SEARCH · Search NASA
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.
An algorithm is developed for finding the inverse of polynomial matrices in the irreducible form. The computational method involves the use of the left (right) matrix division method and the determination of linearly dependent vectors of the remainders. The obtained transfer function matrix has no nontrivial common factor between the elements of the numerator polynomial matrix and the denominator polynomial.
The least-squares transformation of a discrete-time multivariable linear system into a desired one by convolving the first with a polynomial system yields optimal polynomial solutions to the problems of system compensation, inversion, and approximation. The polynomial coefficients are obtained from the solution to a so-called normal linear matrix equation, whose coefficients are shown to be the weighting patterns of certain linear systems. These, in turn, can be used in the recursive solution of the normal equation.
The authors consider the dynamical modeling of robot manipulators whose joint actuators consist of motors driving the joints through gears. The dynamical models for such manipulators are significantly more complex than those for direct drive manipulators. The authors develop recursive O(n) inverse and forward dynamics algorithms as well as recursive O(n2) algorithms for the computation of the mass matrix for geared manipulators. It is shown that, despite the added complexity of the dynamical models for geared manipulators, the algorithms closely resemble the corresponding algorithms for direct drive manipulators, and that the additional algorithmic or computational complexity is relatively insignificant. As a consequence, with little additional cost, existing direct drive algorithms can be easily extended to handle the effects of gearing at the joints.
A technique is developed for systematically deriving a 'prolongation structure' - a set of interrelated potentials and pseudopotentials - for nonlinear partial differential equations in two independent variables. When this is applied to the Korteweg-de Vries equation, a new infinite set of conserved quantities is obtained. Known solution techniques are shown to result from the discovery of such a structure: related partial differential equations for the potential functions, linear 'inverse scattering' equations for auxiliary functions, Backlund transformations. Generalizations of these techniques will result from the use of irreducible matrix representations of the prolongation structure.
THe investigation of two insensitive controller synthesis techniques was reported. The finite dimensional inverse approach produces a time varying insensitive controller and/or parameter identifier by constructing inverse functions derived from a finite number of input output pair relationships. The MD/IM concept relies on the information matrix theory that was developed in the estimation and identification field. The MD/IM synthesis technique is based on the hypothesis that minimizing the information matrix will reduce system identifiability and consequently system sensitivity to uncertain parameters. The controllers designed with both techniques were evaluated on a realistic C-5A aircraft flight control problem. Results indicate that the FDI controller is more suited to trajectory type problems because of its time varying nature. The MD/IM controller performed as well as the top-rated controllers of the initial effort and has direct application to aircraft flight control problems.
We test an innovative inversion scheme using Green’s functions from an array of pressure sources embedded in finite-element method (FEM) models to image, without assuming an a-priori geometry, the composite and complex shape of a volcano deformation source. We invert interferometric synthetic aperture radar (InSAR) data to estimate the pressurization and shape of the magma reservoir of Rabaul caldera, Papua New Guinea. The results image the extended shallow magmatic system responsible for a broad and long-term subsidence of the caldera between 2007 February and 2010 December. Elastic FEM solutions are integrated into the regularized linear inversion of InSAR data of volcano surface displacements in order to obtain a 3-D image of the source of deformation. The Green’s function matrix is constructed from a library of forward line-of-sight displacement solutions for a grid of cubic elementary deformation sources. Each source is sequentially generated by removing the corresponding cubic elements from a common meshed domain and simulating the injection of a fluid mass flux into the cavity, which results in a pressurization and volumetric change of the fluidfilled cavity. The use of a single mesh for the generation of all FEM models avoids the computationally expensive process of non-linear inversion and remeshing a variable geometry domain. Without assuming an a-priori source geometry other than the configuration of the 3-D grid that generates the library of Green’s functions, the geodetic data dictate the geometry of the magma reservoir as a 3-D distribution of pressure (or flux of magma) within the source array. The inversion of InSAR data of Rabaul caldera shows a distribution of interconnected sources forming an amorphous, shallow magmatic system elongated under two opposite sides of the caldera. The marginal areas at the sides of the imaged magmatic system are the possible feeding reservoirs of the ongoing Tavurvur volcano eruption of andesitic products on the east side and of the past Vulcan volcano eruptions of more evolved materials on the west side. The interconnection and spatial distributions of sources correspond to the petrography of the volcanic products described in the literature and to the dynamics of the single and twin eruptions that characterize the caldera. The ability to image the complex geometry of deformation sources in both space and time can improve our ability to monitor active volcanoes, widen our understanding of the dynamics of active volcanic systems and improve the predictions of eruptions.
