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All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

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.↗
NASA NTRS2012

International Space Station Modal Correction Analysis

This paper summarizes the on-orbit modal test and the related modal analysis, model validation and correlation performed for the ISS Stage ULF4, DTF S4-1A, October 11,2010, GMT 284/06:13:00.00. The objective of this analysis is to validate and correlate analytical models with the intent to verify the ISS critical interface dynamic loads and improve fatigue life prediction. For the ISS configurations under consideration, on-orbit dynamic responses were collected with Russian vehicles attached and without the Orbiter attached to the ISS. ISS instrumentation systems that were used to collect the dynamic responses during the DTF S4-1A included the Internal Wireless Instrumentation System (IWIS), External Wireless Instrumentation System (EWIS), Structural Dynamic Measurement System (SDMS), Space Acceleration Measurement System (SAMS), Inertial Measurement Unit (IMU) and ISS External Cameras. Experimental modal analyses were performed on the measured data to extract modal parameters including frequency, damping and mode shape information. Correlation and comparisons between test and analytical modal parameters were performed to assess the accuracy of models for the ISS configuration under consideration. Based on the frequency comparisons, the accuracy of the mathematical models is assessed and model refinement recommendations are given. Section 2.0 of this report presents the math model used in the analysis. This section also describes the ISS configuration under consideration and summarizes the associated primary modes of interest along with the fundamental appendage modes. Section 3.0 discusses the details of the ISS Stage ULF4 DTF S4-1A test. Section 4.0 discusses the on-orbit instrumentation systems that were used in the collection of the data analyzed in this paper. The modal analysis approach and results used in the analysis of the collected data are summarized in Section 5.0. The model correlation and validation effort is reported in Section 6.0. Conclusions and recommendations drawn from this analysis are included in Section 7.0.

Fotz[atrocl. Lrostom↗
NASA NTRS2013

Using Response Surface Methods to Correlate the Modal Test of an Inflatable Test Article

This paper presents a practical application of response surface methods (RSM) to correlate a finite element model of a structural modal test. The test article is a quasi‐cylindrical inflatable structure which primarily consists of a fabric weave, with an internal bladder and metallic bulkheads on either end. To mitigate model size, the fabric weave was simplified by representing it with shell elements. The task at hand is to represent the material behavior of the weave. The success of the model correlation is measured by comparing the four major modal frequencies of the analysis model to the four major modal frequencies of the test article. Given that only individual strap material properties were provided and material properties of the overall weave were not available, defining the material properties of the finite element model became very complex. First it was necessary to determine which material properties (modulus of elasticity in the hoop and longitudinal directions, shear modulus, Poisson's ratio, etc.) affected the modal frequencies. Then a Latin Hypercube of the parameter space was created to form an efficiently distributed finite case set. Each case was then analyzed with the results input into RSM. In the resulting response surface it was possible to see how each material parameter affected the modal frequencies of the analysis model. If the modal frequencies of the analysis model and its corresponding parameters match the test with acceptable accuracy, it can be said that the model correlation is successful.

Gupta, Anju↗
NASA NTRS2018

Performing a Large-Scale Modal Test on the B2 Stand Crane at NASA's Stennis Space Center

A modal test of NASA's Space Launch System (SLS) Core Stage is scheduled to occur at the Stennis Space Center B2 test stand. A derrick crane with a 150-ft long boom, located at the top of the stand, will be used to suspend the Core Stage in order to achieve defined boundary conditions. During this suspended modal test, it is expected that dynamic coupling will occur between the crane and the Core Stage. Therefore, a separate modal test was performed on the B2 crane itself, in order to evaluate the varying dynamic characteristics and correlate math models of the crane. Performing a modal test on such a massive structure was challenging and required creative test setup and procedures, including implementing both AC and DC accelerometers, and performing both classical hammer and operational modal analysis. This paper describes the logistics required to perform this large-scale test, as well as details of the test setup, the modal test methods used, and an overview and application of the results.

Stasiunas, Eric C.↗
NASA NTRS2018

Performing a Large-Scale Modal Test on the B2 Stand Crane at NASA's Stennis Space Center

A modal test of NASA’s Space Launch System (SLS) Core Stage is scheduled to occur prior to propulsion system verification testing at the Stennis Space Center B2 test stand. A derrick crane with a 180-ft long boom, located at the top of the stand, will be used to suspend the Core Stage in order to achieve defined boundary conditions. During this suspended modal test, it is expected that dynamic coupling will occur between the crane and the Core Stage. Therefore, a separate modal test was performed on the B2 crane itself, in order to evaluate the varying dynamic characteristics and correlate math models of the crane. Performing a modal test on such a massive structure was challenging and required creative test setup and procedures, including implementing both AC and DC accelerometers, and performing both classical hammer and operational modal analysis. This paper describes the logistics required to perform this large-scale test, as well as details of the test setup, the modal test methods used, and an overview of the results.

