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At least 199 records · Page 11

An Interesting Correlation Between the Peak Slope and Peak Value of a Sunspot Cycle

The maximum slope of the sunspot number during the rising phase of a sunspot cycle has an excellent correlation with the maximum value of the sunspot number during that cycle. This is demonstrated using a Savitzky–Golay filter to both smooth and calculate the derivative of the sunspot-number data. Version 2 of the International Sunspot Number (S) is used to represent solar activity. The maximum of the slope during the rising phase of each cycle was correlated against the peaks of solar activity. Using three different correlation fits, the average predicted amplitude for Solar Cycle 25 is 130.7 ± 0.5, among the best correlations in solar predictions. A possible explanation for this correlation is given by the similar behavior of a shape function representing the time variation of the sunspot number. This universal function also provides the timing of the solar maximum by the time from the slope maximum to the peak in the function as late 2023 or early 2024. A Hilbert transform gives similar results, which are caused by the dominance of the 11-yr sunspot-cycle period in a Fourier fit of the sunspot number.

W. Dean Pesnell↗

A General Procedure to Formulate 3D Elements for Finite Element Applications

This paper presents a general procedure to formulate and implement 3D elements of arbitrary order in meshes with multiple element types. This procedure includes obtaining shape functions and integration quadrature and establishing an approach for checking the generated element’s compatibility with adjacent elements’ surfaces. This procedure was implemented in Matlab, using its symbolic and graphics toolbox, and complied as a GUI interface named ShapeGen3D to provide finite element users with a tool to tailor elements according to their analysis needs. ShapeGen3D also outputs files with the element formulation needed to enable users to implement the generated elements in other programming languages or through user elements in commercial finite element software. Currently, finite element (FE) users are limited to employing element formulation available in the literature, commercial software, or existing element libraries. Thus, the developed procedure implemented in ShapeGen3D offers FEM users the possibility to employ elements beyond those readily available. The procedure was tested by generating the formulation for a brick element, a brick transition element, and higher-order hexahedron and tetrahedron elements that can be used in a spectral finite element analysis. The formulation obtained for the 20-node element was in perfect agreement with the formulation available in the literature. In addition, the results showed that the interpolation condition was met for all the generated elements, which provides confidence in the implementation of the process. Researchers and educators can use this procedure to efficiently develop and illustrate three-dimensional elements.

higher-order elements↗

Applications of Displacement Transfer Functions to Deformed Shape Predictions of the GIII Swept-Wing Structure

The displacement transfer functions (DTFs) were applied to the GIII swept wing for the deformed shape prediction. The calculated deformed shapes are very close to the correlated finite element results as well as the measured data. The convergence study showed that using 17 strain stations, the wing-tip displacement prediction error was 1.6 percent, and that there is no need to use a large number of strain stations for G-III wing shape predictions.

on board string sensing system↗

Biomimetic/Optical Sensors for Detecting Bacterial Species

Biomimetic/optical sensors have been proposed as means of real-time detection of bacteria in liquid samples through real-time detection of compounds secreted by the bacteria. Bacterial species of interest would be identified through detection of signaling compounds unique to those species. The best-characterized examples of quorum-signaling compounds are acyl-homoserine lactones and peptides. Each compound, secreted by each bacterium of an affected species, serves as a signal to other bacteria of the same species to engage in a collective behavior when the population density of that species reaches a threshold level analogous to a quorum. A sensor according to the proposal would include a specially formulated biomimetic film, made of a molecularly imprinted polymer (MIP), that would respond optically to the signaling compound of interest. The MIP film would be integrated directly onto an opticalwaveguide- based ring resonator for optical readout. Optically, the sensor would resemble the one described in Chemical Sensors Based on Optical Ring Resonators (NPO-40601), NASA Tech Briefs, Vol. 29, No. 10 (October 2005), page 32. MIPs have been used before as molecular- recognition compounds, though not in the manner of the present proposal. Molecular imprinting is an approach to making molecularly selective cavities in a polymer matrix. These cavities function much as enzyme receptor sites: the chemical functionality and shape of a cavity in the polymer matrix cause the cavity to bind to specific molecules. An MIP matrix is made by polymerizing monomers in the presence of the compound of interest (template molecule). The polymer forms around the template. After the polymer solidifies, the template molecules are removed from the polymer matrix by decomplexing them from their binding sites and then dissolving them, leaving cavities that are matched to the template molecules in size, shape, and chemical functionality. The cavities thus become molecular-recognition sites that bind only to molecules matched to the sites; other molecules are excluded. In a sensor according to the proposal, the MIP would feature molecular recognition sites that would bind the specific signaling molecules selectively according to their size, shape, and chemical functionality (see figure). As the film took up the signaling molecules in the molecular recognition sites, the index of refraction and thickness of the film would change, causing a wavelength shift of the peak of the resonance spectrum. It has been estimated that by measuring this wavelength shift, it should be possible to detect as little as 10 picomoles of a peptide signaling compound.

