Search NASA⌕ Search

SEARCH · Search NASA

Results for “residual function”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 73 records · Page 4

Analysis of altimetry over the Aral Sea

Satellite based altimetric data taken by GEOS-3, SEASAT, and GEOSAT over the Aral Sea are analyzed and a least squares collocation technique is used to predict the geoid undulations on a 0.25 by 0.25 degree grid and to transform these geoid undulations to free air gravity anomalies. Rapp's 180 by 180 geopotential model is taken as the empirical model. The collocation procedure is performed with a set of local residual empirical covariance functions. For comparison, Rapp's global covariance functions and Jordan's self-consistent theoretical covariance functions based on Jordan's formulation and on locally derived parameters are also used to grid geoid undulations and to predict gravity anomalies. The sensitivity of the collocation results to the choice of covariance functions is discussed.

Au, Andrew Y.↗

Statistical Analysis of Strength Data for an Aerospace Aluminum Alloy

Aerospace vehicles are produced in limited quantities that do not always allow development of MIL-HDBK-5 A-basis design allowables. One method of examining production and composition variations is to perform 100% lot acceptance testing for aerospace Aluminum (Al) alloys. This paper discusses statistical trends seen in strength data for one Al alloy. A four-step approach reduced the data to residuals, visualized residuals as a function of time, grouped data with quantified scatter, and conducted analysis of variance (ANOVA).

Neergaard, Lynn↗

Statistical Analysis of Strength Data for an Aerospace Aluminum Alloy

Aerospace vehicles are produced in limited quantities that do not always allow development of MIL-HDBK-5 A-basis design allowables. One method of examining production and composition variations is to perform 100% lot acceptance testing for aerospace Aluminum (Al) alloys. This paper discusses statistical trends seen in strength data for one Al alloy. A four-step approach reduced the data to residuals, visualized residuals as a function of time, grouped data with quantified scatter, and conducted analysis of variance (ANOVA).

Neergaard, L.↗

A New Technique for Retrieval of Tropospheric and Stratospheric Ozone Profiles using Sky Radiance Measurements at Multiple View Angles: Application to a Brewer Spectrometer

This paper describes and applies a new technique for retrieving diurnal variability in tropospheric ozone vertical distribution using ground-based measurements of ultraviolet sky radiances. The measured radiances are obtained by a polarization-insensitive modified Brewer double spectrometer located at Goddard Space Flight Center, in Greenbelt, Maryland, USA. Results demonstrate that the Brewer angular (0-72deg viewing zenith angle) and spectral (303-320 nm) measurements of sky radiance in the solar principal plane provide sufficient information to derive tropospheric ozone diurnal variability. In addition, the Brewer measurements provide stratospheric ozone vertical distributions at least twice per day near sunrise and sunset. Frequent measurements of total column ozone amounts from direct-sun observations are used as constraints in the retrieval. The vertical ozone profile resolution is shown in terms of averaging kernels to yield at least four points in the troposphere-low stratosphere, including good information in Umkehr layer 0 (0-5 km). The focus of this paper is on the derivation of stratospheric and tropospheric ozone profiles using both simulated and measured radiances. We briefly discuss the necessary modifications of the Brewer spectrometer that were used to eliminate instrumental polarization sensitivity so that accurate sky radiances can be obtained in the presence of strong Rayleigh scattering and aerosols. The results demonstrate that including a site-specific and time-dependent aerosol correction, based on Brewer direct-sun observations of aerosol optical thickness, is critical to minimize the sky radiance residuals as a function of observing angle in the optimal estimation inversion algorithm and improve the accuracy of the retrieved ozone profile.

Tzortziou, Maria↗

Discretization formulas for unstructured grids

The Galerkin weighted residual technique using linear triangular weight functions is employed to develop finite difference formula in cartesian coordinates for the Laplacian operator, first derivative operators and the function for unstructured triangular grids. The weighted residual coefficients associated with the weak formulation of the Laplacian operator are shown to agree with the Taylor series approach on a global average. In addition, a simple algorithm is presented to determine the Voronoi (finite difference) area of an unstructured grid.

