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At least 397 records · Page 22

Some Continuum Aspects of Data Assimilation

A long-sought goal in data assimilation is to build more fully the time dimension into the data assimilation process. Truly four-dimensional data assimilation requires evolving second-moment information, namely the estimation error covariance, along with the state estimate itself. The continuum evolution equations for the estimation error covariance constitute a system of partial differential equations in six space dimensions, forced by a model error covariance and by the observations themselves. The high dimensionality of this system poses a difficult computational problem. Numerous methods have been proposed for approximate, discrete solution of this system of equations. Four-dimensional variational schemes solve these equations indirectly, while schemes based on Kalman filtering solve the equations more directly, usually on a small subspace of the full six-dimensional space. In both cases, most proposed solution methods are not derived from the continuum covariance evolution equations themselves. Instead, most methods simply inherit the discretization used for evolving the state estimate, either in the form of a discrete tangent linear model or, in the case of ensemble schemes, in the form of a fully nonlinear discrete model. In this lecture we show that solutions of the continuum covariance evolution equations possess simple properties that are not readily satisfied upon discretization of the equations. we give numerical examples illustrating that "inherited" discretizations sometimes fail to produce meaningfully accurate solutions. Finally, we suggest alternative discretization methods that may yield more faithful approximate solutions of the continuum problem.

Cohn, Stephen E.↗

The dynamics and control of large flexible space structures, part 11

A mathematical model is developed to predict the dynamics of the proposed Spacecraft Control Laboratory Experiment during the stationkeeping phase. The Shuttle and reflector are assumed to be rigid, while the mass connecting the Shuttle to the reflector is assumed to be flexible with elastic deformations small as compared with its length. It is seen that in the presence of gravity-gradient torques, the system assumes a new equilibrium position primarily due to the offset in the mass attachment point to the reflector from the reflector's mass center. Control is assumed to be provided through the Shuttle's three torquers and throught six actuators located by painrs at two points on the mass and at the reflector mass center. Numerical results confirm the robustness of an LQR derived control strategy during stationkeeping with maximum control efforts significantly below saturation levels. The linear regulator theory is also used to derive control laws for the linearized model of the rigidized SCOLE configuration where the mast flexibility is not included. It is seen that this same type of control strategy can be applied for the rapid single axis slewing of the SCOLE through amplitudes as large as 20 degrees. These results provide a definite trade-off between the slightly larger slewing times with the considerable reduction in over-all control effort as compared with the results of the two point boundary value problem application of Pontryagin's Maximum Principle.

Bainum, Peter M.↗

GPS Auto-Navigation Design for Unmanned Air Vehicles

A GPS auto-navigation system is designed for Unmanned Air Vehicles. The objective is to enable the air vehicle to be used as a test-bed for novel flow control concepts. The navigation system uses pre-programmed GPS waypoints. The actual GPS position, heading, and velocity are collected by the flight computer, a PC104 system running in Real-Time Linux, and compared with the desired waypoint. The navigator then determines the necessity of a heading correction and outputs the correction in the form of a commanded bank angle, for a level coordinated turn, to the controller system. This controller system consists of 5 controller! (pitch rate PID, yaw damper, bank angle PID, velocity hold, and altitude hold) designed for a closed loop non-linear aircraft model with linear aerodynamic coefficients. The ability and accuracy of using GPS data, is validated by a GPS flight. The autopilots are also validated in flight. The autopilot unit flight validations show that the designed autopilots function as designed. The aircraft model, generated on Matlab SIMULINK is also enhanced by the flight data to accurately represent the actual aircraft.

Nilsson, Caroline C. A.↗

Asymptotic modal analysis and statistical energy analysis

Asymptotic Modal Analysis (AMA) is a method which is used to model linear dynamical systems with many participating modes. The AMA method was originally developed to show the relationship between statistical energy analysis (SEA) and classical modal analysis (CMA). In the limit of a large number of modes of a vibrating system, the classical modal analysis result can be shown to be equivalent to the statistical energy analysis result. As the CMA result evolves into the SEA result, a number of systematic assumptions are made. Most of these assumptions are based upon the supposition that the number of modes approaches infinity. It is for this reason that the term 'asymptotic' is used. AMA is the asymptotic result of taking the limit of CMA as the number of modes approaches infinity. AMA refers to any of the intermediate results between CMA and SEA, as well as the SEA result which is derived from CMA. The main advantage of the AMA method is that individual modal characteristics are not required in the model or computations. By contrast, CMA requires that each modal parameter be evaluated at each frequency. In the latter, contributions from each mode are computed and the final answer is obtained by summing over all the modes in the particular band of interest. AMA evaluates modal parameters only at their center frequency and does not sum the individual contributions from each mode in order to obtain a final result. The method is similar to SEA in this respect. However, SEA is only capable of obtaining spatial averages or means, as it is a statistical method. Since AMA is systematically derived from CMA, it can obtain local spatial information as well.

