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All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Damage growth in composite laminates with interleaves

The influence of interleaves on the fracture behavior of laminated composites is investigated. The geometry of the composite consists of a cracked layer, bonded between two half-planes, which is separated by thin, low modulus, interleaves. The interleaves are modeled as uncoupled tension and shear springs. A stress analysis is carried out for a crack which may grow up to and spread along the interface. Integral transform techniques are used to develop the solution in terms of singular integral equations. An asymptotic analysis reveals logarithmic singularities in the critical stresses for the case of a broken layer. The equations are solved numerically and the effect of damage on critical stresses is studied. Initial results indicate that the interleaf gives a significant reduction in stresses in the adjacent regions and, if properly selected, should result in a more damage tolerant laminate.

Goree, James G.↗
NASA NTRS2006

On Certain Theoretical Developments Underlying the Hilbert-Huang Transform

One of the main traditional tools used in scientific and engineering data spectral analysis is the Fourier Integral Transform and its high performance digital equivalent - the Fast Fourier Transform (FFT). Both carry strong a-priori assumptions about the source data, such as being linear and stationary, and of satisfying the Dirichlet conditions. A recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang Transform (HHT), proposes a novel approach to the solution for the nonlinear class of spectral analysis problems. Using a-posteriori data processing based on the Empirical Mode Decomposition (EMD) sifting process (algorithm), followed by the normalized Hilbert Transform of the decomposed data, the HHT allows spectral analysis of nonlinear and nonstationary data. The EMD sifting process results in a non-constrained decomposition of a source real-value data vector into a finite set of Intrinsic Mode Functions (IMF). These functions form a nearly orthogonal derived from the data (adaptive) basis. The IMFs can be further analyzed for spectrum content by using the classical Hilbert Transform. A new engineering spectral analysis tool using HHT has been developed at NASA GSFC, the HHT Data Processing System (HHT-DPS). As the HHT-DPS has been successfully used and commercialized, new applications pose additional questions about the theoretical basis behind the HHT and EMD algorithms. Why is the fastest changing component of a composite signal being sifted out first in the EMD sifting process? Why does the EMD sifting process seemingly converge and why does it converge rapidly? Does an IMF have a distinctive structure? Why are the IMFs nearly orthogonal? We address these questions and develop the initial theoretical background for the HHT. This will contribute to the development of new HHT processing options, such as real-time and 2-D processing using Field Programmable Gate Array (FPGA) computational resources,

Kizhner, Semion↗
NASA NTRS1972

A layered composite with a broken laminate

The problem of a laminate composite in the presence of a crack located normal to the bond lines is considered. Stress analysis of the limiting case when the crack extends to the bond lines is carried out. An integral transform technique is used to formulate the problem in terms of a singular integral equation. The power of stress singularity around the crack tip terminating at the interface is obtained using the above technique. The singular integral equation is solved numerically and the effect of material properties on the stress intensity factor is calculated.

Gupta, G. D.↗
NASA NTRS1973

A layered composite with a broken laminate.

The problem of a laminate composite in presence of a crack located normal to the bond lines is considered. Stress analysis of the limiting case when the crack extends to the bond lines is carried out. Integral transform technique is used to formulate the problem in terms of a singular integral equation from which the power of stress singularity around the crack tip terminating at the interface is obtained. The singular integral equation is solved numerically and the effect of material properties on the stress intensity factor is calculated.

Gupta, G. D.↗
NASA NTRS2005

On the Hilbert-Huang Transform Theoretical Developments

One of the main heritage tools used in scientific and engineering data spectrum analysis is the Fourier Integral Transform and its high performance digital equivalent - the Fast Fourier Transform (FFT). Both carry strong a-priori assumptions about the source data, such as linearity, of being stationary, and of satisfying the Dirichlet conditions. A recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang Transform (HHT), proposes a novel approach to the solution for the nonlinear class of spectrum analysis problems. Using a-posteriori data processing based on the Empirical Mode Decomposition (EMD) sifting process (algorithm), followed by the normalized Hilbert Transform of the decomposition data, the HHT allows spectrum analysis of nonlinear and nonstationary data. The EMD sifting process results in a non-constrained decomposition of a source real value data vector into a finite set of Intrinsic Mode Functions (IMF). These functions form a near orthogonal adaptive basis, a basis that is derived from the data. The IMFs can be further analyzed for spectrum interpretation by the classical Hilbert Transform. A new engineering spectrum analysis tool using HHT has been developed at NASA GSFC, the HHT Data Processing System (HHT-DPS). As the HHT-DPS has been successfully used and commercialized, new applications post additional questions about the theoretical basis behind the HHT and EMD algorithms. Why is the fastest changing component of a composite signal being sifted out first in the EMD sifting process? Why does the EMD sifting process seemingly converge and why does it converge rapidly? Does an IMF have a distinctive structure? Why are the IMFs near orthogonal? We address these questions and develop the initial theoretical background for the HHT. This will contribute to the developments of new HHT processing options, such as real-time and 2-D processing using Field Programmable Array (FPGA) computational resources, enhanced HHT synthesis, and broaden the scope of HHT applications for signal processing.