Baumeister, Kenneth J.↗

Discretization formulas for unstructured grids

The Galerkin weighted residual technique using linear triangular weight functions is employed to develop finite difference formula in cartesian coordinates for the Laplacian operator, first derivative operators and the function for unstructured triangular grids. The weighted residual coefficients associated with the weak formulation of the Laplacian operator are shown to agree with the Taylor series approach on a global average. In addition, a simple algorithm is presented to determine the Voronoi (finite difference) area of an unstructured grid.

Baumeister, Kenneth J.↗

Surveillance system and method having an adaptive sequential probability fault detection test

System and method providing surveillance of an asset such as a process and/or apparatus by providing training and surveillance procedures that numerically fit a probability density function to an observed residual error signal distribution that is correlative to normal asset operation and then utilizes the fitted probability density function in a dynamic statistical hypothesis test for providing improved asset surveillance.

Herzog, James P.↗

Surveillance system and method having an adaptive sequential probability fault detection test

System and method providing surveillance of an asset such as a process and/or apparatus by providing training and surveillance procedures that numerically fit a probability density function to an observed residual error signal distribution that is correlative to normal asset operation and then utilizes the fitted probability density function in a dynamic statistical hypothesis test for providing improved asset surveillance.

Bickford, Randall L.↗

Surveillance System and Method having an Adaptive Sequential Probability Fault Detection Test

System and method providing surveillance of an asset such as a process and/or apparatus by providing training and surveillance procedures that numerically fit a probability density function to an observed residual error signal distribution that is correlative to normal asset operation and then utilizes the fitted probability density function in a dynamic statistical hypothesis test for providing improved asset surveillance.

Bickford, Randall L.↗

Multibody dynamics: Modeling component flexibility with fixed, free, loaded, constraint, and residual modes

The assumed-modes method in multibody dynamics allows the elastic deformation of each component in the system to be approximated by a sum of products of spatial and temporal functions commonly known as modes and modal coordinates respectively. The choice of component modes used to model articulating and non-articulating flexible multibody systems is examined. Attention is directed toward three classical Component Mode Synthesis (CMS) methods whereby component normal modes are generated by treating the component interface (I/F) as either fixed, free, or loaded with mass and stiffness contributions from the remaining components. The fixed and free I/F normal modes are augmented by static shape functions termed constraint and residual modes respectively. A mode selection procedure is outlined whereby component modes are selected from the Craig-Bampton (fixed I/F plus constraint), MacNeal-Rubin (free I/F plus residual), or Benfield-Hruda (loaded I/F) mode sets in accordance with a modal ordering scheme derived from balance realization theory. The success of the approach is judged by comparing the actuator-to-sensor frequency response of the reduced order system with that of the full order system over the frequency range of interest. A finite element model of the Galileo spacecraft serves as an example in demonstrating the effectiveness of the proposed mode selection method.

Spanos, John T.↗

Implicit application of polynomial filters in a k-step Arnoldi method

The Arnoldi process is a well known technique for approximating a few eigenvalues and corresponding eigenvectors of a general square matrix. Numerical difficulties such as loss of orthogonality and assessment of the numerical quality of the approximations as well as a potential for unbounded growth in storage have limited the applicability of the method. These issues are addressed by fixing the number of steps in the Arnoldi process at a prescribed value k and then treating the residual vector as a function of the initial Arnoldi vector. This starting vector is then updated through an iterative scheme that is designed to force convergence of the residual to zero. The iterative scheme is shown to be a truncation of the standard implicitly shifted QR-iteration for dense problems and it avoids the need to explicitly restart the Arnoldi sequence. The main emphasis of this paper is on the derivation and analysis of this scheme. However, there are obvious ways to exploit parallelism through the matrix-vector operations that comprise the majority of the work in the algorithm. Preliminary computational results are given for a few problems on some parallel and vector computers.

