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NASA NTRS1991

Model correlation and damage location for large space truss structures: Secant method development and evaluation

On-orbit testing of a large space structure will be required to complete the certification of any mathematical model for the structure dynamic response. The process of establishing a mathematical model that matches measured structure response is referred to as model correlation. Most model correlation approaches have an identification technique to determine structural characteristics from the measurements of the structure response. This problem is approached with one particular class of identification techniques - matrix adjustment methods - which use measured data to produce an optimal update of the structure property matrix, often the stiffness matrix. New methods were developed for identification to handle problems of the size and complexity expected for large space structures. Further development and refinement of these secant-method identification algorithms were undertaken. Also, evaluation of these techniques is an approach for model correlation and damage location was initiated.

Smith, Suzanne Weaver↗

NASA NTRS1992

An evidential reasoning extension to quantitative model-based failure diagnosis

The detection and diagnosis of failures in physical systems characterized by continuous-time operation are studied. A quantitative diagnostic methodology has been developed that utilizes the mathematical model of the physical system. On the basis of the latter, diagnostic models are derived each of which comprises a set of orthogonal parity equations. To improve the robustness of the algorithm, several models may be used in parallel, providing potentially incomplete and/or conflicting inferences. Dempster's rule of combination is used to integrate evidence from the different models. The basic probability measures are assigned utilizing quantitative information extracted from the mathematical model and from online computation performed therewith.

Gertler, Janos J.↗

NASA NTRS1994

An investigation of the use of temporal decomposition in space mission scheduling

This research involves an examination of techniques for solving scheduling problems in long-duration space missions. The mission timeline is broken up into several time segments, which are then scheduled incrementally. Three methods are presented for identifying the activities that are to be attempted within these segments. The first method is a mathematical model, which is presented primarily to illustrate the structure of the temporal decomposition problem. Since the mathematical model is bound to be computationally prohibitive for realistic problems, two heuristic assignment procedures are also presented. The first heuristic method is based on dispatching rules for activity selection, and the second heuristic assigns performances of a model evenly over timeline segments. These heuristics are tested using a sample Space Station mission and a Spacelab mission. The results are compared with those obtained by scheduling the missions without any problem decomposition. The applicability of this approach to large-scale mission scheduling problems is also discussed.

Bullington, Stanley E.↗

NASA NTRS1979

Numerical simulation of dynamics of brushless dc motors for aerospace and other applications. Volume 1: Model development and applications, part A

The development, fabrication and evaluation of a prototype electromechanical actuator (EMA) is discussed. Application of the EMA as a motor for control surfaces in aerospace flight is examined. A mathematical model of the EMA is developed for design optimization. Nonlinearities which complicate the mathematical model are discussed. The dynamics of the EMA from the underlying physical principles are determined and a discussion of similating the control logic by means of equivalent boolean expressions is presented.

Demerdash, N. A. O.↗

NASA NTRS2000

Modal Analysis and Correlation of International Space Station Early Configurations

This paper will summarize the modal analysis and model refinement results for the International Space Station (ISS) Flight-2A mated configuration. To maintain structural integrity of the ISS, structural loading distributions have been rigorously analyzed through numerical simulation and taken into account during the design of the structure and mission operations. The accuracy of the analysis results is directly affected by the precision of mathematical models and estimated input forces. A mathematical model of an ISS configuration is composed of individual component math models. Each component model is required to be correlated with ground test data.

Kaouk, Mohamed↗

NASA NTRS1987

Effects of Structural Errors on Parameter Estimates

Paper introduces concept of near equivalence in probability between different parameters or mathematical models of physical system. One in series of papers, each establishes different part of rigorous theory of mathematical modeling based on concepts of structural error, identifiability, and equivalence. This installment focuses upon effects of additive structural errors on degree of bias in estimates parameters.

Hadaegh, F. Y.↗

NASA NTRS1990

More About Multiple-Boundary-Condition Testing

Measured shapes of vibrational modes used to update mathematical models. Report extends discussion of multiple-boundary-condition vibrational testing techniques. Emphasis on further refinement of mathematical model by use of differences between measured eigenvectors and eigenvectors predicted by model to be refined.

Kuo, Chin-Po↗

NASA NTRS1989

Flutter suppression control law synthesis for the Active Flexible Wing model

The Active Flexible Wing Project is a collaborative effort between the NASA Langley Research Center and Rockwell International. The objectives are the validation of methodologies associated with mathematical modeling, flutter suppression control law development and digital implementation of the control system for application to flexible aircraft. A flutter suppression control law synthesis for this project is described. The state-space mathematical model used for the synthesis included ten flexible modes, four control surface modes and rational function approximation of the doublet-lattice unsteady aerodynamics. The design steps involved developing the full-order optimal control laws, reducing the order of the control law, and optimizing the reduced-order control law in both the continuous and the discrete domains to minimize stochastic response. System robustness was improved using singular value constraints. An 8th order robust control law was designed to increase the symmetric flutter dynamic pressure by 100 percent. Preliminary results are provided and experiences gained are discussed.

