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DOE OSTI2024

Multi-Attribute Subset Selection enables prediction of representative phenotypes across microbial populations

The interpretation of complex biological datasets requires the identification of representative variables that describe the data without critical information loss. This is particularly important in the analysis of large phenotypic datasets (phenomics). Here we introduce Multi-Attribute Subset Selection (MASS), an algorithm which separates a matrix of phenotypes (e.g., yield across microbial species and environmental conditions) into predictor and response sets of conditions. Using mixed integer linear programming, MASS expresses the response conditions as a linear combination of the predictor conditions, while simultaneously searching for the optimally descriptive set of predictors. We apply the algorithm to three microbial datasets and identify environmental conditions that predict phenotypes under other conditions, providing biologically interpretable axes for strain discrimination. MASS could be used to reduce the number of experiments needed to identify species or to map their metabolic capabilities. The generality of the algorithm allows addressing subset selection problems in areas beyond biology.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2020

Global ocean dimethyl sulfide climatology estimated from observations and an artificial neural network

Marine dimethyl sulfide (DMS) is important to climate due to the ability of DMS to alter Earth's radiation budget. Knowledge of the global-scale distribution, seasonal variability, and sea-to-air flux of DMS is needed in order to improve understanding of atmospheric sulfur, aerosol/cloud dynamics, and albedo. Here we examine the use of an artificial neural network (ANN) to extrapolate available DMS measurements to the global ocean and produce a global climatology with monthly temporal resolution. A global database of 82 996 ship-based DMS measurements in surface waters was used along with a suite of environmental parameters consisting of latitude–longitude coordinates, time of day, time of year, solar radiation, mixed layer depth, sea surface temperature, salinity, nitrate, phosphate, and silicate. Linear regressions of DMS against the environmental parameters show that on a global-scale mixed layer depth and solar radiation are the strongest predictors of DMS. These parameters capture ~9 % and ~7 % of the raw DMS data variance, respectively. Multilinear regression can capture more of the raw data variance (~39 %) but strongly underestimates DMS in high-concentration regions. In contrast, the artificial neural network captures ~66 % of the raw data variance in our database. Like prior climatologies our results show a strong seasonal cycle in surface ocean DMS with the highest concentrations and sea-to-air fluxes in the high-latitude summertime oceans. We estimate a lower global sea-to-air DMS flux (20.12±0.43 Tg S yr –1 ) than the prior estimate based on a map interpolation method when the same gas transfer velocity parameterization is used. Our sensitivity test results show that DMS concentration does not change unidirectionally with each of the environmental parameters, which emphasizes the interactions among these parameters. The ANN model suggests that the flux of DMS from the ocean to the atmosphere will increase with global warming. Given that larger DMS fluxes induce greater cloud albedo, this corresponds to a negative climate feedback.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2017

Indirect Validation of Probe Speed Data on Arterial Corridors

This study aimed to estimate the accuracy of probe speed data on arterial corridors on the basis of roadway geometric attributes and functional classification. It was assumed that functional class (medium and low) along with other road characteristics (such as weighted average of the annual average daily traffic, average signal density, average access point density, and average speed) were available as correlation factors to estimate the accuracy of probe traffic data. This study tested these factors as predictors of the fidelity of probe traffic data by using the results of an extensive validation exercise. This study showed strong correlations between these geometric attributes and the accuracy of probe data when they were assessed by using average absolute speed error. Linear models were regressed to existing data to estimate appropriate models for medium- and low-type arterial corridors. The proposed models for medium- and low-type arterials were validated further on the basis of the results of a slowdown analysis. These models can be used to predict the accuracy of probe data indirectly in medium and low types of arterial corridors.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2026

