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At least 451 records · Page 25

Multifrequency, Multipolarization External Calibration of the SIR-C/X-SAR Radars

Progress and the future plans for the following objectives are discussed: (1) Assess the accuracy at which the SIR-C/X-SAR standard data products can be calibrated through the use of ground calibrators to estimate the end-to-end system polarization calibration constants (or distortion parameters) and incorporate the constants into the data processing; (2) Study the cross-calibration between three multipolarization systems: SIR-C, the National Aeronautics and Space Administration/Jet Propulsion Laboratory (NASA/JPL) DC-8 SAR, and the University of Michigan ground-based polarimetric scatterometer; (3) Evaluate the calibration "stability" of SIR-C/X-SAR (measured by variations in the calibration constants) over the range swath width and over a specified distance in azimuth. Variations over a 12-hour period (between ascending and descending passes) will also be studied; and (4) Develop a cost-effective calibration plan including development of inexpensive polarimetric active calibrators.

Freeman, Anthony↗

CARES/Life Ceramics Durability Evaluation Software Enhanced for Cyclic Fatigue

The CARES/Life computer program predicts the probability of a monolithic ceramic component's failure as a function of time in service. The program has many features and options for materials evaluation and component design. It couples commercial finite element programs--which resolve a component's temperature and stress distribution--to reliability evaluation and fracture mechanics routines for modeling strength-limiting defects. The capability, flexibility, and uniqueness of CARES/Life have attracted many users representing a broad range of interests and has resulted in numerous awards for technological achievements and technology transfer. Recent work with CARES/Life was directed at enhancing the program s capabilities with regards to cyclic fatigue. Only in the last few years have ceramics been recognized to be susceptible to enhanced degradation from cyclic loading. To account for cyclic loads, researchers at the NASA Lewis Research Center developed a crack growth model that combines the Power Law (time-dependent) and the Walker Law (cycle-dependent) crack growth models. This combined model has the characteristics of Power Law behavior (decreased damage) at high R ratios (minimum load/maximum load) and of Walker law behavior (increased damage) at low R ratios. In addition, a parameter estimation methodology for constant-amplitude, steady-state cyclic fatigue experiments was developed using nonlinear least squares and a modified Levenberg-Marquardt algorithm. This methodology is used to give best estimates of parameter values from cyclic fatigue specimen rupture data (usually tensile or flexure bar specimens) for a relatively small number of specimens. Methodology to account for runout data (unfailed specimens over the duration of the experiment) was also included.

Nemeth, Noel N.↗

Top-of-the-Atmosphere Shortwave Flux Estimation from UV Observations: An Empirical Approach

Measurements of top of the atmosphere (TOA) radiation are essential to the understanding of Earth's climate. Clouds, aerosols, and ozone (0,) are among the most important agents impacting the Earth's short-wave (SW) radiation budget. There are several sensors in orbit that provide independent information related to the Earth's SW radiation budget. Having coincident information from these sensors is important for understanding their potential contributions. The A-train constellation of satellites provides a unique opportunity to analyze near-simultaneous data from several of these sensors. They include the Ozone Monitoring Instrument (OMI), on the NASA Aura satellite, that makes TOA hyper-spectral measurements from ultraviolet (UV) to visible wavelengths, and Clouds and the Earth's Radiant Energy System (CERES) instrument, on the NASA Aqua satellite, that makes broadband measurements in both the long- and short-wave. OMI measurements have been successfully utilized to derive the information on trace gases (e.g., 0 1, NO" and SO,), clouds, and absorbing aerosols. TOA SW fluxes are estimated using a combination of data from CERES and the Aqua MODerate-resolution Imaging Spectroradiometer (MODIS). In this paper, OMI retrievals of cloud/aerosol parameters and 0 1 have been collocated with CERES TOA SW flux retrievals. We use this collocated data to develop a neural network that estimates TOA shortwave flux globally over ocean using data from OMI and meteorological analyses. This input data include the effective cloud fraction, cloud optical centroid pressure (OCP), total-column 0" and sun-satellite viewing geometry from OMI as well as wind speed and water vapor from the Goddard Earth Observing System 5 Modern Era Retrospective-analysis for Research and Applications (GEOS-5 MERRA) along with a climatology of chlorophyll content. We train the neural network using a subset of CERES retrievals of TOA SW flux as the target output (truth) and withhold a different subset of the CERES data to be used for validation.