Stasiunas, Eric C.↗
NASA NTRSDate not supplied

Modal Test and Model Correlation of NASA Plum Brook Station Mechanical Vibration Facility Head Expander –Lessons Learned from the Perspective of an Early-Career Engineer

In preparation for the Sierra Nevada Corporation’s (SNC) Dream Chaser spacecraft vibration test campaign at the Mechanical Vibration Facility (MVF) at NASA Plum Brook Station (PBS) in Sandusky, Ohio, a test-verified model of MVF is needed in order to be able to perform accurate pretest analysis used for determining response limits and abort levels. MVF was designed to vibration test MPCV Orion and was used to perform the system level vibration test of the European Service Module Structural Test Article (E-STA) in 2016. MVF is comprised of an 18 ft diameter annulus table that is driven with sixteen hydraulic vertical actuator assemblies and four hydraulic horizontal actuator assemblies, which allow it to perform single axis vibration testing in the vertical axis and in each of the two orthogonal horizontal axes without the need for reconfiguring the test article. A head expander for the MVF Table has been designed and built that fills in the center opening providing a continuous flat mounting surface with a maximum diameter of 16.25feet that expands the vibration testing capabilities of MVF. The MVF Table with this head expander will be used during the SNC Dream Chaser spacecraft vibration test campaign. Therefore, a critical element in a test-verified model of the MVF will be a test correlated finite element model (FEM) of the head expander. To obtain this, engineers from the Structural Dynamics Lab (SDL) at NASA Glenn Research Center (GRC) in Cleveland, Ohio performed a modal pretest analysis, conducted a modal test in July 2019, and most recently correlated the head expander finite element model to the modal test data up to 300 Hz. From the initial test preparations to the final delivery of a correlated finite element model, all efforts mentioned were led by the same early-career engineers at NASA GRC. From the viewpoint of an early-career engineer, lessons learned about modal pretest analysis, modal testing, and finite element model correlation of the MVF Table expander head will be presented and discussed. This will include the importance of understanding the limitations of using uncorrelated finite element models in the modal pretest analysis and planning, the importance of orthogonality metrics in judging adequacy and accuracy of test mode shapes, and the importance of having the FEM match the as built hardware in the model correlation effort.

Emma L Pierson↗
NASA NTRS2022

Accelerance Decoupling: An Approach for Removing the Influence of the Test Stand from the Integrated Modal Test

The main objective for launch vehicle (LV) modal testing is to quantify the LV’s modal properties in the free-free state (post pad separation). However, given the size of most LV systems, free-free testing is a challenge and often not feasible. With this, a test stand, typically the launch pad itself, is introduced as the means of support. This shifts the challenge to developing robust numerical methods for removing the influence of the launch pad from the integrated system modal test. The Space Launch System (SLS) is no exception where the mobile launcher (ML) is used to support the vehicle for the integrated modal test (IMT). For the IMT, it is well understood from pre-test analysis with finite element models (FEMs) of the SLS and SLS coupled to ML that the ML has a significant influence on the SLS modal properties especially in the lower frequency range where the primary SLS bending modes exist. An accelerance decoupling (AD) method has been formulated for the purpose of “subtracting out” the influence of the ML from the IMT results. With AD, the SLS decoupled frequency response functions (FRFs) are directly extracted from the IMT FRFs. The subject approach is aimed to utilize measured data only and achieve a robust FRF decoupling scheme. AD is derived from a widely used coupling technique called “Receptance Coupling” (RC). The AD core equation reverses the RC process and utilizes a pair of auxiliary equations that enable the core equation to be resolved based on measured data only. In AD, the decoupled component FRFs are extracted from the coupled system FRFs with a transformation to remove the contribution of the “subtractive component”. This paper addresses the AD’s operational flexibility to resolve SLS free-free modal properties from coupled system measured data but also the possibility to include data from FEM if there is enough confidence in the FEM or if it is asserted that the effect to the final outcome is reasonable.