Bayesian chain graph models to characterize microbe-environment dynamics

Microbiome data require statistical models that can simultaneously decode microbes' reaction to the environment and interactions among microbes. While a multiresponse linear regression model seems like a straight-forward solution, we argue that treating it as a graphical model is problematic given that the regression coefficient matrix does not encode the conditional dependence structure between response and predictor nodes. This observation is especially important in biological settings when we have prior knowledge on the edges from specific experimental interventions that can only be properly encoded under a conditional dependence model. Here, we propose a chain graph model with two sets of nodes (predictors and responses) whose solution yields a graph with edges that indeed represent conditional dependence, thus agreeing with the experimenter's intuition on the average behavior of nodes under treatment. The solution to our model is sparse via the Bayesian linear regression (LASSO). In addition, we propose an adaptive extension so that different shrinkages can be applied to different edges to incorporate edge-specific prior knowledge. Our model is computationally inexpensive through an efficient Gibbs sampling algorithm and can account for binary, counting, and compositional responses via an appropriate hierarchical structure. We test the performance of our model in a variety of simulated datasets, thereby showing superior performance to state-of-the-art approaches. We further apply our model to human gut and soil microbial compositional datasets, and we highlight that CG-LASSO can estimate biologically meaningful network structures in the data.

compositional data↗

NASA NTRS2004

Objective Lightning Forecasting at Kennedy Space Center/Cape Canaveral Air Force Station using Cloud-to-Ground Lightning Surveillance System Data

The 45th Weather Squadron (45 WS) forecasters at Cape Canaveral Air Force Station (CCAFS) in Florida include a probability of thunderstorm occurrence in their daily morning briefings. This information is used by personnel involved in determining the possibility of violating Launch Commit Criteria, evaluating Flight Rules for the Space Shuttle, and daily planning for ground operation activities on Kennedy Space Center (KSC)/CCAFS. Much of the current lightning probability forecast is based on a subjective analysis of model and observational data. The forecasters requested that a lightning probability forecast tool based on statistical analysis of historical warm-season (May - September) data be developed in order to increase the objectivity of the daily thunderstorm probability forecast. The tool is a set of statistical lightning forecast equations that provide a lightning occurrence probability for the day by 1100 UTC (0700 EDT) during the warm season. This study used 15 years (1989-2003) of warm season data to develop the objective forecast equations. The local CCAFS 1000 UTC sounding was used to calculate stability parameters for equation predictors. The Cloud-to-Ground Lightning Surveillance System (CGLSS) data were used to determine lightning occurrence for each day. The CGLSS data have been found to be more reliable indicators of lightning in the area than surface observations through local informal analyses. This work was based on the results from two earlier research projects. Everitt (1999) used surface observations and rawinsonde data to develop logistic regression equations that forecast the daily thunderstorm probability at CCAFS. The Everitt (1999) equations showed an improvement in skill over the Neumann-Pfeffer thunderstorm index (Neumann 1971), which uses multiple linear regression, and also persistence and climatology forecasts. Lericos et al. (2002) developed lightning distributions over the Florida peninsula based on specific flow regimes. The flow regimes were inferred from the average wind direction in the 1000-700 mb layer at Miami (MIA), Tampa (TBW), and Jacksonville (JAX), Florida, and the lightning data were from the National Lightning Detection Network. The results suggested that the daily flow regime may be an important predictor of lightning occurrence on KSC/CCAFS.

Lambert, Winifred↗

DOE OSTI2026

Data for Propagation Method and Planting Density Influence Canopy Developmental Transition and Biomass Productivity in Miscanthus × giganteus

Understanding how establishment practices influence the mechanisms underlying Miscanthus × giganteus (miscanthus) productivity and canopy development is critical for optimizing management. Data was collected during the juvenile (2011–2013) and mature (2024) phases of a long-term field experiment established in Urbana, Illinois, to evaluate the effects of propagation method (plug propagation [PP] and rhizome propagation [RP]), planting density (1.0, 0.75, and 0.25 plants m⁻²), and nitrogen application (0 and 67 kg N ha⁻¹) on end-of-season biomass yield, tiller mass, tiller density, and tiller height. Linear regression models identified the dominant predictors of yield across stand ages and management regimes. Planting density, nitrogen (N) application, and propagation method significantly influenced early yield and canopy development. During the juvenile phase, biomass yield was driven by tiller density due to canopy expansion; in the mature phase, yield became driven by tiller mass. The PP plots produced higher tiller density than the RP plots, resulting in faster canopy closure and higher juvenile-phase yields. Rhizome-propagated (RP) plots produced lower tiller density, but individual tillers were 3.3–6.4 g tiller−1 heavier than PP tillers. After the canopy reached equilibrium, the PP and RP yields were similar because greater RP tiller mass compensated for its lower tiller density. Higher planting density resulted in greater yield and tiller density during the second year (2012), but this effect was absent from the third year (2013) onward. In the juvenile phase, N fertilization enhanced yield by 1.6–3.4 Mg ha−1. Initiating fertilization in 2013 on unfertilized plots produced biomass similar to that in fertilized plots, suggesting yield recovery in the mature phase. These findings revealed that establishment strategies, including propagation method and planting density, influence juvenile miscanthus canopy development and productivity, transitioning from tiller-density- to mass-dominated yields, but not mature phase productivity.

