Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “fixed point method”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

On the connection between least squares, regularization, and classical shadows

Classical shadows (CS) offer a resource-efficient means to estimate quantum observables, circumventing the need for exhaustive state tomography. Here, we clarify and explore the connection between CS techniques and least squares (LS) and regularized least squares (RLS) methods commonly used in machine learning and data analysis. By formal identification of LS and RLS ``shadows'' completely analogous to those in CS---namely, point estimators calculated from the empirical frequencies of single measurements---we show that both RLS and CS can be viewed as regularizers for the underdetermined regime, replacing the pseudoinverse with invertible alternatives. Through numerical simulations, we evaluate RLS and CS from three distinct angles: the tradeoff in bias and variance, mismatch between the expected and actual measurement distributions, and the interplay between the number of measurements and number of shots per measurement. Compared to CS, RLS attains lower variance at the expense of bias, is robust to distribution mismatch, and is more sensitive to the number of shots for a fixed number of state copies---differences that can be understood from the distinct approaches taken to regularization. Conceptually, our integration of LS, RLS, and CS under a unifying ``shadow'' umbrella aids in advancing the overall picture of CS techniques, while practically our results highlight the tradeoffs intrinsic to these measurement approaches, illuminating the circumstances under which either RLS or CS would be preferred, such as unverified randomness for the former or unbiased estimation for the latter.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2012

Wavefront Sensing for WFIRST with a Linear Optical Model

In this paper we develop methods to use a linear optical model to capture the field dependence of wavefront aberrations in a nonlinear optimization-based phase retrieval algorithm for image-based wavefront sensing. The linear optical model is generated from a ray trace model of the system and allows the system state to be described in terms of mechanical alignment parameters rather than wavefront coefficients. This approach allows joint optimization over images taken at different field points and does not require separate convergence of phase retrieval at individual field points. Because the algorithm exploits field diversity, multiple defocused images per field point are not required for robustness. Furthermore, because it is possible to simultaneously fit images of many stars over the field, it is not necessary to use a fixed defocus to achieve adequate signal-to-noise ratio despite having images with high dynamic range. This allows high performance wavefront sensing using in-focus science data. We applied this technique in a simulation model based on the Wide Field Infrared Survey Telescope (WFIRST) Intermediate Design Reference Mission (IDRM) imager using a linear optical model with 25 field points. We demonstrate sub-thousandth-wave wavefront sensing accuracy in the presence of noise and moderate undersampling for both monochromatic and polychromatic images using 25 high-SNR target stars. Using these high-quality wavefront sensing results, we are able to generate upsampled point-spread functions (PSFs) and use them to determine PSF ellipticity to high accuracy in order to reduce the systematic impact of aberrations on the accuracy of galactic ellipticity determination for weak-lensing science.

Jurling, Alden S.↗
NASA NTRS1973

On Lidar Sounding of the Atmosphere to Estimate Static and Dynamic Characteristics of Aerosol Inhomogeneities

1. A possible application of intensity fluctuations of a pulse light signal reflected by atmospheric aerosols is analyzed by the correlation method to evaluate static (medium sizes, shape) and dynamic (speed and direction of movement, lifetime) characteristics of aerosol inhomogeneities. The aerosol inhomogeneities are assumed to be expanded, pressed, disintegrated and originated constantly in accordance with random laws, the set of inhomogeneities as a whole traveling together with air masses and having predominant movement in wind direction. It is shown that the characteristics of aerosol inhomogeneities considered can be expressed by the coefficients of the correlation function expansion of the reflected signal fluctuation intensity in Tailor series. 2/ Correlation systems for evaluating static and dynamic characteristics of driving objects can be divided into two types according to the kind and quantity of used information: the systems with coordinates of the information removal "points" to be fixed in space, and the systems with a parallel simultaneous information removal at discrete moments of time. The systems for determination of wind direction considered in are the examples of the first type system. However, the operating information removal for two points is insufficient to estimate completely static and dynamic characteristics of inhomogenities, their quantity ought to be increased up to three of them for two-dimensional problem and up to four of them for three-dimensional problem as it is usually done in the ionospheric studies. The second type systems are used for the investigation of a medium shape and speed of the clouds according to photographs made from satellites. These systems are also used for solution of navigation problems. The use of optical quantum generators with a scanning beam is seen to increase greatly the working information removal in comparison with the first type systems. Nevertheless, scanning rate is not sufficient sometimes in order· to consider a general picture of aerosol inhomogeneities to be stationary. In this connection the use of the systems of second type treatment becomes a matter of essential difficulty. 3. Aerosol inhomogeneities simulation has been carried out on the basis of the digital computer experiments with the aim of estimating static and dynamic characteristics of inhomogeneities by an optical beam in the atmosphere at different scanning procedures. The dependence of determination accuracy of these characteristics on the type of chosen laws of aerosol particle distribution in the atmosphere, the parameters of inhomogeneities geometry, their speed and the law of scanning have been obtained.

