Efficiency of generalized matrix inversion methods
Efficiency of computer programs to calculate generalized inverse of arbitrary real matrix
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Efficiency of computer programs to calculate generalized inverse of arbitrary real matrix
The two remote sensing problems of temperature profiling and aerosol characterization (complex refractive index, size distribution) are considered. These problems differ only in the explicit form of the source function which, for aerosols, includes contributions from both single and multiple scattering processes. When the observables are the spectral extinction or the single scattering of the source radiation, the associated problem is completely analogous to the linearized temperature inversion problem. Methods for obtaining the solution of the linear problem are classified following three main categories: (1) derivation of properties that all solutions satisfy, which must then be properties of the actual solution; (2) regularization of the ill-posed problem; and (3) data changes within their domain of uncertainty in order to avoid the basic instability. A number of unexplored methods are indicated.
The research activities in Italy on inverse design and optimization are reviewed. The review is focused on aerodynamic aspects in turbomachinery and wing section design. Inverse design of blade rows and ducts of turbomachinery in subsonic and transonic regime are illustrated by the Politecnico di Torino and turbomachinery industry (FIAT AVIO).
The application of Chahine's (1970) inversion technique to remote sensing problems utilizing the limb viewing geometry is discussed. The problem considered here involves occultation-type measurements and limb radiance-type measurements from either spacecraft or balloon platforms. The kernel matrix of the inversion problem is either an upper or lower triangular matrix. It is demonstrated that the Chahine inversion technique always converges, provided the diagonal elements of the kernel matrix are nonzero.
An inverse technique was used to calculate through-thickness fatigue crack closure behavior. The through-thickness variation in crack opening stress-intensity factor was calculated by considering the variation in the three-dimensional stress-intensity factor, the variation in crack growth rate along the crack front, and a relationship between the crack growth rate and effective stress-intensity factor range (da/dN-Delta-K(eff)). The three-dimensional stress-intensity factor variation was obtained from an elastic finite element analysis of specific crack-front profiles observed experimentally. The variation in crack growth rate along the crack front was obtained experimentally from comparison of observed crack front changes. The da/dN-Delta-K(eff) relationship was estimated from high stress ratio, constant load amplitude, and fatigue crack growth tests. The through-thickness crack opening stress-intensity factor results agreed with crack opening measurements obtained from fatigue striations, near-tip strain gages, and remote strain and displacement gages.
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A document describes research into the problem of detecting a case breach formation at an early stage of a rocket flight. An inversion algorithm for case breach allocation is proposed and analyzed. It is shown how the case breach can be allocated at an early stage of its development by using the rocket sensor data and the output data from the control block of the rocket navigation system. The results are simulated with MATLAB/Simulink software. The efficiency of an inversion algorithm for a case breach location is discussed. The research was devoted to the analysis of the ARES-l flight during the first 120 seconds after the launch and early prediction of case breach failure. During this time, the rocket is propelled by its first-stage Solid Rocket Booster (SRB). If a breach appears in SRB case, the gases escaping through it will produce the (side) thrust directed perpendicular to the rocket axis. The side thrust creates torque influencing the rocket attitude. The ARES-l control system will compensate for the side thrust until it reaches some critical value, after which the flight will be uncontrollable. The objective of this work was to obtain the start time of case breach development and its location using the rocket inertial navigation sensors and GNC data. The algorithm was effective for the detection and location of a breach in an SRB field joint at an early stage of its development.
Several methods for inverting the lidar equation are suggested as means to derive the cirrus optical properties (beta backscatter, alpha extinction coefficients, and delta optical depth) at one wavelength. The lidar equation can be inverted in a linear or logarithmic form; either solution assumes a linear relationship: beta = kappa(alpha), where kappa is the lidar ratio. A number of problems prevent us from calculating alpha (or beta) with a good accuracy. Some of these are as follows: (1) the multiple scattering effect (most authors neglect it); (2) an absolute calibration of the lidar system (difficult and sometimes not possible); (3) lack of accuracy on the lidar ratio k (taken as constant, but in fact it varies with range and cloud species); and (4) the determination of boundary condition for logarithmic solution which depends on signal to noise ration (SNR) at cloud top. An inversion in a linear form needs an absolute calibration of the system. In practice one uses molecular backscattering below the cloud to calibrate the system. This method is not permanent because the lower atmosphere turbidity is variable. For a logarithmic solution, a reference extinction coefficient (alpha(sub f)) at cloud top is required. Several methods to determine alpha(sub f) were suggested. We tested these methods at low SNR. This led us to propose two new methods referenced as S1 and S2.