Gupta, P.↗

Photon Counting Detector Array Algorithms for Deep Space Optical Communications

For deep-space optical communications systems utilizing an uplink optical beacon, a single-photon-counting detector array on the flight terminal can be used to simultaneously perform uplink tracking and communications as well as accurate downlink pointing at photon-starved (pW/sq. m) power levels. In this paper, we discuss concepts and algorithms for uplink signal acquisition, tracking, and parameter estimation using a photon-counting camera. Statistical models of detector output data and signal processing algorithms are presented, incorporating realistic effects such as Earth background and detector/readout blocking. Analysis and simulation results are validated against measured laboratory data using state-of-the-art commercial photon-counting detector arrays, demonstrating sub-microradian tracking errors under channel conditions representative of deep space optical links.

beacon tracking↗

Steam Condensation Scaled Experiment in the Presence of Non-condensable Gas for Reactor Containment Passive Safety Analysis

This study presents scaled experiments using steam condensation with non-condensable gas (NCG)—helium, simulating hydrogen—as these experiments are pivotal for water-cooled reactor passive containment cooling system (PCCS) design and analysis. Research into PCCSs for small modular reactors (SMRs) is especially important in light of SMR system design; however, studies in the literature reflect limitations due to test geometry and operational condition variations, without considering SMR prototypic design. To address these challenges, a scaled test facility was developed to accurately replicate SMR PCCSs. This facility includes vertical down-flow condensing test sections with 1-, 2-, and 4-in.-diameter condensing tubes, accompanied by annular water cooling. Experiments were conducted using both superheated and saturated steam, with steam mass flow rates varying from 55 to 66 kg/hr., in the presence of helium as the NCG mass flow rate ranges from 1.8 to 22 kg/hr. Test data were collected on (a) the axial temperatures of the annular cooling water; (b) the outer wall temperature of the condensers; and (c) the mass flow rate, temperature, and pressure at the test section inlets and outlets. These primary test data were used in conjunction with a standard data reduction methodology to estimate essential thermal parameters such as heat fluxes, heat transfer coefficients, and condensation rates. The effects of NCGs on steam condensation within the geometry of the scaled test sections were then presented in regard to various testing conditions.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Presentation: Steam Condensation Scaled Experiment in the Presence of Non-condensable Gas for Reactor Containment Passive Safety Analysis

This study presents scaled experiments using steam condensation with non-condensable gas (NCG)—helium, simulating hydrogen—as these experiments are pivotal for water-cooled reactor passive containment cooling system (PCCS) design and analysis. Research into PCCSs for small modular reactors (SMRs) is especially important in light of SMR system design; however, studies in the literature reflect limitations due to test geometry and operational condition variations, without considering SMR prototypic design. To address these challenges, a scaled test facility was developed to accurately replicate SMR PCCSs. This facility includes vertical down-flow condensing test sections with 1-, 2-, and 4-in.-diameter condensing tubes, accompanied by annular water cooling. Experiments were conducted using both superheated and saturated steam, with steam mass flow rates varying from 55 to 66 kg/hr., in the presence of helium as the NCG mass flow rate ranges from 1.8 to 22 kg/hr. Test data were collected on (a) the axial temperatures of the annular cooling water; (b) the outer wall temperature of the condensers; and (c) the mass flow rate, temperature, and pressure at the test section inlets and outlets. These primary test data were used in conjunction with a standard data reduction methodology to estimate essential thermal parameters such as heat fluxes, heat transfer coefficients, and condensation rates. The effects of NCGs on steam condensation within the geometry of the scaled test sections were then presented in regard to various testing conditions.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Imprecise global sensitivity analysis using bayesian multimodel inference and importance sampling

