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NASA NTRS1993

Model reduction in integrated controls-structures design

It is the objective of this paper to present a model reduction technique developed for the integrated controls-structures design of flexible structures. Integrated controls-structures design problems are typically posed as nonlinear mathematical programming problems, where the design variables consist of both structural and control parameters. In the solution process, both structural and control design variables are constantly changing; therefore, the dynamic characteristics of the structure are also changing. This presents a problem in obtaining a reduced-order model for active control design and analysis which will be valid for all design points within the design space. In other words, the frequency and number of the significant modes of the structure (modes that should be included) may vary considerably throughout the design process. This is also true as the locations and/or masses of the sensors and actuators change. Moreover, since the number of design evaluations in the integrated design process could easily run into thousands, any feasible order-reduction method should not require model reduction analysis at every design iteration. In this paper a novel and efficient technique for model reduction in the integrated controls-structures design process, which addresses these issues, is presented.

Maghami, Peiman G.↗

NASA NTRS1992

Model reduction for Space Station Freedom

Model reduction is an important practical problem in the control of flexible spacecraft, and a considerable amount of work has been carried out on this topic. Two of the best known methods developed are modal truncation and internal balancing. Modal truncation is simple to implement but can give poor results when the structure possesses clustered natural frequencies, as often occurs in practice. Balancing avoids this problem but has the disadvantages of high computational cost, possible numerical sensitivity problems, and no physical interpretation for the resulting balanced 'modes'. The purpose of this work is to examine the performance of the subsystem balancing technique developed by the investigator when tested on a realistic flexible space structure, in this case a model of the Permanently Manned Configuration (PMC) of Space Station Freedom. This method retains the desirable properties of standard balancing while overcoming the three difficulties listed above. It achieves this by first decomposing the structural model into subsystems of highly correlated modes. Each subsystem is approximately uncorrelated from all others, so balancing them separately and then combining yields comparable results to balancing the entire structure directly. The operation count reduction obtained by the new technique is considerable: a factor of roughly r(exp 2) if the system decomposes into r equal subsystems. Numerical accuracy is also improved significantly, as the matrices being operated on are of reduced dimension, and the modes of the reduced-order model now have a clear physical interpretation; they are, to first order, linear combinations of repeated-frequency modes.

Williams, Trevor↗

NASA NTRS1981

Problems in the application of multivariable adaptive control to flexible spacecraft

The present investigation is concerned with the application of adaptive control to distributed parameter systems (DPS) which arise in the modeling of large space structures (LSS). Distributed parameter and multivariable models for LSS are introduced and the decoupled adaptive control of such models is considered. Possibilities to achieve adaptive control in connection with a more general model are also examined. It is found that, in concept, adaptive control appears to be a natural choice for solving attitude and shape perturbation problems in LSS. However, due to the distributed parameter nature of such structures and the current lack of experience in their control, the problem must be phrased in general terms which are very difficult to deal with. In particular, detailed a priori plant knowledge is currently required so that decoupling and/or reduced order models of sufficient accuracy can be provided.

Lawrence, D. A.↗

NASA NTRS1987

Adaptive wall testing sections (AWTS)

The lecture starts with conventional techniques of minimizing wall interference and explains the principle of wall streamlining. The history of AWTS development is highlighted, along with the benefits of wall streamlining, including minimized boundary interference, increased model size, reduced tunnel drive power, noise, and volume, as well as multiple flow field simulations to be performed using one test section. AWTS-associated problems coming from the need to adjust the test-section boundaries for each test condition are assessed, along with the requirements of a boundary-adjustment strategy. Examples of two- and three-dimensional test sections are presented, and attention is focused on residual interference and the effects of compressibility and model lift on flexible-wall contours.

