A sensitive far infrared detection system
An infrared field optics system was designed which achieves the maximum flux concentration allowed by the Abbe sine inequality and provides efficient coupling to bolometer-type detectors.
Hildebrand, R. H.↗
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Turbulence effects in radio occultation studies of atmospheric scale heights
Atmospheric scale heights derived from radio occultation measurements of a turbulent planetary atmosphere would be accurate if the average angle of refraction through the turbulent atmosphere were equal to the refraction angle for the corresponding quiescent atmosphere. These two angles are not equal (although their difference may not be large enough to cause significant error). If necessary, it should be possible to correct for the systematic error introduced by this inequality by using measurements of signal spectra to determine characteristics of the turbulence. Sensitive dual-frequency measurements could help define the effects of turbulence in future radio occultation experiments. It does not appear that the angular offset due to turbulence has been important in past experiments, although it may become significant and require corrective analysis when improved equipment is used to probe deep into turbulent atmospheres with greater measurement precision.
Eshleman, V. R.↗
Effect of the mass center shift for force-free flexible spacecraft
For a spinning flexible spacecraft the mass center generally shifts relative to the nominal undeformed position. It is thought that this shift of center complicates spacecraft stability analysis. It is proved, on the basis of results achieved by Meirovitch and Calico (1972), that for the general class of force-free single-spin flexible spacecraft it is possible to ignore this shift of center without affecting the stability criteria in any significant way. A new theorem on inequalities for quadratic forms is proved to demonstrate the validity of the stability analysis.
Meirovitch, L.↗
Optimization of multi-constrained structures based on optimality criteria
A weight-reduction algorithm is developed for the optimal design of structures subject to several multibehavioral inequality constraints. The structural weight is considered to depend linearly on the design variables. The algorithm incorporates a simple recursion formula derived from the Kuhn-Tucker necessary conditions for optimality, associated with a procedure to delete nonactive constraints based on the Gauss-Seidel iterative method for linear systems. A number of example problems is studied, including typical truss structures and simplified wings subject to static loads and with constraints imposed on stresses and displacements. For one of the latter structures, constraints on the fundamental natural frequency and flutter speed are also imposed. The results obtained show that the method is fast, efficient, and general when compared to other competing techniques. Extensions to the generality of the method to include equality constraints and nonlinear merit functions is discussed.
Rizzi, P.↗
Disjoint design spaces in the optimization of harmonically excited structures
The paper deals with a method of optimizing harmonically or dynamically excited structures which removes the frequency constraint (that specifies that the structure's first natural frequency of vibration must be greater than the excitation frequency), replaces the displacement constraint by an inequality constraint on the allowable stress and applies finite element approximations to the continuous one-dimensional structures. When the problem is posed in this manner, the feasible design space is disconnected or 'disjoint'. An attempt is made to explain this disjointness by studying the optimal design of a thin-walled cantilevered rod subjected to steady, simple harmonic torsional excitation. The finite element method is applied to the optimization of a harmonically excited structure with an arbitrary number of design variables, with the disjointness of the design space, a complicating factor.
Johnson, E. H.↗
DHARMA - Discriminant hyperplane abstracting residuals minimization algorithm for separating clusters with fuzzy boundaries
Learning of discriminant hyperplanes in imperfectly supervised or unsupervised training sample sets with unreliably labeled samples along the fuzzy joint boundaries between sample clusters is discussed, with the discriminant hyperplane designed to be a least-squares fit to the unreliably labeled data points. (Samples along the fuzzy boundary jump back and forth from one cluster to the other in recursive cluster stabilization and are considered unreliably labeled.) Minimization of the distances of these unreliably labeled samples from the hyperplanes does not sacrifice the ability to discriminate between classes represented by reliably labeled subsets of samples. An equivalent unconstrained linear inequality problem is formulated and algorithms for its solution are indicated. Landsat earth sensing data were used in confirming the validity and computational feasibility of the approach, which should be useful in deriving discriminant hyperplanes separating clusters with fuzzy boundaries, given supervised training sample sets with unreliably labeled boundary samples.