Global Sensitivity Analysis (GSA) aims to understand the relative importance of uncertain input variables to model response. Conventional GSA involves calculating sensitivity (Sobol’) indices for a model with known model parameter distributions. However, model parameters are affected by aleatory and epistemic uncertainty, with the latter often caused by lack of data. In this paper, we propose a new framework to quantify uncertainty in probability model-form and model parameters resulting from small datasets and integrate these uncertainties into Sobol’ index estimates. First, the process establishes, through Bayesian multimodel inference, a set of candidate probability models and their associated probabilities. Imprecise Sobol’ indices are calculated from these probability models using an importance sampling reweighting approach. This results in probabilistic Sobol’ indices, whose distribution characterizes uncertainty in the sensitivity resulting from small dataset size. The imprecise Sobol’ indices thus provide a measure of confidence in the sensitivity estimate and, moreover, can be used to inform data collection efforts targeted to minimize the impact of uncertainties. Through an example studying the parameters of a Timoshenko beam, we show that these probabilistic Sobol’ indices converge to the true/deterministic Sobol’ indices as the dataset size increases and hence, distribution-form uncertainty reduces. The approach is then applied to assess the sensitivity of the out-of-plane properties of an E-glass fiber composite material to its constituent properties. This second example illustrates the approach for an important class of materials with wide-ranging applications when data may be lacking for some input parameters.

42 ENGINEERING↗

Graphite Characterization: Baseline Variability Analysis Report

The Idaho National INL’s Baseline Material Property program provides many measurements of different material properties on a variety of nuclear graphite grades being investigated for irradiation-induced changes in material properties. The baseline material properties provide an unirradiated reference for comparison with measurements of those properties after irradiation. This study describes how uncertainty, or variance, in estimates of important material properties, like compressive strength, may depend on sample size, sample distribution and parameter estimation methods. Compressive strength data from two large collections of specimens from a billet of PCEA graphite (sample size = 230) and a billet of IG-110 graphite (sample size = 48) are used to illustrate these dependencies. The grades of graphite used represent approximate end members in terms of relative variability in strength measurements. Monte Carlo simulation and bootstrapping methods were used to examine variance in Weibull-parameter estimates as a function of sample size. Results were consistent with what previous statistical analyses have shown about the relationship between sample size and width of the confidence interval for maximum likelihood (ML) estimated parameters when samples are repeatedly drawn from a Weibull distribution. As a function of sample size, the precision of the modulus estimate increases faster than that of the characteristic strength. The modulus maximum likelihood estimates (MLEs) are biased for low sample sizes. The American Society for Testing and Materials document ASTM D7846-16 provides equations that describe the dependence of the variance of parameter MLEs on sample size. Using the same methodology, we show that the polynomials provided for variance dependence on sample size are inaccurate for sample sizes greater than ~120. We provide approximations to that relationship that illustrate relative constancy for sample size > ~10, in the logspace relationship of the modulus variance and the log transformed characteristic strength variance. Bootstrapping provided a means of comparing Weibull parameters obtained using ASME’s guidance for specimen collection to those obtained using different weighting in a case where strength is related to position in a billet and to grain orientation and a single distribution is used to characterize the billet. ASME specifies that samples be collected with equal representation in all locations and grain orientations. Parameter values obtained using ASME’s method were different from those obtained using random sampling of the complete data sets, and this was particularly true for the PCEA data. In addition, while the ASME approach yielded more conservative parameters for the PCEA data, the opposite was true for the IG-110 data. The difference observed for the PCEA data set likely reflects the larger number of against-grain specimens collected, which had generally higher strength than the with-grain specimens. This emphasizes the importance of the dependence of strength on location or grain orientation and suggests that it may be prudent to weight specimen collection toward the weaker subgroups if a conservative estimate as desired, as the equal weighting method recommended by ASME would will not always provide the most conservative Weibull parameters. Because spatial correlations commonly exist in certain grades of graphite, future work may involve developing a methodology for parameter inference that relaxes the assumption of independent specimens. ASTM and ASME codes recommend different parameter estimation methods and models of the Weibull distribution in different situations. Descriptions of the effects on parameter estimates for the example billets used in this study provide an example of how the method may affect the parameter estimate, and how—in this case—that compares to differences due to other factors, such as sample size and dependence on grain orientation or sample location.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Comparative Analyses of Bioequivalence Assessment Methods for In Vitro Permeation Test Data

