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Recent developments in two areas of structural sensitivity analysis are reviewed. These are the sensitivity of static and transient response, and the sensitivity of vibration and buckling eigenproblems. Recent developments from the point of view of computational cost, accuracy, and ease of implementation are considered.
In this paper, an integrated approach to structural/control design is proposed in which variables in both the passive (structural) and active (control) disciplines of an optimization process are changed simultaneously. The global sensitivity equation (GSE) method of Sobieszczanski-Sobieski (1988) is used to obtain the behavior sensitivity derivatives necessary for the linear approximations used in the parallel multidisciplinary synthesis problem. The GSE allows for the decoupling of large systems into smaller subsystems and thus makes it possible to determine the local sensitivities of each subsystem's outputs to its inputs and parameters. The advantages in using the GSE method are demonstrated using a finite-element representation of a truss structure equipped with active lateral displacement controllers, which is undergoing forced vibration.
The relationship in plants between the sensitivity to auxin and differential growth and bending was investigated experimentally. Decapitated and marked sunflower hypocotyl sections were immersed in buffered auxin solutions of different concentrations (0, 10 to the -8th, or 0.001 molar) and were photographed at 1/2 hr intervals; the negatives were analyzed with a digitizer/computer to evaluate surface-length changes in terms of Michaelis-Menten enzyme kinetics. It was found that bending decreased with increasing concentration of auxin. Increasing the auxin concentration inhibits the elongation growth of lower surfaces but promotes upper-surface growth, indicating that the lower surfaces have a greater Km sensitivity to applied auxin than the upper surfaces. At optimum auxin levels (maximum growth), the growth of bottom surfaces exceeded that of top surfaces, indicating that bottom tissues had a greater Vmax sensitivity.
Initial measurements of the position sensitivity of a visible-light multianode microchannel array detector show that centroid calculations for image spots are accurate to better than 0.04 pixels even with sources that are essentially delta functions at the photocathode.Subpixel sensitivity variations of 10-15 percent are typically found for pixels in the array. Variations as large as 30 percent are possible in the worst conditions. These variations limit the photometric accuracy of the detector when very small scale features are observed. The photometric accuracy and the position sensitivity of the detector appear to be limited by cross-coupling effects within the anode array. Initial measurements with more recent designs of the detector show that most or all of this cross-coupling has been eliminated.
A linear, primitive equation stationary wave model having high vertical and meridional resolution is used to examine the sensitivity of orographically forced (primarily by Himalayas) stationary waves at middle and high latitudes to variations in the basic state zonal wind distribution. We find relatively little sensitivity to the winds in high latitudes, but remarkable sensitivity to small variations in the subtropical jet. Fluctuations well within the range of observed variability in the jet can lead to large variations in the stationary waves of the high latitude stratosphere, and to large changes even in tropospheric stationary waves. Implications for both sudden warmings and large-scale weather are discussed.
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 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.
Progress performed on each task is described. Order of magnitude analyses related to liquid zone sensitivity and thermo-capillary flow sensitivity are covered. Progress with numerical models of the sensitivity of isothermal liquid zones is described. Progress towards a numerical model of coupled buoyancy-driven and thermo-capillary convection experiments is also described. Interaction with NASA personnel is covered. Results to date are summarized and they are discussed in terms of the predicted space station acceleration environment. Work planned for the second year is also discussed.
A Monte Carlo simulation shows that EGRET (Energetic Gamma-Ray Experimental Telescope) does not even have sufficient sensitivity to detect 100 percent polarized gamma-rays. This is confirmed by analysis of calibration data. A Monte Carlo study shows that the sensitivity of EGRET to polarization peaks around 100 MeV. However, more than 10 (exp 5) gamma-ray events with 100 percent polarization would be required for a 3 sigma significance detection - more than available from calibration, and probably more than will result from a single score source during flight. A drift chamber gamma ray telescope under development (Hunter and Cuddapah 1989) will offer better sensitivity to polarization. The lateral position uncertainty will be improved by an order of magnitude. Also, if pair production occurs in the drift chamber gas (xenon at 2 bar) instead of tantalum foils, the effects of multiple Coulomb scattering will be reduced.