Zuev, V. E.↗
DOE OSTI2022

Toward Better Understanding of Microphysical Processes and Resulting Precipitation Physics: A Merger Of Observations and Cloud Models (Final Report)

A large database of global disdrometer observations and a diverse set of simulations from the Regional Atmospheric Modeling System (RAMS) were compared using principal component analysis (PCA) in order to better understand warm and ice-based precipitation processes. The analysis demonstrated that six distinct precipitation groups (PGs) with common characteristics were revealed in both the observations and model simulations. These PGs were defined by similar co-variability of rain parameters. However, the model showed large concentrations of drops with a given size compared to the observations. Detailed investigations determined the parameterization of drop breakup was forcing the drops to an equilibrium size with a stronger constraint than was indicated by the observations. A series of sensitivity studies permutating the rain shape parameter in the RAMS 2-moment bulk scheme demonstrated how the assumed shape of the rain distribution influences the microphysics as well as precipitation characteristics. Results were compared to the same simulations performed with a bin microphysics scheme where the rain shape parameter is freely evolving. In the bin scheme, a wide range of shape parameters were found, with horizontal and vertical variability, in addition to being a function of storm lifetime. The results of this study highlight the limitations of a fixed assumed rain distribution in 2-moment microphysics schemes. Model simulations were used to probe the microphysical origins of the six PGs. Rain budgets from a supercell case showed that several of the groups hypothesized to be associated with strong ice microphysical processes had significant contributions from melting hail, but the complexity of ice and warm-rain processes in the supercell precluded definitive determination of microphysical origins for many of the PGs. A case study from the Mid-latitude Continental Convection and Clouds Experiment (MC3E) compared the model PGs to disdrometer observations, and demonstrated the spatial and temporal variability of the PGs which is not possible from disdrometer point measurements alone. The analyses performed during this project demonstrated how statistical analysis can provide a robust method for comparing model simulations and observations, which ultimately resulted identification of limitations in some current microphysics parameterizations as well as insights into precipitation variability which ultimately benefits both observations and modeling efforts.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1984

Flight tests of the Digital Integrated Automatic Landing System (DIALS)

The design, development, implementation and flight tests of the Digital Integrated Automatic Landing System (DIALS) are discussed. The system was implemented and flight tested on the Transport Systems Research Vehicle (TSRV), a Boeing 737-100. The design uses modern optimal control methods. The direct digital design obtained uses a 10 Hz rate for the sampling of sensors and the control commands. The basic structure of the control law consists of a steady state Kalman filter followed by a control gain matrix. The sensor information used includes Microwave Landing System (MLS) position, attitude, calibrated airspeed, and body accelerations. The phases of the final approach considered are localized and steep glideslope capture (which may be performed simultaneously or independently), localizer and glideslope track, crab/decrab, and flare to touchdown. The system can capture, track, and flare from conventional, as well as steep, glideslopes ranging from 2.5 deg to 5.5 deg. All of the modes of the control law including the Kalman filters were implemented on the TSRV flight computers which use fixed point arithmetic with 16 bit words. The implementation considerations are described as well as an analysis of the flight test results.

