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Methodologies for Verification and Validation of Space Launch System (SLS) Structural Dynamic Models: Appendices

Verification and validation (V&V) is a highly challenging undertaking for SLS structural dynamics models due to the magnitude and complexity of SLS subassemblies and subassemblies. Responses to challenges associated with V&V of Space Launch System (SLS) structural dynamics models are presented in Volume I of this paper. Four methodologies addressing specific requirements for V&V are discussed. (1) Residual Mode Augmentation (RMA). (2) Modified Guyan Reduction (MGR) and Harmonic Reduction (HR, introduced in 1976). (3) Mode Consolidation (MC). Finally, (4) Experimental Mode Verification (EMV). This document contains the appendices to Volume I.

Coppolino, Robert N.

A simplified dynamic model of Space Shuttle Main Engine

A simplified dynamic model is presented of the Space Shuttle Main Engine (SSME) dynamics valid within the range of operation of the engine. This model is obtained by linking the linearized point models obtained at 25 different operating points of SSME. The simplified model was developed for use with a model-based diagnostic scheme for failure detection and diagnostics studies, as well as control design purposes.

Duyar, Ahmet

Multi-Dimensional Calibration of Impact Dynamic Models

NASA Langley, under the Subsonic Rotary Wing Program, recently completed two helicopter tests in support of an in-house effort to study crashworthiness. As part of this effort, work is on-going to investigate model calibration approaches and calibration metrics for impact dynamics models. Model calibration of impact dynamics problems has traditionally assessed model adequacy by comparing time histories from analytical predictions to test at only a few critical locations. Although this approach provides for a direct measure of the model predictive capability, overall system behavior is only qualitatively assessed using full vehicle animations. In order to understand the spatial and temporal relationships of impact loads as they migrate throughout the structure, a more quantitative approach is needed. In this work impact shapes derived from simulated time history data are used to recommend sensor placement and to assess model adequacy using time based metrics and orthogonality multi-dimensional metrics. An approach for model calibration is presented that includes metric definitions, uncertainty bounds, parameter sensitivity, and numerical optimization to estimate parameters to reconcile test with analysis. The process is illustrated using simulated experiment data.

Horta, Lucas G.

Nonlinear Dynamic Models in Advanced Life Support

To facilitate analysis, ALS systems are often assumed to be linear and time invariant, but they usually have important nonlinear and dynamic aspects. Nonlinear dynamic behavior can be caused by time varying inputs, changes in system parameters, nonlinear system functions, closed loop feedback delays, and limits on buffer storage or processing rates. Dynamic models are usually cataloged according to the number of state variables. The simplest dynamic models are linear, using only integration, multiplication, addition, and subtraction of the state variables. A general linear model with only two state variables can produce all the possible dynamic behavior of linear systems with many state variables, including stability, oscillation, or exponential growth and decay. Linear systems can be described using mathematical analysis. Nonlinear dynamics can be fully explored only by computer simulations of models. Unexpected behavior is produced by simple models having only two or three state variables with simple mathematical relations between them. Closed loop feedback delays are a major source of system instability. Exceeding limits on buffer storage or processing rates forces systems to change operating mode. Different equilibrium points may be reached from different initial conditions. Instead of one stable equilibrium point, the system may have several equilibrium points, oscillate at different frequencies, or even behave chaotically, depending on the system inputs and initial conditions. The frequency spectrum of an output oscillation may contain harmonics and the sums and differences of input frequencies, but it may also contain a stable limit cycle oscillation not related to input frequencies. We must investigate the nonlinear dynamic aspects of advanced life support systems to understand and counter undesirable behavior.

Jones, Harry

Approximate dynamic model of a turbojet engine

An approximate dynamic nonlinear model of a turbojet engine is elaborated on as a tool in studying the aircraft control loop, with the turbojet engine treated as an actuating component. Approximate relationships linking the basic engine parameters and shaft speed are derived to simplify the problem, and to aid in constructing an approximate nonlinear dynamic model of turbojet engine performance useful for predicting aircraft motion.

Artemov, O. A.

Dynamic models for simulation of the 70-M antenna axis servos

Dynamic models for the various functional elements of the 70 m antenna axis servos are described. The model representing the digital position controller, the linear and nonlinear properties of the physical hardware, and the dynamics of the flexible antenna structure are encoded in six major function blocks. The general modular structure of the function blocks facilitates their adaptation to a variety of dynamic simulation studies. Model parameter values were calculated from component specifications and design data. A simulation using the models to predict limit cycle behavior produced results in excellent agreement with field test data from the DSS 14 70-m antenna.

Hill, R. E.

