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SLS Integrated Modal Test Uncertainty Quantification using the Hybrid Parametric Variation Method

Uncertainty in structural loading during launch is a significant concern in the development of spacecraft and launch vehicles. Small variations in launch vehicle and payload mode shapes and their interaction can result in significant variation in system loads. In many cases involving large aerospace systems it is difficult, not economical, or impossible to perform a system modal test. However, it is still vital to obtain test results that can be compared with analytical predictions to validate models. Instead, the “Building Block Approach” is used in which system components are tested individually. Component models are correlated and updated to agree as best they can with test results. The Space Launch System consists of a number of components that are assembled into a launch vehicle. Finite element models of the components are developed, reduced to Hurty/Craig-Bampton models and assembled to represent different phases of flight. The only opportunity to obtain modal test data from an assembled Space Launch System will be during the Integrated Modal Test. There is always uncertainty in every model, which flows into uncertainty in predicted system results. Uncertainty Quantification is used to determine statistical bounds on prediction accuracy based on model uncertainty. For the Space Launch System, model uncertainty is at the Hurty/Craig-Bampton component level. Uncertainty in the Hurty/Craig-Bampton components is quantified using the hybrid parametric variation approach that combines parametric and nonparametric uncertainty. Uncertainty in model form is one of the biggest contributors to uncertainty in complex built-up structures. This type of uncertainty cannot be represented by variations infinite element model input parameters and thus cannot be included in a parametric approach. However, model-form uncertainty can be modeled using a nonparametric approach based on random matrix theory. The hybrid parametric variation method requires the selection of dispersion values for the Hurty/Craig-Bampton fixed-interface eigenvalues, and the Hurty/Craig-Bampton stiffness matrices. Component test/analysis frequency error is used to identify the fixed-interface eigenvalue dispersions, while test/analysis cross-orthogonality is used to identify stiffness dispersion values. The hybrid parametric variation uncertainty quantification approach is applied to the Space Launch System Integrated Modal Test configuration. Monte Carlo analysis is performed, and statistics are determined for modal correlation metrics, frequency response from Integrated Modal Test shakers to selected accelerometers, as well as other metrics for determining how well target modes are excited and identified. If the predicted uncertainty envelopes future Integrated Modal Test results, then there will be increased confidence in the utility of the component-based hybrid parametric variation uncertainty quantification approach.

Uncertainty Quantification↗
NASA NTRS1982

Modal vector estimation for closely spaced frequency modes

Techniques for obtaining improved modal vector estimates for systems with closely spaced frequency modes are discussed. In describing the dynamical behavior of a complex structure modal parameters are often analyzed: undamped natural frequency, mode shape, modal mass, modal stiffness and modal damping. From both an analytical standpoint and an experimental standpoint, identification of modal parameters is more difficult if the system has repeated frequencies or even closely spaced frequencies. The more complex the structure, the more likely it is to have closely spaced frequencies. This makes it difficult to determine valid mode shapes using single shaker test methods. By employing band selectable analysis (zoom) techniques and by employing Kennedy-Pancu circle fitting or some multiple degree of freedom (MDOF) curve fit procedure, the usefulness of the single shaker approach can be extended.

Craig, R. R., Jr.↗
NASA NTRS2009

Recovering Aerodynamic Side Loads on Rocket Nozzles using Quasi-Static Strain-Gage Measurements

During over-expanded operation of rocket nozzles, which is defined to be when the exit pressure is greater than internal pressure over some part of the nozzle, the nozzle will experience a transverse forcing function due to the pressure differential across the nozzle wall. Over-expansion occurs during the nozzle start-up and shutdown transient, even in high-altitude engines, because most test facilities cannot completely reproduce the near-vacuum pressures at those altitudes. During this transient, the pressure differential moves axially down the nozzle as it becomes pressurized, but this differential is never perfectly symmetric circumferentially. The character of the forcing function is highly complex and defined by a series of restricted and free shock separations. The subject of this paper is the determination of the magnitude of this loading during sub-scale testing via measurement of the structural dynamic response of the nozzle and its support structure. An initial attempt at back-calculating this load using the inverse of the transfer function was performed, but this attempt was shown to be highly susceptible to numerical error. The final method chosen was to use statically calibrated strain data and to filter out the system fundamental frequency such that the measured response yields close to the correct dynamic loading function. This method was shown to capture 93% of the pressure spectral energy using controlled load shaker testing. This method is one of the only practical ways for the inverse determination of the forcing function for non-stationary excitations, and, to the authors' knowledge, has not been described in the literature to date.

