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NASA NTRS1989

An investigation of new methods for estimating parameter sensitivities

The method proposed for estimating sensitivity derivatives is based on the Recursive Quadratic Programming (RQP) method and in conjunction a differencing formula to produce estimates of the sensitivities. This method is compared to existing methods and is shown to be very competitive in terms of the number of function evaluations required. In terms of accuracy, the method is shown to be equivalent to a modified version of the Kuhn-Tucker method, where the Hessian of the Lagrangian is estimated using the BFS method employed by the RQP algorithm. Initial testing on a test set with known sensitivities demonstrates that the method can accurately calculate the parameter sensitivity.

Beltracchi, Todd J.↗

NASA NTRS1989

Shape sensitivity analysis of flutter response of a laminated wing

A method is presented for calculating the shape sensitivity of a wing aeroelastic response with respect to changes in geometric shape. Yates' modified strip method is used in conjunction with Giles' equivalent plate analysis to predict the flutter speed, frequency, and reduced frequency of the wing. Three methods are used to calculate the sensitivity of the eigenvalue. The first method is purely a finite difference calculation of the eigenvalue derivative directly from the solution of the flutter problem corresponding to the two different values of the shape parameters. The second method uses an analytic expression for the eigenvalue sensitivities of a general complex matrix, where the derivatives of the aerodynamic, mass, and stiffness matrices are computed using a finite difference approximation. The third method also uses an analytic expression for the eigenvalue sensitivities, but the aerodynamic matrix is computed analytically. All three methods are found to be in good agreement with each other.

Kapania, Rakesh K.↗

NASA NTRS1989

Computational Aspects of Sensitivity Calculations in Linear Transient Structural Analysis

A study has been performed focusing on the calculation of sensitivities of displacements, velocities, accelerations, and stresses in linear, structural, transient response problems. One significant goal was to develop and evaluate sensitivity calculation techniques suitable for large-order finite element analyses. Accordingly, approximation vectors such as vibration mode shapes are used to reduce the dimensionality of the finite element model. Much of the research focused on the accuracy of both response quantities and sensitivities as a function of number of vectors used. Two types of sensitivity calculation techniques were developed and evaluated. The first type of technique is an overall finite difference method where the analysis is repeated for perturbed designs. The second type of technique is termed semianalytical because it involves direct, analytical differentiation of the equations of motion with finite difference approximation of the coefficient matrices. To be computationally practical in large-order problems, the overall finite difference methods must use the approximation vectors from the original design in the analyses of the perturbed models.

Greene, William H.↗

NASA NTRS1990

Loading rate sensitivity of open-hole composite specimens in compression

The results are reported of an experimental study on the compressive, time-dependent behavior of graphite fiber reinforced polymer composite laminates with open holes. The effect of loading rate on compressive strength was determined for six material systems ranging from brittle epoxies to thermoplastics at both 75 F and 220 F. Specimens were loaded to failure using different loading rates. The slope of the strength versus elapsed time-to-failure curve was used to rank the materials' loading rate sensitivity. All of the materials had greater strength at 75 F than at 220 F. All the materials showed loading rate effects in the form of reduced failure strength for longer elapsed-time-to-failure. Loading rate sensitivity was less at 220 F than the same material at 70 F. However, C12000/ULTEM and IM7/8551-7 were more sensitive to loading rate than the other materials at 220 F. AS4/APC2 laminates with 24, 32, and 48 plies and 1/16 and 1/4 inch diameter holes were tested. The sensitivity to loading rate was less for either increasing number of plies or larger hole size. The failure of the specimens made from brittle resins was accompanied by extensive delaminations while the failure of the roughened systems was predominantly by shear crippling. Fewer delamination failures were observed at the higher temperature.

