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At least 343 records · Page 19

Diurnal Variability of Vertical Structure from a TRMM Passive Microwave "Virtual Radar" Retrieval

Robust description of the diurnal cycle from TRMM observations is complicated by the limitations of Low Earth Orbit (LEO) sampling; from a 'climatological' perspective, sufficient sampling must exist to control for both spatial and seasonal variability, before tackling an additional diurnal component (e.g., with 8 additional 3-hourly or 24 1-hourly bins). For documentation of vertical structure, the narrow sample swath of the TRMM Precipitation Radar limits the resolution of any of these components. A neural-network based 'virtual radar" retrieval has been trained and internally validated, using multifrequency / multipolarization passive microwave(TM1) brightness temperatures and textures parameters and lightning (LIS) observations, as inputs, and PR volumetric reflectivity as targets (outputs). By training the algorithms (essentially highly multivariate, nonlinear regressions) on a very large sample of high-quality co-located data from the center of the TRMM swath, 3D radar reflectivity and derived parameters (VIL, IWC, Echo Tops, etc.) can be retrieved across the entire TMI swath, good to 8-9% over the dynamic range of parameters. As a step in the retrieval (and as an output of the process), each TMI multifrequency pixel (at 85 GHz resolution) is classified into one of the 25 archetypal radar profile vertical structure "types", previously identified using cluster analysis. The dynamic range of retrieved vertical structure appears to have higher fidelity than the current (Version 6) experimental GPROF hydrometeor vertical structure retrievals. This is attributable to correct representation of the prior probabilities of vertical structure variability in the neural network training data, unlike the GPROF cloud-resolving model training dataset used in the V6 algorithms. The LIS lightning inputs are supplementary inputs, and a separate offline neural network has been trained to impute (predict) LIS lightning from passive-microwave-only data. The virtual radar retrieval is thus, in principle, extensible to Aqua/AMSR-E and NPOESS/CMIS passive microwave instruments. The virtual radar approach yields a threefold increase in effective sampling from the mission, albeit of lower-quality "retrieved" data, reducing the variance of local estimates by one third (or the standard deviation by-0.57). In this talk, the variance reduction is leveraged to more finely resolve global diurnal variability in both space and time (local hour).

Boccippio, Dennis J.↗

Cascade Optimization for Aircraft Engines With Regression and Neural Network Analysis - Approximators

The NASA Engine Performance Program (NEPP) can configure and analyze almost any type of gas turbine engine that can be generated through the interconnection of a set of standard physical components. In addition, the code can optimize engine performance by changing adjustable variables under a set of constraints. However, for engine cycle problems at certain operating points, the NEPP code can encounter difficulties: nonconvergence in the currently implemented Powell's optimization algorithm and deficiencies in the Newton-Raphson solver during engine balancing. A project was undertaken to correct these deficiencies. Nonconvergence was avoided through a cascade optimization strategy, and deficiencies associated with engine balancing were eliminated through neural network and linear regression methods. An approximation-interspersed cascade strategy was used to optimize the engine's operation over its flight envelope. Replacement of Powell's algorithm by the cascade strategy improved the optimization segment of the NEPP code. The performance of the linear regression and neural network methods as alternative engine analyzers was found to be satisfactory. This report considers two examples-a supersonic mixed-flow turbofan engine and a subsonic waverotor-topped engine-to illustrate the results, and it discusses insights gained from the improved version of the NEPP code.

Patnaik, Surya N.↗

Lost in space: Onboard star identification using CCD star tracker data without an a priori attitude

There are many algorithms in use today which determine spacecraft attitude by identifying stars in the field of view of a star tracker. Some methods, which date from the early 1960's, compare the angular separation between observed stars with a small catalog. In the last 10 years, several methods have been developed which speed up the process and reduce the amount of memory needed, a key element to onboard attitude determination. However, each of these methods require some a priori knowledge of the spacecraft attitude. Although the Sun and magnetic field generally provide the necessary coarse attitude information, there are occasions when a spacecraft could get lost when it is not prudent to wait for sunlight. Also, the possibility of efficient attitude determination using only the highly accurate CCD star tracker could lead to fully autonomous spacecraft attitude determination. The need for redundant coarse sensors could thus be eliminated at substantial cost reduction. Some groups have extended their algorithms to implement a computation intense full sky scan. Some require large data bases. Both storage and speed are concerns for autonomous onboard systems. Neural network technology is even being explored by some as a possible solution, but because of the limited number of patterns that can be stored and large overhead, nothing concrete has resulted from these efforts. This paper presents an algorithm which, by descretizing the sky and filtering by visual magnitude of the brightness observed star, speeds up the lost in space star identification process while reducing the amount of necessary onboard computer storage compared to existing techniques.

