Search NASA⌕ Search

SEARCH · Search NASA

Results for “ITERATIVE NETWORK”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Application of multigrid methods to the solution of liquid crystal equations on a SIMD computer

We will describe a finite difference code for computing the equilibrium configurations of the order-parameter tensor field for nematic liquid crystals in rectangular regions by minimization of the Landau-de Gennes Free Energy functional. The implementation of the free energy functional described here includes magnetic fields, quadratic gradient terms, and scalar bulk terms through the fourth order. Boundary conditions include the effects of strong surface anchoring. The target architectures for our implementation are SIMD machines, with interconnection networks which can be configured as 2 or 3 dimensional grids, such as the Wavetracer DTC. We also discuss the relative efficiency of a number of iterative methods for the solution of the linear systems arising from this discretization on such architectures.

Farrell, Paul A.↗
DOE OSTI2024

Super Resolving Unrolled Neural Networks for Remote Sensing

In remote sensing systems, the capabilities of the system are constrained by the complex interactions between size, weight, and power (SWAP) of potential designs. In electro-optical (EO) systems, examples of these critical parameters include the system’s sensitivity and resolution. Those parameters can be increased by ever larger optical apertures and focal planes but at the cost of more SWAP. Multi-image super resolution (MISR) techniques allow resolution to be enhanced via computation rather than more sophisticated optical hardware. These algorithms combine multiple images together into a single, higher resolution image, trading temporal resolution and computation for spatial resolution. Fielded MISR techniques, such as Drizzle, can require several hundred images to create a single super resolved image, implying reduced temporal resolution, increased data acquisition load, and limiting mission applications. Iterative techniques, such as model-based image reconstruction and compressive sensing, have been shown to create super resolved images using fewer images than Drizzle. They do this by posing an optimization problem that balances accuracy between a highly accurate physical model and an image model. In the case of super resolution, the physical model is defined by the relation between low resolution input images and the desired high resolution output image. The image model encodes some assumptions about the super resolved image. These assumptions are meant to suppress reconstruction artifacts that arise due to deterministic physical model error, stochastic measurement noise, and potential undersampling. In practice, the performance of iterative methods are limited by imaging models compatible with optimization. Deep learning-based methods can effectively learn image models of arbitrary complexity, but lack the theoretical explainability and robustness of iterative techniques. Consensus equilibrium (CE) generalizes the iterative techniques beyond optimization, enabling blackbox algorithms such as traditional and neural image denoisers to be used as the image model. CE-based approaches retain much of the explainability and robustness of iterative techniques while allowing the expressiveness of machine learning image models to be used. Additionally, by unrolling iterations of CE with an embedded image denoiser, the image denoiser can be further trained and specialized to the specific application with potentially higher quality reconstructions. Under this project, we demonstrated the feasibility of training an unrolled neural network based upon CE. While we didn’t train one, we showed that the CE process is differentiable and its gradient can be tractably computed. We also explored the usage of a variants of CE akin to generative neural works. Most importantly, we applied the CE framework to a number of problems including non-blind deconvolution, upsampling, single-image super resolution, MISR, event-based sensing, and saturated deconvolution. Our MISR prototype creates high quality reconstructions with an order of magnitude fewer images than previous approaches and, critically, produces these reconstructions fast enough for practical usage.

47 OTHER INSTRUMENTATION↗
NASA NTRS2022

A Novel Atmospheric Correction Algorithm to Exploit the Diurnal Variability in Hypertemporal Geostationary Observations

This study developed a new atmospheric correction algorithm, GeoNEX-AC, that is independent from the traditional use of spectral band ratios but dedicated to exploiting information from the diurnal variability in the hypertemporal geostationary observations. The algorithm starts by evaluating smooth segments of the diurnal time series of the top-of-atmosphere (TOA) reflectance to identify clear-sky and snow-free observations. It then attempts to retrieve the Ross-Thick–Li-Sparse (RTLS) surface bi-directional reflectance distribution function (BRDF) parameters and the daily mean atmospheric optical depth (AOD) with an atmospheric radiative transfer model (RTM) to optimally simulate the observed diurnal variability in the clear-sky TOA reflectance. Once the initial RTLS parameters are retrieved after the algorithm’s burn-in period, they serve as the prior information to estimate the AOD levels for the following days and update the surface BRDF information with the new clear-sky observations. This process is iterated through the full time span of the observations, skipping only totally cloudy days or when surface snow is detected. We tested the algorithm over various Aerosol Robotic Network (AERONET) sites and the retrieved results well agree with the ground-based measurements. This study demonstrates that the high-frequency diurnal geostationary observations contain unique information that can help to address the atmospheric correction problem from new directions.

