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NASA NTRS1983

Developing sensitivity coefficients for a state variable model of a flexible spacecraft with modular attitude control

The numerical value for the sensitivity coefficient of each scalar state variable with respect to each parameter of a five body model of the rotational dynamics of a flexible spacecraft with modular attitude control is generated. The maximum magnitudes of these sensitivity coefficients are arranged in descending order in one table while the final time (steady state) values of these sensitivity coefficients are arranged in order of descending magnitude in a second table.

Chichester, F. D.↗

NASA NTRS1986

Some influences of approximate values for velocity, density and total temperature sensitivities on hot wire anemometer results

There is a renewed interest in hot wire anemometry at transonic speeds. Recent results were published which indicate that at transonic speeds a heated wire is sensitive only to mass flow and total temperature, results similar to those obtained for supersonic flows. Other results were obtained to show that the sensitivity is a function of velocity, density, and total temperature, results in agreement with many of those obtained in the 1950s. An analysis of anemometry results was made to evaluate possible errors when various assumptions were made concerning the sensitivity of a heated wire to fluid flow variables.

Stainback, P. C.↗

NASA NTRS1986

Sensitivity analysis and approximation methods for general eigenvalue problems

Optimization of dynamic systems involving complex non-hermitian matrices is often computationally expensive. Major contributors to the computational expense are the sensitivity analysis and reanalysis of a modified design. The present work seeks to alleviate this computational burden by identifying efficient sensitivity analysis and approximate reanalysis methods. For the algebraic eigenvalue problem involving non-hermitian matrices, algorithms for sensitivity analysis and approximate reanalysis are classified, compared and evaluated for efficiency and accuracy. Proper eigenvector normalization is discussed. An improved method for calculating derivatives of eigenvectors is proposed based on a more rational normalization condition and taking advantage of matrix sparsity. Important numerical aspects of this method are also discussed. To alleviate the problem of reanalysis, various approximation methods for eigenvalues are proposed and evaluated. Linear and quadratic approximations are based directly on the Taylor series. Several approximation methods are developed based on the generalized Rayleigh quotient for the eigenvalue problem. Approximation methods based on trace theorem give high accuracy without needing any derivatives. Operation counts for the computation of the approximations are given. General recommendations are made for the selection of appropriate approximation technique as a function of the matrix size, number of design variables, number of eigenvalues of interest and the number of design points at which approximation is sought.

Murthy, D. V.↗

NASA NTRS1987

Alternative methods for calculating sensitivity of optimized designs to problem parameters

Optimum sensitivity is defined as the derivative of the optimum design with respect to some problem parameter, P. The problem parameter is usually fixed during optimization, but may be changed later. Thus, optimum sensitivity is used to estimate the effect of changes in loads, materials or constraint bounds on the design without expensive re-optimization. Here, the general topic of optimum sensitivity is discussed, available methods identified, examples given, and the difficulties encountered in calculating this information in nonlinear constrained optimization are identified.

Vanderplaats, G. N.↗

NASA NTRS1987

Behavior sensitivities for control augmented structures

During the past few years it has been recognized that combining passive structural design methods with active control techniques offers the prospect of being able to find substantially improved designs. These developments have stimulated interest in augmenting structural synthesis by adding active control system design variables to those usually considered in structural optimization. An essential step in extending the approximation concepts approach to control augmented structural synthesis is the development of a behavior sensitivity analysis capability for determining rates of change of dynamic response quantities with respect to changes in structural and control system design variables. Behavior sensitivity information is also useful for man-machine interactive design as well as in the context of system identification studies. Behavior sensitivity formulations for both steady state and transient response are presented and the quality of the resulting derivative information is evaluated.

Manning, R. A.↗

NASA NTRS1987

The case for aerodynamic sensitivity analysis

No specific solutions are offered, nor verified by applications, for its subject problem which is sensitivity analysis in Computational Fluid Dynamics (CFD). Instead, a plea is made to the CFD community for extending their present capability to include sensitivity analysis. The plea is made from the viewpoint of an aeronautical engineer, not an expert in CFD methods, who needs the sensitivity information when working at the junction of aerodynamics, structures, active controls, and other disciplines whose inputs need to be integrated in aircraft design.