ABSTRACT For topical, dermatological drug products, an in vitro option to determine bioequivalence (BE) between test and reference products is recommended. In particular, in vitro permeation test (IVPT) data analysis uses a reference‐scaled approach for two primary endpoints, cumulative penetration amount (AMT) and maximum flux ( J max ), which takes the within donor variability into consideration. In 2022, the Food and Drug Administration (FDA) published a draft IVPT guidance that includes statistical analysis methods for both balanced and unbalanced cases of IVPT study data. This work presents a comprehensive evaluation of various methodologies used to estimate critical parameters essential in assessing BE. Specifically, we investigate the performance of the FDA draft IVPT guidance approach alongside alternative empirical and model‐based methods utilizing mixed‐effects models. Our analyses include both simulated scenarios and real‐world studies. In simulated scenarios, empirical formulas consistently demonstrate robustness in approximating the true model, particularly in effectively addressing treatment–donor interactions. Conversely, the effectiveness of model‐based approaches heavily relies on precise model selection, which significantly influences their results. The research emphasizes the importance of accurate model selection in model‐based BE assessment methodologies. It sheds light on the advantages of empirical formulas, highlighting their reliability compared to model‐based approaches and offers valuable implications for BE assessments. Our findings underscore the significance of robust methodologies and provide essential insights to advance their understanding and application in the assessment of BE, employed in IVPT data analysis.

Leon, Sami↗

Application of a Kalman filter identification technique to flight data from the X-22A variable stability V/STOL aircraft

A digital identification technique based on Kalman filter theory was developed for the estimation of V/STOL aircraft stability and control parameters from flight data. The application of this technique to flight data from flying qualities experiments using the variable stability X-22A V/STOL aircraft is discussed. The estimation algorithm is briefly reviewed, experimental and data acquisition procedures used in the X-22A flight programs are outlined, and specific problem areas such as the determination of noise statistics and selection of pilot inputs to enhance identifiability are discussed. Results are presented for a wide range of simulated dynamic configurations.

Lebacqz, J. V.↗

Tightly-coupled camera/LiDAR integration for point cloud generation from GNSS/INS-assisted UAV mapping systems

Unmanned aerial vehicles (UAVs) equipped with integrated global navigation satellite systems/inertial navigation systems (GNSS/INS) together with cameras and/or LiDAR sensors are being widely used for topographic mapping in a variety of applications such as precision agriculture, coastal monitoring, and archaeological documentation. Integration of image-based and LiDAR point clouds can provide a comprehensive 3D model of the area of interest. For such integration, ensuring a good alignment between data from the different sources is critical. Although many works have been conducted on this topic, there is still a need for a rigorous integration approach that minimizes the discrepancy between camera and LiDAR data caused by inaccurate system calibration parameters and/or trajectory artifacts. This study proposes an automated tightly-coupled camera/LiDAR integration workflow for GNSS/INS-assisted UAV systems. The proposed strategy is conducted in three main steps. First, an image-based point cloud is generated using a LiDAR/GNSS/INS-assisted structure from motion (SfM) strategy. Then, feature correspondences between image-based and LiDAR point clouds are automatically identified. Finally, an integrated-bundle adjustment procedure including image points, LiDAR raw measurements, and GNSS/INS information is conducted to minimize the discrepancy between point clouds from different sensors while estimating system calibration parameters and refining the trajectory information. The proposed SfM strategy and integration framework are evaluated using five datasets. The SfM results show that using LiDAR data can facilitate feature matching and further increase the number of reconstructed 3D points. The experimental results also illustrate that the developed automated camera/LiDAR integration strategy is capable of accurately estimating system calibration parameters to achieve good alignment among camera/LiDAR data from single/multiple systems. Finally, an absolute accuracy in the range of 3–5 cm is achieved for the image/LiDAR point clouds after the integration process.

42 ENGINEERING↗

Synthesis of observed and simulated rain microphysics to inform a new Bayesian statistical framework for microphysical parameterization in climate models (Final Scientific Report)