Miscanthus↗

DOE OSTI2023

Uncertainty quantification of a deep learning fuel property prediction model

Deep learning models are being widely used in the field of combustion. Given the black-box nature of typical neural network based models, uncertainty quantification (UQ) is critical to ensure the reliability of predictions as well as the training datasets, and for a principled quantification of noise and its various sources. Deep learning surrogate models for predicting properties of chemical compounds and mixtures have been recently shown to be promising for enabling data-driven fuel design and optimization, with the ultimate goal of improving efficiency and lowering emissions from combustion engines. In this study, UQ is performed for a multi-task deep learning model that simultaneously predicts the research octane number (RON), Motor Octane Number (MON), and Yield Sooting Index (YSI) of pure components and multicomponent blends. The deep learning model is comprised of three smaller networks: Extractor 1, Extractor 2, and Predictor, and a mixing operator. The molecular fingerprints of individual components are encoded via Extractor 1 and Extractor 2, the mixing operator generates fingerprints for mixtures/blends based on linear mixing operation, and the predictor maps the fingerprint to the target properties. Two different classes of UQ methods, Monte Carlo ensemble methods and Bayesian neural networks (BNNs), are employed for quantifying the epistemic uncertainty. Combinations of Bernoulli and Gaussian distributions with DropConnect and DropOut techniques are explored as ensemble methods. All the DropConnect, DropOut and Bayesian layers are applied to the predictor network. Aleatoric uncertainty is modeled by assuming that each data point has an independent uncertainty associated with it. The results of the UQ study are further analyzed to compare the performance of BNN and ensemble methods. Although this study is confined to UQ of fuel property prediction, the methodologies are applicable to other deep learning frameworks that are being widely used in the combustion community.

33 ADVANCED PROPULSION SYSTEMS↗

NASA NTRS1996

Thrust Vectoring on the NASA F-18 High Alpha Research Vehicle

Investigations into a multiaxis thrust-vectoring system have been conducted on an F-18 configuration. These investigations include ground-based scale-model tests, ground-based full-scale testing, and flight testing. This thrust-vectoring system has been tested on the NASA F-18 High Alpha Research Vehicle (HARV). The system provides thrust vectoring in pitch and yaw axes. Ground-based subscale test data have been gathered as background to the flight phase of the program. Tests investigated aerodynamic interaction and vane control effectiveness. The ground-based full-scale data were gathered from static engine runs with image analysis to determine relative thrust-vectoring effectiveness. Flight tests have been conducted at the NASA Dryden Flight Research Center. Parameter identification input techniques have been developed. Individual vanes were not directly controlled because of a mixer-predictor function built into the flight control laws. Combined effects of the vanes have been measured in flight and compared to combined effects of the vanes as predicted by the cold-jet test data. Very good agreement has been found in the linearized effectiveness derivatives.

Bowers, Albion H.↗

NASA NTRS2012

Hardware Implementation of Lossless Adaptive Compression of Data From a Hyperspectral Imager