Halyo, N.↗
DOE OSTI2021

Follow the power—pathways to steady-state tokamak reactors

Abstract Diagramming pathways of dimensionless power is a potent method for extrapolating between operating points on present-day tokamaks and future burning plasma devices. The heat transport power, current drive power, H-mode threshold power and other ‘plasma physics’ powers can be expressed in dimensionally correct (or normalized) form as Pa 3/4 , where P is the power and a is the plasma minor radius, with the relative gyroradius ( ρ * ) dependence ranging from gyro-Bohm-like for transport ( P a 3 / 4 ∝ ρ * − 3 / 2 ), Bohm-like for current drive ( P a 3 / 4 ∝ ρ * − 5 / 2 ) and worse than Bohm-like for H-mode threshold ( P a 3 / 4 ∝ ρ * − 3 ). The D–T fusion power cannot be normalized in the same fashion since it is governed by nuclear physics, but at fixed B T it scales like P a 3 / 4 ∝ ρ * − 9 / 2 . Other ‘mixed physics’ powers can be incorporated into the dimensionless power framework by holding B T fixed in the same manner. Diagramming these dimensionless powers vs ρ * shows how the pathway to a steady-state reactor can be optimized relative to various operational boundaries. Using a steady-state hybrid discharge with β N = 3.2 from DIII-D as the starting point, a multi-parameter optimization finds an attractive pathway to steady-state operation on ITER using 76 MW of current drive power (fusion gain of Q fus = 8), along with a pathway to Q fus = 20 in a JET-sized steady-state reactor with B T = 10 T.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1981

Non-E x B ordered ion beams upstream of the earth's bow shock

The unexpected appearance of spin modulations in the fixed voltage electrostatic analyzer detectors on ISEE 1 and 2 has made it possible to study the plasma properties of the upstream ions in high time resolution. Using an isotropic flowing Maxwellian distribution to model the count rate modulations, estimates have been obtained of the local plasma temperature and three-dimensional flow velocity of the observed upstream ion population. It is found that in almost all of the observations of upstream particles there exist beam-like ions with temperatures in the range 5-80 eV. Their flow velocities cannot be ordered by E x B. This last point separates these observations from the previously reported reflected and diffuse populations of upstream ions. Mechanisms that can gyrophase bunch the ions reflected at the bow shock are discussed as a method of explaining the data.

Gurgiolo, C.↗
DOE OSTI2020

Adaptive Activation Functions Accelerate Convergence in Deep and Physics-informed Neural Networks

We employ adaptive activation functions for regression in deep and physics-informed neural networks (PINNs) to approximate smooth and discontinuous functions as well as solutions of linear and nonlinear partial differential equations. In particular, we solve the nonlinear Klein-Gordon equation, which has smooth solutions, the nonlinear Burgers equation, which can admit high gradient solutions, and the Helmholtz equation. We introduce a scalable hyper-parameter in the activation function, which can be optimized to achieve best performance of the network as it changes dynamically the topology of the loss function involved in the optimization process. The adaptive activation function has better learning capabilities than the traditional one (fixed activation) as it improves greatly the convergence rate, especially at early training, as well as the solution accuracy. To better understand the learning process, we plot the neural network solution in the frequency domain to examine how the network captures successively different frequency bands present in the solution. We consider both forward problems, where the approximate solutions are obtained, as well as inverse problems, where parameters involved in the governing equation are identified. Our simulation results show that the proposed method is a very simple and effective approach to increase the efficiency, robustness and accuracy of the neural network approximation of nonlinear functions as well as solutions of partial differential equations, especially for forward problems. We theoretically prove that in the proposed method, gradient descent algorithms are not attracted to suboptimal critical points or local minima.

machine leaning, Bad minima, Inverse problems, Phy↗
NASA NTRS2016

Spiral Lamber's Problem with Generalized Logarithmic Spirals

Lambert’s problem subject to a continuous acceleration is solved using the family of generalized logarithmic spirals. Thanks to the existence of two first integrals related to the energy and angular momentum surprising analogies with the Keplerian case are found. A minimum-energy spiral transfer exists. Increasing the value of the constant of the generalized energy yields pairs of conjugate spiral trajectories. The properties of such spirals are strongly connected with the properties of conjugate Keplerian orbits. When the generalized constant of the energy reaches a critical value the two solutions degenerate into a pair of parabolic spirals, one of which connects the two vectors through infinity. From that point the spiral transfers become hyperbolic. Generalized logarithmic spirals admit closed-form solutions to all the required magnitudes including the time of flight, providing a deep insight into the dynamics of the problem. In addition, the maximum acceleration along the transfer is found analytically so the solutions that violate the design constraints on the maximum thrust acceleration can be rejected without any further computations. When the time of flight is fixed there is still a degree of freedom in the solution, related to a control parameter. Resonant transfers appear naturally thanks to the symmetry properties of the generalized logarithmic spirals. The problem of designing a low-thrust transfer between two bodies can be reduced to solving the corresponding spiral Lambert’s problem. In order to show the versatility of the method it is applied to the design of an asteroid tour and to explore launch opportunities to Mars.\