Accelerance decoupling↗
NASA NTRS2022

Accelerance Decoupling: An Approach for Removing the Influence of the Test Stand from the Integrated Modal Test

The main objective for launch vehicle (LV) modal testing is to quantify the LV’s modal properties in the free-free state (post pad separation). However, given the size of most LV systems, free-free testing is a challenge and often not feasible. With this, a test stand, typically the launch pad itself, is introduced as the means of support. This shifts the challenge to developing robust numerical methods for removing the influence of the launch pad from the integrated system modal test. The Space Launch System (SLS) is no exception where the mobile launcher (ML) is used to support the vehicle for the integrated modal test (IMT). For the IMT, it is well understood from pre-test analysis with finite element models (FEMs) of the SLS and SLS coupled to ML that the ML has a significant influence on the SLS modal properties especially in the lower frequency range where the primary SLS bending modes exist. An accelerance decoupling (AD) method has been formulated for the purpose of “subtracting out” the influence of the ML from the IMT results. With AD, the SLS decoupled frequency response functions (FRFs) are directly extracted from the IMT FRFs. The subject approach is aimed to utilize measured data only and achieve a robust FRF decoupling scheme. AD is derived from a widely used coupling technique called “Receptance Coupling” (RC). The AD core equation reverses the RC process and utilizes a pair of auxiliary equations that enable the core equation to be resolved based on measured data only. In AD, the decoupled component FRFs are extracted from the coupled system FRFs with a transformation to remove the contribution of the “subtractive component”. This paper addresses the AD’s operational flexibility to resolve SLS free-free modal properties from coupled system measured data but also the possibility to include data from FEM if there is enough confidence in the FEM or if it is asserted that the effect to the final outcome is reasonable.

Accelerance decoupling↗
NASA NTRS2022

Accelerance Decoupling: An Approach for Removing the Influence of the Test Stand from the Integrated Modal Test

The main objective for launch vehicle (LV) modal testing is to quantify the LV’s modal properties in the free-free state (post pad separation). However, given the size of most LV systems, free-free testing is a challenge and often not feasible. With this, a test stand, typically the launch pad itself, is introduced as the means of support. This shifts the challenge to developing robust numerical methods for removing the influence of the launch pad from the integrated system modal test. The Space Launch System (SLS) is no exception where the mobile launcher (ML) is used to support the vehicle for the integrated modal test (IMT). For the IMT, it is well understood from pre-test analysis with finite element models (FEMs) of the SLS and SLS coupled to ML that the ML has a significant influence on the SLS modal properties especially in the lower frequency range where the primary SLS bending modes exist. An accelerance decoupling (AD) method has been formulated for the purpose of “subtracting out” the influence of the ML from the IMT results. With AD, the SLS decoupled frequency response functions (FRFs) are directly extracted from the IMT FRFs. The subject approach is aimed to utilize measured data only and achieve a robust FRF decoupling scheme. AD is derived from a widely used coupling technique called “Receptance Coupling” (RC). The AD core equation reverses the RC process and utilizes a pair of auxiliary equations that enable the core equation to be resolved based on measured data only. In AD, the decoupled component FRFs are extracted from the coupled system FRFs with a transformation to remove the contribution of the “subtractive component”. This paper addresses the AD’s operational flexibility to resolve SLS free-free modal properties from coupled system measured data but also the possibility to include data from FEM if there is enough confidence in the FEM or if it is asserted that the effect to the final outcome is reasonable.

Accelerance decoupling↗
NASA NTRSDate not supplied

Using Distributed Fiber-optic Strain Sensing to Estimate Generalized Modal Coordinates from Flight-test Data

A method for estimating the generalized modal coordinates of an aircraft during flight has been developed. The Fiber-optic Sensing System (FOSS) offers an efficient and cost-effective method of measuring the strain at thousands of points along the wings. The estimation of modal coordinates was implemented as a two-step process. First, a maximum likelihood method is used to estimate the statistical properties of the sensors and generalized modal coordinates. Second, the strain mode shapes from the finite element model are used along with the statistical properties from the first step to estimate the generalized modal coordinates over time. Using simulated data from the X-56A Multi-Utility Technology Testbed (MUTT), different methods of modal coordinate estimation were compared to demonstrate the benefits and weaknesses of each. These were compared against the exact solution and an ordinary least squares (a more traditional method) estimate. Modal coordinate estimation methods were then applied to flight-test data from the X-56A aircraft to show that the method continues to work well with actual test data. The new estimation method provides insights unavailable from more classical approaches.

Jeffrey Ouellette↗
DOE OSTI2015

A Modal Model to Simulate Typical Structural Dynamic Nonlinearity

Some initial investigations have been published which simulate nonlinear response with almost traditional modal models: instead of connecting the modal mass to ground through the traditional spring and damper, a nonlinear Iwan element was added. This assumes that the mode shapes do not change with amplitude and there are no interactions between modal degrees of freedom. This work expands on these previous studies. An impact experiment is performed on a structure which exhibits typical structural dynamic nonlinear response, i.e. weak frequency dependence and strong damping dependence on the amplitude of vibration. Use of low level modal test results in combination with high level impacts are processed using various combinations of modal filtering, the Hilbert Transform and band-pass filtering to develop response data that are then fit with various nonlinear elements to create a nonlinear pseudo-modal model. Simulations of forced response are compared with high level experimental data for various nonlinear element assumptions.