Efficient onboard data compression can reduce the data volume from hyperspectral imagers on NASA and DoD spacecraft in order to return as much imagery as possible through constrained downlink channels. Lossless compression is important for signature extraction, object recognition, and feature classification capabilities. To provide onboard data compression, a hardware implementation of a lossless hyperspectral compression algorithm was developed using a field programmable gate array (FPGA). The underlying algorithm is the Fast Lossless (FL) compression algorithm reported in Fast Lossless Compression of Multispectral- Image Data (NPO-42517), NASA Tech Briefs, Vol. 30, No. 8 (August 2006), p. 26 with the modification reported in Lossless, Multi-Spectral Data Comressor for Improved Compression for Pushbroom-Type Instruments (NPO-45473), NASA Tech Briefs, Vol. 32, No. 7 (July 2008) p. 63, which provides improved compression performance for data from pushbroom-type imagers. An FPGA implementation of the unmodified FL algorithm was previously developed and reported in Fast and Adaptive Lossless Onboard Hyperspectral Data Compression System (NPO-46867), NASA Tech Briefs, Vol. 36, No. 5 (May 2012) p. 42. The essence of the FL algorithm is adaptive linear predictive compression using the sign algorithm for filter adaption. The FL compressor achieves a combination of low complexity and compression effectiveness that exceeds that of stateof- the-art techniques currently in use. The modification changes the predictor structure to tolerate differences in sensitivity of different detector elements, as occurs in pushbroom-type imagers, which are suitable for spacecraft use. The FPGA implementation offers a low-cost, flexible solution compared to traditional ASIC (application specific integrated circuit) and can be integrated as an intellectual property (IP) for part of, e.g., a design that manages the instrument interface. The FPGA implementation was benchmarked on the Xilinx Virtex IV LX25 device, and ported to a Xilinx prototype board. The current implementation has a critical path of 29.5 ns, which dictated a clock speed of 33 MHz. The critical path delay is end-to-end measurement between the uncompressed input data and the output compression data stream. The implementation compresses one sample every clock cycle, which results in a speed of 33 Msample/s. The implementation has a rather low device use of the Xilinx Virtex IV LX25, making the total power consumption of the implementation about 1.27 W.

Keymeulen, Didlier↗

NASA NTRS1986

Anisotropic constitutive model for nickel base single crystal alloys: Development and finite element implementation

A tool for the mechanical analysis of nickel base single crystal superalloys, specifically Rene N4, used in gas turbine engine components is developed. This is achieved by a rate dependent anisotropic constitutive model implemented in a nonlinear three dimensional finite element code. The constitutive model is developed from metallurigical concepts utilizing a crystallographic approach. A non Schmid's law formulation is used to model the tension/compression asymmetry and orientation dependence in octahedral slip. Schmid's law is a good approximation to the inelastic response of the material in cube slip. The constitutive equations model the tensile behavior, creep response, and strain rate sensitivity of these alloys. Methods for deriving the material constants from standard tests are presented. The finite element implementation utilizes an initial strain method and twenty noded isoparametric solid elements. The ability to model piecewise linear load histories is included in the finite element code. The constitutive equations are accurately and economically integrated using a second order Adams-Moulton predictor-corrector method with a dynamic time incrementing procedure. Computed results from the finite element code are compared with experimental data for tensile, creep and cyclic tests at 760 deg C. The strain rate sensitivity and stress relaxation capabilities of the model are evaluated.

Dame, L. T.↗

NASA NTRS1990

Real-Time Digital Compression Of Television Image Data

Digital encoding/decoding system compresses color television image data in real time for transmission at lower data rates and, consequently, lower bandwidths. Implements predictive coding process, in which each picture element (pixel) predicted from values of prior neighboring pixels, and coded transmission expresses difference between actual and predicted current values. Combines differential pulse-code modulation process with non-linear, nonadaptive predictor, nonuniform quantizer, and multilevel Huffman encoder.

Barnes, Scott P.↗

DOE OSTI2022

Multifidelity Ensemble Kalman Filtering Using Surrogate Models Defined by Theory-Guided Autoencoders

Data assimilation is a Bayesian inference process that obtains an enhanced understanding of a physical system of interest by fusing information from an inexact physics-based model, and from noisy sparse observations of reality. The multifidelity ensemble Kalman filter (MFEnKF) recently developed by the authors combines a full-order physical model and a hierarchy of reduced order surrogate models in order to increase the computational efficiency of data assimilation. The standard MFEnKF uses linear couplings between models, and is statistically optimal in case of Gaussian probability densities. This work extends the MFEnKF into to make use of a broader class of surrogate model such as those based on machine learning methods such as autoencoders non-linear couplings in between the model hierarchies. We identify the right-invertibility property for autoencoders as being a key predictor of success in the forecasting power of autoencoder-based reduced order models. We propose a methodology that allows us to construct reduced order surrogate models that are more accurate than the ones obtained via conventional linear methods. Numerical experiments with the canonical Lorenz'96 model illustrate that nonlinear surrogates perform better than linear projection-based ones in the context of multifidelity ensemble Kalman filtering. We additionality show a large-scale proof-of-concept result with the quasi-geostrophic equations, showing the competitiveness of the method with a traditional reduced order model-based MFEnKF.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1992