Roa, Javier↗
NASA NTRS1991

Transformation of two and three-dimensional regions by elliptic systems

A reliable linear system is presented for grid generation in 2-D and 3-D. The method is robust in the sense that convergence is guaranteed but is not as reliable as other nonlinear elliptic methods in generating nonfolding grids. The construction of nonfolding grids depends on having reasonable approximations of cell aspect ratios and an appropriate distribution of grid points on the boundary of the region. Some guidelines are included on approximating the aspect ratios, but little help is offered on setting up the boundary grid other than to say that in 2-D the boundary correspondence should be close to that generated by a conformal mapping. It is assumed that the functions which control the grid distribution depend only on the computational variables and not on the physical variables. Whether this is actually the case depends on how the grid is constructed. In a dynamic adaptive procedure where the grid is constructed in the process of solving a fluid flow problem, the grid is usually updated at fixed iteration counts using the current value of the control function. Since the control function is not being updated during the iteration of the grid equations, the grid construction is a linear procedure. However, in the case of a static adaptive procedure where a trial solution is computed and used to construct an adaptive grid, the control functions may be recomputed at every step of the grid iteration.

Mastin, C. Wayne↗
NASA NTRS1994

Theoretical study of the incompressible Navier-Stokes equations by the least-squares method

Usually the theoretical analysis of the Navier-Stokes equations is conducted via the Galerkin method which leads to difficult saddle-point problems. This paper demonstrates that the least-squares method is a useful alternative tool for the theoretical study of partial differential equations since it leads to minimization problems which can often be treated by an elementary technique. The principal part of the Navier-Stokes equations in the first-order velocity-pressure-vorticity formulation consists of two div-curl systems, so the three-dimensional div-curl system is thoroughly studied at first. By introducing a dummy variable and by using the least-squares method, this paper shows that the div-curl system is properly determined and elliptic, and has a unique solution. The same technique then is employed to prove that the Stokes equations are properly determined and elliptic, and that four boundary conditions on a fixed boundary are required for three-dimensional problems. This paper also shows that under four combinations of non-standard boundary conditions the solution of the Stokes equations is unique. This paper emphasizes the application of the least-squares method and the div-curl method to derive a high-order version of differential equations and additional boundary conditions. In this paper, an elementary method (integration by parts) is used to prove Friedrichs' inequalities related to the div and curl operators which play an essential role in the analysis.

Jiang, Bo-Nan↗
NASA NTRS2024

X-57 Cruise Motor GVT Using Fixed-Base Correction Technique

The National Aeronautics and Space Administration (NASA) Armstrong Flight Research Center (AFRC) completed a modal survey of the X-57 Maxwell aircraft cruise motor system to help inform cruise motor redesign efforts. X-57 Maxwell was an electric propulsion demonstrator aircraft developed by NASA to inform airworthiness standards for electrified-aircraft. The cruise motor system modal survey was completed in spring of 2023 utilizing the fixed-base correction (FBC) ground vibration test (GVT) technique developed by ATA Engineering, to decouple the motor modes from the aircraft modes. Previously during the full aircraft GVT, a detailed modal assessment of the cruise motors was not performed. Owing to the X-57 project’s phase in the aircraft development cycle when the motor redesign effort occurred, the cruise motor GVT could only be performed with the cruise motor system installed on the aircraft, with most of its installation hardware (wiring, baffling, sensors, etc.) attached. An impact hammer was used to provide excitation input at various locations within the tight confines of the cruise motor installation. To better support motor redesign efforts, the FBC methodology was utilized to fix, separate and de-couple the cruise motor modes from aircraft modal response. During the GVT, this required additional impact tap tests on candidate fixed-boundary points for each degree of freedom (DOF) to be fixed. Additional triaxial accelerometers installed at the candidate points were used to compute frequency response functions (FRFs) in X, Y, and Z directions to enable those DOFs to be numerically fixed. Test data was acquired using Hottinger Brüel & Kjær’s LAN-XI data acquisition hardware and BK Connect software. FBC post-test processing was performed using the Structural Modification Using Frequency Response Functions (SMURF) technique with ATA Engineering’s Interface between MATLAB, Analysis, Test (IMAT) software. Utilizing the FBC technique relieved test engineers from having to instrument the entire aircraft to identify and separate aircraft response from cruise motor modes of interest. The FBC technique also permitted structural analysis engineers to omit secondary components from their finite element model (FEM) of the cruise motor system. This FBC modal survey was successful, and the first time NASA AFRC utilized the FBC method on an aircraft rather than a test fixture, and also using an impact hammer rather than multiple shakers allowing significant project schedule and cost savings