This project aimed to investigate a new approach to bulk microphysics schemes. We identified the need to move beyond the fixed structural assumptions and approximation of existing schemes. For example, most schemes assume some functional form for the rain drop size distribution (e.g. a gamma or exponential distribution). Most schemes then evolve some number of statistical moments of that distribution via various processes, such as evaporation, sedimentation, collision-coalescence, and collisional breakup. These microphysical processes, in turn, are typically some fixed functional form derived from either some other (more detailed) model, or using some single-particle rates that are then integrated over the size distribution. While these process rate functions may have some free parameters to adjust, in other cases doing so is impossible (e.g. when the process rates are analytical or piecewise solutions to some target function). Our goal was to build and test a scheme that assumed no size distribution form, and used a series of power laws as the basis for the process rates. Moments of the size distribution would be predicted, but no underlying size distribution would be specified. Any number or choice of size distribution moments could be used, and any number of power laws could be employed to model the process rates. Thus, our approach is flexible, and can seamlessly scale across levels of complexity, as demanded by the data. Bayesian inference then would provide the formalism to estimate the model parameters and structure, allowing for robust uncertainty quantification. We proposed testing this framework in idealized simulations using bin microphysical schemes as a data source. We also proposed using real data to inform our microphysics scheme, and also that we would integrate our scheme into WRF.

58 GEOSCIENCES↗

Kinetics of simultaneous hydrodesulfurization and hydrodenitrogenation reactions using CoMoP/Al 2 O 3 and NiMoP/Al 2 O 3

Hydrodesulfurization (HDS) is a key reaction to achieve diesel production at the specified low sulfur levels and is highly affected by a competing reaction involving nitrogen removal through hydrodenitrogenation (HDN). This work evaluated kinetic parameters of simultaneous reactions of HDS of dibenzothiophene (DBT) and HDN of quinoline (Q) using CoMoP/Al 2 O 3 and NiMoP/Al 2 O 3 catalysts under operational conditions that allow a wide range of reagent conversions. Estimated parameters were evaluated using rigorous statistical 2 analysis. Good fits for the evaluated experimental data were provided by both power-law and Langmuir-Hinshelwood models. Further, turnover frequency values highlight adsorption and competition effects between nitrogen-containing compounds and sulfur-containing compounds. NiMoP catalyst showed higher hydrogenating power than CoMoP, with larger absolute value of the estimated adsorption enthalpy (-120 kJ.mol -1 for NiMoP and -75 kJ.mol -1 for CoMoP), suggesting strong adsorption of nitrogen compounds. A catalyst with more hydrogenating power is also more capable of performing both HDN and HDS reactions simultaneously.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

MEDLI2: MISP Inferred Aerothermal Environment and Flow Transition Assessment

The Mars Entry, Descent, and Landing Instrumentation 2 (MEDLI2) sensor suite on the Mars2020 mission contained multiple sensors on the aeroshell to measure the aerothermal environment during entry into the Martian atmosphere. These sensors performed superbly and successfully returned forebody and aftbody heating measurements. Analysis of MEDLI2 data indicated flow transitioning from a laminar to turbulent state on the heatshield. No evidence of flow transition was observed on the backshell. Two methods were used to estimate flow transition times on the heatshield: (1) temperature gradient of near-surface thermocouple data and (2) heat flux gradient from an inverse reconstruction approach using thermocouple data and material response modeling. Both methods produced similar transition times with an estimated accuracy of ±1 s. To assess various transition criteria, transition parameters were evaluated at each sensor location using flow field solutions from computational fluid dynamics (CFD) simulations. The idea was to use conservative values inferred from MEDLI2 data as transition criteria for other Mars missions. To test this hypothesis, MEDLI data from the Mars Science Laboratory (MSL) mission was used to compare predicted vs. actual flow transition times. The comparisons suggest smooth wall transition criteria are not well-suited in modeling the rapid progression of a turbulent transition front. Transition criteria containing a roughness element parameter agreed better with the flight data. In summary, critical transition values derived from MEDLI2 data may be used as a starting point in constructing a flow transition model for future Mars missions.

Chun Y Tang↗

Convergence in simulating global soil organic carbon by structurally different models after data assimilation

Abstract Current biogeochemical models produce carbon–climate feedback projections with large uncertainties, often attributed to their structural differences when simulating soil organic carbon (SOC) dynamics worldwide. However, choices of model parameter values that quantify the strength and represent properties of different soil carbon cycle processes could also contribute to model simulation uncertainties. Here, we demonstrate the critical role of using common observational data in reducing model uncertainty in estimates of global SOC storage. Two structurally different models featuring distinctive carbon pools, decomposition kinetics, and carbon transfer pathways simulate opposite global SOC distributions with their customary parameter values yet converge to similar results after being informed by the same global SOC database using a data assimilation approach. The converged spatial SOC simulations result from similar simulations in key model components such as carbon transfer efficiency, baseline decomposition rate, and environmental effects on carbon fluxes by these two models after data assimilation. Moreover, data assimilation results suggest equally effective simulations of SOC using models following either first‐order or Michaelis–Menten kinetics at the global scale. Nevertheless, a wider range of data with high‐quality control and assurance are needed to further constrain SOC dynamics simulations and reduce unconstrained parameters. New sets of data, such as microbial genomics‐function relationships, may also suggest novel structures to account for in future model development. Overall, our results highlight the importance of observational data in informing model development and constraining model predictions.