Artificial neural network implementation of a near-ideal error prediction controller

A theory has been developed at the University of Virginia which explains the effects of including an ideal predictor in the forward loop of a linear error-sampled system. It has been shown that the presence of this ideal predictor tends to stabilize the class of systems considered. A prediction controller is merely a system which anticipates a signal or part of a signal before it actually occurs. It is understood that an exact prediction controller is physically unrealizable. However, in systems where the input tends to be repetitive or limited, (i.e., not random) near ideal prediction is possible. In order for the controller to act as a stability compensator, the predictor must be designed in a way that allows it to learn the expected error response of the system. In this way, an unstable system will become stable by including the predicted error in the system transfer function. Previous and current prediction controller include pattern recognition developments and fast-time simulation which are applicable to the analysis of linear sampled data type systems. The use of pattern recognition techniques, along with a template matching scheme, has been proposed as one realizable type of near-ideal prediction. Since many, if not most, systems are repeatedly subjected to similar inputs, it was proposed that an adaptive mechanism be used to 'learn' the correct predicted error response. Once the system has learned the response of all the expected inputs, it is necessary only to recognize the type of input with a template matching mechanism and then to use the correct predicted error to drive the system. Suggested here is an alternate approach to the realization of a near-ideal error prediction controller, one designed using Neural Networks. Neural Networks are good at recognizing patterns such as system responses, and the back-propagation architecture makes use of a template matching scheme. In using this type of error prediction, it is assumed that the system error responses be known for a particular input and modeled plant. These responses are used in the error prediction controller. An analysis was done on the general dynamic behavior that results from including a digital error predictor in a control loop and these were compared to those including the near-ideal Neural Network error predictor. This analysis was done for a second and third order system.

Mcvey, Eugene S.↗

DOE OSTI2021

Environmental predictors of pulmonary nontuberculous mycobacteria (NTM) sputum positivity among persons with cystic fibrosis in the state of Florida

Nontuberculous mycobacteria (NTM) are opportunistic human pathogens that are commonly found in soil and water, and exposure to these organisms may cause pulmonary nontuberculous mycobacterial disease. Persons with cystic fibrosis (CF) are at high risk for developing pulmonary NTM infections, and studies have shown that prolonged exposure to certain environments can increase the risk of pulmonary NTM. It is therefore important to determine the risk associated with different geographic areas. Using annualized registry data obtained from the Cystic Fibrosis Foundation Patient Registry for 2010 through 2017, we conducted a geospatial analysis of NTM infections among persons with CF in Florida. A Bernoulli model in SaTScan was used to identify clustering of ZIP codes with higher than expected numbers of NTM culture positive individuals. Generalized linear mixed models with a binomial distribution were used to test the association of environmental variables and NTM culture positivity. We identified a significant cluster of M . abscessus and predictors of NTM sputum positivity, including annual precipitation and soil mineral levels.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2026

Meteoric 10Be Flux Calibration Data for the East River Watershed, Colorado, USA

This data package contains tabular and geospatial data used to quantify and model meteoric beryllium-10 fluxes in the East River watershed, Colorado, USA. The tabular component includes calibration-site data from five glacial moraine sites and includes environmental variables used to evaluate spatial controls on meteoric 10Be delivery, including elevation, mean annual precipitation (MAP), mean snow depth, and mean snow water equivalent (SWE). These site-level data were used to compare observed fluxes with environmental gradients across the watershed and to evaluate the effects of erosion correction on flux estimates. The package also includes supporting slope and curvature values used to assess topographic inputs to the erosion analysis. A second component of the data package contains updated manuscript tables and regression outputs used to summarize the relationships between meteoric 10Be flux and environmental predictors. These tables include meteoric 10Be sample information and AMS results, site-level environmental values, site-level meteoric 10Be inventory and flux values, watershed-averaged predicted fluxes, soil bulk density measurements, fine-fraction values, soil pH measurements, and regression statistics including slope, intercept, coefficient of determination, and p-value. The regression products include both standard linear regressions and regressions in which the intercept is constrained to pass through zero, and they support the analyses presented in the companion manuscript. Together, these tabular files provide the numerical basis for the manuscript tables and the regression-based interpretation of meteoric 10Be flux variability in a snow-dominated mountain watershed. The geospatial component of the package consists of GeoTIFF raster files used to generate the map products presented in Figures 2 and 6 of the companion manuscript. These rasters represent watershed-scale spatial layers for environmental variables and regression-based predictions of meteoric 10Be flux. This dataset contains comma-separated values files (.csv), Microsoft Excel files (.xlsx), GeoTIFF raster files (.tif), and upporting metadata files, including CSV data dictionaries and readme text files (.csv, .txt). The tabular files can be opened with standard spreadsheet software, and the raster files can be viewed and analyzed in GIS software such as ArcGIS Pro or QGIS. Together, these files document the numerical and spatial datasets used to calibrate and predict meteoric 10Be delivery in the East River watershed.