atmospheric correction↗
NASA NTRS1986

An optimization model for the US Air-Traffic System

A systematic approach for monitoring U.S. air traffic was developed in the context of system-wide planning and control. Towards this end, a network optimization model with nonlinear objectives was chosen as the central element in the planning/control system. The network representation was selected because: (1) it provides a comprehensive structure for depicting essential aspects of the air traffic system, (2) it can be solved efficiently for large scale problems, and (3) the design can be easily communicated to non-technical users through computer graphics. Briefly, the network planning models consider the flow of traffic through a graph as the basic structure. Nodes depict locations and time periods for either individual planes or for aggregated groups of airplanes. Arcs define variables as actual airplanes flying through space or as delays across time periods. As such, a special case of the network can be used to model the so called flow control problem. Due to the large number of interacting variables and the difficulty in subdividing the problem into relatively independent subproblems, an integrated model was designed which will depict the entire high level (above 29000 feet) jet route system for the 48 contiguous states in the U.S. As a first step in demonstrating the concept's feasibility a nonlinear risk/cost model was developed for the Indianapolis Airspace. The nonlinear network program --NLPNETG-- was employed in solving the resulting test cases. This optimization program uses the Truncated-Newton method (quadratic approximation) for determining the search direction at each iteration in the nonlinear algorithm. It was shown that aircraft could be re-routed in an optimal fashion whenever traffic congestion increased beyond an acceptable level, as measured by the nonlinear risk function.

Mulvey, J. M.↗
NASA NTRS1986

On the structure of parallelism in a highly concurrent PDE solver

A parallel multigrid algorithm for solving elliptic partial differential equations is developed and evaluated. A V-cycle multigrid method is altered to increase the degree of parallelism. A numerical analysis of the resulting concurrent-iteration multigrid algorithm is performed; its architectural implications are considered; highly parallel systems without shared memory are examined (including mesh-connected arrays, mesh-shuffle-connected systems, permutation networks, and direct VLSI embeddings); and the results of numerical experiments are presented in tables and graphs.

Gannon, D.↗
NASA NTRS2018

Deep Neural Network for Precision Multi-band Infrared Image Segmentation

Image segmentation is one of the fundamental steps in computer vision. Separating targets from background clutter with high precision is a challenging operation for both humans and computers. Currently, segmenting objects from IR images is done by tedious manual work. The implementation of a Deep Neural Network (DNN) to perform precision segmentation of multi-band IR video images is presented. A customized pix2pix DNN with multiple layers of generative encoder/decoder and discriminator architecture is used in the IR image segmentation process. Real and synthetic images and ground truths are employed to train the DNN. Iterative training is performed to achieve optimum accuracy of segmentation using a minimal number of training data. Special training images are created to enhance the missing features and to increase the segmentation accuracy of the objects. Retraining strategies are developed to minimize the DNN training time. Single pixel accuracy has been achieved in IR target boundary segmentation using DNNs. The segmentation accuracy between the customized pix2pix DNN and simple thresholding, GraphCut, simple neural network and ResNet models are compared.