Sorensen, D. C.↗

Axial residual stresses in boron fibers

The axial residual stress distribution as a function of radius was determined from the fiber surface to the core including the average residual stress in the core. Such measurements on boron on tungsten (B/W) fibers show that the residual stresses for 102, 142, 203, and 366 micron diameter fibers were similar, being compressive at the surface and changing monotonically to a region of tensile within the boron. At approximately 25 percent of the original radius, the stress reaches a maximum tensile stress of about 860 mn/sq.m and then decreases to a compressive stress near the tungsten boride core. Data were presented for 203 micron diameter B/W fibers that show annealing above 900 C reduces the residual stresses. A comparison between 102 micron diameter B/W and boron on carbon (b/C) shows that the residual stresses were similar in the outer regions of the fibers, but that large differences near and in the core were observed. The effects of these residual stresses on the fracture of boron fibers were discussed.

Behrendt, D. R.↗

Axial residual stresses in boron fibers

A method of measuring axial residual stresses in boron fibers is presented. With this method, the axial residual stress distribution as a function of radius is determined from the fiber surface to the core including the average residual stress in the core. Such measurements on boron on tungsten (B/W) fibers show that the residual stresses for 102, 142, 203, and 366 micron diam fibers are similar, being compressive at the surface and changing monotonically to a region of tensile stress within the boron. At approximately 25% of the original radius, the stress reaches a maximum tensile stress of about 860 MN sq m and then decreases to a compressive stress near the tungsten boride core. Data are presented for 203-micron diam B/W fibers that show annealing above 900 C reduces the residual stresses. A comparison between 102-micron diam B/W and boron on carbon (B/C) show that the residual stresses are similar in the outer regions of the fibers, but that large differences near and in the core are observed. Fracture of boron fibers is discussed.

Behrendt, D. R.↗

Fabrication and properties of functionally graded NiAl/Al2O3 composites

A modified sedimentation process was used in the production of a functionally gradient material (FGM), NiAl/Al2O3. A simple finite element model was used to guide our design and fabrication efforts by estimating residual stress states as a function of composite structure. This approach could lead to tailored designs that enhance or avoid specific residual stress states. Thermal cycling tests were factored into the model to predict time dependent or steady-state internal temperature and stress profiles. Four-point bend tests were conducted to establish the mechanical load-displacement behavior of a single interlayer FGM at room temperature, 800 and 1000 K. Room temperature bend strength of the FGM was 3-4 times that of the base NiAl. At elevated temperatures, composite fracture occurred in a gradual, noncatastrophic mode involving NiAl retardation of a succession of cracks originating in the alumina face.

Miller, D. P.↗

Implicit Formulation of Muscle Dynamics in OpenSim

Astronauts lose bone and muscle mass during spaceflight. Exercise countermeasure is the primary method for counteracting bone and muscle mass loss in space. New spacecraft exercise device concepts are currently being developed for the NASAs new crew exploration vehicle. The NASA Digital Astronaut Project (DAP) uses computational modeling to help determine if the new exercise devices will be effective as countermeasures. The NASA Digital Astronaut Project is developing the ability to utilize predictive simulation to provide insight into the change in kinematics and kinetics with a change in device and gravitational environment (1-g versus 0-g). For example, in space exercise the subject's body weight is applied in addition to the loads prescribed for musculoskeletal maintenance. How and where these loads are applied obviously directly impacts bone and tissue loads. Additionally, due to space vehicle structural requirements, exercise devices are often placed on vibration isolation systems. This changes the apparent impedance or stiffness of the device as seen by the user. Data collection under these conditions is often impractical and limited. Predictive modeling provides a means to have a virtual subject to test hypotheses. Predictive simulation provides a virtual subject for which we are able to perform studies such as sensitivity to device loading and vibration isolation without the need for laboratory kinematic or kinetic test data.Direct Collocation optimization provides an efficient means to perform task based optimization and predictive modeling. It is relatively straight forward to structure a physical exercise task in a Direct Collocation mathematical formulation: perform a motion such that you start at an initial pose, achieve a given amount of deflection i.e a squat, return to the initial pose, and minimize muscle activation cost. Direct Collocation is advantageous in that it does not require numerical integration to evaluate the objective function. Instead, the system dynamics are transformed to discrete time and the optimizer is constrained such that the solution is not considered to be a valid unless the dynamic equations are satisfied at all time points. The simulation and optimization are effectively done simultaneously. Due to the implicit integration, time steps can be more coarse than in a differential equation solver. In a gait scenario this means that that the model constraints and cost function are evaluated at 100 nodes in the gait cycle versus 10,000 integration steps in a variable-step forward dynamic simulation. Furthermore, no time is wasted on accurate simulations of movements that are far from the optimum. Constrained optimization algorithms require a Jacobian matrix that contains the partial derivatives of each of the dynamic constraints with respect to of each of the state and control variables at all time points. This is a large but sparse matrix. An implicit dynamics formulation requires computation of the dynamic residuals f as a function of the states x and their derivatives, and controls u:f(x, dxdt, u) 0If the dynamics of musculoskeletal system are formulated implicitly, the Jacobian elements are often available analytically, eliminating the need for numerical differentiation; this is obviously computationally advantageous. Additionally, implicit formulation of musculoskeletal dynamics do not suffer from singularities from low mass bodies, zero muscle activation, or other stiff system or