Wolf, Stephen W. D.↗

NASA NTRS2001

The 3D Recognition, Generation, Fusion, Update and Refinement (RG4) Concept

This paper describes an active (real time) recognition strategy whereby information is inferred iteratively across several viewpoints in descent imagery. We will show how we use inverse theory within the context of parametric model generation, namely height and spectral reflection functions, to generate model assertions. Using this strategy in an active context implies that, from every viewpoint, the proposed system must refine its hypotheses taking into account the image and the effect of uncertainties as well. The proposed system employs probabilistic solutions to the problem of iteratively merging information (images) from several viewpoints. This involves feeding the posterior distribution from all previous images as a prior for the next view. Novel approaches will be developed to accelerate the inversion search using novel statistic implementations and reducing the model complexity using foveated vision. Foveated vision refers to imagery where the resolution varies across the image. In this paper, we allow the model to be foveated where the highest resolution region is called the foveation region. Typically, the images will have dynamic control of the location of the foveation region. For descent imagery in the Entry, Descent, and Landing (EDL) process, it is possible to have more than one foveation region. This research initiative is directed towards descent imagery in connection with NASA's EDL applications. Three-Dimensional Model Recognition, Generation, Fusion, Update, and Refinement (RGFUR or RG4) for height and the spectral reflection characteristics are in focus for various reasons, one of which is the prospect that their interpretation will provide for real time active vision for automated EDL.

Maluf, David A.↗

NASA NTRS1994

Effect of lightning on the concentration of odd nitrogen species in the lower stratosphere: An update

Revised model estimates of the effect of lightning on the lower stratospheric NOy are presented. Several changes in the Atmospheric and Environmental Research Incorporated model were made since the last evaluation of the impact of lightning. Improvements were made in the model circulation and location of tropopause in the tropics, which is now calculated from the National Meteorological Center temperature data. Changes in model circulation reduced the mass flux from the troposphere to the tropical stratosphere. The calculated mass fluxes are found to agree better with some recent estimates. The circulation changes also reduced the advective mass flux from the tropical lower stratosphere to the midlatitudes. The change in circulation and the change in the tropopause height lead to increases in the calculated concentration of N2O, O3 and NOy in the tropical lower stratosphere. The effect of lightning is to increase the calculated concentration of NOy around 64 mbar by a factor of 2, compared to a factor of 10 enhancement in the previous calculations. Comparison with the Stratosphere Troposphere Exchange Project 1987 data indicates that the inclusion of a lightning source brings the model results in closer agreement with the observations.

Kotamarthi, V. R.↗

NASA NTRS1980

Application of digital terrain data to quantify and reduce the topographic effect on LANDSAT data

Integration of LANDSAT multispectral scanner (MSS) data with 30 m U.S. Geological Survey (USGS) digital terrain data was undertaken to quantify and reduce the topographic effect on imagery of a forested mountain ridge test site in central Pennsylvania. High Sun angle imagery revealed variation of as much as 21 pixel values in data for slopes of different angles and aspects with uniform surface cover. Large topographic effects were apparent in MSS 4 and 5 was due to a combination of high absorption by the forest cover and the MSS quantization. Four methods for reducing the topographic effect were compared. Band ratioing of MSS 6/5 and MSS 7/5 did not eliminate the topographic effect because of the lack of variation in MSS 4 and 5 radiances. The three radiance models examined to reduce the topographic effect required integration of the digital terrain data. Two Lambertian models increased the variation in the LANDSAT radiances. The nonLambertian model considerably reduced (86 per cent) the topographic effect in the LANDSAT data. The study demonstrates that high quality digital terrain data, as provided by the USGS digital elevation model data, can be used to enhance the utility of multispectral satellite data.

Justice, C. O.↗

NASA NTRS2017

Vertical Profiles of Mars 1.27 Micrometer O2 Dayglow from MRO CRISM Limb Spectra: Seasonal/global Behaviors, Comparisons to LMDGCM Simulations, and a Global Definition for Mars Water Vapor Profiles