Torres, Gil↗
NASA NTRS2004

Subsonic Aircraft With Regression and Neural-Network Approximators Designed

At the NASA Glenn Research Center, NASA Langley Research Center's Flight Optimization System (FLOPS) and the design optimization testbed COMETBOARDS with regression and neural-network-analysis approximators have been coupled to obtain a preliminary aircraft design methodology. For a subsonic aircraft, the optimal design, that is the airframe-engine combination, is obtained by the simulation. The aircraft is powered by two high-bypass-ratio engines with a nominal thrust of about 35,000 lbf. It is to carry 150 passengers at a cruise speed of Mach 0.8 over a range of 3000 n mi and to operate on a 6000-ft runway. The aircraft design utilized a neural network and a regression-approximations-based analysis tool, along with a multioptimizer cascade algorithm that uses sequential linear programming, sequential quadratic programming, the method of feasible directions, and then sequential quadratic programming again. Optimal aircraft weight versus the number of design iterations is shown. The central processing unit (CPU) time to solution is given. It is shown that the regression-method-based analyzer exhibited a smoother convergence pattern than the FLOPS code. The optimum weight obtained by the approximation technique and the FLOPS code differed by 1.3 percent. Prediction by the approximation technique exhibited no error for the aircraft wing area and turbine entry temperature, whereas it was within 2 percent for most other parameters. Cascade strategy was required by FLOPS as well as the approximators. The regression method had a tendency to hug the data points, whereas the neural network exhibited a propensity to follow a mean path. The performance of the neural network and regression methods was considered adequate. It was at about the same level for small, standard, and large models with redundancy ratios (defined as the number of input-output pairs to the number of unknown coefficients) of 14, 28, and 57, respectively. In an SGI octane workstation (Silicon Graphics, Inc., Mountainview, CA), the regression training required a fraction of a CPU second, whereas neural network training was between 1 and 9 min, as given. For a single analysis cycle, the 3-sec CPU time required by the FLOPS code was reduced to milliseconds by the approximators. For design calculations, the time with the FLOPS code was 34 min. It was reduced to 2 sec with the regression method and to 4 min by the neural network technique. The performance of the regression and neural network methods was found to be satisfactory for the analysis and design optimization of the subsonic aircraft.

Patnaik, Surya N.↗
NASA NTRS2006

Dynamics and Adaptive Control for Stability Recovery of Damaged Aircraft

This paper presents a recent study of a damaged generic transport model as part of a NASA research project to investigate adaptive control methods for stability recovery of damaged aircraft operating in off-nominal flight conditions under damage and or failures. Aerodynamic modeling of damage effects is performed using an aerodynamic code to assess changes in the stability and control derivatives of a generic transport aircraft. Certain types of damage such as damage to one of the wings or horizontal stabilizers can cause the aircraft to become asymmetric, thus resulting in a coupling between the longitudinal and lateral motions. Flight dynamics for a general asymmetric aircraft is derived to account for changes in the center of gravity that can compromise the stability of the damaged aircraft. An iterative trim analysis for the translational motion is developed to refine the trim procedure by accounting for the effects of the control surface deflection. A hybrid direct-indirect neural network, adaptive flight control is proposed as an adaptive law for stabilizing the rotational motion of the damaged aircraft. The indirect adaptation is designed to estimate the plant dynamics of the damaged aircraft in conjunction with the direct adaptation that computes the control augmentation. Two approaches are presented 1) an adaptive law derived from the Lyapunov stability theory to ensure that the signals are bounded, and 2) a recursive least-square method for parameter identification. A hardware-in-the-loop simulation is conducted and demonstrates the effectiveness of the direct neural network adaptive flight control in the stability recovery of the damaged aircraft. A preliminary simulation of the hybrid adaptive flight control has been performed and initial data have shown the effectiveness of the proposed hybrid approach. Future work will include further investigations and high-fidelity simulations of the proposed hybrid adaptive Bight control approach.

Nguyen, Nhan↗
DOE OSTI2025

Neural network-based classification and regression of magnetohydrodynamic modes in tokamaks

We present a machine learning-based magnetohydrodynamic (MHD) classifier and regressor that utilizes real or complex-valued 3D magnetic sensor array data to determine neoclassical tearing mode (NTM) onset times in tokamaks with millisecond accuracy. The input dataset consists of poloidal profiles of complex Fourier amplitudes with an n = 1 toroidal mode number from 144 human-labeled ITER Baseline Scenario discharges in the DIII-D tokamak, spanning both tearing-dominated and sawtooth-dominated regimes. Since m, n = 2,1 NTMs frequently emerge alongside sawteeth at the same frequency in this scenario, the focus is on isolating the m = 1 and m = 2 components of the n = 1 MHD mode near the tearing onset. To improve model regularization and prediction stability, singular value decomposition was applied to balance the sawtooth and tearing datasets. The enriched datasets facilitated training neural networks that learn the key distinguishing features of sawtooth and tearing modes in the poloidal profiles of their magnetic amplitude and phase. When the modes occur independently, the networks achieve perfect classification due to the modes’ distinct characteristics and low measurement noise. In the more experimentally relevant case where both modes coexist, the networks maintain exceptional performance across key metrics. Tests on synthetic data with known ground truth demonstrate the superior accuracy of the neural network trained on complex-valued input compared to models using real amplitude, phase, or pseudo-complex data, achieving both a mean time delay and standard deviation below 1 ms. Notably, standard linear regression methods fitting the dominant singular modes to the data closely match the neural network’s performance. Applying these methods across a broad range of H-mode scenarios will enable future studies to systematically identify dominant NTM triggers as scenario-specific variables, paving the way for more effective tearing mode avoidance strategies in future fusion reactor designs.

