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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Model Reduction by Generalized Falk Method for Efficient Field-Circuit Simulations

The Generalized Falk Method (GFM) for coordinate transformation, together with two model-reduction strategies based on this method, are presented for efficient coupled field-circuit simulations. Each model-reduction strategy is based on a decision to retain specific linearly-independent vectors, called trial vectors, to construct a vector basis for coordinate transformation. The reduced-order models are guaranteed to be stable and passive since the GFM is a congruence transformation of originally symmetric positive definite systems. We also show that, unlike the Pad´e-via-Lanczos (PVL) method, the GFM does not generate unstable positive poles while reducing the order of circuit problems. Further, the proposed GFM is also faster when compared to methods of the type Lanczos (or Krylov) that are already widely used in circuit simulations for electrothermal and electromagnetic problems. The concept of response participation factors is introduced for the selection of the trial vectors in the proposed model-reduction methods. Further, we present methods to develop simple equivalent circuit networks for the field component of the overall field-circuit system. The implementation of these equivalent circuit networks in circuit simulators is discussed. With the proposed model-reduction strategies, significant improvement on the efficiency of the generalized Falk method is illustrated for coupled field-circuit problems.

42 ENGINEERING↗
NASA NTRS1989

Model reduction in the physical coordinate system

In the dynamics modeling of a flexible structure, finite element analysis employs reduction techniques, such as Guyan's reduction, to remove some of the insignificant physical coordinates, thus producing a dynamics model that has smaller mass and stiffness matrices. But this reduction is limited in the sense that it removes certain degrees of freedom at a node points themselves in the model. From the standpoint of linear control design, the resultant model is still too large despite the reduction. Thus, some form of the model reduction is frequently used in control design by approximating a large dynamical system with a fewer number of state variables. However, a problem arises from the placement of sensors and actuators in the reduced model, because a model usually undergoes, before being reduced, some form of coordinate transformations that do not preserve the physical meanings of the states. To correct such a problem, a method is developed that expresses a reduced model in terms of a subset of the original states. The proposed method starts with a dynamic model that is originated and reduced in finite element analysis. Then the model is converted to the state space form, and reduced again by the internal balancing method. At this point, being in the balanced coordinate system, the states in the reduced model have no apparent resemblance to those of the original model. Through another coordinate transformation that is developed, however, this reduced model is expressed by a subset of the original states.

Yae, K. Harold↗
NASA NTRS2011

Range 7 Scanner Integration with PaR Robot Scanning System

An interface bracket and coordinate transformation matrices were designed to allow the Range 7 scanner to be mounted on the PaR Robot detector arm for scanning the heat shield or other object placed in the test cell. A process was designed for using Rapid Form XOR to stitch data from multiple scans together to provide an accurate 3D model of the object scanned. An accurate model was required for the design and verification of an existing heat shield. The large physical size and complex shape of the heat shield does not allow for direct measurement of certain features in relation to other features. Any imaging devices capable of imaging the entire heat shield in its entirety suffers a reduced resolution and cannot image sections that are blocked from view. Prior methods involved tools such as commercial measurement arms, taking images with cameras, then performing manual measurements. These prior methods were tedious and could not provide a 3D model of the object being scanned, and were typically limited to a few tens of measurement points at prominent locations. Integration of the scanner with the robot allows for large complex objects to be scanned at high resolution, and for 3D Computer Aided Design (CAD) models to be generated for verification of items to the original design, and to generate models of previously undocumented items. The main components are the mounting bracket for the scanner to the robot and the coordinate transformation matrices used for stitching the scanner data into a 3D model. The steps involve mounting the interface bracket to the robot's detector arm, mounting the scanner to the bracket, and then scanning sections of the object and recording the location of the tool tip (in this case the center of the scanner's focal point). A novel feature is the ability to stitch images together by coordinates instead of requiring each scan data set to have overlapping identifiable features. This setup allows models of complex objects to be developed even if the object is large and featureless, or has sections that don't have visibility to other parts of the object for use as a reference. In addition, millions of points can be used for creation of an accurate model [i.e. within 0.03 in. (=0.8 mm) over a span of 250 in. (=635 mm)].

Schuler, Jason↗
NASA NTRS1976

On differential transformations between Cartesian and curvilinear (geodetic) coordinates

Differential transformations are developed between Cartesian and curvilinear orthogonal coordinates. Only matrix algebra is used for the presentation of the basic concepts. After defining the reference systems used the rotation (R), metric (H), and Jacobian (J) matrices of the transformations between cartesian and curvilinear coordinate systems are introduced. A value of R as a function of H and J is presented. Likewise an analytical expression for J(-1) as a function of H(-2) and R is obtained. Emphasis is placed on showing that differential equations are equivalent to conventional similarity transformations. Scaling methods are discussed along with ellipsoidal coordinates. Differential transformations between elipsoidal and geodetic coordinates are established.