Modal Survey↗
NASA NTRS1976

Space shuttle electromagnetic environment experiment. Phase A: Definition study

Methods for carrying out measurements of earth electromagnetic environment using the space shuttle as a measurement system platform are herein reported. The goal is to provide means for mapping intentional and nonintentional emitters on earth in the frequency range 0.4 to 40 GHz. A survey was made of known emitters using available data from national and international regulatory agencies, and from industry sources. The spatial distribution of sources, power levels, frequencies, degree of frequency re-use, etc., found in the survey, are here presented. A concept is developed for scanning the earth using a directive antenna whose beam is made to rotate at a fixed angle relative to the nadir; the illuminated area swept by the beam is of the form of cycloidal annulus over a sphere. During the beam's sojourn over a point, the receiver sweeps in frequency over ranges in the order of octave width using sweeping filter bandwidths sufficient to give stable readings.

Haber, F.↗
NASA NTRS1991

Experiments with conjugate gradient algorithms for homotopy curve tracking

There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK is a mathematical software package implementing globally convergent homotopy algorithms with three different techniques for tracking a homotopy zero curve, and has separate routines for dense and sparse Jacobian matrices. The HOMPACK algorithms for sparse Jacobian matrices use a preconditioned conjugate gradient algorithm for the computation of the kernel of the homotopy Jacobian matrix, a required linear algebra step for homotopy curve tracking. Here, variants of the conjugate gradient algorithm are implemented in the context of homotopy curve tracking and compared with Craig's preconditioned conjugate gradient method used in HOMPACK. The test problems used include actual large scale, sparse structural mechanics problems.

Irani, Kashmira M.↗
NASA NTRSDate not supplied

Microscale Constitutive Model Sensitivity on Multiscale Modeling of Fiber Reinforced Composites

Fiber reinforced composites are desirable in applications where low weight and high strength are needed, but are susceptible to microscale variability during manufacturing, making failure predictions difficult. The impact microscale variability has on macroscale mechanical response is difficult to predict due to the computational efficiency needed to simulate many, large, high fidelity, microscale models. In this study, a multiscale approach was taken to model 3-point bend, 4-point bend, and tensile experiments of a unidirectional composite from only having microstructure scans of these samples and constituent properties from literature. These scans were sampled with different sized windows, and statistically equivalent microstructures were generated, then simulated for stiffness, strength, and fracture toughness using an efficient micromechanical. Mesoscale models were created where element sizes equaled microstructure size, and properties were assigned through sampling of microscale simulation results. First, this study showed the effect of using Weibull scaling on constituent matrix strength on macroscale response. Then, a comparison was made between different element sizes and experiments. Finally, model dimensions were fixed, and the effect of randomly distributed local properties alone was examined. Results showed that the scatter of strength and stiffness in the experiments could be predicted well using images of the microscale fiber morphologies and that using stochastic properties produced a 3% coefficient of variation of strength for all experiments.