Lubowinski, S. J.↗

NASA NTRS1990

The sensitivity of synthetic aperture radiometers for remote sensing applications from space

Aperture synthesis offers a means of realizing the full potential microwave remote sensing from space by helping to overcome the limitations set by antenna size. The result is a potentially lighter, more adaptable structure for applications in space. However, because the physical collecting area is reduced, the signal-to-noise ratio is also reduced and may adversely affect the radiometric sensitivity. Sensitivity is an especially critical issue for measurements from low earth orbit because the motion of the platform (about 7 km/s) limits the integration time available for forming an image. The purpose of this paper is to develop expressions for the sensitivity of remote sensing systems which use aperture synthesis. The objective is to develop basic equations general enough to be used to obtain the sensitivity of the several variations of aperture synthesis which have been proposed for sensors in space. The conventional microwave imager (a scanning total power radiometer) is treated as a special case, and the paper concludes with a comparison of three synthetic aperture configurations with the conventional imager.

Le Vine, David M.↗

NASA NTRS1990

Environmental sensitivities of quartz crystal oscillators

The frequency, amplitude, and noise of the output signal of a quartz crystal controlled oscillator is affected by a large number of environmental effects. The physical basis for the sensitivity of precision oscillators to temperature, humidity, pressure, vibration, magnetic field, electric field, load, and radiation is discussed. The sensitivity of crystal oscillators to radiation is a very complex topic and poorly understood. Therefore only a few general results are mentioned. The sensitivity to most external influences often varies significantly from one oscillator type to another and from one unit of given type to another. For a given unit, the sensitivity to one parameter often depends on the value of other parameters and history.

Walls, Fred L.↗

NASA NTRS1990

Sensitivity analysis of a wing aeroelastic response

The present shape-sensitivity analysis of wing aeroelastic response proceeds from aeroelastic response sensitivities obtained on the basis of the aerodynamic performance valid for high aspect ratio wings in subsonic, subcritical flow. Attention is given to the shape sensitivity of various static aeroelastic responses; the formulation is general, and assumes that, for a given shape and elastic deformation, the aerodynamic analysis will furnish the distribution of the pressure and the pressure sensitivity derivatives with respect to the shape parameters of interest. Wing displacements are obtained by means of an iterative scheme.

Kapania, Rakesh K.↗

NASA NTRS1991

Sensitivity of control-augmented structure obtained by a system decomposition method

The verification of a method for computing sensitivity derivatives of a coupled system is presented. The method deals with a system whose analysis can be partitioned into subsets that correspond to disciplines and/or physical subsystems that exchange input-output data with each other. The method uses the partial sensitivity derivatives of the output with respect to input obtained for each subset separately to assemble a set of linear, simultaneous, algebraic equations that are solved for the derivatives of the coupled system response. This sensitivity analysis is verified using an example of a cantilever beam augmented with an active control system to limit the beam's dynamic displacements under an excitation force. The verification shows good agreement of the method with reference data obtained by a finite difference technique involving entire system analysis. The usefulness of a system sensitivity method in optimization applications by employing a piecewise-linear approach to the same numerical example is demonstrated. The method's principal merits are its intrinsically superior accuracy in comparison with the finite difference technique, and its compatibility with the traditional division of work in complex engineering tasks among specialty groups.

Sobieszczanski-Sobieski, Jaroslaw↗

NASA NTRS1991

On the accuracy of shape sensitivity

The calculation of sensitivity of the response of a structure modeled by finite elements to shape variation is known to be subject to numerical difficulties. The accuracy of a given method is typically measured against the yard stick of finite-difference sensitivity calculation. The present paper demonstrates with a simple example that this approach may be flawed because of discretization errors associated with the finite element mesh. Seven methods for calculating sensitivity derivatives are compared for a two-material beam problem with a moving interface. It is found that as the mesh is refined, displacement sensitivity derivatives converge more slowly than the displacements. Six of the methods agree fairly well, but the adjoint variational surface method provides substantially different results. However, the difference is found to reflect convergence from another direction to the same answer rather than reduced accuracy. Additionally, it is observed that small derivatives are particularly prone to accuracy problems.

