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Aeroelastic Flight Data Analysis with the Hilbert-Huang Algorithm

This report investigates the utility of the Hilbert Huang transform for the analysis of aeroelastic flight data. It is well known that the classical Hilbert transform can be used for time-frequency analysis of functions or signals. Unfortunately, the Hilbert transform can only be effectively applied to an extremely small class of signals, namely those that are characterized by a single frequency component at any instant in time. The recently-developed Hilbert Huang algorithm addresses the limitations of the classical Hilbert transform through a process known as empirical mode decomposition. Using this approach, the data is filtered into a series of intrinsic mode functions, each of which admits a well-behaved Hilbert transform. In this manner, the Hilbert Huang algorithm affords time-frequency analysis of a large class of signals. This powerful tool has been applied in the analysis of scientific data, structural system identification, mechanical system fault detection, and even image processing. The purpose of this report is to demonstrate the potential applications of the Hilbert Huang algorithm for the analysis of aeroelastic systems, with improvements such as localized online processing. Applications for correlations between system input and output, and amongst output sensors, are discussed to characterize the time-varying amplitude and frequency correlations present in the various components of multiple data channels. Online stability analyses and modal identification are also presented. Examples are given using aeroelastic test data from the F-18 Active Aeroelastic Wing airplane, an Aerostructures Test Wing, and pitch plunge simulation.

Brenner, Martin J.↗

Fast Scattering Code (FSC) User's Manual: Version 2

The Fast Scattering Code (version 2.0) is a computer program for predicting the three-dimensional scattered acoustic field produced by the interaction of known, time-harmonic, incident sound with aerostructures in the presence of potential background flow. The FSC has been developed for use as an aeroacoustic analysis tool for assessing global effects on noise radiation and scattering caused by changes in configuration (geometry, component placement) and operating conditions (background flow, excitation frequency).

Tinetti, Ana F.↗

Airframe Noise Results from the QTD II Flight Test Program

With continued growth in air travel, sensitivity to community noise intensifies and materializes in the form of increased monitoring, regulations, and restrictions. Accordingly, realization of quieter aircraft is imperative, albeit only achievable with reduction of both engine and airframe components of total aircraft noise. Model-scale airframe noise testing has aided in this pursuit; however, the results are somewhat limited due to lack of fidelity of model hardware, particularly in simulating full-scale landing gear. Moreover, simulation of true in-flight conditions is non-trivial if not infeasible. This paper reports on an investigation of full-scale landing gear noise measured as part of the 2005 Quiet Technology Demonstrator 2 (QTD2) flight test program. Conventional Boeing 777-300ER main landing gear were tested, along with two noise reduction concepts, namely a toboggan fairing and gear alignment with the local flow, both of which were down-selected from various other noise reduction devices evaluated in model-scale testing at Virginia Tech. The full-scale toboggan fairings were designed by Goodrich Aerostructures as add-on devices allowing for complete retraction of the main gear. The baseline-conventional gear, faired gear, and aligned gear were all evaluated with the high-lift system in the retracted position and deployed at various flap settings, all at engine idle power setting. Measurements were taken with flyover community noise microphones and a large aperture acoustic phased array, yielding far-field spectra, and localized sources (beamform maps). The results were utilized to evaluate qualitatively and quantitatively the merit of each noise reduction concept. Complete similarity between model-scale and full-scale noise reduction levels was not found and requires further investigation. Far-field spectra exhibited no noise reduction for both concepts across all angles and frequencies. Phased array beamform maps show inconclusive evidence of noise reduction at selective frequencies (1500 to 3000 Hz) but are otherwise in general agreement with the far-field spectra results (within measurement uncertainty).

Elkoby, Ronen↗

Comparison of Predicted and Measured Attenuation of Turbine Noise from a Static Engine Test

Aircraft noise has become an increasing concern for commercial airlines. Worldwide demand for quieter aircraft is increasing, making the prediction of engine noise suppression one of the most important fields of research. The Low-Pressure Turbine (LPT) can be an important noise source during the approach condition for commercial aircraft. The National Aeronautics and Space Administration (NASA), Pratt & Whitney (P&W), and Goodrich Aerostructures (Goodrich) conducted a joint program to validate a method for predicting turbine noise attenuation. The method includes noise-source estimation, acoustic treatment impedance prediction, and in-duct noise propagation analysis. Two noise propagation prediction codes, Eversman Finite Element Method (FEM) code [1] and the CDUCT-LaRC [2] code, were used in this study to compare the predicted and the measured turbine noise attenuation from a static engine test. In this paper, the test setup, test configurations and test results are detailed in Section II. A description of the input parameters, including estimated noise modal content (in terms of acoustic potential), and acoustic treatment impedance values are provided in Section III. The prediction-to-test correlation study results are illustrated and discussed in Section IV and V for the FEM and the CDUCT-LaRC codes, respectively, and a summary of the results is presented in Section VI.