Brown, Andrew↗
NASA NTRS1984

Galileo spacecraft modal test and evaluation of testing techniques

The structural configuration, modal test requirements and pre-test activities involved in modeling the expected dynamic environment and responses of the Galileo spacecraft are discussed. The probe will be Shuttle-launched in 1986 and will gather data on the Jupiter system. Loads analysis for the 5300 lb spacecraft were performed with the NASTRAN code, and covered 10,000 static degrees of freedom and 1600 mass degrees of freedom. A modal analysis will be used to verify the predictions for natural frequencies, mode shapes, orthogonality checks, residual mass, modal damping and forces, and generalized forces. Verification of the validity of considering only 70 natural modes in the numerical simulation is being performed by examining the forcing functions of the analysis. The analysis led to requirements that 162 channels of accelerometer data and 118 channels of strain gage data be recorded during shaker tests to reveal areas where design changes will be needed to eliminate vibration peaks.

Chen, J.-C.↗
NASA NTRS2013

Understanding How Kurtosis Is Transferred from Input Acceleration to Stress Response and Its Influence on Fatigue Llife

High cycle fatigue of metals typically occurs through long term exposure to time varying loads which, although modest in amplitude, give rise to microscopic cracks that can ultimately propagate to failure. The fatigue life of a component is primarily dependent on the stress amplitude response at critical failure locations. For most vibration tests, it is common to assume a Gaussian distribution of both the input acceleration and stress response. In real life, however, it is common to experience non-Gaussian acceleration input, and this can cause the response to be non-Gaussian. Examples of non-Gaussian loads include road irregularities such as potholes in the automotive world or turbulent boundary layer pressure fluctuations for the aerospace sector or more generally wind, wave or high amplitude acoustic loads. The paper first reviews some of the methods used to generate non-Gaussian excitation signals with a given power spectral density and kurtosis. The kurtosis of the response is examined once the signal is passed through a linear time invariant system. Finally an algorithm is presented that determines the output kurtosis based upon the input kurtosis, the input power spectral density and the frequency response function of the system. The algorithm is validated using numerical simulations. Direct applications of these results include improved fatigue life estimations and a method to accelerate shaker tests by generating high kurtosis, non-Gaussian drive signals.

Kihm, Frederic↗
NASA NTRS1984

Seismic Analysis Capability in NASTRAN

Seismic analysis is a technique which pertains to loading described in terms of boundary accelerations. Earthquake shocks to buildings is the type of excitation which usually comes to mind when one hears the word seismic, but this technique also applied to a broad class of acceleration excitations which are applied at the base of a structure such as vibration shaker testing or shocks to machinery foundations. Four different solution paths are available in NASTRAN for seismic analysis. They are: Direct Seismic Frequency Response, Direct Seismic Transient Response, Modal Seismic Frequency Response, and Modal Seismic Transient Response. This capability, at present, is invoked not as separate rigid formats, but as pre-packaged ALTER packets to existing RIGID Formats 8, 9, 11, and 12. These ALTER packets are included with the delivery of the NASTRAN program and are stored on the computer as a library of callable utilities. The user calls one of these utilities and merges it into the Executive Control Section of the data deck to perform any of the four options are invoked by setting parameter values in the bulk data.

Butler, T. G.↗
NASA NTRS1978

A study of multiple-shaker modal survey testing

The principal objective was to examine and to assess the practical value of a method of multiple-shaker sinusoidal modal vibration testing known as Asher's method. Numerical studies which simulate the application of Asher's method and a unique experimental implementation of the method were completed. Another objective of the research was to develop and to demonstrate with numerical simulation a quantitative method for determining from transfer function data the number of dominant modes of vibration in sinusoidal structural response.

Hallauer, W. L., Jr.↗
NASA NTRS2019

Development of a new method in force limited vibration testing

The force limited vibration test approaches discussed in NASA-HDBK-7004C were developed to reduce overtesting associated with base shake vibration tests of aerospace hardware. This handbook outlines several different methods of specifying force limiting specifications. The basis for deriving force limiting specifications is related to the differences between mechanical impedances of typical aerospace hardware interfacing the mounting structures in flight configurations and the large impedances inherent in shaker vibration testing. Among these approaches, the semi-empirical method is presently the most widely used method to derive the force limiting specifications. This method is developed based on the assumption that the hardware interface responses are coherently excited. The inclusion of the incoherent excitation of the aerospace structures at mounting interfaces provides the basis for developing a more realistic force limiting specification that may be used to qualify flight hardware for launch environments using shaker testing. In this paper the semi-empirical method for defining force limiting specifications discussed in NASA handbook are reviewed using data recently obtained from a series of acoustic and vibration tests. A mathematical formation of a new force limiting approach based on considering the incoherent excitation of the hardware at their mounting interfaces is developed. Results from the analysis, which are correlated to the data obtained from a series of well instrumented acoustic and vibration tests, are discussed. The new approach provides much more realistic force limits that may further remove conservatism inherent in shaker vibration testing not accounted for by methods discussed in the NASA handbook.