We test an innovative inversion scheme using Green’s functions from an array of pressure sources embedded in finite-element method (FEM) models to image, without assuming an a-priori geometry, the composite and complex shape of a volcano deformation source. We invert interferometric synthetic aperture radar (InSAR) data to estimate the pressurization and shape of the magma reservoir of Rabaul caldera, Papua New Guinea. The results image the extended shallow magmatic system responsible for a broad and long-term subsidence of the caldera between 2007 February and 2010 December. Elastic FEM solutions are integrated into the regularized linear inversion of InSAR data of volcano surface displacements in order to obtain a 3-D image of the source of deformation. The Green’s function matrix is constructed from a library of forward line-of-sight displacement solutions for a grid of cubic elementary deformation sources. Each source is sequentially generated by removing the corresponding cubic elements from a common meshed domain and simulating the injection of a fluid mass flux into the cavity, which results in a pressurization and volumetric change of the fluid-filled cavity. The use of a single mesh for the generation of all FEM models avoids the computationally expensive process of non-linear inversion and remeshing a variable geometry domain. Without assuming an a-priori source geometry other than the configuration of the 3-D grid that generates the library of Green’s functions, the geodetic data dictate the geometry of the magma reservoir as a 3-D distribution of pressure (or flux of magma) within the source array. The inversion of InSAR data of Rabaul caldera shows a distribution of interconnected sources forming an amorphous, shallow magmatic system elongated under two opposite sides of the caldera. The marginal areas at the sides of the imaged magmatic system are the possible feeding reservoirs of the ongoing Tavurvur volcano eruption of andesitic products on the east side and of the past Vulcan volcano eruptions of more evolved materials on the west side. The interconnection and spatial distributions of sources correspond to the petrography of the volcanic products described in the literature and to the dynamics of the single and twin eruptions that characterize the caldera. The ability to image the complex geometry of deformation sources in both space and time can improve our ability to monitor active volcanoes, widen our understanding of the dynamics of active volcanic systems and improve the predictions of eruptions.
We formulate and test a series of algorithms for echo mapping the emission-line regions near active galactic nuclei from measurements of correlated variability in their line and continuum light curves. The linear regularization method (LRM) employs a direct inversion of evenly spaced light-curve data, with a regularization parameter that can be used to control the trade-off between noise and resolution. Matrix formulas express the formal solution as well as its variance and covariance in terms of uncertainties in the measurements. Unlike the maximum-entropy method (MEM), LRM applies to kernels with both positive and negative values, but the results are somewhat limited by ringing effects. A positivity constraint proves effective in controlling the ringing. MEM combines regularization and positivity in a natural way, but similar results are also found using positivity constraints with nonentropic regularization functions. Direct inversions of unevenly sampled light curves require interpolating the noisy data. In this case better results are found by solving for both the continuum light curve and kernel function in a simultaneous fit to the data. Our conclusion is that while echo mapping currently gives ambiguous results, the algorithms are not the limiting factor. Progress depends on efforts to increase the accuracy and completeness of sampling of the observed light curves.
The intersubband-Auger-recombination time of electrons under population-inversion conditions in a single quantum well is calculated by taking into account momentum- and energy-conservation rules, and by employing Fermi-Dirac statistics. The screened matrix element of the electron-electron interaction and the overlap integral are calculated for an infinitely deep quantum well. The results are in a good agreement with published experimental data. As a major nonradiative process, the Auger recombination is related to threshold current of infrared lasers based on intersubband transitions in quantum-well structures. The realization of these devices and other limitations to achieving population inversion are discussed. In view of the results, development of these lasers for emission wavelengths corresponding to energies below the LO-phonon energy seems feasible.