East River↗

DOE OSTI2024

Reduced‐Order Modeling for Linearized Representations of Microphysical Process Rates

Abstract Representing cloud microphysical processes in large scale atmospheric models is challenging because many processes depend on the details of the droplet size distribution (DSD, the spectrum of droplets with different sizes in a cloud). While full or partial statistical moments of droplet size distributions are the typical variables used in bulk models, prognostic moments are limited in their ability to represent microphysical processes across the range of conditions experienced in the atmosphere. Microphysical parameterizations employing prognostic moments are known to suffer from structural uncertainty in their representations of inherently higher dimensional cloud processes, which limit model fidelity and lead to forecasting errors. Here we investigate how data‐driven reduced‐order modeling can be used to learn predictors for microphysical process rates in bulk microphysics schemes in an unsupervised manner from higher dimensional bin distributions. Using simulations characteristic of marine stratiform clouds, we simultaneously learn lower dimensional representations of droplet size distributions and predict the evolution of the microphysical state of the system. Droplet collision‐coalescence, the main process for generating warm rain, is estimated to have an intrinsic dimension of three. This intrinsic dimension provides a lower limit on the number of degrees of freedom needed to accurately represent collision‐coalescence in models. We demonstrate how deep learning based reduced‐order modeling can be used to discover intrinsic coordinates describing the microphysical state of the system, where process rates such as collision‐coalescence are globally linearized. These implicitly learned representations of the DSD retain more information about the DSD than typical moment‐based representations.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2019

Effects of Omitting Non-confounding Predictors From General Relative-Risk Models for Binary Outcomes

The effects, in terms of bias and precision, of omitting non-confounding predictive covariates from generalized linear models have been well studied, and it is known that such omission results in attenuation bias but increased precision with logistic regression. However, many epidemiologic risk analyses utilize alternative models that are not based on a linear predictor, and the effect of omitting non-confounding predictive covariates from such models has not been characterized. We employed simulation to study the effects on risk estimation of omitting non-confounding predictive covariates from an excess relative risk (ERR) model and a general additive-multiplicative relative-risk mixture model for binary outcome data in a case-control setting. We also compared the results to the effects with ordinary logistic regression. For these commonly employed alternative relative-risk models, the bias was similar to that with logistic regression when the risk was small. More generally, the bias and standard error of the risk-parameter estimates demonstrated patterns that are similar to those with logistic regression, but with greater magnitude depending on the true value of the risk. The magnitude of bias and standard error had little relation to study size or underlying disease prevalence. Prior conclusions regarding omitted covariates in logistic regression models can be qualitatively applied to the ERR and the general additive-multiplicative relative-risk mixture model without substantial change. Quantitatively, however, these alternative models may have slightly greater omitted-covariate bias, depending on the magnitude of the true risk being estimated.

60 APPLIED LIFE SCIENCES↗

NASA NTRS1982

Application of Zimmerman flutter-margin criterion to a wind tunnel model

The Zimmerman flutter margin criterion was studied by applying it to data obtained from a wind tunnel model. The sensitivity of the flutter margin parameter was explored with a parametric trend study and by calculation of the derivatives with respect to the input frequency and damping parameters. The criterion is simple in concept and application, and it serves as a good flutter onset predictor because it gives a nearly linear variation with dynamic pressure. However, accurate values of both frequency and damping of both modes involved in flutter are required for reliable flutter onset prediction. The simplified version using only frequencies gave a highly nonconservative flutter onset in one case and should not be used in general.

Bennett, R. M.↗