Haftka, R. T.↗

NASA NTRS1991

Eigenvalue sensitivity analysis of planar frames with variable joint and support locations

Two sensitivity equations are derived in this study based upon the continuum approach for eigenvalue sensitivity analysis of planar frame structures with variable joint and support locations. A variational form of an eigenvalue equation is first derived in which all of the quantities are expressed in the local coordinate system attached to each member. Material derivative of this variational equation is then sought to account for changes in member's length and orientation resulting form the perturbation of joint and support locations. Finally, eigenvalue sensitivity equations are formulated in either domain quantities (by the domain method) or boundary quantities (by the boundary method). It is concluded that the sensitivity equation derived by the boundary method is more efficient in computation but less accurate than that of the domain method. Nevertheless, both of them in terms of computational efficiency are superior to the conventional direct differentiation method and the finite difference method.

Chuang, Ching H.↗

NASA NTRS1991

Temperature sensitivity of differential absorption lidar measurements of water vapor in the 720-nm region

Recently measured properties of water vapor (H2O) absorption lines have been used in calculations to evalute the temperature sensitivity of differential absorption lidar (Dial) H2O measurements. This paper estimates the temperature sensitivity of H2O lines in the 717-733-nm region for both H2O mixing ratio and number density measurements, and discusses the influence of the H2O line ground state energies E-double-prime, the H2O absorption linewidths, the linewidth temperature dependence parameter, and the atmospheric temperature and pressure variations with altitude and location on the temperature sensitivity calculations. Line parameters and temperature sensitivity calculations for 67 H2O lines in the 720-nm band are given which can be directly used in field experiments. Water vapor lines with E-double-prime values in the 100-300/cm range were found to be optimum for Dial measurements of H2O number densities, while E-double-prime values in the 250-500/cm range were found to be optimum for H2O mixing ratio measurements.

Browell, Edward V.↗

NASA NTRS1991

Transient thermoelasticity and other body force effects in boundary element shape sensitivity analysis

Structural shape design sensitivity analysis (DSA) is presented for objects subjected to gravity, centrifugal, and general thermal loading. DSA employs implicit differentiation of the governing boundary integral equations. Both a surface integral and a particular integral approach are discussed for computation of these effects in response analysis and sensitivity analysis. It is shown that the particular integral approach is capable of computing the sensitivities of objects subjected to nonharmonic temperature distributions. Attention is also given to several techniques for the modeling of temperature distributions in the DSA process. In particular, an approach that eliminates the need for the incorporation of thermal response analysis and sensitivity analysis is described in the overall shape optimization process. A sharp corner formulation is also presented that can account for the jump in the surface traction components at a sharp corner in an interzone boundary.

Kane, James H.↗

NASA NTRS1991

Sensitivity analysis, approximate analysis, and design optimization for internal and external viscous flows

A gradient-based design optimization strategy for practical aerodynamic design applications is presented, which uses the 2D thin-layer Navier-Stokes equations. The strategy is based on the classic idea of constructing different modules for performing the major tasks such as function evaluation, function approximation and sensitivity analysis, mesh regeneration, and grid sensitivity analysis, all driven and controlled by a general-purpose design optimization program. The accuracy of aerodynamic shape sensitivity derivatives is validated on two viscous test problems: internal flow through a double-throat nozzle and external flow over a NACA 4-digit airfoil. A significant improvement in aerodynamic performance has been achieved in both cases. Particular attention is given to a consistent treatment of the boundary conditions in the calculation of the aerodynamic sensitivity derivatives for the classic problems of external flow over an isolated lifting airfoil on 'C' or 'O' meshes.