Hybrid composites have important applications, such as high-performance and lightweight materials in aerospace and automotive industries. Hybrid composites utilize the synergy of diverse fillers to achieve desired material properties, but usually have more complicated microstructures. While topology optimization can optimize a particular property, designing hybrid composites for customized mechanical performances, e.g. full-range stress–strain curve, remains challenging. Here, a computational framework that integrated finite element analysis (FEA) and artificial intelligence (AI) methods of Conditional Generative Adversarial Networks (cGAN) deep learning and transfer learning was developed to establish inverse structure–property relationships and design tailor-made hybrid composites. Based on FEA-generated datasets of hybrid fiber-particle–matrix microstructures and their corresponding full-range stress–strain curves, a cGAN architecture was trained to generate tailored microstructures and establish structure–property relationships. Similarity in microstructural features and well-matched stress–strain curves based on the AI-generated composites were achieved. In conclusion, transfer learning was used to expand the pre-trained model for designing different materials systems.
The use of structural health monitoring systems on spacecraft structures can play a crucial role in ensuring the safety, reliability, and longevity of the structure by gathering and analyzing onboard sensor data. Of specific importance is monitoring for excessive loading at critical interfaces as any off-nominal structural excitations experienced by spacecraft structures can cause early unpredicted high structural life consumption or damage. The availability and cost of flight-certified sensors along with the size of spacecraft structures and allowable payload mass drives the need for a method to estimate loads using sparsely-located sensors. Numerous approaches such as physics-based, statistical learning, and physics-enhanced statistical learning algorithms have gained popularity among structural prognostics applications. However, developing noise-robust prediction models to assess loads and structural life predictions from a sparse multi-sensor data acquisition system can be a challenging task. This paper discusses the evaluation of physics-based versus machine-learning algorithms for predicting loads and structural life at mission critical locations on the spacecraft structure using a finite element loads analysis with the application of simulated noise and noise reduction techniques. To estimate the loads from accelerations, the physics-based algorithm leverages a loads transformation matrix from a Craig-Bampton reduced finite element model. A System Equivalent Reduction Expansion Process (SEREP) and a pseudo-inverse approach are considered to expand from the onboard sensor degrees of freedom to the Craig-Bampton model degrees of freedom. The machine learning algorithm provides a data driven solution/mapping of the sensor accelerations to the loads at the mission critical locations using a high dimensionality analysis. Although these strategies produce comparable loads prediction without noise, the limitations of these strategies with incorporating simulated noise and noise reduction techniques with low signal to noise ratio signals are evaluated. The study demonstrates the immense potential of statistical learning algorithms for sparse structural prognostic models and enhancing signal denoising techniques. These findings also highlight the need for noise-resilient prognostic models and low-noise data acquisition systems onboard spacecraft structures.
An explicit guidance scheme is outlined which provides the appropriate energy management in order for the shuttle orbiter to reach any location within the required footprint. Considering the orbiter as entering the earth's atmosphere, expressions for the downrange, crossrange, and the time of the termination of the entry phase as functions of the control variables are developed. Performing an order-of-magnitude analysis of the terms in these expressions, only dominant terms are retained. Analytical expressions for the elements of the sensitivity matrix which represents the partial derivatives of the desired range with respect to control variables are formulated. Using the Gauss-Jordan inversion technique, the required change in guidance commands as a function of the deviations in the downrange and crossrange are explicitly computed.
Decorin (DCN), a member of small leucine-rich proteoglycans, is known to modulate collagen fibrillogenesis. In order to investigate the potential roles of DCN in collagen matrix mineralization, several stable osteoblastic cell clones expressing higher (sense-DCN, S-DCN) and lower (antisense-DCN, As-DCN) levels of DCN were generated and the mineralized nodules formed by these clones were characterized. In comparison with control cells, the onset of mineralization by S-DCN clones was significantly delayed; whereas it was markedly accelerated and the number of mineralized nodules was significantly increased in As-DCN clones. The timing of mineralization was inversely correlated with the level of DCN synthesis. In these clones, the patterns of cell proliferation and differentiation appeared unaffected. These results suggest that DCN may act as an inhibitor of collagen matrix mineralization, thus modulating the timing of matrix mineralization.