Dasarathy, B. V.↗
Imaginary-frequency polarizability and van der Waals force constants of two-electron atoms, with rigorous bounds
Variational functionals of Braunn and Rebane (1972) for the imagery-frequency polarizability (IFP) have been generalized by the method of Gramian inequalities to give rigorous upper and lower bounds, valid even when the true (but unknown) unperturbed wavefunction must be represented by a variational approximation. Using these formulas in conjunction with flexible variational trial functions, tight error bounds are computed for the IFP and the associated two- and three-body van der Waals interaction constants of the ground 1(1S) and metastable 2(1,3S) states of He and Li(+). These bounds generally establish the ground-state properties to within a fraction of a per cent and metastable properties to within a few per cent, permitting a comparative assessment of competing theoretical methods at this level of accuracy. Unlike previous 'error bounds' for these properties, the present results have a completely a priori theoretical character, with no empirical input data.
Glover, R. M.↗
Trajectory optimization for the Atlas/Centaur launch vehicle
A method for finding solutions to complex trajectory optimization problems with detailed hardware and launch vehicle constraints is presented. The trajectory optimization problem is formulated as a constrained function minimization problem by modeling the control by a function of a finite number of parameters. Although any parametric control model may be selected, the natural choice of parameters is the actual parameters of the parametric guidance equations flown on the flight digital computer. A variation of the method of multipliers is presented for performing the constrained function minimization. A functional is proposed that allows incorporation of state variable inequality constraints. Finally, optimization of the HEAO-A direct-ascent trajectory is discussed. The HEAO-A mission demonstrates profile optimization to meet range safety, tracking, heating, structural integrity, and attitude rate constraints.
Brusch, R. G.↗
Curvilinear projection developments
Gradient projection is a powerful algorithm for minimization of a function subject to constraints. Constraint nonlinearities hamper projection computations. The constraints must then be restored before another projection cycle. The restoration steps taken in the process of following nonlinear constraint surfaces can be used as a guide to the construction of a curve which more nearly follows the constraints than does the straight line in the projected gradient direction. This scheme, termed 'curvilinear projection', was explored in earlier research. The study presently reported carries out some computational experiments using a related version of the technique. Some other details of projection computations which turn out to be practically important are taken up: rules for updating the variable metric in projection when early termination of the one-dimensional search on constraint violation occurs, and active-constraint logic for screening inequalities that makes use of the Kuhn-Tucker necessary conditions.
Kelley, H. J.↗
Expansion and broadening of coronal loop transients - A theoretical explanation
Consequences are examined of the assumption that an observed coronal loop transient is a twisted rope of magnetic-field lines expanding and broadening in the background coronal plasma and magnetic field. It is shown that the expansion can be accounted for by the azimuthal component of the field; the observed broadening of the loop as it moves outward can be accounted for by the longitudinal component of the field. In order to have a net outward force and at the same time avoid a classical pinch (sausage) instability, the two components of the field must satisfy a certain inequality. It is predicted that, as the loop rises, the width (h) of its top portion should vary proportionally with distance (R) from the sun's center. This is in good agreement with measurements that show h is proportional to the 0.8 power of R. The prediction that the radius of curvature of the top portion of the loop should be proportional to R differs from the measured variation. The difference could be accounted for by a drag due to the background coronal field that flattens the loop's top.
Mouschovias, T. CH.↗
Supercritical tests of a self-optimizing, variable-Camber wind tunnel model
A testing procedure was used in a 16-foot Transonic Propulsion Wind Tunnel which leads to optimum wing airfoil sections without stopping the tunnel for model changes. Being experimental, the optimum shapes obtained incorporate various three-dimensional and nonlinear viscous and transonic effects not included in analytical optimization methods. The method is a closed-loop, computer-controlled, interactive procedure and employs a Self-Optimizing Flexible Technology wing semispan model that conformally adapts the airfoil section at two spanwise control stations to maximize or minimize various prescribed merit functions subject to both equality and inequality constraints. The model, which employed twelve independent hydraulic actuator systems and flexible skins, was also used for conventional testing. Although six of seven optimizations attempted were at least partially convergent, further improvements in model skin smoothness and hydraulic reliability are required to make the technique fully operational.
Levinsky, E. S.↗
Optimal analytic rendezvous using Clohessy-Wiltshire equations
The optimal solution time that minimizes the sum of the two applied impulses necessary to rendezvous is obtained analytically for the Clohessy-Wiltshire equations with a linear gravity model assumption. A plume impingement inequality constraint on the solution is examined, and an optimal policy is developed. Numerical tests are conducted to verify the analysis and to illustrate the optimal solution algorithm.