machine learning↗
DOE OSTI2025

From disorganized data to emergent dynamic models: Questionnaires to partial differential equations

Starting with sets of disorganized observations of spatially varying and temporally evolving systems, obtained at different (also disorganized) sets of parameters, we demonstrate the data-driven derivation of parameter dependent, evolutionary partial differential equation (PDE) models capable of generating the data. This tensor type of data is reminiscent of shuffled (multidimensional) puzzle tiles. The independent variables for the evolution equations (their “space” and “time”) as well as their effective parameters are all emergent , i.e. determined in a data-driven way from our disorganized observations of behavior in them. We use a diffusion map based questionnaire approach to build a smooth parametrization of our emergent space/time/parameter space for the data. This approach iteratively processes the data by successively observing them on the “space,” the “time” and the “parameter” axes of a tensor. Once the data become organized, we use machine learning (here, neural networks) to approximate the operators governing the evolution equations in this emergent space. Our illustrative examples are based (i) on a simple advection–diffusion model; (ii) on a previously developed vertex-plus-signaling model of Drosophila embryonic development; and (iii) on two complex dynamic network models (one neuronal and one coupled oscillator model) for which no obvious smooth embedding geometry is known a priori. This allows us to discuss features of the process like symmetry breaking, translational invariance, and autonomousness of the emergent PDE model, as well as its interpretability.

generative models↗
NASA NTRS1999

Time-of-Arrival Lightning Location Retrieval Using an Oblate Spheroidal Earth Model

The problem of retrieving lightning ground strike location on an oblate spheroidal Earth using a network of 4 or more time-of-arrival sensors is considered. A recently developed analytic method for obtaining such retrievals on a spherical Earth surface is perturbed resulting in an iterative procedure to get correction terms. The perturbation procedure consists of applying a vector Newton's method to eqs. relating the distances from the lightning location to each sensor along a geodesic and the times of arrival of the wave produced by the lightning source at each sensor.

Solakiewicz, Richard↗
DOE OSTI2024

Multi deep learning-based stochastic microstructure reconstruction and high-fidelity micromechanics simulation of time-dependent ceramic matrix composite response

A multi deep learning-based framework is developed for efficient, automated microstructure reconstruction and generation of stochastic representative volume elements (SRVEs) with periodic boundary conditions (PBCs) for accurate modeling of ceramic matrix composite (CMC) response. The methodology comprises a convolutional neural network coupled with regression layers to act as a vanilla regression network for semantic segmentation of the microstructure, allowing accurate characterization of the phases and their distributions at the microscale. Scanning electron microscope and confocal microscope are used to obtain C/SiNC and SiC/SiNC CMCs micrographs for vanilla regression testing. Microstructure variability in terms of fiber volume fraction and porosity are quantified through the output regression layer, ensuring accurate representation of material variability in SRVE construction. Generative adversarial network (GAN) and its variants are designed to produce high-fidelity SRVE, spanning CMCs microstructure variability space. A circular padding algorithm is developed to generate SRVEs with PBCs during training of GANs. The accuracy of the generated SRVEs is established through micromechanics simulations, where an efficient formulation of the high-fidelity generalized methods of cells (HFGMC) approach is used to compute the effective mechanical properties. Furthermore, an iterative algorithm is implemented in the HFGMC solver to simulate time-dependent deformation of SiC/SiNC subjected to creep loading conditions.