Progress Toward a Format Standard for Flight Dynamics Models

In the beginning, there was FORTRAN, and it was... not so good. But it was universal, and all flight simulator equations of motion were coded with it. Then came ACSL, C, Ada, C++, C#, Java, FORTRAN-90, Matlab/Simulink, and a number of other programming languages. Since the halcyon punch card days of 1968, models of aircraft flight dynamics have proliferated in training devices, desktop engineering and development computers, and control design textbooks. With the rise of industry teaming and increased reliance on simulation for procurement decisions, aircraft and missile simulation models are created, updated, and exchanged with increasing frequency. However, there is no real lingua franca to facilitate the exchange of models from one simulation user to another. The current state-of-the-art is such that several staff-months if not staff-years are required to 'rehost' each release of a flight dynamics model from one simulation environment to another one. If a standard data package or exchange format were to be universally adopted, the cost and time of sharing and updating aerodynamics, control laws, mass and inertia, and other flight dynamic components of the equations of motion of an aircraft or spacecraft simulation could be drastically reduced. A 2002 paper estimated over $ 6 million in savings could be realized for one military aircraft type alone. This paper describes the efforts of the American Institute of Aeronautics and Astronautics (AIAA) to develop a standard flight dynamic model exchange standard based on XML and HDF-5 data formats.

Jackson, E. Bruce

Development of an Integrated Nonlinear Aeroservoelastic Flight Dynamic Model of the NASA Generic Transport Model

This paper describes a recent development of an integrated fully coupled aeroservoelastic flight dynamic model of the NASA Generic Transport Model (GTM). The integrated model couples nonlinear flight dynamics to a nonlinear aeroelastic model of the GTM. The nonlinearity includes the coupling of the rigid-body aircraft states in the partial derivatives of the aeroelastic angle of attack. Aeroservoelastic modeling of the control surfaces which are modeled by the Variable Camber Continuous Trailing Edge Flap is also conducted. The R.T. Jones' method is implemented to approximate unsteady aerodynamics. Simulations of the GTM are conducted with simulated continuous and discrete gust loads..

Aeroservoelasticit

A statistical rain attenuation prediction model with application to the advanced communication technology satellite project. Part 2: Theoretical development of a dynamic model and application to rain fade durations and tolerable control delays for fade countermeasures

A dynamic rain attenuation prediction model is developed for use in obtaining the temporal characteristics, on time scales of minutes or hours, of satellite communication link availability. Analagous to the associated static rain attenuation model, which yields yearly attenuation predictions, this dynamic model is applicable at any location in the world that is characterized by the static rain attenuation statistics peculiar to the geometry of the satellite link and the rain statistics of the location. Such statistics are calculated by employing the formalism of Part I of this report. In fact, the dynamic model presented here is an extension of the static model and reduces to the static model in the appropriate limit. By assuming that rain attenuation is dynamically described by a first-order stochastic differential equation in time and that this random attenuation process is a Markov process, an expression for the associated transition probability is obtained by solving the related forward Kolmogorov equation. This transition probability is then used to obtain such temporal rain attenuation statistics as attenuation durations and allowable attenuation margins versus control system delay.

Manning, Robert M.

Dynamic Aeroelastic Flight Dynamic Modeling of Mach 0.745 Transonic Truss-Braced Wing

This paper presents a modeling approach for dynamic aeroelastic flight dynamic analysis of the Mach0.745 Transonic Truss-Braced Wing. The modeling approach is based on a transonic correction method to correct the Theodorsen’s theory for transonic flow. CFD unsteady Reynolds-averaged Navier-Stokes equations (RANS) simulations are conducted using FUN3D solver for a series of wing sections from the Mach 0.745Transonic Truss-Braced Wing in pitch and plunge oscillations. Unsteady lift and pitching moment coefficients are obtained and used to develop the correction terms in the Theodorsen’s theory to account for transonic aerodynamics. The unsteady lift and pitching moment derivatives with respect to the unsteady angle of attack are obtained as functions of the reduced frequency. These derivatives are used to compute the unsteady lift and pitching moment contributions by the angle of attack, pitch rate, and roll rate. They are then approximated using a frequency-domain regression to obtain the dynamic stability derivatives for the Mach 0.745 Transonic Truss-Braced Wing. The structural dynamic mode shapes of the Mach 0.745 TTBW are extracted from a NAS-TRAN finite-element model. These mode shapes are used to compute the generalized unsteady aerodynamic forces. The aerodynamic mass, damping, and stiffness and the aerodynamic lag states are constructed to couple the dynamic aeroelastic contribution to the flight dynamic model of the Mach 0.745 Transonic Truss-Braced Wing. The coupled dynamic aeroelastic flight dynamic equations of motion are formulated. The eigenvalues of the coupled system are computed. All the flight dynamic modes and structural dynamic modes are stable at Match 0.745. The effect of transonic aerodynamics generally causes all the dynamic modes to have lower damping values

Flight Dynamics

Comprehensive Static and Dynamic Modeling of a Magnetic Suspension and Balance System

Magnetic Suspension and Balance Systems (MSBS) are inherently complex multi-degree-of-freedom dynamic systems. Comprehensive, high-fidelity dynamic models are increasingly important due to the application of model-based controllers as well as demands for unsteady aerodynamic data derived from post-test system identification. This paper reviews some aspects of the development of a dynamic model of the NASA/ODU 6-inch MSBS.

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Comprehensive Static and Dynamic Modeling of a Magnetic Suspension and Balance System

Magnetic Suspension and Balance Systems (MSBS) are inherently complex multi-degree-of-freedom dynamic systems. Comprehensive, high-fidelity dynamic models are increasingly important due to the application of model-based controllers as well as demands for unsteady aerodynamic data derived from post-test system identification. This paper reviews some aspects of the development of a dynamic model of the NASA/ODU 6-inch MSBS.

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