Chien, Eugene W.↗

Advanced Airfoils Boost Helicopter Performance

Carson Helicopters Inc. licensed the Langley RC4 series of airfoils in 1993 to develop a replacement main rotor blade for their Sikorsky S-61 helicopters. The company's fleet of S-61 helicopters has been rebuilt to include Langley's patented airfoil design, and the helicopters are now able to carry heavier loads and fly faster and farther, and the main rotor blades have twice the previous service life. In aerial firefighting, the performance-boosting airfoils have helped the U.S. Department of Agriculture's Forest Service control the spread of wildfires. In 2003, Carson Helicopters signed a contract with Ducommun AeroStructures Inc., to manufacture the composite blades for Carson Helicopters to sell

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Fiber Optic Wing Shape Sensing on NASA's Ikhana UAV

This document discusses the development of fiber optic wing shape sensing on NASA's Ikhana vehicle. The Dryden Flight Research Center's Aerostructures Branch initiated fiber-optic instrumentation development efforts in the mid-1990s. Motivated by a failure to control wing dihedral resulting in a mishap with the Helios aircraft, new wing displacement techniques were developed. Research objectives for Ikhana included validating fiber optic sensor measurements and real-time wing shape sensing predictions; the validation of fiber optic mathematical models and design tools; assessing technical viability and, if applicable, developing methodology and approaches to incorporate wing shape measurements within the vehicle flight control system; and, developing and flight validating approaches to perform active wing shape control using conventional control surfaces and active material concepts.

Richards, Lance↗

F15B-Quiet Spike Aeroservoelastic Flight Test Data Analysis

Airframe structural morphing technologies designed to mitigate sonic boom strength are being developed by Gulfstream Aerospace Corporation (GAC). Among these technologies is a concept in which an aircraft's frontend would be extended prior to supersonic acceleration. This morphing would effectively lengthen the vehicle, reducing peak sonic boom amplitude, but is also expected to partition the otherwise strong bow shock into a series of reduced-strength, non-coalescing shocklets. This combination of boom shaping techniques is predicted to transform the classic, high-impulse N-wave pattern typically generated by an aircraft traveling at supersonic speed into a signature more closely resembling a sinusoidal wave with a greatly reduced perceived loudness. 'QuietSpike' is GAC's nomenclature for its recently patented front-end vehicle morphing arrangement. The ability of Quiet Spike to effectively shape a vehicle's far- field sonic boom signature is highly dependent on the area distribution characteristics of the aircraft. The full aeroacoustic benefits of front-end morphing at farfield are only possible when the QuietSpike article and vehicle configuration are designed in consideration of each other. Adding QuietSpike technology to the airframe of an existing, non-boom-optimized supersonic vehicle is unlikely to result in an improved far-field signature due to the generally over-powering influence of wing- and inlet-generated shocks. Therefore, it is generally recognized within NASA and the industry that a clean-sheet vehicle design is required to demonstrate the theoretically predicted far-field aeroacoustic benefits of QuietSpike type morphing and other boom- mitigating concepts. NASA's Aeronautics Research Mission Directorate (ARMD) Supersonics Division has placed increased priority on near-term development and flight-testing of such a vehicle. To help achieve this objective, static and dynamic aerostructural proof-of-concept testing was considered a prudent step prior to a clean-sheet effort in order to reduce risk associated with a follow-on test program. Following a survey of potential test platforms, NASA Dryden's F-15B was selected as the target test vehicle primarily because of its unique ability to carry a largescale test apparatus to relevant supersonic flight speeds, so called the F15 -QS. The QuietSpike test article was constructed primarily of composite materials and attached to the forward fuselage of the F-1 5B bulkhead (see Figures 1,2). The QuietSpike test article replaces the current flight test noseboom and radome assembly. Power is supplied to the Quiet Spike motor assembly in order to extend and retract the Spike, and the Quiet Spike test article was appropriately instrumented with accelerometers, strain gages, pressure transducers, and thermocouples.