54 ENVIRONMENTAL SCIENCES↗

Estimation of multidimensional precipitation parameters by areal estimates of oceanic rainfall

The parameters of the multidimensional precipitation model proposed by Waymire et al. (1984) are estimated using the areal-averaged radar measurements of precipitation of the Global Atlantic Tropical Experiment (GATE) data set. The procedure followed was the fitting of the first- and second-order moments at different aggregation scales by nonlinear regression techniques. The numerical estimates of the parameters using different subsets of GATE information were reasonably stable, i.e., they were not affected by changes of the area-averaging size, temporal length of the records, and percentage of areal coverage of rainfall. This suggests that the estimation procedure is relatively robust and suitable to estimate the parameters of the multidimensional model in areas of sparse density of rain gages. The use of the space-time spectrum of rainfall to help in the determination of sampling errors due to intermittent visits of future space-borne low-altitude sensors of precipitation is also discussed.

Valdes, J. B.↗

Modeling Substrate Utilization, Metabolite Production, and Uranium Immobilization in Shewanella oneidensis Biofilms

In this study, we developed a two-dimensional mathematical model to predict substrate utilization and metabolite production rates in Shewanella oneidensis MR-1 biofilm in the presence and absence of uranium (U). In our model, lactate and fumarate are used as the electron donor and the electron acceptor, respectively. The model includes the production of extracellular polymeric substances (EPS). The EPS bound to the cell surface and the EPS distributed in the biofilm were considered bound EPS (bEPS) and loosely associated EPS (laEPS), respectively. COMSOL ® Multiphysics finite element analysis software was used to solve the model numerically (model file provided in the Supplementary Material). The input variables of the model were the lactate and fumarate concentrations, cell density, EPS density, half saturation constant for fumarate, and diffusion coefficients of the substrates and metabolites. To estimate unknown parameters and calibrate the model, we used a custom designed biofilm reactor placed inside a nuclear magnetic resonance (NMR) microimaging and spectroscopy system and measured substrate utilization and metabolite production rates. From these data we estimated the yield coefficients, maximum substrate utilization rate, half saturation constant for lactate, stoichiometric ratio of fumarate and acetate to lactate and stoichiometric ratio of succinate to fumarate. These parameters are critical to predicting the activity of biofilms and are not available in the literature. Lastly, the model was used to predict uranium immobilization in S. oneidensis MR-1 biofilms by considering reduction and adsorption processes in the cells and in the EPS. We found that the majority of immobilization was due to cells, and that EPS were less efficient at immobilizing U. Furthermore, most of the immobilization occurred within the top 10 µm of the biofilm. To the best of our knowledge, this research is one of the first biofilm immobilization mathematical models based on experimental observation. It has the ability to predict the relative contributions to U immobilization of laEPS, bEPS and cells.

59 BASIC BIOLOGICAL SCIENCES↗

Autonomous Modal Identification of the Space Shuttle Tail Rudder

Autonomous modal identification automates the calculation of natural vibration frequencies, damping, and mode shapes of a structure from experimental data. This technology complements damage detection techniques that use continuous or periodic monitoring of vibration characteristics. The approach shown in the paper incorporates the Eigensystem Realization Algorithm (ERA) as a data analysis engine and an autonomous supervisor to condense multiple estimates of modal parameters using ERA's Consistent-Mode Indicator and correlation of mode shapes. The procedure was applied to free-decay responses of a Space Shuttle tail rudder and successfully identified the seven modes of the structure below 250 Hz. The final modal parameters are a condensed set of results for 87 individual ERA cases requiring approximately five minutes of CPU time on a DEC Alpha computer.

Pappa, Richard S.↗