Ketchum, Eleanor A.↗

Application of Machine Learning Techniques in Calibration and Data Reduction of Multi-Hole Probes

This work presents procedures to implement machine learning methods in the existing algorithms for multi-hole probe calibrations and data reduction. It is shown here, that utilizing artificial neural networks (ANNs) can reduce the amount of calibration data that needs to be acquired in order to obtain a specific calibration uncertainty, by more than 50% while simultaneously reducing data reduction times significantly. ANNs were used instead of the surface fitting methods, where first, the directional calibration coefficients related to the flow angles are calculated based on the pressure measurements, and then the flow angles are used as a set of the input parameters for the following ANNs to define Mach number and static and total pressure iteratively. In a second approach, novel calibration coefficients were used to directly relate the pressure measurements from five-hole probe to the quantities of interest thus, eliminating the need for iterative algorithms used in the conventional surface fitting methods. The advantageous features of this method are an average increase of less than 1% in the calibration uncertainty for flow angles and significant reduction of the data reduction times (few seconds). In addition, we confirmed the methodology to avoid over-fitting and under-fitting.

Machine Learning↗

Optical fiber sensors for damage analysis in aerospace materials

Under this grant, fiber optic sensors were investigated for use in the nondestructive evaluation of aging aircraft. Specifically, optical fiber sensors for detection and location of impacts on a surface, and for detection of corrosion in metals were developed. The use of neural networks was investigated for determining impact location by processing the output of a network of fiberoptic strain sensors distributed on a surface. This approach employs triangulation to determine location by comparing the arrival times at several sensors, of the acoustic signal generated by the impact. For this study, a neural network simulator running on a personal computer was used to train a network using a back-propagation algorithm. Fiber optic extrinsic Fabry-Perot interferometer (EFPI) strain sensors are attached to or embedded in the surface, so that stress waves emanating from an impact can be detected. The ability of the network to determine impact location by time-or-arrival of acoustic signals was assessed by comparing network outputs with actual experimental results using impacts on a panel instrumented with optical fiber sensors. Using the neural network to process the sensor outputs, the impact location can be inferred to centimeter range accuracy directly from the arrival time data. In addition, the network can be trained to determine impact location, regardless of material anisotropy. Results demonstrate that a back-propagation network identifies impact location for an anisotropic graphite/bismaleimide plate with the same accuracy as that for an isotropic aluminum plate. Two different approaches were investigated for the development of fiber optic sensors for corrosion detection in metals, both utilizing optical fiber sensors with metal coatings. In the first approach, an extrinsic Fabry-Perot interferometric fiber optic strain sensor was placed under tensile stress, and while in the resulting strained position, a thick coating of metal was applied. Due to an increase in the quantity of material, the sensor does not return to its original position upon removal of the applied stress, and some residual strain is maintained within the sensor element. As the metal thickness decreases due to corrosion, this strain is released, providing the sensing mechanism for corrosion detection. In the second approach, photosensitive optical fibers with long period Bragg gratings in the core were coated with metal. The Bragg gratings serve to couple core modes at discrete wavelengths to cladding modes. Since cladding modes interact with the metal coating surrounding the fiber cladding, the specific wavelengths coupled from core to cladding depend on the refractive index of the metal coating. Therefore, as the metal corrodes, the resulting change in index of the coating may be measured by measuring the change in wavelength of the coupled mode. Results demonstrate that both approaches can be successfully used to track the loss in metal coating on the optical fiber sensors due to corrosion.