Kolaini, Ali R.↗
NASA NTRS2003

An Integrated Analysis-Test Approach

This viewgraph presentation provides an overview of a project to develop a computer program which integrates data analysis and test procedures. The software application aims to propose a new perspective to traditional mechanical analysis and test procedures and to integrate pre-test and test analysis calculation methods. The program also should also be able to be used in portable devices and allows for the 'quasi-real time' analysis of data sent by electronic means. Test methods reviewed during this presentation include: shaker swept sine and random tests, shaker shock mode tests, shaker base driven model survey tests and acoustic tests.

Kaufman, Daniel↗
NASA NTRS1999

Vibration and Acoustic Testing for Mars Micromission Spacecraft

The objective of the Mars Micromission program being managed by the Jet Propulsion Laboratory (JPL) for NASA is to develop a common spacecraft that can carry telecommunications equipment and a variety of science payloads for exploration of Mars. The spacecraft will be capable of carrying robot landers and rovers, cameras, probes, balloons, gliders or aircraft, and telecommunications equipment to Mars at much lower cost than recent NASA Mars missions. The lightweight spacecraft (about 220 Kg mass) will be launched in a cooperative venture with CNES as a TWIN auxiliary payload on the Ariane 5 launch vehicle. Two or more Mars Micromission launches are planned for each Mars launch opportunity, which occur every 26 months. The Mars launch window for the first mission is November 1, 2002 through April 2003, which is planned to be a Mars airplane technology demonstration mission to coincide with the 100 year anniversary of the Kittyhawk flight. Several subsequent launches will create a telecommunications network orbiting Mars, which will provide for continuous communication with lenders and rovers on the Martian surface. Dedicated science payload flights to Mars are slated to start in 2005. This new cheaper and faster approach to Mars exploration calls for innovative approaches to the qualification of the Mars Micromission spacecraft for the Ariane 5 launch vibration and acoustic environments. JPL has in recent years implemented new approaches to spacecraft testing that may be effectively applied to the Mars Micromission. These include 1) force limited vibration testing, 2) combined loads, vibration and modal testing, and 3) direct acoustic testing. JPL has performed nearly 200 force limited vibration tests in the past 9 years; several of the tests were on spacecraft and large instruments, including the Cassini and Deep Space One spacecraft. Force limiting, which measures and limits the spacecraft base reaction force using triaxial force gages sandwiched between the spacecraft and the test fixture, alleviates the severe overtest at spacecraft resonances inherent in rigid fixture vibration tests. It has the distinct advantage over response limiting that the method is not dependent on the accuracy of a detailed dynamic model of the spacecraft. Combined loads, vibration, and modal testing were recently performed on the QuikSCAT spacecraft. The combined tests were performed in a single test setup per axis on a vibration shaker, reducing test time by a factor of two or three. Force gages were employed to measure the true c.g. acceleration of the spacecraft for structural loads verification using a sine burst test, to automatically notch random vibration test input accelerations at spacecraft resonances based on predetermined force limits, and to directly measure modal masses in a base drive modal test. In addition to these combined tests on the shaker, the QuikSCAT spacecraft was subjected to a direct field acoustic test by surrounding the spacecraft, still on the vibration shaker, with rock concert type acoustic speakers. Since the spacecraft contractor does not have a reverberant field acoustic test facility, performing a direct field acoustic test -saved the program nearly two weeks schedule time that would have been required for packing / unpacking and shipping of the spacecraft. This paper discusses the rationale behind and advantages of the above test approaches and provides examples of their actual implementation and comparisons to flight data. The applicability of the test approaches to Mars Micromission spacecraft qualification is discussed.