Homer, Margie↗

Applications of Displacement Transfer Functions to Deformed Shape Predictions of the G-III Swept-Wing Structure

In support of the Adaptive Compliant Trailing Edge [ACTE] project at the NASA Armstrong Flight Research Center, displacement transfer functions were applied to the swept wing of a Gulfstream G-III airplane (Gulfstream Aerospace Corporation, Savannah, Georgia) to obtain deformed shape predictions. Four strainsensing lines (two on the lower surface, two on the upper surface) were used to calculate the deformed shape of the G III wing under bending and torsion. There being an insufficient number of surface strain sensors, the existing G III wing box finite element model was used to generate simulated surface strains for input to the displacement transfer functions. The resulting predicted deflections have good correlation with the finite-element generated deflections as well as the measured deflections from the ground load calibration test. The convergence study showed that the displacement prediction error at the G III wing tip can be reduced by increasing the number of strain stations (for each strain-sensing line) down to a minimum error of l.6 percent at 17 strain stations; using more than 17 strain stations yielded no benefit because the error slightly increased to 1.9% when 32 strain stations were used.

displacement theory↗

Improved Displacement Transfer Functions for Structure Deformed Shape Predictions Using Discretely Distributed Surface Strains

In the formulations of earlier Displacement Transfer Functions for structure shape predictions, the surface strain distributions, along a strain-sensing line, were represented with piecewise linear functions. To improve the shape-prediction accuracies, Improved Displacement Transfer Functions were formulated using piecewise nonlinear strain representations. Through discretization of an embedded beam (depth-wise cross section of a structure along a strain-sensing line) into multiple small domains, piecewise nonlinear functions were used to describe the surface strain distributions along the discretized embedded beam. Such piecewise approach enabled the piecewise integrations of the embedded beam curvature equations to yield slope and deflection equations in recursive forms. The resulting Improved Displacement Transfer Functions, written in summation forms, were expressed in terms of beam geometrical parameters and surface strains along the strain-sensing line. By feeding the surface strains into the Improved Displacement Transfer Functions, structural deflections could be calculated at multiple points for mapping out the overall structural deformed shapes for visual display. The shape-prediction accuracies of the Improved Displacement Transfer Functions were then examined in view of finite-element-calculated deflections using different tapered cantilever tubular beams. It was found that by using the piecewise nonlinear strain representations, the shape-prediction accuracies could be greatly improved, especially for highly-tapered cantilever tubular beams.

Ko, William L.↗

Scattering from arbitrarily shaped microstrip patch antennas

The scattering properties of arbitrarily shaped microstrip patch antennas are examined. The electric field integral equation for a current element on a grounded dielectric slab is developed for a rectangular geometry based on Galerkin's technique with subdomain rooftop basis functions. A shape function is introduced that allows a rectangular grid approximation to the arbitrarily shaped patch. The incident field on the patch is expressed as a function of incidence angle theta(i), phi(i). The resulting system of equations is then solved for the unknown current modes on the patch, and the electromagnetic scattering is calculated for a given angle. Comparisons are made with other calculated results as well as with measurements.