Since July of 2009, The Compact Reconnaissance Imaging Spectral Mapper (CRISM) onboard the Mars Re- connaissance Orbiter (MRO) has periodically obtained pole-to-pole observations (i.e., full MRO orbits) of limb scanned visible/near IR spectra (lambda= 0.4 - 4.0 micrometers, delta lambda approx. 10 nm- Murchie et al., 2007). These CRISM limb observations support the first seasonally and spatially extensive set of Mars 1.27 micometers O2 (1 delta(sub g)) day-glow profile retrievals (approx. 1100) over greater than or equal to 8-80 km altitudes. Their comparison to Laboratoire de Meteorologie Dynamique (LMD) global climate model (GCM) simulated O2 (1 delta(sub g)) volume emission rate (VER) profiles, as a function of altitude, latitude, and season (solar longitude, L(sub s), supports several key conclusions regarding Mars atmospheric water vapor (which is derived from O2 (1 delta(sub g)) emission rates), Mars O3, and the collisional de-excitation of O2 (1 delta(sub g)) in the Mars CO2 atmosphere. Current (Navarro et al., 2014) LMDGCM simulations of Mars atmospheric water vapor fall 2-3 times below CRISM derived water vapor abundances at 20-40 km altitudes over low-to-mid latitudes in northern spring (L(sub s) = 30-60 deg), and northern mid-to-high latitudes over northern summer (L(sub s) = 60-140 deg). In contrast, LMDGCM simulated water vapor is 2-5 times greater than CRISM derived values at all latitudes and seasons above 40 km, within the aphelion cloud belt (ACB), and over high-southern to mid-southern latitudes in southern summer (L(sub s) = 190-340 deg) at 15-35 km altitudes. Overall, the solstitial summer-to-winter hemisphere gradients in water vapor are reversed between the LMDGCM modeled versus the CRISM derived water vapor abundances above 10-30 km altitudes. LMDGCM-CRISM differences in water vapor profiles correlate with LMDGCM-CRISM differences in cloud mixing profiles; and likely reflect limitations in simulating cloud microphysics and radiative forcing, both of which restrict meridional transport of water from summer- to-winter hemispheres on Mars (Clancy et al., 1996; Montmessin et al., 2004; Steele et al., 2014; Navarro et al., 2014) and depend on uncertain cloud microphysical properties (Navarro et al., 2014). The derived low-to-mid latitude changes in Mars water vapor vertical distributions should reduce current model- data disagreements in column O3 and H2O2 abundances over low-to-mid latitudes (e.g., within the ACB; Lefevre et al., 2008; Encrenaz et al., 2015; Clancy et al., 2016). Lastly, the global/seasonal average com- parison of CRISM and LMDGCM O2 (1 delta(sub g)) VER below 20 km altitudes indicates a factor of approx. 3 times lower value (0.25 x 10(exp -20) cu cm sec(exp -1)) for the CO2 collisional de-excitation rate coefficient of O2 (1 delta(sub g)) than derived recently by Guslyakova et al. (2016).

Clancy, R. Todd↗

NASA NTRS1995

The ocean response to operational westerly wind bursts during the 1991 - 1992 El Nino

Numerical simulations of the remotely forced ocean response to westerly wind bursts prior to and during the 1991 - 1992 El Nino are examined; the models are forced by wind stress from the U.S. Navy's atmospheric global operational analysis/forecast system. The study focuses on (1) the relative response of the first and second internal modes to a single episode of westerly bursts; (2) the role of westerly bursts in producing the eastern Pacific sea level variations from October 1990 to February 1992; and (3) the relative importance of the remotely forced sea level responses generated by central and western Pacific wind anomalies. The simulation use the Naval Research Laboratory global multilayer formulation; the suite of experiments includes hydrodynamic simulations that use both one- and three- active-layer reduced gravity models as well as an experiment that also includes thermodynamic effects. The models are executed from January 1, 1990, to March 1, 1992, a period that includes 10 significant westerly wind bursts or burst clusters and the 1991 - 1992 El Nino event. The numerical experiments reveal an ability to accurately simulate the eastern Pacific sea level variations during this period. In response to a single burst, the three-layer hydrodynamic simulation reveals that the second internal mode Kelvin wave yields a sea level change at the eastern boundary that is approximately one third that of the first mode and a surface velocity signature that is equivalent to the first mode. During the onset of the El Nino event the inclusion of higher modes also produces a more realistic representation of the observed eastern boundary sea level signal. Furthermore, by comparing the model response to particular wind bursts with the observed sea level at Baltra, Galapagos, a value of 2.5 - 2.6 m/s is suggested as the most appropriate mean speed for the first internal mode Kelvin wave during the onset phase. A scenario for the onset of the 1991 - 1992 El Nino is given.

Kindle, John C.↗

NASA NTRS2014

4D-Var Developement at GMAO

The Global Modeling and Assimilation Offce (GMAO) is currently using an IAU-based 3D-Var data assimilation system. GMAO has been experimenting with a 3D-Var-hybrid version of its data assimilation system (DAS) for over a year now, which will soon become operational and it will rapidly progress toward a 4D-EnVar. Concurrently, the machinery to exercise traditional 4DVar is in place and it is desirable to have a comparison of the traditional 4D approach with the other available options, and evaluate their performance in the Goddard Earth Observing System (GEOS) DAS. This work will also explore the possibility for constructing a reduced order model (ROM) to make traditional 4D-Var computationally attractive for increasing model resolutions. Part of the research on ROM will be to search for a suitably acceptable space to carry on the corresponding reduction. This poster illustrates how the IAU-based 4D-Var assimilation compares with our currently used IAU-based 3D-Var.