Kern, Dennis L.↗
NASA NTRS2020

Multiple Shaker Placement for Ground Vibration Test of X-59 Aircraft Using Topology Optimization

A multiple shaker placement methodology is developed and tested using a topology optimization technique. Current multiple shaker placement methodology requires optimum accelerometer placement and optimum single-shaker placement techniques. The proposed methodology is tested using a finite element model of the X-59 Low Boom Flight Demonstrator aircraft. The effective independence and the driving point acceleration transfer function (DPATF) methods are used for the accelerometer placement study. In this study, four shakers are used to excite each mode more effectively during the ground vibration test; all the modes of interest thus are separated into four groups. Each shaker takes care of a separate group of modes. Grouping the modes of interest is performed utilizing topology optimization. The number of modes for each group therefore will be automatically decided during grouping. For each group of modes, perform the following two steps to determine optimal location of four shakers: 1) At each accelerometer location, compare the magnitude of DPATF values at natural frequencies, select the minimum value, and make a vector with these minimum values of the DPATF magnitudes for each group; and 2) Select the degrees of freedom corresponding to the maximum value of this vector. The objective function value is the maximum value of the vector with minimum value of the magnitude of the superposed acceleration transfer function. This objective function value is maximized by changing the modes for each group. Forty accelerometers are enough to have good correlation between mode shapes obtained from the reduced order model and the simulated ground vibration test.

Optimization Analysis↗
NASA NTRS2011

A Procedure for Accurately Measuring the Shaker Overturning Moment During Random Vibration Tests

Motivation: For large system level random vibration tests, there may be some concerns about the shaker's capability for the overturning moment. It is the test conductor's responsibility to predict and monitor the overturning moment during random vibration tests. If the predicted moment is close to the shaker's capability, test conductor must measure the instantaneous moment at low levels and extrapolate to higher levels. That data will be used to decide whether it is safe to proceed to the next test level. Challenge: Kistler analog formulation for computing the real-time moment is only applicable to very limited cases in which we have 3 or 4 load cells installed at shaker interface with hardware. Approach: To overcome that limitation, a simple procedure was developed for computing the overturning moment time histories using the measured time histories of the individual load cells.

predict overturning↗
DOE OSTI2021

Structural Health Monitoring: Using an Autoencoder to Identify Damage in a Bolted Joint [Capstone Project]

Los Alamos National Laboratory (LANL) is an important fixture in the United States Department of Energy’s (DOE) National Nuclear Security Agency (NNSA) complex. LANL is one of the largest national laboratories in the country, and the laboratory’s primary mission is to support the nation’s nuclear stockpile. The lab functions as a design agencies for the NNSA and performs extensive testing on weapons as part of that mission. The shock and vibration test team at LANL utilizes electrodynamic shaker systems for important qualification testing in support of the laboratory’s mission. Modern engineering relies heavily on bolted joints to connect two objects. During these shaker tests, engineers depend on bolted joints to secure the test article to a fixture and the fixture to the table. The test article may be hazardous and contain high explosives which could create a safety issue if a bolted joint failed. A loss of preload in a bolt will affect the way energy is input to the system and may introduce nonlinearities as the joint opens and closes. The loss of preload can create challenges controlling the test and make acquired signals useless. Being able to monitor preload within bolted joints during testing can improve the quality of the data and keep workers safe.

42 ENGINEERING↗
NASA NTRS1982

Test program to develop vibroacoustics test criteria for the Galileo bus

In order to define random vibration test requirements for Galileo bus-mounted hardware, an extensive vibroacoustics test program was conducted on hardware available from the previous Voyager spacecraft development program. The Galileo test program consisted of acoustic tests on three configurations of the Voyager Dynamic Test Model bus and shaker random vibration tests on two flight-like bus equipment bay assemblies and one dummy equipment bay assembly. The primary goal of the acoustic tests was to define vibration levels at locations on the bus structure representative of inputs to bus equipment bay assemblies and to obtain response data on bus bay subassemblies for correlation with the vibration tests response data. The primary purpose of the vibration tests was to determine if the vibration tests excited subassembly responses at least as severely as the bus acoustic tests.

Kern, D. L.↗
NASA NTRS2011

Application of the Semi-Empirical Force-Limiting Approach for the CoNNeCT SCAN Testbed

The semi-empirical force-limited vibration method was developed and implemented for payload testing to limit the structural impedance mismatch (high force) that occurs during shaker vibration testing. The method has since been extended for use in analytical models. The Space Communications and Navigation Testbed (SCAN Testbed), known at NASA Glenn Research Center (GRC) as, the Communications, Navigation, and Networking re-Configurable Testbed (CoNNeCT) project utilized force-limited testing and analysis following the semi-empirical approach. This presentation presents the steps in performing a force-limited analysis and then compares the results to test data recovered during the CoNNeCT force-limited random vibration qualification test that took place at NASA Glenn Research Center (GRC) in the Structural Dynamics Laboratory (SDL) December 19, 2010 - January 7, 2011. A compilation of lessons learned and considerations for future force-limited tests is also included.

Staab, Lucas↗