Soler, T.↗
NASA NTRS1978

Forebody and afterbody solutions of the Navier-Stokes equations for supersonic flow over blunt bodies in a generalized orthogonal coordinate system

A coordinate transformation, which can approximate many different two-dimensional and axisymmetric body shapes with an analytic function, is used as a basis for solving the Navier-Stokes equations for the purpose of predicting 0 deg angle of attack supersonic flow fields. The transformation defines a curvilinear, orthogonal coordinate system in which coordinate lines are perpendicular to the body and the body is defined by one coordinate line. This system is mapped in to a rectangular computational domain in which the governing flow field equations are solved numerically. Advantages of this technique are that the specification of boundary conditions are simplified and, most importantly, the entire flow field can be obtained, including flow in the wake. Good agreement has been obtained with experimental data for pressure distributions, density distributions, and heat transfer over spheres and cylinders in supersonic flow. Approximations to the Viking aeroshell and to a candidate Jupiter probe are presented and flow fields over these shapes are calculated.

Gnoffo, P. A.↗
NASA NTRSDate not supplied

Sonic Boom Propagation Model Based on a Single-Ray Jacobian

A sonic boom is a nonlinear event whose propagation can be modeled involving two stages. The first stage consists of ray path calculations using linear approximations, while the second stage deals with a nonlinear transport of the acoustic energy along these paths. This presentation discusses a second-order finite difference numerical approach used to predict the ray paths in range-dependent atmospheres and compares it to existing finite difference schemes. The approach is validated using exact solutions obtained for stratified atmospheres. In the second stage, the geometrical spreading effect needed in determining sonic boom waveforms from a Burgers' equation is obtained using a method that only needs a single ray rather than four rays required by most existing sonic boom propagation codes. The single-ray method calculates the Jacobian, associated with the coordinate transformation from a suitable ray coordinate system to the Cartesian coordinate system, directly from the ray tracing equations. While the four-ray method approximates the geometrical spreading using a finite difference scheme involving the four rays, the single-ray method does not rely on this approximation and instead depends purely on the acoustical kinematic properties of the atmosphere. Comparisons of results using these two methods are discussed.

sonic boom↗
DOE OSTI2022

Analytic descriptions of parabolic X-ray mirrors

On X-ray beamlines and telescopes, glancing-incidence mirrors with parabolic profiles are used to collimate, focus, and collect light. Here, analytic descriptions for paraboloidal, plane-parabolic, and parabolic cylindrical mirrors in several congruent geometries that are commonly used in fabrication, metrology, and modeling are provided. The exact expressions are derived directly from Fermat's principle, without coordinate transformations, in several mirror-centered coordinate systems, including one with the surface tangent to the central point of intersection. Coefficients for a sixth-order polynomial series approximation are calculated for that coordinate system.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1984

A rapid method for obtaining frequency-response functions for multiple input photogrammetric data

A two-digital-camera photogrammetric technique for measuring the motion of a vibrating spacecraft structure or wing surface and an applicable data-reduction algorithm are presented. The 3D frequency-response functions are obtained by coordinate transformation from averaged cross and autopower spectra derived from the 4D camera coordinates by Fourier transformation. Error sources are investigated analytically, and sample results are shown in graphs.

Kroen, M. L.↗
NASA NTRS1999

Integration of vestibular and head movement signals in the vestibular nuclei during whole-body rotation

Single-unit recordings were obtained from 107 horizontal semicircular canal-related central vestibular neurons in three alert squirrel monkeys during passive sinusoidal whole-body rotation (WBR) while the head was free to move in the yaw plane (2.3 Hz, 20 degrees /s). Most of the units were identified as secondary vestibular neurons by electrical stimulation of the ipsilateral vestibular nerve (61/80 tested). Both non-eye-movement (n = 52) and eye-movement-related (n = 55) units were studied. Unit responses recorded when the head was free to move were compared with responses recorded when the head was restrained from moving. WBR in the absence of a visual target evoked a compensatory vestibulocollic reflex (VCR) that effectively reduced the head velocity in space by an average of 33 +/- 14%. In 73 units, the compensatory head movements were sufficiently large to permit the effect of the VCR on vestibular signal processing to be assessed quantitatively. The VCR affected the rotational responses of different vestibular neurons in different ways. Approximately one-half of the units (34/73, 47%) had responses that decreased as head velocity decreased. However, the responses of many other units (24/73) showed little change. These cells had signals that were better correlated with trunk velocity than with head velocity. The remaining units had responses that were significantly larger (15/73, 21%) when the VCR produced a decrease in head velocity. Eye-movement-related units tended to have rotational responses that were correlated with head velocity. On the other hand, non-eye-movement units tended to have rotational responses that were better correlated with trunk velocity. We conclude that sensory vestibular signals are transformed from head-in-space coordinates to trunk-in-space coordinates on many secondary vestibular neurons in the vestibular nuclei by the addition of inputs related to head rotation on the trunk. This coordinate transformation is presumably important for controlling postural reflexes and constructing a central percept of body orientation and movement in space.

Non-NASA Center↗