kilometers). For the analysis of correlation between empirical sound data and local atmospheric sound- propagation conditions, #e concept of analytical classification of sound-velocity profiles has been developed. Examination of over a quarter-million individual sound-velocity profiles indicates that 33 profile types for heights up to 3 kilometers constitute the empirical possibilities of sound-propagation conditions in southeastern United States. Since the focusing qualities of each sound- velocity profile can be determined as a class characteristic, the overall probabilities of focusing occurrence can he obtained. The severity of focusing, as based upon lateral spread of focusing areas, has been determined. The data for MTF indicate focusing is most severe in winter, with the direction toward east being most affected. Sound propagation is a fluctuating phenomenon because atmospheric conditions vary continuously. A measuring system for analyzing the nonstationary sound-propagation phenomena has been established. The analysis of the acoustic fluctuation data is sup- posed to provide "dynamic” perturbation functions of sound, which are to be superimposed on the related characteristic sound-velocity-profile type. The ultimate result of the program will be the establishment of reliable contingency tables showing the relationship between atmospheric parameters and far-field sound intensities. These data will be the basis for more accurate sound-propagation forecasting for static firing tests.

STATIC TESTING↗

Size distribution of dust grains: A problem of self-similarity

Distribution functions describing the results of natural processes frequently show the shape of power laws, e.g., mass functions of stars and molecular clouds, velocity spectrum of turbulence, size distributions of asteroids, micrometeorites and also interstellar dust grains. It is an open question whether this behavior is a result simply coming about by the chosen mathematical representation of the observational data or reflects a deep-seated principle of nature. The authors suppose the latter being the case. Using a dust model consisting of silicate and graphite grains Mathis et al. (1977) showed that the interstellar extinction curve can be represented by taking a grain radii distribution of power law type n(a) varies as a(exp -p) with 3.3 less than or equal to p less than or equal to 3.6 (example 1) as a basis. A different approach to understanding power laws like that in example 1 becomes possible by the theory of self-similar processes (scale invariance). The beta model of turbulence (Frisch et al., 1978) leads in an elementary way to the concept of the self-similarity dimension D, a special case of Mandelbrot's (1977) fractal dimension. In the frame of this beta model, it is supposed that on each stage of a cascade the system decays to N clumps and that only the portion beta N remains active further on. An important feature of this model is that the active eddies become less and less space-filling. In the following, the authors assume that grain-grain collisions are such a scale-invarient process and that the remaining grains are the inactive (frozen) clumps of the cascade. In this way, a size distribution n(a) da varies as a(exp -(D+1))da (example 2) results. It seems to be highly probable that the power law character of the size distribution of interstellar dust grains is the result of a self-similarity process. We can, however, not exclude that the process leading to the interstellar grain size distribution is not fragmentation at all. It could be, e.g., diffusion-limited growth discussed by Sander (1986), who applied the theory of fractal geometry to the classification of non-equilibrium growth processes. He received D=2.4 for diffusion-limited aggregation in 3d-space.

Henning, TH.↗