GMAO↗

NASA NTRS1991

Controls for space structures

Assembly and operation of large space structures (LSS) in orbit will require robot-assisted docking and berthing of partially-assembled structures. These operations require new solutions to the problems of controls. This is true because of large transient and persistent disturbances, controller-structure interaction with unmodeled modes, poorly known structure parameters, slow actuator/sensor dynamical behavior, and excitation of nonlinear structure vibrations during control and assembly. For on-orbit assembly, controllers must start with finite element models of LSS and adapt on line to the best operating points, without compromising stability. This is not easy to do, since there are often unmodeled dynamic interactions between the controller and the structure. The indirect adaptive controllers are based on parameter estimation. Due to the large number of modes in LSS, this approach leads to very high-order control schemes with consequent poor stability and performance. In contrast, direct model reference adaptive controllers operate to force the LSS to track the desirable behavior of a chosen model. These schemes produce simple control algorithms which are easy to implement on line. One problem with their use for LSS has been that the model must be the same dimension as the LSS - i.e., quite large. A control theory based on the command generator tracker (CGT) ideas of Sobel, Mabins, Kaufman and Wen, Balas to obtain very low-order models based on adaptive algorithms was developed. Closed-loop stability for both finite element models and distributed parameter models of LSS was proved. In addition, successful numerical simulations on several LSS databases were obtained. An adaptive controller based on our theory was also implemented on a flexible robotic manipulator at Martin Marietta Astronautics. Computation schemes for controller-structure interaction with unmodeled modes, the residual mode filters or RMF, were developed. The RMF theory was modified to compensate slow actuator/sensor dynamics. These new ideas are being applied to LSS simulations to demonstrate the ease with which one can incorporate slow actuator/sensor effects into our design. It was also shown that residual mode filter compensation can be modified for small nonlinearities to produce exponentially stable closed-loop control. A theory for disturbance accommodating controllers based on reduced order models of structures was developed, and stability results for these controllers in closed-loop with large-scale finite element models of structures were obtained.

Balas, Mark↗

NASA NTRSDate not supplied

Development and Validation of a Slosh-Based Ullage Collapse Model

Ullage collapse modeling is an essential tool for the success of spacecraft powered by cryogenic propellants. The degree of ullage collapse can have a major impact on the design of cryogenic propellant tanks as well as the mission’s concept of operations. Additional commodities (e.g., helium gas for pressure control) and their quantities are dependent on the amount of heat transfer and phase change of propellants expected during flight. Currently, high-fidelity computational fluid dynamics (CFD) with heat transfer and phase change is the most accurate method for predicting ullage collapse. CFD simulations of this kind, however, can become very costly for problems requiring large domains, long simulation times, or significant liquid motion. Consequently, there is a need for a reduced order model to provide fast responses which can be used in engineering design decisions. The proposed numerical model is a nodal approach, augmented by outputs from CFD analyses that are generated rapidly and reliably. These outputs include transient values for liquid-vapor interface area, interface velocity, and liquid position using a volume of fluid (VoF) method. There are several benefits of combining a nodal approach with slosh predictions from CFD simulations: leveraging of the Loci/STREAM-VoF solver that has been validated in high-g and low-g environments, rapid modeling of VoF with isothermal propellant simplifications and relatively coarse meshes, and improved model predictions from the nodal tool. The nodal approach, informed by the slosh predictions from CFD, assumes uniform conditions in the liquid and gas domains. Modifications to account for temperature stratification in the liquid and gas may be implemented as a future improvement. Thermodynamic changes within the tank are solved at user-defined timesteps. First, impacts due to mass entering or leaving the control volume are captured. Second, heat transfer impacts are accounted for by tracking the volume of the gas which has been contacted by liquid in that timestep and rebalancing the internal energy. Finally, phase change is approximated using the area and velocity of the interface. The tank conditions are re-computed by conserving mass and energy. Calibration of the model to several test flights and experiments are required to baseline the predictive power and uncertainty. The final product will enable designers and engineers to create quick-turnaround predictions for ullage collapse and inform design feasibility.