Jezewski, D. J.↗
The near-wake structure of the Atmosphere Explorer C /AE-C/ satellite - A parametric investigation
Measurements of ion current, electron temperature, and values of space potential obtained from the cylindrical electrostatic probe on board the Atmosphere Explorer C (AE-C) satellite were used to examine, in a parametric manner, the angular distribution of charge around the satellite. Interest is focused on nighttime equatorial data in the altitude range 275-620 km, which yields a wide range for the parameter R sub D (the radius of the satellite divided by the ambient value of the Debye lengths), including R sub D greater than 100, which is of practical significance to large space platforms. The variations of normalized ion current in the wake zone of the AE-C satellite appear to display an exponential dependence on R sub D for 'constant' values of other relevant parameters. The angular variations of electron temperature and space potential in the close vicinity of the satellite's surface were examined and compared with results from the Explorer 31 satellite. The variation of the ratio of measured to computed space potential with electron temperature was examined using data from both the AE-C and Explorer 31 satellites. It was found that the ratio is greater than unity. Possible causes for the above inequality are discussed.
Samir, U.↗
Stability bounds for the control of large space structures
Balas (1977) has discussed the stability problem of reduced-order regulators and estimators in terms of control and observation 'spillover'. The term 'control spillover' was used to define that part of the feedback control which excites the uncontrolled (or residual) modes, and 'observation spillover' was used to define that part of the measurement which is contaminated by residual modes. In this paper, two sufficient conditions are derived via Lyapunov methods for asymptotic stability of large space structures using a class of reduced-order controllers. These conditions give allowable bounds on the spectral norms of control and observation spillover terms. The sufficient condition given by a specified inequality equation appears to be less conservative, and should be useful as a design tool for the control of large space structures.
Joshi, S. M.↗
An analytic approach to optimal rendezvous using Clohessy-Wiltshire equations
An analytic approach is used to obtain the optimal solution time that minimizes the sum of the two applied impulses necessary to rendezvous for the Clohessy-Wiltshire equations. A plume impingement inequality constraint on the solution is examined, and an optimal policy is developed. Numerical tests are conducted to verify the analysis and to illustrate the optimal solution algorithm.
Jezewski, D. J.↗
Application of constrained optimization to active control of aeroelastic response
Active control of aeroelastic response is a complex in which the designer usually tries to satisfy many criteria which are often conflicting. To further complicate the design problem, the state space equations describing this type of control problem are usually of high order, involving a large number of states to represent the flexible structure and unsteady aerodynamics. Control laws based on the standard Linear-Quadratic-Gaussian (LQG) method are of the same high order as the aeroelastic plant. To overcome this disadvantage of the LQG mode, an approach developed for designing low order optimal control laws which uses a nonlinear programming algorithm to search for the values of the control law variables that minimize a composite performance index, was extended to the constrained optimization problem. The method involves searching for the values of the control law variables that minimize a basic performance index while satisfying several inequality constraints that describe the design criteria. The method is applied to gust load alleviation of a drone aircraft.
Newsom, J. R.↗
Current research on shear buckling and thermal loads with PASCO: Panel Analysis and Sizing Code
The PASCO computer program to obtain the detailed dimensions of optimum stiffened composite structural panels is described. Design requirements in terms of inequality constraints can be placed on buckling loads or vibration frequencies, lamina stresses and strains, and overall panel stiffness for each of many load conditions. General panel cross sections can be treated. An analysis procedure involving a smeared orthotropic solution was investigated. The conservatism in the VIPASA solution and the danger in a smeared orthotropic solution is explored. PASCO's capability to design for thermal loadings is also described. It is emphasized that design studies illustrate the importance of the multiple load condition capability when thermal loads are present.
Stroud, W. J.↗
Asymptotic form of the longitudinal correlation function for isotropic homogeneous turbulence
An asymptotic form is derived for the longitudinal correlation function for isotropic homogeneous turbulence in an incompressible fluid governed by the Navier-Stokes equation. The result is obtained from an analysis of the algebraic-differential structure of the two-point correlation tensor contained in the complex-valued Fourier transform of the probability measure over the turbulence ensemble, which reveals that the Hopf characteristic functional (the complex-valued Fourier transform of the probability measure) satisfies the Fourier interference inequality. Consequences of the expression obtained, in which the correlation function is a positive definite function of the inverse cube of the spatial coordinate as it approaches infinity, are shown to include the nonexistence of the Loitsianskii invariant, and the solution is shown to be consistent with empirical formulas.
Rosen, G.↗