42 ENGINEERING↗
DOE OSTI2023

Sensitivity Analysis of Modal Parameters of a Jacket Offshore Wind Turbine to Operational Conditions

Accurate estimation of offshore wind turbine (OWT) modal parameters has a prominent effect on the design loads, lifetime prediction, and dynamic response of the system. Modal parameters can vary during the operation of OWTs. This paper studies the variation and sensitivity analysis of an OWT’s modal parameters with respect to operational and environmental conditions. Three finite element models of a jacket-supported OWT at the Block Island Wind Farm are created within the OpenSees, SAP2000, and OpenFAST platforms and validated using experimental measurements. The OpenFAST model is used to simulate the modal parameters of the turbine under various wind speed, rotor speed, power, yaw angle, mean sea level, blade pitch angle, and soil spring values. The model-predicted modal parameters of the first fore–aft (FA) and side–side (SS) modes are compared to those identified from experimental measurements. Results from the simulations show that the first FA natural frequency and damping ratio mostly depend on the rotor speed and wind speed, respectively, while yaw angle and mean sea level do not have a visible effect. It is observed that there is about 8% stiffening in the first FA frequency and an aerodynamic damping of 7.5% during the operation of the OWT.

17 WIND ENERGY↗
DOE OSTI2019

Estimation of full-field, full-order experimental modal model of cable vibration from digital video measurements with physics-guided unsupervised machine learning and computer vision

Cables are critical components for a variety of structures such as stay cables and suspenders of cable-stayed bridges and suspension bridges. When in operational service, they are vulnerable to cumulative fatigue damage induced by dynamic loads (e.g., the cyclic vehicle loads and wind excitation). To accurately analyze and predict their dynamics behaviors and performance that could be spatially local and temporal transient, it is essential to perform high-resolution vibration measurements, from which their dynamics properties are identified and, subsequently, a high spatial resolution, full-modal-order dynamics model of cable vibration can be established. In this study, we develop a physics-guided, unsupervised machine learning-based video processing approach that can blindly and efficiently extract the full-field (as many points as the pixel number of the video frame) modal parameters of cable vibration using only the video of an operating (output-only) cable. In particular, by incorporating the physics of cable vibration (taut string model), a novel automated modal motion filtering method is proposed to enable autonomous identification of full-order (as many modes as possible) dynamic parameters, including those weakly excited modes that used to be challenging to identify in operational modal analysis. Therefore, a full-field, full-order modal model of cable vibration is established by the proposed method. Furthermore, this new approach provides a low-cost and noncontact technique to estimate the cable tension using only the video of the vibrating cable where the fundamental frequency is automatically and efficiently estimated to compute the cable tension according to the taut string equation. Laboratory experiments on a bench-scale cable are conducted to validate the developed approach.

42 ENGINEERING↗
DOE OSTI2026

Multi-Modal Bayesian Neural Network Surrogates with Conjugate Last-Layer Estimation

As data collection and simulation capabilities advance, multi-modal learning, the task of learning from multiple modalities and sources of data, is becoming an increasingly important area of research. Surrogate models that learn from data of multiple auxiliary modalities to support the modeling of a highly expensive quantity of interest have the potential to aid outer loop applications such as optimization, inverse problems, or sensitivity analyses when multi-modal data are available. We develop two multi-modal Bayesian neural network surrogate models and leverage conditionally conjugate distributions in the last layer to estimate model parameters using stochastic variational inference (SVI). We provide a method to perform this conjugate SVI estimation in the presence of partially missing observations. Here, we demonstrate improved prediction accuracy and uncertainty quantification compared to unimodal surrogate models for both scalar and time series data.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2007

Characterization of Mid-Infrared Single Mode Fibers as Modal Filters

We present a technique for measuring the modal filtering ability of single mode fibers. The ideal modal filter rejects all input field components that have no overlap with the fundamental mode of the filter and does not attenuate the fundamental mode. We define the quality of a nonideal modal filter Q(sub f) as the ratio of transmittance for the fundamental mode to the transmittance for an input field that has no overlap with the fundamental mode. We demonstrate the technique on a 20 cm long mid-infrared fiber that was produced by the U.S. Naval Research Laboratory. The filter quality Q(sub f) for this fiber at 10.5 micron wavelength is 1000 +/- 300. The absorption and scattering losses in the fundamental mode are approximately 8 dB/m. The total transmittance for the fundamental mode, including Fresnel reflections, is 0.428 +/- 0.002. The application of interest is the search for extrasolar Earthlike planets using nulling interferometry. It requires high rejection ratios to suppress the light of a bright star, so that the faint planet becomes visible. The use of modal filters increases the rejection ratio (or, equivalently, relaxes requirements on the wavefront quality) by reducing the sensitivity to small wavefront errors. We show theoretically that, exclusive of coupling losses, the use of a modal filter leads to the improvement of the rejection ratio in a two-beam interferometer by a factor of Q(sub f).