Knowledge of particle sizes and number densities of polar stratospheric clouds (PSCs) is highly important, because they are critical parameters for the modeling of the ozone chemistry of the stratosphere. In situ measurements of PSC particles are rare. the main instrument for the accumulation of PSC data are lidar systems. Therefore the derivation of some microphysical properties of PSCS from the optical parameters measured by lidars would be highly beneficial for ozone research. Inversion of lidar data obtained in the presence of PSCs formed from crystalline particles type 11 and the various nitric acid tri Ydrrate (NAT) types cannot be easily accomplished, because a suitable scattering theory for small faceted crystals has not been readily available tip to now. As a consequence, the T-matrix method is commonly used for the interpretation of these PSC lidar data. Here the assumption is made that the optical properties of an ensemble of spheroids resemble those of crystalline PSCs, and microphysical properties of the PSC are inferred from the optical signatures of the PSC at two or more wavelengths. The problem with the T-matrix approach is that the assumption of spheroidal instead of faceted particles can lead to dramatically wrong results: Usually cloud particle properties are deduced from analysis of lidar profiles of backscatter ratio and depolarization ratio. The particle contribution to the backscatter ratio is given by the product of the particle number density and the backscattering cross section. The latter is proportional to the value of the particle's scattering phase function at 180 degrees scattering angle. At 180 degrees however, the phase functions of rough, faceted crystals and of spheroids with same maximum dimension differ by a factor of 6. From this it follows that for a PSC consisting of faceted crystals, the particle number density is underestimated by roughly the same factor if spheroidal particles are unrealistically assumed. We are currently developing a retrieval technique for determining the microphysical parameters of crystalline PSCs that takes into account the faceted shape of the PSC particles. This approach utilizes finite-difference time-domain (FDTD) calculations of particle optical properties. The accuracy and the free choice of the shape of the scattering particle make the FDTD technique a promising tool for the inversion of PSC lidar data. A first comparison of FDTD and T-matrix calculations will be presented.
Study of environmental hydrogen embrittlement of a Ti-6 Al-4 alloy as a function of test displacement rate and of variations in alpha-beta microstructure. Embrittlement in low-pressure (about 1 atm) gaseous hydrogen was inversely dependent on test displacement rate and strongly dependent on microstructure. At a given displacement rate, microstructures having a continuous alpha-phase matrix were less severely embrittled than those having a continuous beta-phase matrix. Further, brittle fracture occurred in the former microstructures by transgranular cleavage and in the latter microstructures by intergranular separation. These observations are consistent with previous studies made on slow strain-rate embrittlement of hydrogen-charged titanium alloys and are explained in terms of relative hydrogen transport rates within the alpha-phase and beta-phase titanium.
Theoretical modeling as well as laboratory and field measurement were coupled with analysis of aircraft data obtained from controlled sites in an effort to enhance understanding of the microwave response due to soil moisture so as to specify sensor parameters and develop inversion algorithms. Models to predict the complex dielectric constant were produced which led to the interpretation of the results in terms of a matrix potential rather than simply moisture content. Similar advances were made in the development of coherent and incoherent radiative transfer models and rough surface scattering models.
An inversion algorithm is presented, which is used to process Nimbus-7 solar backscattered UV (SBUV) data collected between November 1978 and October 1980. The SBUV experiment utilizes a double monochromator in the nadir position which measures the backscattered solar radiation in twelve 1-nm bands; a separate photometer measures the radiance at 343.0 nm in the field of view coincident with the monochromator. The primary output of the inversion is the total ozone content in umkehr layers in units of m atm cm. In addition, the diagonal elements of the covariance matrix are reported; they represent the uncertainty in the derived ozone content in each layer. The solution covariance is noted to be independent of the measurements.
Numerical technique increases the efficiencies of the numerical methods involving Toeplitz matrices by reducing the number of multiplications required by an N-order Toeplitz matrix from N-cubed to N-squared multiplications. Some efficient algorithms are given.