Sobieszczanski-Sobieski, Jaroslaw↗

NASA NTRS1987

Modal sensitivity for structural systems with repeated frequencies

Repeated or closely packed modal frequencies are common physical occurrences for vibrating structures which are complex or possess multi-planes of symmetry. The computation of the sensitivity to structural modifications for these frequencies and mode shapes is made difficult by the fact that the mode shapes are not unique, since any linear combination of eigenvectors corresponding to a repeated eigenvalue is also an eigenvector. The work of Chen and Pan is extended, who used modal expansion techniques for accommodating the sensitivity analysis of structures with repeated eigenvalues. Starting with a discussion of the physical significance of sensitivity analysis for repeated frequency modes, a derivation is presented of the governing equations for the derivatives of a repeated eigenvalue. This is followed with a small example to illustrate the results. An efficient computation procedure, based upon an expansion of Nelson's ideas for large banded systems, is then proposed for systems with repeated or closely spaced eigenvalues.

Ojalvo, I. U.↗

NASA NTRS1987

Application of design sensitivity analysis for greater improvement on machine structural dynamics

Methodologies are presented for greatly improving machine structural dynamics by using design sensitivity analyses and evaluative parameters. First, design sensitivity coefficients and evaluative parameters of structural dynamics are described. Next, the relations between the design sensitivity coefficients and the evaluative parameters are clarified. Then, design improvement procedures of structural dynamics are proposed for the following three cases: (1) addition of elastic structural members, (2) addition of mass elements, and (3) substantial charges of joint design variables. Cases (1) and (2) correspond to the changes of the initial framework or configuration, and (3) corresponds to the alteration of poor initial design variables. Finally, numerical examples are given for demonstrating the availability of the methods proposed.

Yoshimura, Masataka↗

NASA NTRS1987

Shape design sensitivity analysis and optimal design of structural systems

The material derivative concept of continuum mechanics and an adjoint variable method of design sensitivity analysis are used to relate variations in structural shape to measures of structural performance. A domain method of shape design sensitivity analysis is used to best utilize the basic character of the finite element method that gives accurate information not on the boundary but in the domain. Implementation of shape design sensitivty analysis using finite element computer codes is discussed. Recent numerical results are used to demonstrate the accuracy obtainable using the method. Result of design sensitivity analysis is used to carry out design optimization of a built-up structure.

Choi, Kyung K.↗

NASA NTRS1986

Design sensitivity analysis using EAL. Part 1: Conventional design parameters

A numerical implementation of design sensitivity analysis of builtup structures is presented, using the versatility and convenience of an existing finite element structural analysis code and its database management system. The finite element code used in the implemenatation presented is the Engineering Analysis Language (EAL), which is based on a hybrid method of analysis. It was shown that design sensitivity computations can be carried out using the database management system of EAL, without writing a separate program and a separate database. Conventional (sizing) design parameters such as cross-sectional area of beams or thickness of plates and plane elastic solid components are considered. Compliance, displacement, and stress functionals are considered as performance criteria. The method presented is being extended to implement shape design sensitivity analysis using a domain method and a design component method.

Dopker, B.↗

NASA NTRS1986

Design component method for sensitivity analysis of built-up structures

A 'design component method' that provides a unified and systematic organization of design sensitivity analysis for built-up structures is developed and implemented. Both conventional design variables, such as thickness and cross-sectional area, and shape design variables of components of built-up structures are considered. It is shown that design of components of built-up structures can be characterized and system design sensitivity expressions obtained by simply adding contributions from each component. The method leads to a systematic organization of computations for design sensitivity analysis that is similar to the way in which computations are organized within a finite element code.

Choi, Kyung K.↗

NASA NTRS1987

Practical implementation of an accurate method for multilevel design sensitivity analysis

Solution techniques for handling large scale engineering optimization problems are reviewed. Potentials for practical applications as well as their limited capabilities are discussed. A new solution algorithm for design sensitivity is proposed. The algorithm is based upon the multilevel substructuring concept to be coupled with the adjoint method of sensitivity analysis. There are no approximations involved in the present algorithm except the usual approximations introduced due to the discretization of the finite element model. Results from the six- and thirty-bar planar truss problems show that the proposed multilevel scheme for sensitivity analysis is more effective (in terms of computer incore memory and the total CPU time) than a conventional (one level) scheme even on small problems. The new algorithm is expected to perform better for larger problems and its applications on the new generation of computer hardwares with 'parallel processing' capability is very promising.

Nguyen, Duc T.↗

NASA NTRS1987

Physically based sensitivity derivatives for finite-element programs

Attention is given to a virtual-work approach to the definition of sensitivity in terms of physical quantities; sensitivity fields are treated as a solution to loadings that consist of body forces, initial strains, and initial stresses. The method can accordingly be implemented in a finite element package, with only minimal knowledge of its programming detail and without access to its source code. The application of the approach to one- and two-dimensional problems is demonstrated. The sensitivity of the structural response for truss structures was computed with respect to the cross-sectional areas of the members.