Shively, David G.↗

Magnetopause shape as a bivariate function of interplanetary magnetic field B(sub z) and solar wind dynamic pressure

We present a new method for determining the shape of the magnetopause as a bivariate function of the hourly averaged solar wind dynamic pressure (p) and the north-south component of the interplanetary magnetic field (IMF) B(sub z). We represent the magnetopause (for X(sub GSE) greater than -40 R(sub E)) as an ellipsoid of revolution in solar-wind-aberrated coordinates and express the (p, B(sub z)) dependence of each of the three ellipsoid parameters as a second-order (6-term) bivariate expansion in Inp and B(sub z). We define 12 overlapping bins in a normalized dimensionless (p, B(sub z)) `control space' and fit an ellipsoid to those magnetopause crossings having (p, B(sub z)) values within each bin. We also calculate the bivariate (Inp, B(sub z)) moments to second order over each bin in control space. We can then calculate the six control-space expansion coefficients for each of the three ellipsoid parameters in configuration space. From these coefficients we can derive useful diagnosis of the magnetopause shape as joint functions of p and B(sub z): the aspect ratio of the ellipsoid's minor-to-major axes; the flank distance, radius of curvature, and flaring angle (at X(sub GSE) = 0); and the subsolar distance and radius of curvature. We confirm and quantify previous results that during periods of southward B(sub z) the subsolar magnetopause moves inward, while at X(sub GSE) = 0 the flank magnetopause moves outward and the flaring angle increases.

Roelof, Edmond C.↗

Structural Shape Sensing from Strain Data Using the Basis Function Method

An aircraft shape must be measured during flight to implement an active trim shape control, such as an active dihedral control for a highly flexible aircraft with a high-aspect-ratio wing, and an active sonic boom control for a supersonic transport aircraft. A basis function method for linear as well as geometrically nonlinear structural shape sensing is proposed in this study. Basis functions can be mode shapes, linear static deformation shapes, or geometrically nonlinear static deformation shapes. The proposed basis function method is validated using a high-aspect-ratio wing, a swept test plate, and the National Aeronautics and Space Administration Low Boom Flight Demonstration mission X-59 Quiet Supersonic Technology (QueSST) aircraft (Lockheed Martin, Bethesda, Maryland). A large structural deformation of a high-aspect-ratio wing is successfully captured using the proposed basis function method with less than 0.3-percentprediction error at the wing-tip section. The basis function method gives excellent deformation prediction, even with stress concentration. Performance of the basis functions is compared using the X-59 stabilator sample case. In most of the sample load cases, static deformations give a better correlation with the target deformation than do mode shapes. Wing shape sensing with sparse strain data is also demonstrated in this study using the X-59 QueSST aircraft. Predicted structural deformations match reasonably with the target deformations even without strain gauges on some structural components. The predicted deformations have a good match with the target deformations.

Chan-gi Pak↗

Shape Servoing of Deformable Objects Using Model Estimation and Barrier Lyapunov Function

An adaptive shape servoing control method is presented in this article to manipulate a deformable object into a desired shape in 3-D. A finite-point-based representation of the deformable object is used and the deformation Jacobian matrix is approximated using Fourier series basis functions. The unknown parameters of the deformation Jacobian are learned by using the velocity applied to a control point on the object and corresponding change of positions of the points describing the entire object. An integral concurrent learning (ICL)-based parameter update law is designed along with a constrained controller to satisfy the state constraints on the motion of the control point using Barrier Lyapunov function analysis. ICL-based parameter update law uses data history of velocity and corresponding positions of the points along with their current values. An efficient algorithm to update the history stack using singular value maximization is proposed based on the structure of the regressor matrix. Simulations using a physical simulator and experiments using a robot platform are performed to validate the performance of the proposed controller on two different deformable objects.

Vrithik Raj Guthikonda↗

Automation of Geometric Accuracy Assessment Algorithm

When end-users are using multiple satellite images for a study the first step is often the assessment and rectification of geolocation offsets. We have developed an automated algorithm to calculate the geometric offsets between two satellite images. It splits both images into subset images (chips) and resamples them to a common resolution. Offsets are imposed on matching chips and the Pearson Cross Correlation (PCC) value calculated for each offset, where the best PCC gives the true offsets. With the true offsets corrected for, a quality of image registration is calculated, measurement uncertainty (MU). The MU threshold value is non-uniform across sensors because it depends on spectral characteristics of each sensor. Previously, the MU threshold was determined by manual inspection for each new sensor assessed. In this study, we automated MU threshold determination. 1/MU vs calculated offset approximates a Gaussian function in shape, see abstract image. A Gaussian function is fit to this dataset, and the root of the third derivative is calculated and applied as a quality threshold, removing the data of lower quality from the final assessment of image offsets. We apply this algorithm to commercial satellite data for proof of concept.