Brenner, Martin J.↗

2007 Research and Engineering Annual Report

Selected research and technology activities at NASA Dryden Flight Research Center are summarized. These following activities exemplify the Center's varied and productive research efforts: Developing a Requirements Development Guide for an Automatic Ground Collision Avoidance System; Digital Terrain Data Compression and Rendering for Automatic Ground Collision Avoidance Systems; Nonlinear Flutter/Limit Cycle Oscillations Prediction Tool; Nonlinear System Identification Using Orthonormal Bases: Application to Aeroelastic/Aeroservoelastic Systems; Critical Aerodynamic Flow Feature Indicators: Towards Application with the Aerostructures Test Wing; Multidisciplinary Design, Analysis, and Optimization Tool Development Using a Genetic Algorithm; Structural Model Tuning Capability in an Object-Oriented Multidisciplinary Design, Analysis, and Optimization Tool; Extension of Ko Straight-Beam Displacement Theory to the Deformed Shape Predictions of Curved Structures; F-15B with Phoenix Missile and Pylon Assembly--Drag Force Estimation; Mass Property Testing of Phoenix Missile Hypersonic Testbed Hardware; ARMD Hypersonics Project Materials and Structures: Testing of Scramjet Thermal Protection System Concepts; High-Temperature Modal Survey of the Ruddervator Subcomponent Test Article; ARMD Hypersonics Project Materials and Structures: C/SiC Ruddervator Subcomponent Test and Analysis Task; Ground Vibration Testing and Model Correlation of the Phoenix Missile Hypersonic Testbed; Phoenix Missile Hypersonic Testbed: Performance Design and Analysis; Crew Exploration Vehicle Launch Abort System-Pad Abort-1 (PA-1) Flight Test; Testing the Orion (Crew Exploration Vehicle) Launch Abort System-Ascent Abort-1 (AA-1) Flight Test; SOFIA Flight-Test Flutter Prediction Methodology; SOFIA Closed-Door Aerodynamic Analyses; SOFIA Handling Qualities Evaluation for Closed-Door Operations; C-17 Support of IRAC Engine Model Development; Current Capabilities and Future Upgrade Plans of the C-17 Data Rack; Intelligent Data Mining Capabilities as Applied to Integrated Vehicle Health Management; STARS Flight Demonstration No. 2 IP Data Formatter; Space-Based Telemetry and Range Safety (STARS) Flight Demonstration No. 2 Range User Flight Test Results; Aerodynamic Effects of the Quiet Spike(tm) on an F-15B Aircraft; F-15 Intelligent Flight Controls-Increased Destabilization Failure; F-15 Integrated Resilient Aircraft Control (IRAC) Improved Adaptive Controller; Aeroelastic Analysis of the Ikhana/Fire Pod System; Ikhana: Western States Fire Missions Utilizing the Ames Research Center Fire Sensor; Ikhana: Fiber-Optic Wing Shape Sensors; Ikhana: ARTS III; SOFIA Closed-Door Flutter Envelope Flight Testing; F-15B Quiet Spike(TM) Aeroservoelastic Flight Test Data Analysis; and UAVSAR Platform Precision Autopilot Flight Results.

Stoliker, Patrick↗

New Flutter Analysis Technique for CFD-based Unsteady Aeroelasticity

This paper presents a flutter analysis technique for the transonic flight regime. The technique uses an iterative approach to determine the critical dynamic pressure for a given mach number. Unlike other CFD-based flutter analysis methods, each iteration solves for the critical dynamic pressure and uses this value in subsequent iterations until the value converges. This process reduces the iterations required to determine the critical dynamic pressure. To improve the accuracy of the analysis, the technique employs a known structural model, leaving only the aerodynamic model as the unknown. The aerodynamic model is estimated using unsteady aeroelastic CFD analysis combined with a parameter estimation routine. The technique executes as follows. The known structural model is represented as a finite element model. Modal analysis determines the frequencies and mode shapes for the structural model. At a given mach number and dynamic pressure, the unsteady CFD analysis is performed. The output time history of the surface pressure is converted to a nodal aerodynamic force vector. The forces are then normalized by the given dynamic pressure. A multi-input multi-output parameter estimation software, ERA, estimates the aerodynamic model through the use of time histories of nodal aerodynamic forces and structural deformations. The critical dynamic pressure is then calculated using the known structural model and the estimated aerodynamic model. This output is used as the dynamic pressure in subsequent iterations until the critical dynamic pressure is determined. This technique is demonstrated on the Aerostructures Test Wing-2 model at NASA's Dryden Flight Research Center.