statistical microstructure↗
NASA NTRS1982

Engineering sciences area and module performance and failure analysis area

Photovoltaic-array/power-conditioner interface studies are updated. An experiment conducted to evaluate different operating-point strategies, such as constant voltage and pilot cells, and to determine array energy losses when the array is operated off the maximum power points is described. Initial results over a test period of three and a half weeks showed a 2% energy loss when the array is operated at a fixed voltage. Degraded-array studies conducted at NE RES that used a range of simulated common types of degraded I-V curves are reviewed. The instrumentation installed at the JPL field-test site to obtain the irradiance data was described. Experiments using an optical filter to adjust the spectral irradiance of the large-area pulsed solar simulator (LAPSS) to AM1.5 are described. Residential-array research activity is reviewed. Voltage isolation test results are described. Experiments performed on one type of module to determine the relationship between leakage current and temperature are reviewed. An encapsulated-cell testing approach is explained. The test program, data reduction methods, and initial results of long-duration module testing are described.

Ross, R. G., Jr.↗
DOE OSTI2024

Reduced-order modeling on a near-term quantum computer

Quantum computing is an advancing area of research in which computer hardware and algorithms are developed to take advantage of quantum mechanical phenomena. In recent studies, quantum algorithms have shown promise in solving linear systems of equations as well as systems of linear ordinary differential equations (ODEs) and partial differential equations (PDEs). Reducedorder modeling (ROM) algorithms for studying fluid dynamics have shown success in identifying linear operators that can describe flowfields, where dynamic mode decomposition (DMD) is a particularly useful method in which a linear operator is identified from data. In this work, DMD is reformulated as an optimization problem to propagate the state of the linearized dynamical system on a quantum computer. This reformulation was chosen as a means of facilitating implementation on a near-term quantum computer. Quadratic unconstrained binary optimization (QUBO), a technique for optimizing quadratic polynomials in binary variables, allows for quantum annealing algorithms to be applied. A quantum circuit model (quantum approximation optimization algorithm, QAOA) is utilized to obtain predictions of the state trajectories. Results are shown for the quantum-ROM predictions for flow over a 2D cylinder at Re = 220 and flow over a NACA0009 airfoil at Re = 500 and α = 15°. The quantum-ROM predictions are found to depend on the number of bits utilized for a fixed point representation and the truncation level of the DMD model. Comparisons with DMD predictions from a classical computer algorithm are made, as well as an analysis of the computational complexity and prospects for future, more fault-tolerant quantum computers.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2003

Blind Leak Detection for Closed Systems

The current inspection technique for locating interstitial leaking in the Space Shuttle Main Engine nozzles is the application of a liquid leak check solution in the openings where the interstitials space between the tubing and the structural jacket vent out the aft end of the nozzle, while its cooling tubes are pressurized to 25 psig with Helium. When a leak is found, it is classified, and if the leak is severe enough the suspect tube is cut open so that a boroscope can be inserted to find the leak point. Since the boroscope can only cover a finite tube length and since it is impossible to identify which tube (to the right or left of the identified interstitial) is leaking, many extra and undesired repairs have been made to fix just one leak. In certain instances when the interstitials are interlinked by poor braze bonding, many interstitials will show indications of leaking from a single source. What is desired is a technique that can identify the leak source so that a single repair can be performed. Dr, Samuel Russell and James Walker, both with NASA/MSFC have developed a thermographic inspection system that addresses a single repair approach. They have teamed with Boeing/Rocketdyne to repackage the inspection processes to be suitable to address full scale Shuttle development and flight hardware and implement the process at NASA centers. The methods and results presented address the thermographic identification of interstitial leaks in the Space Shuttle Main Engine nozzles. A highly sensitive digital infrared camera (capable of detecting a delta temperature difference of 0.025 C) is used to record the cooling effects associated with a leak source, such as a crack or pinhole, hidden within the nozzle wall by observing the inner hot wall surface as the nozzle is pressurized, These images are enhanced by digitally subtracting a thermal reference image taken before pressurization. The method provides a non-intrusive way of locating the tube that is leaking and the exact leak source position to within a very small axial distance. Many of the factors that influence the inspectability of the nozzle are addressed; including pressure rate, peak pressure, gas type, ambient temperature and surface preparation. Other applications for this thermographic inspection system are the Reinforced-Carbon-Carbon (RCC) leading edge of the Space Shuttle orbiter and braze joint integrity.

Oelgoetz, Peter↗