single mode fibers↗
NASA NTRS2017

Fixed Base Modal Survey of the MPCV Orion European Service Module Structural Test Article

Recently, the MPCV Orion European Service Module Structural Test Article (E-STA) underwent sine vibration testing using the multi-axis shaker system at NASA GRC Plum Brook Station Mechanical Vibration Facility (MVF). An innovative approach using measured constraint shapes at the interface of E-STA to the MVF allowed high-quality fixed base modal parameters of the E-STA to be extracted, which have been used to update the E-STA finite element model (FEM), without the need for a traditional fixed base modal survey. This innovative approach provided considerable program cost and test schedule savings. This paper documents this modal survey, which includes the modal pretest analysis sensor selection, the fixed base methodology using measured constraint shapes as virtual references and measured frequency response functions, and post-survey comparison between measured and analysis fixed base modal parameters.

modal testing↗
NASA NTRSDate not supplied

Green Run Modal Test of the NASA Space Launch System Core Stage

The Core Stage of the new NASA Space Launch System (SLS) is a 212-foot tall rocket assembly—consisting primarily of two fuel tanks, an engine section, and four RS-25 rocket engines—capable of sending crew and large payloads to the moon and beyond with 1.6 million pounds of thrust. Currently, the Core Stage is in the B2 Test Stand at Stennis Space Center, undergoing a series of structural and functional tests, designated the Green Run test series. The ultimate goal of Green Run is to verify analytical models and confirm proper subsystem operation of the Core Stage. In January 2020, Green Run testing began with an experimental modal analysis test performed by the Marshal Space Flight Center modal test team. The desired free boundary condition of the Core Stage was achieved by suspending the massive spacecraft from the B2 Test Stand crane. Modal excitation was provided by a pair of 250-lb electro-dynamic shakers for multi-shaker random vibration testing, as well as a 12-pound impact hammer for impact testing. Modal response was measured with 550 accelerometers channels distributed on both the Core Stage and the B2 Test Stand crane. Following one very long night of testing, frequency response functions were calculated from the measured time histories in the target mode frequency range of 2.5 Hz to 15 Hz, and mode shapes, frequencies, and damping values were successfully extracted. The case-study presented in this paper will discuss the SLS Core Stage, the modal test setup and procedure, as well as a brief overview of the test results. Challenges associated with testing such a large, suspended structure in an outdoor environment will be discussed as well.

Green Run↗
NASA NTRSDate not supplied

Green Run Modal Test of the NASA Space Launch System Core Stage

The Core Stage of the new NASA Space Launch System (SLS) is a 212-foot-tall rocket assembly—consisting primarily of two cryogenic propellant tanks, an engine section, and four RS-25 rocket engines—that will send crew and large payloads to the moon and beyond for NASA’s Artemis program. Prior to SLS assembly, the Core Stage completed a series of structural and functional tests in the B-2 Test Stand at Stennis Space Center, designated Green Run. The goal of Green Run was to verify analytical models, confirm proper subsystem operation, and test-fire all four RS-25 engines of the Core Stage. In January 2020, Green Run testing began with an experimental modal analysis test, performed by the Marshal Space Flight Center modal test team. A free-boundary test condition of the Core Stage was simulated as close as possible by suspending the massive launch vehicle from the B-2 Test Stand crane. Modal excitation was provided by a pair of 250-lb electro-dynamic shakers for multi-shaker random vibration testing, as well as a 12-pound instrumented hammer for impact testing. Modal response was measured with 550 accelerometer channels distributed on both the Core Stage and the B-2 Test Stand derrick crane. Following one very long day of testing, frequency response functions were calculated from the measured time histories in the target mode frequency range of 5 Hz to 15 Hz, and mode shapes, frequencies, and damping values were successfully estimated. The case-study presented in this paper will discuss Green Run, the SLS Core Stage, the modal test setup and execution, as well as a brief overview of the test results. Challenges associated with testing such a large, suspended structure in an outdoor environment will be discussed as well.

Space Launch System↗