Kizhner, Semion↗
NASA NTRS1977

Feasibility investigation of integrated optics Fourier transform devices

The possibility of producing an integrated optics data processing device based upon Fourier transformations or other parallel processing techniques, and the ways in which such techniques may be used to upgrade the performance of present and projected NASA systems were investigated. Activities toward this goal include; (1) production of near-diffraction-limited geodesic lenses in glass waveguides; (2) development of grinding and polishing techniques for the production of geodesic lenses in LiNbO3 waveguides; (3) development of a characterization technique for waveguide lenses; and (4) development of a theory for corrected aspheric geodesic lenses. A holographic subtraction system was devised which should be capable of rapid on-board preprocessing of a large number of parallel data channels. The principle involved is validated in three demonstrations.

Verber, C. M.↗
NASA NTRS2003

On the Hilbert-Huang Transform Data Processing System Development

One of the main heritage tools used in scientific and engineering data spectrum analysis is the Fourier Integral Transform and its high performance digital equivalent - the Fast Fourier Transform (FFT). The Fourier view of nonlinear mechanics that had existed for a long time, and the associated FFT (fairly recent development), carry strong a-priori assumptions about the source data, such as linearity and of being stationary. Natural phenomena measurements are essentially nonlinear and nonstationary. A very recent development at the National Aeronautics and Space Administration (NASA) Goddard Space Flight Center (GSFC), known as the Hilbert-Huang Transform (HHT) proposes a novel approach to the solution for the nonlinear class of spectrum analysis problems. Using the Empirical Mode Decomposition (EMD) followed by the Hilbert Transform of the empirical decomposition data (HT), the HHT allows spectrum analysis of nonlinear and nonstationary data by using an engineering a-posteriori data processing, based on the EMD algorithm. This results in a non-constrained decomposition of a source real value data vector into a finite set of Intrinsic Mode Functions (IMF) that can be further analyzed for spectrum interpretation by the classical Hilbert Transform. This paper describes phase one of the development of a new engineering tool, the HHT Data Processing System (HHTDPS). The HHTDPS allows applying the "T to a data vector in a fashion similar to the heritage FFT. It is a generic, low cost, high performance personal computer (PC) based system that implements the HHT computational algorithms in a user friendly, file driven environment. This paper also presents a quantitative analysis for a complex waveform data sample, a summary of technology commercialization efforts and the lessons learned from this new technology development.

Kizhner, Semion↗
NASA NTRS1972

An integral equation approach to the strip problem

A semi-infinite strip held rigidly on its short end is considered. Loads in the strip at infinity (far away from the fixed end) are prescribed. Integral transform technique is used to provide an exact formulation of the problem in terms of a singular integral equation. Stress singularity at the strip corner is obtained from the singular integral equation which is then solved numerically. Stresses along the rigid end are determined and the effect of the material properties on the stress intensity factor is presented. The method can also be applied to the problem of a laminate composite with a flat inclusion normal to the interfaces.

Gupta, G. D.↗
NASA NTRS1973

An integral equation approach to the semi-infinite strip problem.

A semi-infinite strip held rigidly on its short end is considered. Loads in the strip at infinity (far away from the fixed end) are prescribed. The integral transform technique is used to provide an exact formulation of the problem in terms of a singular integral equation. The stress singularity at the strip corner is obtained from the singular integral equation, which is then solved numerically. Stresses along the rigid end are determined, and the effect of the material properties on the stress-intensity factor is presented. The method can also be applied to the problem of a laminate composite with a flat inclusion normal to the interfaces.

Gupta, G. D.↗
NASA NTRS2016

On Holo-Hilbert Spectral Analysis: A Full Informational Spectral Representation for Nonlinear and Non-Stationary Data

The Holo-Hilbert spectral analysis (HHSA) method is introduced to cure the deficiencies of traditional spectral analysis and to give a full informational representation of nonlinear and non-stationary data. It uses a nested empirical mode decomposition and Hilbert-Huang transform (HHT) approach to identify intrinsic amplitude and frequency modulations often present in nonlinear systems. Comparisons are first made with traditional spectrum analysis, which usually achieved its results through convolutional integral transforms based on additive expansions of an a priori determined basis, mostly under linear and stationary assumptions. Thus, for non-stationary processes, the best one could do historically was to use the time- frequency representations, in which the amplitude (or energy density) variation is still represented in terms of time. For nonlinear processes, the data can have both amplitude and frequency modulations (intra-mode and inter-mode) generated by two different mechanisms: linear additive or nonlinear multiplicative processes. As all existing spectral analysis methods are based on additive expansions, either a priori or adaptive, none of them could possibly represent the multiplicative processes. While the earlier adaptive HHT spectral analysis approach could accommodate the intra-wave nonlinearity quite remarkably, it remained that any inter-wave nonlinear multiplicative mechanisms that include cross-scale coupling and phase-lock modulations were left untreated. To resolve the multiplicative processes issue, additional dimensions in the spectrum result are needed to account for the variations in both the amplitude and frequency modulations simultaneously. HHSA accommodates all the processes: additive and multiplicative, intra-mode and inter-mode, stationary and nonstationary, linear and nonlinear interactions. The Holo prefix in HHSA denotes a multiple dimensional representation with both additive and multiplicative capabilities.