Mukhopadhyay, Vivek↗

NASA NTRS1989

Flutter suppression control law synthesis for the active flexible wing model

Mukhopadhyay, Vivek↗

NASA NTRS1973

Modeling a particular class of multiple-input/multiple-output black boxes with stochastic integral equations and identifying the required parameters

A method is given for obtaining a mathematical model of a class of black boxes having multiple inputs and multiple outputs in terms of Ito stochastic integral equations. This method is applicable to the class of black boxes having ergodic correlation functions when there is zero applied input. The point of view adopted in this paper is phenomenological in that it is desired that calculations made using the mathematical model should be close to what is actually observed at the output of the black box. How close is defined in the problem statement.

Eyman, E. D.↗

NASA NTRS1982

Wind tunnel tests of a free-wing/free-trimmer model

The riding qualities of an aircraft with low wing loading can be improved by freeing the wing to rotate about its spanwise axis. A trimming surface also free to rotate about its spanwise axis can be added at the wing tips to permit the use of high lift devices. Wind tunnel tests of the free wing/free trimmer model with the trimmer attached to the wing tips aft of the wing chord were conducted to validate a mathematical model developed to predict the dynamic characteristics of a free wing/free trimmer aircraft. A model consisting of a semispan wing with the trimmer mounted on with the wing on an air bearing and the trimmer on a ball bearing was displaced to various angles of attack and released. The damped oscillations of the wing and trimmer were recorded. Real and imaginary parts of the characteristic equations of motion were determined and compared to values predicted using the mathematical model.

Sandlin, D. R.↗

NASA NTRS1980

Experience in the control of a continuous flow cyrogenic tunnel

The concept of using liquid nitrogen to cool the test gas of a wind tunnel to cryogenic temperatures lead to the achievement of very high Reynolds number flows in relatively small transonic tunnels. The economical operation of liquid nitrogen cooled cryogenic tunnels is critically dependent on fast and accurate control of the tunnel variables. The control problem of a continuous flow fan driven cryogenic tunnel was addressed, first by developing a lumped multivariable mathematical model of a tunnel and validating the model by reconciling the responses of the Langley 0.3 m transonic cryogenic tunnel to the responses of the mathematical model on a simulator. Finally, the development of laws for the closed loop control of the tunnel pressure and temperature and the successful implementation of a control system for the 0.3 m transonic cryogenic tunnel based on these laws are presented.

Kilgore, R. A.↗

NASA NTRS2006

Advances in Measurement of Skin Friction in Airflow

The surface interferometric skin-friction (SISF) measurement system is an instrument for determining the distribution of surface shear stress (skin friction) on a wind-tunnel model. The SISF system utilizes the established oil-film interference method, along with advanced image-data-processing techniques and mathematical models that express the relationship between interferograms and skin friction, to determine the distribution of skin friction over an observed region of the surface of a model during a single wind-tunnel test. In the oil-film interference method, a wind-tunnel model is coated with a thin film of oil of known viscosity and is illuminated with quasi-monochromatic, collimated light, typically from a mercury lamp. The light reflected from the outer surface of the oil film interferes with the light reflected from the oil-covered surface of the model. In the present version of the oil-film interference method, a camera captures an image of the illuminated model and the image in the camera is modulated by the interference pattern. The interference pattern depends on the oil-thickness distribution on the observed surface, and this distribution can be extracted through analysis of the image acquired by the camera. The oil-film technique is augmented by a tracer technique for observing the streamline pattern. To make the streamlines visible, small dots of fluorescentchalk/oil mixture are placed on the model just before a test. During the test, the chalk particles are embedded in the oil flow and produce chalk streaks that mark the streamlines. The instantaneous rate of thinning of the oil film at a given position on the surface of the model can be expressed as a function of the instantaneous thickness, the skin-friction distribution on the surface, and the streamline pattern on the surface; the functional relationship is expressed by a mathematical model that is nonlinear in the oil-film thickness and is known simply as the thin-oil-film equation. From the image data acquired as described, the time-dependent oil-thickness distribution and streamline pattern are extracted and by inversion of the thin-oil-film equation it is then possible to determine the skin-friction distribution. In addition to a quasi-monochromatic light source, the SISF system includes a beam splitter and two video cameras equipped with filters for observing the same area on a model in different wavelength ranges, plus a frame grabber and a computer for digitizing the video images and processing the image data. One video camera acquires the interference pattern in a narrow wavelength range of the quasi-monochromatic source. The other video camera acquires the streamline image of fluorescence from the chalk in a nearby but wider wavelength range. The interference- pattern and fluorescence images are digitized, and the resulting data are processed by an algorithm that inverts the thin-oil-film equation to find the skin-friction distribution.