Pak, Chan-gi↗

Application of Reduced Order Transonic Aerodynamic Influence Coefficient Matrix for Design Optimization

Supporting the Aeronautics Research Mission Directorate guidelines, the National Aeronautics and Space Administration [NASA] Dryden Flight Research Center is developing a multidisciplinary design, analysis, and optimization [MDAO] tool. This tool will leverage existing tools and practices, and allow the easy integration and adoption of new state-of-the-art software. Today s modern aircraft designs in transonic speed are a challenging task due to the computation time required for the unsteady aeroelastic analysis using a Computational Fluid Dynamics [CFD] code. Design approaches in this speed regime are mainly based on the manual trial and error. Because of the time required for unsteady CFD computations in time-domain, this will considerably slow down the whole design process. These analyses are usually performed repeatedly to optimize the final design. As a result, there is considerable motivation to be able to perform aeroelastic calculations more quickly and inexpensively. This paper will describe the development of unsteady transonic aeroelastic design methodology for design optimization using reduced modeling method and unsteady aerodynamic approximation. The method requires the unsteady transonic aerodynamics be represented in the frequency or Laplace domain. Dynamically linear assumption is used for creating Aerodynamic Influence Coefficient [AIC] matrices in transonic speed regime. Unsteady CFD computations are needed for the important columns of an AIC matrix which corresponded to the primary modes for the flutter. Order reduction techniques, such as Guyan reduction and improved reduction system, are used to reduce the size of problem transonic flutter can be found by the classic methods, such as Rational function approximation, p-k, p, root-locus etc. Such a methodology could be incorporated into MDAO tool for design optimization at a reasonable computational cost. The proposed technique is verified using the Aerostructures Test Wing 2 actually designed, built, and tested at NASA Dryden Flight Research Center. The results from the full order model and the approximate reduced order model are analyzed and compared.

Pak, Chan-gi↗

Subspace Iteration Method for Complex Eigenvalue Problems with Nonsymmetric Matrices in Aeroelastic System

Modern airplane design is a multidisciplinary task which combines several disciplines such as structures, aerodynamics, flight controls, and sometimes heat transfer. Historically, analytical and experimental investigations concerning the interaction of the elastic airframe with aerodynamic and in retia loads have been conducted during the design phase to determine the existence of aeroelastic instabilities, so called flutter .With the advent and increased usage of flight control systems, there is also a likelihood of instabilities caused by the interaction of the flight control system and the aeroelastic response of the airplane, known as aeroservoelastic instabilities. An in -house code MPASES (Ref. 1), modified from PASES (Ref. 2), is a general purpose digital computer program for the analysis of the closed-loop stability problem. This program used subroutines given in the International Mathematical and Statistical Library (IMSL) (Ref. 3) to compute all of the real and/or complex conjugate pairs of eigenvalues of the Hessenberg matrix. For high fidelity configuration, these aeroelastic system matrices are large and compute all eigenvalues will be time consuming. A subspace iteration method (Ref. 4) for complex eigenvalues problems with nonsymmetric matrices has been formulated and incorporated into the modified program for aeroservoelastic stability (MPASES code). Subspace iteration method only solve for the lowest p eigenvalues and corresponding eigenvectors for aeroelastic and aeroservoelastic analysis. In general, the selection of p is ranging from 10 for wing flutter analysis to 50 for an entire aircraft flutter analysis. The application of this newly incorporated code is an experiment known as the Aerostructures Test Wing (ATW) which was designed by the National Aeronautic and Space Administration (NASA) Dryden Flight Research Center, Edwards, California to research aeroelastic instabilities. Specifically, this experiment was used to study an instability known as flutter. ATW was a small-scale airplane wing comprised of an airfoil and wing tip boom. This wing was formulated based on a NACA-65A004 airfoil shape with a 3.28 aspect ratio. The wing had a span of 18 inch with root chord length of 13.2 inch and tip chord length of 8.7 inch. The total area of this wing was 197 square inch. The wing tip boom was a 1 inch diameter hollow tube of length 21.5 inch. The total weight of the wing was 2.66 lbs.