Computational Fluid Dynamics↗

NASA NTRS2026

Developing a Pyrolysis Gas Thermal Blocking Model for Reentry Demise

In NASA’s Object Reentry Survival Analysis Tool (ORSAT), aerodynamic drag and aerothermal heating coefficients are computed for each of the free-molecular, continuum, and transitional flow regimes using analytical and semi-analytical methods. These heating coefficients were derived for typical metallic materials that melt and do not have a strong gas-phase contribution to the flow in the boundary layer. Modern satellites typically feature fiber-reinforced polymer (FRP) components, such as solar array booms, facesheets of sandwich panels, or overwraps for composite-overwrapped pressure vessels (COPV). These FRP materials do not behave the same as metals in the reentry environment, but instead will pyrolyze and develop significant volumes of gas into the boundary layer. Accurately predicting the reentry demise of FRP components is critical to assessing the reentry casualty risk for modern spacecraft. Research in recent years has shown that this demisability can depend heavily on how the expulsion of gaseous pyrolysis products through the outer surface of the material affects the heat flux at the surface. The ODPO has been developing a reduced-order model of the effect of pyrolysis gas blowing on the heat flux based on correlations between a blowing factor and a non-dimensional heat flux to be incorporated in the upcoming version 7.3 of the Object Reentry Survivability Analysis Tool (ORSAT). This presentation discusses the progress of this development project and the challenges remaining for generalizing the model across families of FRP materials.

Benton Greene↗

NASA NTRS2007

Lightning Charge Retrievals: Dimensional Reduction, LDAR Constraints, and a First Comparison w/ LIS Satellite Data

A "dimensional reduction" (DR) method is introduced for analyzing lightning field changes whereby the number of unknowns in a discrete two-charge model is reduced from the standard eight to just four. The four unknowns are found by performing a numerical minimization of a chi-squared goodness-of-fit function. At each step of the minimization, an Overdetermined Fixed Matrix (OFM) method is used to immediately retrieve the best "residual source". In this way, all 8 parameters are found, yet a numerical search of only 4 parameters is required. The inversion method is applied to the understanding of lightning charge retrievals. The accuracy of the DR method has been assessed by comparing retrievals with data provided by the Lightning Detection And Ranging (LDAR) instrument. Because lightning effectively deposits charge within thundercloud charge centers and because LDAR traces the geometrical development of the lightning channel with high precision, the LDAR data provides an ideal constraint for finding the best model charge solutions. In particular, LDAR data can be used to help determine both the horizontal and vertical positions of the model charges, thereby eliminating dipole ambiguities. The results of the LDAR-constrained charge retrieval method have been compared to the locations of optical pulses/flash locations detected by the Lightning Imaging Sensor (LIS).

Koshak, William↗

NASA NTRS2010

Simulation of Turbine Tone Noise Generation Using a Turbomachinery Aerodynamics Solver

As turbofan engine bypass ratios continue to increase, the contribution of the turbine to the engine noise signature is receiving more attention. Understanding the relative importance of the various turbine noise generation mechanisms and the characteristics of the turbine acoustic transmission loss are essential ingredients in developing robust reduced-order models for predicting the turbine noise signature. A computationally based investigation has been undertaken to help guide the development of a turbine noise prediction capability that does not rely on empiricism. As proof-of-concept for this approach, two highly detailed numerical simulations of the unsteady flow field inside the first stage of a modern high-pressure turbine were carried out. The simulations were computed using TURBO, which is an unsteady Reynolds-Averaged Navier-Stokes code capable of multi-stage simulations. Spectral and modal analysis of the unsteady pressure data from the numerical simulation of the turbine stage show a circumferential modal distribution that is consistent with the Tyler-Sofrin rule. Within the high-pressure turbine, the interaction of velocity, pressure and temperature fluctuations with the downstream blade rows are all possible tone noise source mechanisms. We have taken the initial step in determining the source strength hierarchy by artificially reducing the level of temperature fluctuations in the turbine flowfield. This was accomplished by changing the vane cooling flow temperature in order to mitigate the vane thermal wake in the second of the two simulations. The results indicated that, despite a dramatic change in the vane cooling flow, the computed modal levels changed very little indicating that the contribution of temperature fluctuations to the overall pressure field is rather small compared with the viscous and potential field interaction mechanisms.