Huang, Norden E.↗
NASA NTRS2014

On the Computation of High Order Rys Quadrature Weights and Nodes

Since its introduction in 1976, the Rys Quadrature method has proven a very attractive method for evaluating electron repulsion integrals for calculations using Gaussian type orbitals. Since then, there have been considerable refinements of the method, but at it's core, Gaussian weights and nodes are used to exactly evaluate using a numerical approach to the transform integral. One of the powers of the Rys Quadrature method is the relative ease in evaluating integrals involving functions of high angular momentum. In this work we report on the complete resolution of these numerical difficulties, and we have easily computed accurate quadrature weights and nodes up to order 101. All calculations were carried out using 128-bit precision.

Computation↗
NASA NTRS1996

Hypercars: The next industrial revolution

The auto industry -- one-seventh of the GNP, and the highest expression of the Iron Age -- is about to trigger the biggest transformation in industrial structure since the microchip. Ultralight cars molded from net-shape advanced composites can be several-fold lighter than present steel cars, yet safer, sportier, and more comfortable, durable, and beautiful. Modern hybrid-electric drives boost efficiency approximately 1.3-1.5x in heavy steel cars, but approximately 5-20x in ultralight, very slippery plafforms. Synergistically combined into ultralight-hybrid 'hypercars,' these elements can yield state-of-the-shelf family cars that average 150-300+ mi/gal -- twice that with state-of-the-art technologies -- yet can also be superior in all other respects, probably including cost: carbon-fiber monocoques can actually be cheaper to mass-produce that steel unibodies. Designing cars more like aircraft and less like tanks requires not only an approximately 400-500 kg curb mass and very low air and road drag, but also an aerospace philosophy of engineering integration. Mass, cost, and complexity turn out to compound with heavy hybrids but to decompound with ultralight hybrids, owing partly to radical simplification. Excellent aerodynamics, preferable including advanced techniques for passive boundary-layer control, will be the key to successful design integration. Transforming automaking is a competitive and environmental imperative, could form the nucleus of a green industrial Renaissance, and would enhance national security by, among other things, saving as much oil as OPEC now extracts. However, this transformation faces serious cultural barriers. For example, hypercars will be more like computers with wheels than like cars with chips -- they'll have an order of magnitude more code than today's cars -- but Detroit is not a software culture. Just the transition from stamped and welded steel to integrated and adhesive-joined synthetics is difficult enough. Nonetheless, hypercars are rapidly heading to market in the late 1990s, because approximately 25 current and intending automakers are eager to capture their potentially decisive competitive advantages -- including order-of-magnitude reductions in product cycle time, tooling cost, assembly effort, and parts count. Hypercars will succeed, and may well sweep the market, not because of mandates or subsidies, but because of manufacturers' quest for competitive advantage and customers' desire for better, smarter cars.

Lovins, Amory B.↗
NASA NTRS2012

Rainbow Fourier Transform

We present a novel technique for remote sensing of cloud droplet size distributions. Polarized reflectances in the scattering angle range between 135deg and 165deg exhibit a sharply defined rainbow structure, the shape of which is determined mostly by single scattering properties of cloud particles, and therefore, can be modeled using the Mie theory. Fitting the observed rainbow with such a model (computed for a parameterized family of particle size distributions) has been used for cloud droplet size retrievals. We discovered that the relationship between the rainbow structures and the corresponding particle size distributions is deeper than it had been commonly understood. In fact, the Mie theory-derived polarized reflectance as a function of reduced scattering angle (in the rainbow angular range) and the (monodisperse) particle radius appears to be a proxy to a kernel of an integral transform (similar to the sine Fourier transform on the positive semi-axis). This approach, called the rainbow Fourier transform (RFT), allows us to accurately retrieve the shape of the droplet size distribution by the application of the corresponding inverse transform to the observed polarized rainbow. While the basis functions of the proxy-transform are not exactly orthogonal in the finite angular range, this procedure needs to be complemented by a simple regression technique, which removes the retrieval artifacts. This non-parametric approach does not require any a priori knowledge of the droplet size distribution functional shape and is computationally fast (no look-up tables, no fitting, computations are the same as for the forward modeling).

Alexandrov, Mikhail D.↗