Pak, Chan-gi↗

Application of Approximate Unsteady Aerodynamics for Flutter Analysis

A technique for approximating the modal aerodynamic influence coefficient (AIC) matrices by using basis functions has been developed. A process for using the resulting approximated modal AIC matrix in aeroelastic analysis has also been developed. The method requires the unsteady aerodynamics in frequency domain, and this methodology can be applied to the unsteady subsonic, transonic, and supersonic aerodynamics. The flutter solution can be found by the classic methods, such as rational function approximation, k, p-k, p, root locus et cetera. The unsteady aeroelastic analysis using unsteady subsonic aerodynamic approximation is demonstrated herein. The technique presented is shown to offer consistent flutter speed prediction on an aerostructures test wing (ATW) 2 and a hybrid wing body (HWB) type of vehicle configuration with negligible loss in precision. This method computes AICs that are functions of the changing parameters being studied and are generated within minutes of CPU time instead of hours. These results may have practical application in parametric flutter analyses as well as more efficient multidisciplinary design and optimization studies.

Pak, Chan-gi↗

Application of Approximate Unsteady Aerodynamics for Flutter Analysis

A technique for approximating the modal aerodynamic influence coefficient (AIC) matrices by using basis functions has been developed. A process for using the resulting approximated modal AIC matrix in aeroelastic analysis has also been developed. The method requires the unsteady aerodynamics in frequency domain, and this methodology can be applied to the unsteady subsonic, transonic, and supersonic aerodynamics. The flutter solution can be found by the classic methods, such as rational function approximation, k, p-k, p, root locus et cetera. The unsteady aeroelastic analysis using unsteady subsonic aerodynamic approximation is demonstrated herein. The technique presented is shown to offer consistent flutter speed prediction on an aerostructures test wing (ATW) 2 and a hybrid wing body (HWB) type of vehicle configuration with negligible loss in precision. This method computes AICs that are functions of the changing parameters being studied and are generated within minutes of CPU time instead of hours. These results may have practical application in parametric flutter analyses as well as more efficient multidisciplinary design and optimization studies.

Pak, Chan-gi↗

Basis Function Approximation of Transonic Aerodynamic Influence Coefficient Matrix

A technique for approximating the modal aerodynamic influence coefficients [AIC] matrices by using basis functions has been developed and validated. An application of the resulting approximated modal AIC matrix for a flutter analysis in transonic speed regime has been demonstrated. This methodology can be applied to the unsteady subsonic, transonic and supersonic aerodynamics. The method requires the unsteady aerodynamics in frequency-domain. The flutter solution can be found by the classic methods, such as rational function approximation, k, p-k, p, root-locus et cetera. The unsteady aeroelastic analysis for design optimization using unsteady transonic aerodynamic approximation is being demonstrated using the ZAERO(TradeMark) flutter solver (ZONA Technology Incorporated, Scottsdale, Arizona). The technique presented has been shown to offer consistent flutter speed prediction on an aerostructures test wing [ATW] 2 configuration with negligible loss in precision in transonic speed regime. These results may have practical significance in the analysis of aircraft aeroelastic calculation and could lead to a more efficient design optimization cycle

Li, Wesley Waisang↗

Distributed Aerodynamic Sensing and Processing Toolbox

A Distributed Aerodynamic Sensing and Processing (DASP) toolbox was designed and fabricated for flight test applications with an Aerostructures Test Wing (ATW) mounted under the fuselage of an F-15B on the Flight Test Fixture (FTF). DASP monitors and processes the aerodynamics with the structural dynamics using nonintrusive, surface-mounted, hot-film sensing. This aerodynamic measurement tool benefits programs devoted to static/dynamic load alleviation, body freedom flutter suppression, buffet control, improvement of aerodynamic efficiency through cruise control, supersonic wave drag reduction through shock control, etc. This DASP toolbox measures local and global unsteady aerodynamic load distribution with distributed sensing. It determines correlation between aerodynamic observables (aero forces) and structural dynamics, and allows control authority increase through aeroelastic shaping and active flow control. It offers improvements in flutter suppression and, in particular, body freedom flutter suppression, as well as aerodynamic performance of wings for increased range/endurance of manned/ unmanned flight vehicles. Other improvements include inlet performance with closed-loop active flow control, and development and validation of advanced analytical and computational tools for unsteady aerodynamics.