An approach toward improving supersonic ignition and combustion efficiency was investigated under a feasibility program with NASA-Ames. The idea is to selectively irradiate targetted species in the combustion zone. The ensuing photodissociation reactions produce highly reactive radicals which modify the gas phase kinetics. The overall objective of this research was to demonstrate photosensitized ignition of H2/O2 mixtures, and to gain a preliminary understanding of the ignition mechanism, especially as it pertains to the concept of supersonic combustion. To this end, a series of experiments were performed with a model sensitizer, NO2. At subatmospheric pressures and moderate temperatures (above 100 F), mixtures of H2/O2/NO2 are ignitable by a pulsed eximer laser at 308 nm, 115 to 200 mJ. Ignitability was found to be a function of NO2 pressure, temperature, laser energy per pulse, and laser lens focal length (fluence at focal volume). Mixtures could not be ignited in the absence of the sensitizer. While increasing temperature improved sensitized ignition in the lower temperature range, a retarding effect was observed at the highest temperatures. To more thoroughly understand these thermal effects, the UV-Vis and IR spectra of NO2 and H2/O2/NO2 mixtures were studied over the temperature range 70 to 900 F. Initially, increasing temperature shifts the N2O4 in a reversible reaction to 2 NO2 equilibrium toward NO2, favoring photochemical ignition. However, at still higher temperature, NO2 converts to non-absorbing NO + 1/2 O2, thus preventing photosensitized ignition.
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.
This paper derives an error magnification index for assessing the sensitivity of the displacement field to errors in the load vector. It is shown that the error magnification index is less conservative than the stiffness-matrix condition number and that, for some cases, no error magnification occurs even when the condition number is very high. The proposed index was used to calculate the derivatives of beam response to changes in the beam structural parameters, using a semianalytical method. It is shown that the proposed index discriminates well between the calculation of the derivative with respect to length, which is very sensitive to errors, and the calculation of the derivative with respect to cross-sectional height, which is not sensitive.
The purpose of the study is to assess the Mars orbiters with regard to their sensitivity to the Mars gravity field. The sensitivity is evaluated and quantified in terms of the magnitude and frequency of the orbiter position and velocity perturbations. The strengths and weaknesses of each orbiter, including Mariner 9, Viking 1 and 2, Mars Observer, Phobos, and Deimos, when used as a sensor of the Mars gravity field are assessed. It is shown that Mariner 9 and Viking data supply strong information on the low degree and order coefficients, with Mariner 9 contributing to the even-ordered terms out to about degrees 10 to 12. Phobos and Deimos are shown to be able to contribute to the lowest degrees of the gravity field, while the Mars Observer, in addition to the lower-degree and -order harmonics, will be responsive to coefficients as high as degree and order 50. Emphasis is placed on the spacecraft orbit plane orientation allowing the radial velocity perturbations to be measured by the Doppler data, thus enhancing the sensitivity to the gravitational signal.
An overview is given of methodology and test results pertaining to the characterization of ultra sensitive accelerometers. Two issues are of primary concern. The terminology ultra sensitive accelerometer is used to imply instruments whose noise floors and resolution are at the state of the art. Hence, the typical approach of verifying an instrument's performance by measuring it with a yet higher quality instrument (or standard) is not practical. Secondly, it is difficult to find or create an environment with sufficiently low background acceleration. The typical laboratory acceleration levels will be at several orders of magnitude above the noise floor of the most sensitive accelerometers. Furthermore, this background must be treated as unknown since the best instrument available is the one to be tested. A test methodology was developed in which two or more like instruments are subjected to the same but unknown background acceleration. Appropriately selected spectral analysis techniques were used to separate the sensors' output spectra into coherent components and incoherent components. The coherent part corresponds to the background acceleration being measured by the sensors being tested. The incoherent part is attributed to sensor noise and data acquisition and processing noise. The method works well for estimating noise floors that are 40 to 50 dB below the motion applied to the test accelerometers. The accelerometers being tested are intended for use as feedback sensors in a system to actively stabilize an inertial guidance component test platform.