physical exercise↗

Progress on Inverse Estimation Technique of Non-Linear Pitch Damping Coefficient Curves Using Free-Flight CFD Generated Trajectories

Characterization of entry vehicle pitch damping coefficient curves is crucial to ensure appropriate re-entry and overall mission success. The pitch damping coefficient (C_(m_q )+C_(m_α ̇ )) is used to encapsulate the oscillatory growth or decay of a body during a trajectory. The inverse estimation technique utilizes an existing Free-Flight CFD (FF-CFD) dataset and wraps a reconstruction algorithm in an optimizer. The reconstruction integrates the planar equations of motion derived by Schoenenberger, Queen [1] using Python’s scipy.integrate.solve_ivp. The optimizer’s objective function is the normalized 𝐿2 residual of the angle of attack peaks between the reconstructed trajectory and the original data produced with FF-CFD. Inclusion of the peak times in this residual calculation allows for simultaneous optimization of the pitch moment coefficient, C_(m_α ). This residual equation is shown below in Eq. 1. The optimizer scipy.optimize.minimize was used with the gradient-based Powell method for the analysis presented, however the differential evolution method was investigated as means of comparison, and was found to produce marginally lower residual values with prohibitively longer run times. Further, the pitch damping curve is found by fitting a cubic interpolation function to a set of (α, (C_(m_q )+C_(m_α ̇ ))) control points, where the α points are held constant and the (C_(m_q )+C_(m_α ̇ )) values are the optimized parameters. The pitch moment curve uses a linear interpolation between the minimum and maximum α in the dataset. FF-CFD generated trajectories using the Dragonfly capsule geometry with the Genesis ballistic range model parameters were simulated and used for this analysis. These FF-CFD trajectories simulate planar motion, as restricted by the reconstructing the equations of motion, of three different cases: 1-DoF (free-to-pitch), 2-DoF (free-to-pitch and heave), and 3-DoF (free-to-pitch, heave, and decelerate). Pitch damping coefficient curves generated using this inverse estimation curve technique with FF-CFD 1-DoF Dragonfly data are found in Fig. 1. Preliminary results reconstructing ballistic range shots using these FF-CFD derived predictions of the pitch damping curve (Fig. 1) are shown in Fig. 2. It should be noted that the ballistic range shot used a Genesis model whereas the FF-CFD data used a Dragonfly geometry, however these geometries are similar.

entry↗

Fatigue of notched fiber composite laminates - Analytical and experimental evaluation

Axial cracking in the load direction and transverse cracking across notched boron/epoxy laminate specimens subjected to tension/tension fatigue loading are studied both theoretically and experimentally. The fatigue analysis, which allows for the computation of residual strength and the determination of the preferred mode of crack propagation, is reviewed; static and fatigue data for boron/epoxy lamina are investigated with the aim of characterizing fatigue growth and residual strength as a function of the number of load cycles. It is suggested that correlation between the theory and the experiment may be limited by lack of a capability to predict the growth of delaminations.

Kulkarni, S. V.↗