VanZante, Dale↗

NASA NTRS2018

Comparison of MERRA-2 and ECCO-V4 Ocean Surface Heat Fluxes: Consequences of Different Forcing Feedbacks on Ocean Circulation and Implications for Climate Data Assimilation

Forcing ocean models with reanalysis data is a common practice in ocean modeling. As part of this practice, prescribed atmospheric state variables and interactive ocean SST (Sea Surface Temperature) are used to calculate fluxes between the ocean and the atmosphere. When forcing an ocean model with reanalysis fields, errors in the reanalysis data, errors in the ocean model and errors in the forcing formulation will generate a different solution compared to other ocean reanalysis solutions (which also have their own errors). As a first step towards a consistent coupled ocean-atmosphere reanalysis, we compare surface heat fluxes from a state-of-the-art atmospheric reanalysis, the Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2), to heat fluxes from a state-of-the-art oceanic reanalysis, the Estimating the Circulation and Climate of the Ocean Version 4, Release 2 (ECCO-v4). Then, we investigate the errors associated with the MITgcm (Massachusetts Institute of Technology general circulation model) ocean model in its ECCO-v4 ocean reanalysis configuration (1992-2011) when it is forced with MERRA- 2 atmospheric reanalysis fields instead of with the ECCO-v4 adjoint optimized ERA-interim state variables. This is done by forcing ECCO-v4 ocean with and without feedbacks from MERRA-2 related to turbulent fluxes of heat and moisture and the outgoing long wave radiation. In addition, we introduce an intermediate forcing method that includes only the feedback from the interactive outgoing long wave radiation. The resulting ocean circulation is compared with ECCO-v4 reanalysis and in-situ observations. We show that, without feedbacks, imbalances in the energy and the hydrological cycles of MERRA-2 (which are directly related to the fact it was created without interactive ocean) result in considerable SST drifts and a large reduction in sea level. The bulk formulae and interactive outgoing long wave radiation, although providing air-sea feedbacks and reducing model-data misfit, strongly relax the ocean to observed SST and may result in unwanted features such as large change in the water budget. These features have implications in a desired forcing recipe to be used. The results strongly and unambiguously argue for next generation data assimilation climate studies to involve fully coupled systems.

MERRA-2↗

NASA NTRS1987

Flexible manipulator control experiments and analysis

Modeling and control design for flexible manipulators, both from an experimental and analytical viewpoint, are described. From the application perspective, an ongoing effort within the laboratory environment at the Ohio State University, where experimentation on a single link flexible arm is underway is described. Several unique features of this study are described here. First, the manipulator arm is slewed by a direct drive dc motor and has a rigid counterbalance appendage. Current experimentation is from two viewpoints: (1) rigid body slewing and vibration control via actuation with the hub motor, and (2) vibration suppression through the use of structure-mounted proof-mass actuation at the tip. Such an application to manipulator control is of interest particularly in design of space-based telerobotic control systems, but has received little attention to date. From an analytical viewpoint, parameter estimation techniques within the closed-loop for self-tuning adaptive control approaches are discussed. Also introduced is a control approach based on output feedback and frequency weighting to counteract effects of spillover in reduced-order model design. A model of the flexible manipulator based on experimental measurements is evaluated for such estimation and control approaches.

Yurkovich, S.↗

NASA NTRS1994

Correlation of finite element free vibration predictions using random vibration test data

Finite element analysis is regularly used during the engineering cycle of mechanical systems to predict the response to static, thermal, and dynamic loads. The finite element model (FEM) used to represent the system is often correlated with physical test results to determine the validity of analytical results provided. Results from dynamic testing provide one means for performing this correlation. One of the most common methods of measuring accuracy is by classical modal testing, whereby vibratory mode shapes are compared to mode shapes provided by finite element analysis. The degree of correlation between the test and analytical mode shapes can be shown mathematically using the cross orthogonality check. A great deal of time and effort can be exhausted in generating the set of test acquired mode shapes needed for the cross orthogonality check. In most situations response data from vibration tests are digitally processed to generate the mode shapes from a combination of modal parameters, forcing functions, and recorded response data. An alternate method is proposed in which the same correlation of analytical and test acquired mode shapes can be achieved without conducting the modal survey. Instead a procedure is detailed in which a minimum of test information, specifically the acceleration response data from a random vibration test, is used to generate a set of equivalent local accelerations to be applied to the reduced analytical model at discrete points corresponding to the test measurement locations. The static solution of the analytical model then produces a set of deformations that once normalized can be used to represent the test acquired mode shapes in the cross orthogonality relation. The method proposed has been shown to provide accurate results for both a simple analytical model as well as a complex space flight structure.

Chambers, Jeffrey A.↗