Dowell, Earl H.↗

Improved Benchmarking of Cohesive Elements in Abaqus Standard for Predicting Disbond and Delamination in Composite Structures

Traditional approaches for aircraft certification require the assumption of an initial flaw condition, either represented as barely visible impact damage (BVID) or through inclusion of a Teflon insert to serve as surrogate damage. Based on the initial composite damage state, the structure must be shown to demonstrate structural durability and damage tolerance (DaDT) according to the following criteria: a. Damage displays no detrimental growth under cyclic loading b. The structure is able to sustain design limit load (DLL) Currently, the only available manner for validating structural performance is through test. Since damage can occur over a wide variety of areas within a structure, this approach has proven to be increasingly expensive and time consuming for composite airframes and acreage structure within the design-test-certification building block. A further complicating factor is the requirement to accurately capture the most critical damage morphologies as a starting condition. To understand the severity of the damage, it is either required to experimentally determine the most critical areas at tremendous expense or rely on legacy data of similar structural testing, which limits design space expansion. A preferred solution is to use advanced analysis to provide improved understanding of load margins for critical locations based on a wide variety of potential starting damage conditions. The standard industry approach for DaDT certification adheres to the use of the traditional virtual crack closure technique (VCCT) method. VCCT is generally a preferred method because it conforms to the current certification principles of damage from a known flaw, and when used correctly, can be effective at predicting delamination propagation under static and cyclic loading. The VCCT method requires the inclusion of an initial flaw in the finite element (FE) model requiring a-priori knowledge of the flaw location. This in turn requires a plethora of analysis cases to be examined to cover a reasonable span of potential damage states. Additionally, the VCCT approach requires node-to-node connectivity rendering it incompatible with the best practices and approaches for using continuum damage mechanics (CDM) based progressive damage and failure analysis (PDFA) tools within a typical FE solver. Alternatives to VCCT have emerged in the form of cohesive elements which utilize the cohesive zone model (CZM). Unlike VCCT which models linear elastic fracture mechanics, cohesive elements couples continuum and fracture based responses through the use of bilinear traction separation laws. These laws are defined based on a penalty stiffness, a cohesive strength, and a strain energy release rate. The approach can be mesh regularized with native cohesive elements within many FE solvers such as Abaqus and LS-DYNA. In Phase I of the NASA Advanced Composites Consortium (ACC) post-buckled stiffened panel with BVID, Strength and Life [1], the performance of cohesive elements were benchmarked in comparison to VCCT and LEFM solutions and showed good agreement using Abaqus explicit [2]. To realize savings on current and future programs, it is still necessary to close technical gaps related to the use of cohesive elements with Abaqus Standard. Within a program environment, standard finite element analysis is the preferred analytical capability for quasi-static loading as it eliminates uncertainty due to oscillatory behavior commonly seen with explicit analysis. This oscillatory behavior creates difficulties in writing margins of safety based on the analysis. The use of negative tangent stiffness material models complicates convergence which typically requires the use of numerical controls such as viscous damping to overcome. To date, there has not been a comprehensive study on how to establish best practices for cohesive element convergence for predictive capability within the Abaqus implicit solver. In pursuit of these goals, under the NASA ACC program, several numerical benchmark problems were proposed including pure mode I (double cantilevered beam – DCB), pure mode II (end notch flexure – ENF), and symmetric/unsymmetric evolving mixed mode (single leg bend – SLB). This paper focuses on the use of cohesive elements to model the delamination through the use of CZM. Specifically, finite element models for the DCB, ENF, symmetric SLB, and unsymmetric SLB, are developed and various solution controls for convergence are studied to develop a best practice. Once the best practice has been developed, the predictive capability of the objective CZM model is used to analyze the hat pull-off strength of a standard hat stiffened configuration under various loading conditions.

Abaqus↗

Multi-Omics Analysis of Mouse Retina Following Low Dose Radiation and/or Hindlimb Unloading