36 MATERIALS SCIENCE↗
NASA NTRS1992

GRAPEVINE: Grids about anything by Poisson's equation in a visually interactive networking environment

A proven 3-D multiple-block elliptic grid generator, designed to run in 'batch mode' on a supercomputer, is improved by the creation of a modern graphical user interface (GUI) running on a workstation. The two parts are connected in real time by a network. The resultant system offers a significant speedup in the process of preparing and formatting input data and the ability to watch the grid solution converge by replotting the grid at each iteration step. The result is a reduction in user time and CPU time required to generate the grid and an enhanced understanding of the elliptic solution process. This software system, called GRAPEVINE, is described, and certain observations are made concerning the creation of such software.

Sorenson, Reese L.↗
NASA NTRSDate not supplied

Leveraging the Multiplatform Precipitation Feature Database of Combined Ground Radar and Satellite Lightning Observations for Convective Studies

The Multiplatform Precipitation Feature (MPF) database combines coincident observations of lightning from space with satellite- and ground-based radar data in a storm-based, feature-defined framework. The concept for the MPF database stems from the motivation to extend the scale and scope of investigations into the complex connections between ice precipitation, updrafts, and lightning in thunderstorms. The earliest iteration of the MPF database incorporates NASA International Space Station Lightning Imaging Sensor (ISS LIS) observations alongside the NASA Global Precipitation Measurement (GPM) Mission Dual-frequency Precipitation Radar (DPR) and Validation Network (VN). Because of the specific role of the GPM VN in forming the first MPFs, this subset is referred to as the VNMPF database. The synthesis of these multi-scale and multi-resolution observations leveraged each platform’s unique insights into convective properties and processes, offering a more complete view of deep convection over the large viewing area afforded by satellite coverage. The VNMPF database established the feasibility and infrastructure to combine microphysical, kinematic, and lightning observations from multiple satellite- and ground-based platforms. Following this successful proof-of-concept, recent progress has expanded the MPF database to make use of coincident ISS LIS lightning observations and data from the operational Weather Surveillance Radar - 1988 Doppler (WSR-88D) network, where individual WSR-88D proximity facilitates vertical wind retrievals via dual-Doppler analysis. These database changes have expanded the scope of the dataset by removing the requirement for coincident GPM and ISS LIS overpasses. This increases the sample size dramatically and facilitates analysis of higher-resolution radar-derived properties. These advancements allow both storm-scale and unprecedented broad statistical analyses of deep convection from electrical, kinematic, and microphysical perspectives over the contiguous United States. This presentation outlines the construction of the new MPF database and introduces some preliminary analyses of the convection captured within it. Early results summarize relationships based on updraft characteristics ascertained from WSR-88D dual-Doppler three-dimensional wind retrievals, properties of ice microphysics gleaned from dual-polarization analyses, and electrical characteristics observed by the ISS LIS. The expanded scale and scope offered by more than five years of ISS LIS observations enable new insights into regional and seasonal variations in the microphysical, kinematic, and electrical relationships of convection. Analysis of the database highlights the potential for advancements in lightning meteorology made possible by combining large-scale spaceborne lightning detection and proven storm interrogation tools such as operational polarimetric Doppler radar.

Lightning↗
NASA NTRS1995

Locomotion training of legged robots using hybrid machine learning techniques

In this study artificial neural networks and fuzzy logic are used to control the jumping behavior of a three-link uniped robot. The biped locomotion control problem is an increment of the uniped locomotion control. Study of legged locomotion dynamics indicates that a hierarchical controller is required to control the behavior of a legged robot. A structured control strategy is suggested which includes navigator, motion planner, biped coordinator and uniped controllers. A three-link uniped robot simulation is developed to be used as the plant. Neurocontrollers were trained both online and offline. In the case of on-line training, a reinforcement learning technique was used to train the neurocontroller to make the robot jump to a specified height. After several hundred iterations of training, the plant output achieved an accuracy of 7.4%. However, when jump distance and body angular momentum were also included in the control objectives, training time became impractically long. In the case of off-line training, a three-layered backpropagation (BP) network was first used with three inputs, three outputs and 15 to 40 hidden nodes. Pre-generated data were presented to the network with a learning rate as low as 0.003 in order to reach convergence. The low learning rate required for convergence resulted in a very slow training process which took weeks to learn 460 examples. After training, performance of the neurocontroller was rather poor. Consequently, the BP network was replaced by a Cerebeller Model Articulation Controller (CMAC) network. Subsequent experiments described in this document show that the CMAC network is more suitable to the solution of uniped locomotion control problems in terms of both learning efficiency and performance. A new approach is introduced in this report, viz., a self-organizing multiagent cerebeller model for fuzzy-neural control of uniped locomotion is suggested to improve training efficiency. This is currently being evaluated for a possible patent by NASA, Johnson Space Center. An alternative modular approach is also developed which uses separate controllers for each stage of the running stride. A self-organizing fuzzy-neural controller controls the height, distance and angular momentum of the stride. A CMAC-based controller controls the movement of the leg from the time the foot leaves the ground to the time of landing. Because the leg joints are controlled at each time step during flight, movement is smooth and obstacles can be avoided. Initial results indicate that this approach can yield fast, accurate results.