Barthelemy, Bruno↗

NASA NTRS1988

A semianalytical technique for sensitivity analysis of unsteady aerodynamic computations

A semianalytical approach is developed for the sensitivity analysis of linear unsteady aerodynamic loads. The semianalytical approach is easier to implement than the analytical approach. It is also computationally less expensive than the finite difference approach when used with panel methods, which require a large number of panels. The semianalytical approach is applied to an isolated airfoil in a 2-D flow and rotating propfan blades in 3-D flow. Sensitivity coefficients with respect to non-shape-dependent variables are shown for some cases. It is expected that the semianalytical approach will be useful in aeroelastic design procedures particularly when mistuning is present, and that it is potentially useful for shape sensitivity analysis of linear unsteady aerodynamics.

Murthy, Durbha V.↗

NASA NTRS1988

On the sensitivity of complex, internally coupled systems

A method is presented for computing sensitivity derivatives with respect to independent (input) variables for complex, internally coupled systems, while avoiding the cost and inaccuracy of finite differencing performed on the entire system analysis. The method entails two alternative algorithms: the first is based on the classical implicit function theorem formulated on residuals of governing equations, and the second develops the system sensitivity equations in a new form using the partial (local) sensitivity derivatives of the output with respect to the input of each part of the system. A few application examples are presented to illustrate the discussion.

Sobieszczanskisobieski, Jaroslaw↗

NASA NTRS1988

Computational aspects of sensitivity calculations in transient structural analysis

A key step in the application of formal automated design techniques to structures under transient loading is the calculation of sensitivities of response quantities to the design parameters. This paper considers structures with general forms of damping acted on by general transient loading and addresses issues of computational errors and computational efficiency. The equations of motion are reduced using the traditional basis of vibration modes and then integrated using a highly accurate, explicit integration technique. A critical point constraint formulation is used to place constraints on the magnitude of each response quantity as a function of time. Three different techniques for calculating sensitivities of the critical point constraints are presented. The first two are based on the straightforward application of the forward and central difference operators, respectively. The third is based on explicit differentiation of the equations of motion. Condition errors, finite difference truncation errors, and modal convergence errors for the three techniques are compared by applying them to a simple five-span-beam problem. Sensitivity results are presented for two different transient loading conditions and for both damped and undamped cases.

Greene, William H.↗

NASA NTRS1988

Relative planetary radar sensitivities: Arecibo and Goldstone

The increase of the Deep Space Network antennas from 64 meter to 70 meter diameter represents the first of several improvements that will be made over the next decade to enhance earth based radar sensitivity to solar system targets. The aperture increase at the Goldstone DSS-14 site, coupled with a proposed increase in transmitter power to 1000 kW, will improve the 3.5 cm radar by about one order of magnitude. Similarly, proposed Arecibo Observatory upgrades of a Gregorian feed structure and an increase of transmitter power to 1000 kW will increase the sensitivity of this radar about 20 fold. In addition, a Goldstone to Very Large Array bistatic observation with horizon to horizon tracking will have 3.5 times more sensitivity than will a Goldstone horizon to horizon monostatic observation. All of these improvements, which should be in place within the next decade, will enrich an already fertile field of planetary exploration.

Renzetti, N. A.↗

NASA NTRS1988

Sensitivity of satellite-derived net shortwave irradiance at the Earth's surface to radiometric calibration

The effect of radiometric calibration uncertainties on satellite-derived net shortwave irradiance at the Earth's surface was examined. Net shortwave irradiance sensitivity to calibration is expressed as a function of two basic components that depend on surface and cloud albedo sensitivities, respectively. The analysis of these sensitivities for a wide range of atmospheric and surface conditions, as well as radiation geometries, shows that a 10 percent uncertainty in the calibration induces up to 40 W/sqm errors in instantaneous net shortwave irradiance (negative when the calibration uncertainty is positive). The maximum relative errors are obtained in overcast conditions when cloud albedos are high. On a monthly time scale, the induced error becomes typically 13 W/sqm in the tropics and 16 W/sqm in higher latitude regions during summer. The error almost vanishes at high latitudes during winter. A 10 percent positive uncertainty in the calibration gives a net shortwave irradiance error similar to that induced by the 3 hr sampling of the ISCCP Project.

Gautier, C.↗