Rodent models have been used as analogs for studying the effects of spaceflight. NASA’s GeneLab provides access to omics datasets generated from spaceflight and ground-based experiments allowing for additional retrospective analysis. We used GeneLab’s GLDS-203, a dataset generated by researchers at Loma Linda University to study the impact of prolonged unloading and/or low-dose radiation on mouse retina. The purpose of this study was to understand the effect of gamma radiation and/or hindlimb unloading on mice retinas through a multi-omics analysis. In the experiment that generated the omics data, mice were irradiated with gamma-ray and/or subjected to hindlimb unloading for 21 days and multi-omics analysis was performed at 7 days, 1 month, or 4 months post exposure. In the current study, for each of the three timepoints, we compared epigenomic profiles for retinas from exposed mice against timepoint-matched controls. We identified a total of 5,271 differentially methylated loci (DML) and 321 differentially methylated regions (DMR; using a sliding window and step size of 500 bp) with methylation difference > 10% and q-value < 0.05 (sliding linear model corrected p-value) across the nine exposure groups. Highest correlation in methylation difference was seen for significant DMLs (q-value < 0.05) across different conditions at same post exposure timepoint (Figure 1).The location of DMLs and DMRs were characterized with respect to CpG islands and shores, putative promoters, gene body, and intergenic regions (Table 1). We analyzed RNA-seq counts and performed gene set enrichment analysis using differential expression results from comparing each exposure group to its timepoint-matched control group. Significant pathways (adjusted p-value <0.05) enriched in all three microgravity-only groups were related to morphogenesis of a branching epithelium, skeletal muscle cell differentiation, and response to fibroblast growth factor. Common processes across all timepoints in the radiation-only groups were retina homeostasis, synaptic vesicle exocytosis-endocytosis, and chemotaxis. In the combination groups, regulation of trans-synaptic signaling, and Rho protein signal transduction were enriched at all three timepoints. Processes related to purine nucleotide metabolism were enriched in all nine exposure groups, with activation at 1 month, and suppression at 7 days and 4 months. A total of 14 genes contained at least one DML and were differentially expressed at adjusted p-value < 0.05, including genes implicated in cataract development (Sipa1l3, Crybb3) and those involved in cytoskeletal organization (Plec, Flnb, Eef1a1). This analysis is part of a larger effort to understand the molecular mechanisms following spaceflight exposures that can help translate effects observed in animal models to human impacts.

Prachi Kothiyal↗

Linearized blade row compression component model. Stability and frequency response analysis of a J85-3 compressor

NASA developed stability and frequency response analysis techniques were applied to a dynamic blade row compression component stability model to provide a more economic approach to surge line and frequency response determination than that provided by time-dependent methods. This blade row model was linearized and the Jacobian matrix was formed. The clean-inlet-flow stability characteristics of the compressors of two J85-13 engines were predicted by applying the alternate Routh-Hurwitz stability criterion to the Jacobian matrix. The predicted surge line agreed with the clean-inlet-flow surge line predicted by the time-dependent method to a high degree except for one engine at 94% corrected speed. No satisfactory explanation of this discrepancy was found. The frequency response of the linearized system was determined by evaluating its Laplace transfer function. The results of the linearized-frequency-response analysis agree with the time-dependent results when the time-dependent inlet total-pressure and exit-flow function amplitude boundary conditions are less than 1 percent and 3 percent, respectively. The stability analysis technique was extended to a two-sector parallel compressor model with and without interstage crossflow and predictions were carried out for total-pressure distortion extents of 180 deg, 90 deg, 60 deg, and 30 deg.

Tesch, W. A.↗

Charged-particle mutagenesis II. Mutagenic effects of high energy charged particles in normal human fibroblasts

The biological effects of high LET charged particles are a subject of great concern with regard to the prediction of radiation risk in space. In this report, mutagenic effects of high LET charged particles are quantitatively measured using primary cultures of human skin fibroblasts, and the spectrum of induced mutations are analyzed. The LET of the charged particles ranged from 25 KeV/micrometer to 975 KeV/micrometer with particle energy (on the cells) between 94-603 MeV/u. The X-chromosome linked hypoxanthine guanine phosphoribosyl transferase (hprt) locus was used as the target gene. Exposure to these high LET charged particles resulted in exponential survival curves; whereas, mutation induction was fitted by a linear model. The Relative Biological Effect (RBE) for cell-killing ranged from 3.73 to 1.25, while that for mutant induction ranged from 5.74 to 0.48. Maximum RBE values were obtained at the LET of 150 keV/micrometer. The inactivation cross-section (alpha i) and the action cross-section for mutant induction (alpha m) ranged from 2.2 to 92.0 micrometer2 and 0.09 to 5.56 x 10(-3) micrometer2, respectively. The maximum values were obtained by 56Fe with an LET of 200 keV/micrometer. The mutagenicity (alpha m/alpha i) ranged from 2.05 to 7.99 x 10(-5) with the maximum value at 150 keV/micrometer. Furthermore, molecular analysis of mutants induced by charged particles indicates that higher LET beams are more likely to cause larger deletions in the hprt locus.