Brown, James L.↗

NASA NTRS1996

Modelling System Processes to Support Uncertainty Analysis and Robustness Evaluation

In the use of advanced systems control techniques in the development of a dynamic system, results from effective mathematical modelling is required. Historically, in some cases the use of a model which only reflects the "expected" or "nominal" important -information about the system's internal processes has resulted in acceptable system performance, but it should be recognized that for those cases success was due to a combination of the remarkable inherent potential of feedback control for robustness and fortuitously wide margins between system performance requirements and system performance capability. In the cases of a CELSS development, no such fortuitous combinations should be expected, and it should be expected that the uncertainty in the information on the system's processes will have to be taken into account in order to generate a performance robust design. In this paper, we develop one perspective of the issue of providing robustness as mathematical modelling impacts it, and present some examples of model formats which serve the needed purpose.

Blackwell, Charles↗

NASA NTRS1987

Validation of a real-time engineering simulation of the UH-60A helicopter

A real-time simulation of the UH-60A Black Hawk Helicopter based on the Sikorsky Gen Hel mathematical model is compared with flight test data and Sikorsky's nonreal-time computer program. An overview of the mathematical model is given, including a description of updates and expansion of the model by NASA. Also, real-time programming requirements and techniques are explained. The simulation displays very good agreement with flight test data and excellent with the nonreal-time program on which it is based. The large dedication of effort required to develop the real-time program suggests a need for development of generalized techniques for real-time simulation of high-fidelity physical models of rotorcraft.

Ballin, Mark G.↗

NASA NTRS1988

Formulation of a General Technique for Predicting Pneumatic Attenuation Errors in Airborne Pressure Sensing Devices

Presented is a mathematical model derived from the Navier-Stokes equations of momentum and continuity, which may be accurately used to predict the behavior of conventionally mounted pneumatic sensing systems subject to arbitrary pressure inputs. Numerical techniques for solving the general model are developed. Both step and frequency response lab tests were performed. These data are compared with solutions of the mathematical model and show excellent agreement. The procedures used to obtain the lab data are described. In-flight step and frequency response data were obtained. Comparisons with numerical solutions of the math model show good agreement. Procedures used to obtain the flight data are described. Difficulties encountered with obtaining the flight data are discussed.

Whitmore, Stephen A.↗

NASA NTRS1992

System/observer/controller identification toolbox

System Identification is the process of constructing a mathematical model from input and output data for a system under testing, and characterizing the system uncertainties and measurement noises. The mathematical model structure can take various forms depending upon the intended use. The SYSTEM/OBSERVER/CONTROLLER IDENTIFICATION TOOLBOX (SOCIT) is a collection of functions, written in MATLAB language and expressed in M-files, that implements a variety of modern system identification techniques. For an open loop system, the central features of the SOCIT are functions for identification of a system model and its corresponding forward and backward observers directly from input and output data. The system and observers are represented by a discrete model. The identified model and observers may be used for controller design of linear systems as well as identification of modal parameters such as dampings, frequencies, and mode shapes. For a closed-loop system, an observer and its corresponding controller gain directly from input and output data.

Juang, Jer-Nan↗

NASA NTRS1994

Interactive visualization of Earth and Space Science computations

Computers have become essential tools for scientists simulating and observing nature. Simulations are formulated as mathematical models but are implemented as computer algorithms to simulate complex events. Observations are also analyzed and understood in terms of mathematical models, but the number of these observations usually dictates that we automate analyses with computer algorithms. In spite of their essential role, computers are also barriers to scientific understanding. Unlike hand calculations, automated computations are invisible and, because of the enormous numbers of individual operations in automated computations, the relation between an algorithm's input and output is often not intuitive. This problem is illustrated by the behavior of meteorologists responsible for forecasting weather. Even in this age of computers, many meteorologists manually plot weather observations on maps, then draw isolines of temperature, pressure, and other fields by hand (special pads of maps are printed for just this purpose). Similarly, radiologists use computers to collect medical data but are notoriously reluctant to apply image-processing algorithms to that data. To these scientists with life-and-death responsibilities, computer algorithms are black boxes that increase rather than reduce risk. The barrier between scientists and their computations can be bridged by techniques that make the internal workings of algorithms visible and that allow scientists to experiment with their computations. Here we describe two interactive systems developed at the University of Wisconsin-Madison Space Science and Engineering Center (SSEC) that provide these capabilities to Earth and space scientists.

Hibbard, William L.↗