Brenner, Martin↗

Unsteady Aerodynamic Model Tuning for Precise Flutter Prediction

A simple method for an unsteady aerodynamic model tuning is proposed in this study. This method is based on the direct modification of the aerodynamic influence coefficient matrices. The aerostructures test wing 2 flight-test data is used to demonstrate the proposed model tuning method. The flutter speed margin computed using only the test validated structural dynamic model can be improved using the additional unsteady aerodynamic model tuning, and then the flutter speed margin requirement of 15 % in military specifications can apply towards the test validated aeroelastic model. In this study, unsteady aerodynamic model tunings are performed at two time invariant flight conditions, at Mach numbers of 0.390 and 0.456. When the Mach number for the unsteady model tuning approaches to the measured fluttering Mach number, 0.502, at the flight altitude of 9,837 ft, the estimated flutter speed is approached to the measured flutter speed at this altitude. The minimum flutter speed difference between the estimated and measured flutter speed is -.14 %.

Pak, Chan-Gi↗

Unsteady Aerodynamic Model Tuning for Precise Flutter Prediction

A simple method for an unsteady aerodynamic model tuning is proposed in this study. This method is based on the direct modification of the aerodynamic influence coefficient matrices. The aerostructures test wing 2 flight-test data is used to demonstrate the proposed model tuning method. The flutter speed margin computed using only the test validated structural dynamic model can be improved using the additional unsteady aerodynamic model tuning, and then the flutter speed margin requirement of 15 percent in military specifications can apply towards the test validated aeroelastic model. In this study, unsteady aerodynamic model tunings are performed at two time invariant flight conditions, at Mach numbers of 0.390 and 0.456. When the Mach number for the unsteady aerodynamic model tuning approaches to the measured fluttering Mach number, 0.502, at the flight altitude of 9,837 ft, the estimated flutter speed is approached to the measured flutter speed at this altitude. The minimum flutter speed difference between the estimated and measured flutter speed is -0.14 percent.

Pak, Chan-gi↗

NASA Tech Briefs, December 2003

Topics covered include: Organic/Inorganic Hybrid Polymer/Clay Nanocomposites; Less-Toxic Coatings for Inhibiting Corrosion of Aluminum; Liquid Coatings for Reducing Corrosion of Steel in Concrete; Processable Polyimides Containing APB and Reactive End Caps; Rod/Coil Block Copolyimides for Ion-Conducting Membranes; Techniques for Characterizing Microwave Printed Antennas; Cylindrical Antenna With Partly Adaptive Phased-Array Feed; Command Interface ASIC - Analog Interface ASIC Chip Set; Predicting Accumulations of Ice on Aerodynamic Surfaces; Analyzing Aeroelasticity in Turbomachines; Software for Allocating Resources in the Deep Space Network; Expert Seeker; High-Speed Recording of Test Data on Hard Disks; Functionally Graded Nanophase Beryllium/Carbon Composites; Thin Thermal-Insulation Blankets for Very High Temperatures; Aerostructures Test Wing; Flight-Test Evaluation of Flutter-Prediction Methods; Piezoelectrically Actuated Microvalve for Liquid Effluents; Larger-Stroke Piezoelectrically Actuated Microvalve; Innovative, High-Pressure, Cryogenic Control Valve: Short Face-to-Face, Reduced Cost; Safer Roadside Crash Walls Would Limit Deceleration; Improved Interactive Medical-Imaging System; Scanning Microscopes Using X Rays and Microchannels; Slotting Fins of Heat Exchangers to Provide Thermal Breaks; Methane Clathrate Hydrate Prospecting; Automated Monitoring with a BSP Fault-Detection Test; Automated Monitoring with a BCP Fault-Decision Test; Vector-Ordering Filter Procedure for Data Reduction; Remote Sensing and Information Technology for Large Farms; Developments at the Advanced Design Technologies Testbed; Spore-Forming Bacteria that Resist Sterilization; and Acoustical Applications of the HHT Method.

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