Alana Semple↗

Optimal rocket thrust profile shaping using third degree spline function interpolation

Optimal solid-rocket thrust profiles for the parallel-burn, solid-rocket-assisted space shuttle are investigated. Solid-rocket thrust profiles are simulated by using third-degree spline functions, with the values of the thrust ordinates defined as parameters. The profiles are optimized parametrically, using the Davidon-Fletcher-Powell penalty function method, by minimizing propellant weight subject to state and control inequality constraints and to terminal boundary conditions. This study shows that optimizing a control variable parametrically by using third-degree spline function interpolation allows the control to be shaped so that inequality constraints are strictly adhered to and all corners are eliminated. The absence of corners, which is realistic in nature, makes this method attractive from the viewpoint of solid rocket grain design.

Johnson, I. L.↗

Experimental determination of the particle motions associated with the low order acoustic modes in enclosures

A procedure for experimentally determining, in terms of the particle motions, the shapes of the low order acoustic modes in enclosures is described. The procedure is based on finding differentiable functions which approximate the shape functions of the low order acoustic modes when these modes are defined in terms of the acoustic pressure. The differentiable approximating functions are formed from polynomials which are fitted by a least squares procedure to experimentally determined values which define the shapes of the low order acoustic modes in terms of the acoustic pressure. These experimentally determined values are found by a conventional technique in which the transfer functions, which relate the acoustic pressures at an array of points in the enclosure to the volume velocity of a fixed point source, are measured. The gradient of the function which approximates the shape of a particular mode in terms of the acoustic pressure is evaluated to give the mode shape in terms of the particle motion. The procedure was tested by using it to experimentally determine the shapes of the low order acoustic modes in a small rectangular enclosure.

Byrne, K. P.↗

A new class of energy based control laws for revolute robot arms - Tracking control, robustness enhancement and adaptive control

A class of joint-level control laws for all-revolute robot arms is introduced. The analysis is similar to the recently proposed energy Liapunov function approach except that the closed-loop potential function is shaped in accordance with the underlying joint space topology. By using energy Liapunov functions with the modified potential energy, a much simpler analysis can be used to show closed-loop global asymptotic stability and local exponential stability. When Coulomb and viscous friction and model parameter errors are present, a sliding-mode-like modification of the control law is proposed to add a robustness-enhancing outer loop. Adaptive control is also addressed within the same framework. A linear-in-the-parameters formulation is adopted, and globally asymptotically stable adaptive control laws are derived by replacing the model parameters in the nonadaptive control laws by their estimates.

Wen, John T.↗

Jig-Shape Optimization of a Low-Boom Supersonic Aircraft

A simple approach for optimizing the jig-shape is proposed in this study. This simple approach is based on an unconstrained optimization problem and applied to a low-boom supersonic aircraft. In this study, the jig-shape optimization is performed using the two-step approach. First, starting design variables are computed using the least-squares surface fitting technique. Next, the jig-shape is further tuned using a numerical optimization procedure based on an in-house object-oriented optimization tool. During the numerical optimization procedure, a design jig-shape is determined by the baseline jig-shape and basis functions. A total of 12 symmetric mode shapes of the cruise-weight configuration, rigid pitch shape, rigid left and right stabilator rotation shapes, and a residual shape are selected as sixteen basis functions. After three optimization runs, the trim shape error distribution is improved, and the maximum trim shape error of 0.9844 inches of the starting configuration becomes 0.00367 inch by the end of the third optimization run.

numerical analysi↗

Development of a Refined Space Vehicle Rollout Forcing Function

For several decades, American manned spaceflight vehicles and the associated launch platforms have been transported from final assembly to the launch pad via a pre-launch phase called rollout. The rollout environment is rich with forced harmonics and higher order effects can be used for extracting structural dynamics information. To enable this utilization, processing tools are needed to move from measured and analytical data to dynamic metrics such as transfer functions, mode shapes, modal frequencies, and damping. This paper covers the range of systems and tests that are available to estimate rollout forcing functions for the Space Launch System (SLS). The specific information covered in this paper includes: the different definitions of rollout forcing functions; the operational and developmental data sets that are available; the suite of analytical processes that are currently in-place or in-development; and the plans and future work underway to solve two immediate problems related to rollout forcing functions. Problem 1 involves estimating enforced accelerations to drive finite element models for developing design requirements for the SLS class of launch vehicles. Problem 2 involves processing rollout measured data in near real time to understand structural dynamics properties of a specific vehicle and the class to which it belongs.

James, George↗