The three dimensional quasi-analytical sensitivity analysis and the ancillary driver programs are developed needed to carry out the studies and perform comparisons. The code is essentially contained in one unified package which includes the following: (1) a three dimensional transonic wing analysis program (ZEBRA); (2) a quasi-analytical portion which determines the matrix elements in the quasi-analytical equations; (3) a method for computing the sensitivity coefficients from the resulting quasi-analytical equations; (4) a package to determine for comparison purposes sensitivity coefficients via the finite difference approach; and (5) a graphics package.
Continuing studies associated with the development of the quasi-analytical (QA) sensitivity method for three dimensional transonic flow about wings are presented. Furthermore, initial results using the quasi-analytical approach were obtained and compared to those computed using the finite difference (FD) approach. The basic goals achieved were: (1) carrying out various debugging operations pertaining to the quasi-analytical method; (2) addition of section design variables to the sensitivity equation in the form of multiple right hand sides; (3) reconfiguring the analysis/sensitivity package in order to facilitate the execution of analysis/FD/QA test cases; and (4) enhancing the display of output data to allow careful examination of the results and to permit various comparisons of sensitivity derivatives obtained using the FC/QA methods to be conducted easily and quickly. In addition to discussing the above goals, the results of executing subcritical and supercritical test cases are presented.
A new and efficient method is presented for aerodynamic design optimization, which is based on a computational fluid dynamics (CFD)-sensitivity analysis algorithm. The method is applied to design a scramjet-afterbody configuration for an optimized axial thrust. The Euler equations are solved for the inviscid analysis of the flow, which in turn provides the objective function and the constraints. The CFD analysis is then coupled with the optimization procedure that uses a constrained minimization method. The sensitivity coefficients, i.e. gradients of the objective function and the constraints, needed for the optimization are obtained using a quasi-analytical method rather than the traditional brute force method of finite difference approximations. During the one-dimensional search of the optimization procedure, an approximate flow analysis (predicted flow) based on a first-order Taylor series expansion is used to reduce the computational cost. Finally, the sensitivity of the optimum objective function to various design parameters, which are kept constant during the optimization, is computed to predict new optimum solutions. The flow analysis of the demonstrative example are compared with the experimental data. It is shown that the method is more efficient than the traditional methods.
Incorporating the full geochemical cycles of stable water isotopes (HDO and H2O-18) into an atmospheric general circulation model (GCM) allows an improved understanding of global delta-D and delta-O-18 distributions and might even allow an analysis of the GCM's hydrological cycle. A detailed sensitivity analysis using the NASA/Goddard Institute for Space Studies (GISS) model II GCM is presented that examines the nature of isotope modeling. The tests indicate that delta-D and delta-O-18 values in nonpolar regions are not strongly sensitive to details in the model precipitation parameterizations. This result, while implying that isotope modeling has limited potential use in the calibration of GCM convection schemes, also suggests that certain necessarily arbitrary aspects of these schemes are adequate for many isotope studies. Deuterium excess, a second-order variable, does show some sensitivity to precipitation parameterization and thus may be more useful for GCM calibration.
Intensive research and development in Computational Fluid Dynamics (CFD) has recently produced many powerful CFD codes to simulate complex aerodynamic phenomena. However, in order to enhance the usefulness of these CFD codes for design practice, development of design sensitivity equations compatible to these codes becomes very important. This paper represents a part of such an effort to develop a sensitivity analysis methodology that enables the sensitivity equations to be implemented into existing CFD codes with minimal code modification. The methodology is based upon a preelimination procedure which accounts for consistently linearized boundary conditions. Formulations of both the direct differentiation and the adjoint variable methods will be presented in the paper.