NASA Center JSC↗

Theory and Practical Design of Phase-locked Receivers, Volume I

This is Volume I of a two-volume work on the theory, of phase-locked receivers, with pertinent reference material on practical receiver design. Volume I is primarily devoted to the performance of carrier-tracking loops, including a rigorous treatment of narrow-band systems having IF limiters. The bulk of the work is based on a theoretical linear model, but a nonlinear method is also presented to predict behavior near the threshold. The emphasis throughout the work is toward completeness, simplicity, and internal consistency of the material assembled. Part I of this Volume is an exposition of the theory, the resulting equations, and the design philosophy that have enabled the phase-lock concept to evolve into the basic principle underlying the most sensitive receivers il, the world today. Part II is a condensed version of Part I, intended as a quick reference to formulas, definitions, and salient design considerations.

RECEIVER↗

Dynamics and Control of Flexible Space Vehicles

The purpose of this report is twofold: (1) to survey the established analytic procedures for the simulation of controlled flexible space vehicles, and (2) to develop in detail methods that employ a combination of discrete and distributed ("modal") coordinates, i.e., the hybrid-coordinate methods. Analytic procedures are described in three categories: (1) discrete-coordinate methods, (2) hybrid-coordinate methods, and (3) vehicle normal-coordinate methods. Each of these approaches is described and analyzed for its advantages and disadvantages, and each is found to have an area of applicability. The hybrid-coordinate method combines the efficiency of the vehicle normal-coordinate method with the versatility of the discrete-coordinate method, and appears to have the widest range of practical application. The results in this report have practical utility in two areas: (1) complex digital computer simulation of flexible space vehicles of arbitrary configuration subject to realistic control laws, and (2) preliminary control system design based on transfer functions for linearized models of dynamics and control laws.

Likins, P. W.↗

The behavior of magnitude dependent systematic errors

The objective grating technique is discussed. From the investigation of actual material, it is established that the effect of coma varies significantly from plate to plate, also that a model linear in diameter and/or coordinate may be inadequate for its removal, and even introduce systematic errors. From this standpoint, the requirements of reference star systems are discussed.

Eichhorn, H.↗

Dynamics of a spinning space station with a counterweight connected by multiple cables.

A unique and relatively simple approach is presented for obtaining the linearized equations of motion. A conservative system consisting of two rigid bodies connected by any number of massless cables with linear axial stiffness is assumed. The cable forces and torques are expanded in a Taylor series about the equilibrium values of the system coordinates which results in a cable stiffness matrix. The method of obtaining the equilibrium values of the coordinates is discussed and results are presented. The range of validity of the linear model is determined by comparing results with a digital simulation of the nonlinear system.

Nixon, D. D.↗

Digital controller for high pressure rocket engine.

Description of a general approach for the design of an adaptive digital control system for liquid bipropellant rocket engines. The technique employs linearized transfer functions derived from perturbations of an engine simulation. The linear models serve as a basis on which to develop candidate closed-loop control laws quickly and economically.

Thompson, Z.↗

The optimal control of merging aircraft - Implementation of the hybrid air traffic controller.

The control of merging aircraft is formulated as a finite-time, quadratic optimal control problem of a linear system with state and control constraints. The purpose of this paper is to demonstrate that the Hybrid Air Traffic Controller (HAC), which has been previously developed as a solution to this problem, may be easily implemented. Use is made of both the properties of the algebraic solution to the matrix Riccati equation and the structure of the linear model. This approach results in a real-time synthesis procedure for the HAC which does not rely on iterative numerical integration techniques.

Schatz, J. G.↗

The influence of a prediction display on the quasi-linear describing function and remnant measured with an adaptive analog-pilot in a closed loop

The effect of a prediction display on the human transfer characteristics is explained with the aid of a quasi-linear model. The prediction display causes an increase of the gain factor and the lead factor, a diminishing of the lag factor and a decrease of the remnant. Altogether, these factors yield a smaller mean square value of the control deviation and a simultaneous decrease of the mean square value of the stick signal.

Dey, D.↗

Estimation of automobile-driver describing function from highway tests using the double steering wheel

The automobile-driver describing function for lateral position control was estimated for three subjects from frequency response analysis of straight road test results. The measurement procedure employed an instrumented full size sedan with known steering response characteristics, and equipped with a lateral lane position measuring device based on video detection of white stripe lane markings. Forcing functions were inserted through a servo driven double steering wheel coupling the driver to the steering system proper. Random appearing, Gaussian, and transient time functions were used. The quasi-linear models fitted to the random appearing input frequency response characterized the driver as compensating for lateral position error in a proportional, derivative, and integral manner. Similar parameters were fitted to the Gabor transformed frequency response of the driver to transient functions. A fourth term corresponding to response to lateral acceleration was determined by matching the time response histories of the model to the experimental results. The time histories show evidence of pulse-like nonlinear behavior during extended response to step transients which appear as high frequency remnant power.

Delp, P.↗