Simon, William E.↗
DOE OSTI2025

Efficient Training of Deep Neural Operator Networks via Randomized Sampling

Neural operators (NOs) employ deep neural networks to learn the mappings between infinitedimensional function spaces. Deep operator network (DeepONet), a popular NO architecture, has demonstrated success in the real-time prediction of complex dynamics across various scientific and engineering applications. In this work, we introduce a random sampling technique to be adopted during the training of DeepONet, aimed at improving the generalization ability of the model, while significantly reducing the computational time. The proposed approach targets the trunk network of the DeepONet model that outputs the basis functions corresponding to the spatiotemporal locations of the bounded domain on which the physical system is defined. While constructing the loss function, DeepONet training traditionally considers a uniform grid of spatiotemporal points at which all the output functions are evaluated for each iteration. This approach leads to a larger batch size, resulting in poor generalization and increased memory demands, due to the limitations of the stochastic gradient descent (SGD) optimizer. The proposed random sampling over the inputs of the trunk net mitigates these challenges, improving generalization and reducing the memory requirements during training, resulting in significant computational gains. We validate our hypothesis through three benchmark examples, demonstrating substantial reductions in training time while achieving comparable or lower overall test errors relative to the traditional training approach. Our results indicate that incorporating randomization in the trunk network inputs during training enhances the efficiency and robustness of DeepONet, offering a promising avenue for improving the framework’s performance in modeling complex physical systems.

Karumuri, Sharmila [Department of Civil & Systems ↗
NASA NTRS1987

Simulated annealing in networks for computing possible arrangements for red and green cones

Attention is given to network models in which each of the cones of the retina is given a provisional color at random, and then the cones are allowed to determine the colors of their neighbors through an iterative process. A symmetric-structure spin-glass model has allowed arrays to be generated from completely random arrangements of red and green to arrays with approximately as much disorder as the parafoveal cones. Simulated annealing has also been added to the process in an attempt to generate color arrangements with greater regularity and hence more revealing moirepatterns than than the arrangements yielded by quenched spin-glass processes. Attention is given to the perceptual implications of these results.

Ahumada, Albert J., Jr.↗
NASA NTRS2013

Assessment of Ice Shape Roughness Using a Self-Orgainizing Map Approach

Self-organizing maps are neural-network techniques for representing noisy, multidimensional data aligned along a lower-dimensional and nonlinear manifold. For a large set of noisy data, each element of a finite set of codebook vectors is iteratively moved in the direction of the data closest to the winner codebook vector. Through successive iterations, the codebook vectors begin to align with the trends of the higher-dimensional data. Prior investigations of ice shapes have focused on using self-organizing maps to characterize mean ice forms. The Icing Research Branch has recently acquired a high resolution three dimensional scanner system capable of resolving ice shape surface roughness. A method is presented for the evaluation of surface roughness variations using high-resolution surface scans based on a self-organizing map representation of the mean ice shape. The new method is demonstrated for 1) an 18-in. NACA 23012 airfoil 2 AOA just after the initial ice coverage of the leading 5 of the suction surface of the airfoil, 2) a 21-in. NACA 0012 at 0AOA following coverage of the leading 10 of the airfoil surface, and 3) a cold-soaked 21-in.NACA 0012 airfoil without ice. The SOM method resulted in descriptions of the statistical coverage limits and a quantitative representation of early stages of ice roughness formation on the airfoils. Limitations of the SOM method are explored, and the uncertainty limits of the method are investigated using the non-iced NACA 0012 airfoil measurements.

Icing↗