Variability in the location and shape of the dayside magnetopause is attributed to magnetic reconnection, a fundamental process that enables the transfer of mass, energy, and momentum from the solar wind into the magnetosphere. The spatial and temporal properties of the magnetopause, under varying solar and magnetospheric conditions, remain largely unknown because empirical studies using in-situ observations are challenging to interpret. Global wide field-of-view (FOV) imaging is the only means to simultaneously observe the spatial distribution of the plasma properties over the vast dayside magnetospheric region and, subsequently, quantify the energy transport from the interplanetary medium into the terrestrial magnetosphere. Two upcoming missions, ESA/CAS SMILE and NASA’s LEXI will provide wide-field imagery of the dayside magnetosheath in soft X-rays, an emission generated by charge exchange interactions between high charge-state heavy ions of solar wind origin and exospheric neutral atoms. High-cadence two-dimensional observations of the magnetosheath will allow the estimation of dynamic properties of its inner boundary, the magnetopause, and enable studies of its response to changes in the solar wind dynamic pressure and interplanetary magnetic field orientation. This work introduces a statistically-based estimation approach based on inverse theory to estimate the spatial distribution of magnetosheath soft X-ray emissivities and, with this, identify the location of the magnetopause over the Sun−Earth line. To do so, we simulate the magnetosheath structure using the MHD-based OpenGGCM model and generate synthetic soft X-ray images using LEXI’s orbit and attitude information. Our results show that 3-D estimations using the described statistically-based technique are robust against Poisson-distributed shot noise inherent to soft X-ray images. Also, our proposed methodology shows that the accuracy of both three-dimensional (3-D) estimation and the magnetopause standoff distance calculation highly depends on the observational point.
The Goddard Laboratory for Atmospheric Sciences approach to temperature sounding from satellite observations is fundamentally different from that of NESS in that heavy reliance is placed on the ability to model accurately the instrumental response to atmospheric and surface conditions, while no use is made of statistical relationships between satellite observations and atmospheric temperature profiles. The method involves starting with a guess set of atmospheric and surface conditions from which expected brightness temperatures for the satellite observations are computed. Then, iterative relaxation of atmospheric and surface conditions is performed according to the difference between observed and computed brightness temperatures until sufficient agreement is reached. In the absence of sufficient agreement, no retrieval is produced for that location.
Goddard Laboratory for Atmospheric Sciences has developed a method to derive atmospheric temperature profiles, sea or land surface temperatures, sea ice extent and snow cover, and cloud heights and fractional cloud, from HIRS2/MSU radiance data. Chapter 1 describes the physics used in the radiative transfer calculations and demonstrates the accuracy of the calculations. Chapter 2 describes the rapid transmittance algorithm used and demonstrates its accuracy. Chapter 3 describes the theory and application of the techniques used to analyze the satellite data. Chapter 4 shows results obtained for January 1979.
For the case of unknown surfaces, which can only be studied by means of remote sensors, roughness scale relative to incident wavelength can be determined through the examination of angular scattering characteristics in both vertically and horizontally polarized states. Generally, an angular backscattering curve without polarization dependence indicates scattering by roughness scales that are larger than the incident wavelength. Over angular regions where both vertical and horizontal returns are well separated, the scattering must be dominated by roughness scales that are small by comparison with wavelength.
The Earth Radiation Budget Experiment carries a three-channel scanning radiometer and a set of nadir-looking wide and medium field-of-view instruments for measuring the radiation emitted from earth and the solar radiation reflected from earth. This paper describes the algorithms which are used to compute the radiant exitances at a reference level ('top of the atmosphere') from these measurements. Methods used to analyze data from previous radiation budget experiments are reviewed, and the rationale for the present algorithms is developed. The scanner data are converted to radiances by use of spectral factors, which account for imperfect spectral response of the optics. These radiances are converted to radiant exitances at the reference level by use of directional models, which account for anisotropy of the radiation as it leaves the earth. The spectral factors and directional models are selected on the basis of the scene, which is identified on the basis of the location and the long-wave and shortwave radiances. These individual results are averaged over 2.5 x 2.5 deg regions. Data from the wide and medium field-of-view instruments are analyzed by use of the traditional shape factor method and also by use of a numerical filter, which permits resolution enhancement along the orbit track.
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Given the current level of jet engine performance, improvement of the various turbomachinery components requires the use of advanced methods in aerodynamics, heat transfer, and aeromechanics. In particular, successful blade design can only be achieved via numerical design methods which make it possible to reach optimized solutions in a much shorter time than ever before. Two design methods which are currently being used throughout the French turbomachinery industry to obtain optimized blade geometries are presented. Examples are presented for compressor and turbine applications. The status of these methods as far as improvement and extension to new fields of applications is also reported.
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