Taylor, Arthur C., III↗

NASA NTRS1991

Computational aspects of sensitivity calculations in linear transient structural analysis

The calculation of sensitivities of displacements, velocities, accelerations, and stresses in linear, structural, and transient response problems is studied. Several existing sensitivity calculation methods and two new methods are compared for three example problems. Approximation vectors such as vibration mode shapes are used to reduce the dimensionality of the finite model. To be computationally practical in large-order problems, the overall finite difference methods must use the approximation vectors from the original design in the analyses of the perturbed models. This was found to result in poor convergence of stress sensitivities in several cases. Two semianalytical techniques are developed to overcome this poor convergence. Both new methods result in very good convergence of the stress sensitivities; the computational cost is much less than would result if the vibration modes were recalculated and then used in an overall finite difference method.

Greene, W. H.↗

NASA NTRS1989

The sensitivity of synthetic aperture radiometers for remote sensing applications from space

Aperture synthesis offers a means of realizing the full potential of microwave remote sensing from space by helping to overcome the limitations set by antenna size. The result is a potentially lighter, more adaptable structure for applications in space. However, because the physical collecting area is reduced, the signal-to-noise ratio is reduced and may adversely affect the radiometric sensitivity. Sensitivity is an especially critical issue for measurements to be made from low earth orbit because the motion of the platform limits the integration time available for forming an image. The purpose is to develop expression for the sensitivity of remote sensing systems which use aperture synthesis. The objective is to develop basic equations general enough to be used to obtain the sensitivity of the several variations of aperture synthesis which were proposed for sensors in space. The conventional microwave imager (a scanning total power radiometer) is treated as a special case and a comparison of three synthetic aperture configurations with the conventional imager is presented.

Levine, D. M.↗

NASA NTRS1992

Sensitivity analysis of hydrodynamic stability operators

The eigenvalue sensitivity for hydrodynamic stability operators is investigated. Classical matrix perturbation techniques as well as the concept of epsilon-pseudoeigenvalues are applied to show that parts of the spectrum are highly sensitive to small perturbations. Applications are drawn from incompressible plane Couette, trailing line vortex flow and compressible Blasius boundary layer flow. Parametric studies indicate a monotonically increasing effect of the Reynolds number on the sensitivity. The phenomenon of eigenvalue sensitivity is due to the non-normality of the operators and their discrete matrix analogs and may be associated with large transient growth of the corresponding initial value problem.

Schmid, Peter J.↗

NASA NTRS1992

Boundary formulations for shape sensitivity of temperature dependent conductivity problems

Used in concert with the Kirchhoff transformation, implicit differentiation of the discretized boundary integral equations governing the conduction of heat in solids with temperature dependent thermal conductivity is shown to generate an accurate and economical approach for computation of shape sensitivities. For problems with specified temperature and heat flux boundary conditions, a linear problem results for both the analysis and sensitivity analysis. In problems with either convection or radiation boundary conditions, a nonlinear problem is generated. Several iterative strategies are presented for the solution of the resulting sets of nonlinear equations and the computational performances examined in detail. Multizone analysis and zone condensation strategies are demonstrated to provide substantive computational economies in this process for models with either localized nonlinear boundary conditions or regions of geometric insensitivity to design variables. A series of nonlinear example problems is presented that have closed form solutions. Exact analytical expressions for the shape sensitivities associated with these problems are developed and these are compared with the sensitivities computed using the boundary element formulation.

Kane, James H.↗

NASA NTRS1992

Transfer of contrast sensitivity in linear visual networks

Contrast sensitivity is a useful measure of the ability of an observer to distinguish contrast signals from noise. Although usually applied to human observers, contrast sensitivity can also be defined operationally for individual visual neurons. In a model linear neuron consisting of a filter and noise source, this operational measure is a function of filter gain, noise power spectrum, signal duration, and a performance criterion. This definition allows one to relate the sensitivities of linear neurons at different levels in the visual pathway. Mathematical formulas describing these relationships are derived, and the general model is applied to the specific problem of relating the sensitivities of parvocellular LGN neurons and cortical simple cells in the primate.

Watson, Andrew B.↗