Schindler, Paul↗

Proceedings of the Second Joint Technology Workshop on Neural Networks and Fuzzy Logic, volume 1

Documented here are papers presented at the Neural Networks and Fuzzy Logic Workshop sponsored by NASA and the University of Houston, Clear Lake. The workshop was held April 11 to 13 at the Johnson Space Flight Center. Technical topics addressed included adaptive systems, learning algorithms, network architectures, vision, robotics, neurobiological connections, speech recognition and synthesis, fuzzy set theory and application, control and dynamics processing, space applications, fuzzy logic and neural network computers, approximate reasoning, and multiobject decision making.

Lea, Robert N.↗

Introduction to a system for implementing neural net connections on SIMD architectures

Neural networks have attracted much interest recently, and using parallel architectures to simulate neural networks is a natural and necessary application. The SIMD model of parallel computation is chosen, because systems of this type can be built with large numbers of processing elements. However, such systems are not naturally suited to generalized communication. A method is proposed that allows an implementation of neural network connections on massively parallel SIMD architectures. The key to this system is an algorithm permitting the formation of arbitrary connections between the neurons. A feature is the ability to add new connections quickly. It also has error recovery ability and is robust over a variety of network topologies. Simulations of the general connection system, and its implementation on the Connection Machine, indicate that the time and space requirements are proportional to the product of the average number of connections per neuron and the diameter of the interconnection network.

Tomboulian, Sherryl↗

Introduction to a system for implementing neural net connections on SIMD architectures

Neural networks have attracted much interest recently, and using parallel architectures to simulate neural networks is a natural and necessary application. The SIMD model of parallel computation is chosen, because systems of this type can be built with large numbers of processing elements. However, such systems are not naturally suited to generalized elements. A method is proposed that allows an implementation of neural network connections on massively parallel SIMD architectures. The key to this system is an algorithm permitting the formation of arbitrary connections between the neurons. A feature is the ability to add new connections quickly. It also has error recovery ability and is robust over a variety of network topologies. Simulations of the general connection system, and its implementation on the Connection Machine, indicate that the time and space requirements are proportional to the product of the average number of connections per neuron and the diameter of the interconnection network.

Tomboulian, Sherryl↗

Neural Network Prediction of Failure of Damaged Composite Pressure Vessels from Strain Field Data Acquired by a Computer Vision Method

This effort used a new and novel method of acquiring strains called Sub-pixel Digital Video Image Correlation (SDVIC) on impact damaged Kevlar/epoxy filament wound pressure vessels during a proof test. To predict the burst pressure, the hoop strain field distribution around the impact location from three vessels was used to train a neural network. The network was then tested on additional pressure vessels. Several variations on the network were tried. The best results were obtained using a single hidden layer. SDVIC is a fill-field non-contact computer vision technique which provides in-plane deformation and strain data over a load differential. This method was used to determine hoop and axial displacements, hoop and axial linear strains, the in-plane shear strains and rotations in the regions surrounding impact sites in filament wound pressure vessels (FWPV) during proof loading by internal pressurization. The relationship between these deformation measurement values and the remaining life of the pressure vessels, however, requires a complex theoretical model or numerical simulation. Both of these techniques are time consuming and complicated. Previous results using neural network methods had been successful in predicting the burst pressure for graphite/epoxy pressure vessels based upon acoustic emission (AE) measurements in similar tests. The neural network associates the character of the AE amplitude distribution, which depends upon the extent of impact damage, with the burst pressure. Similarly, higher amounts of impact damage are theorized to cause a higher amount of strain concentration in the damage effected zone at a given pressure and result in lower burst pressures. This relationship suggests that a neural network might be able to find an empirical relationship between the SDVIC strain field data and the burst pressure, analogous to the AE method, with greater speed and simplicity than theoretical or finite element modeling. The process of testing SDVIC neural network analysis and some encouraging preliminary results are presented in this paper. Details are given concerning the processing of SDVIC output data such that it may be used as back propagation neural network (BPNN) input data. The software written to perform this processing and the BPNN algorithm are also discussed. It will be shown that, with limited training, test results indicate an average error in burst pressure prediction of approximately six percent,

Russell, Samuel S.↗

Comparison of polynomial approximations and artificial neural nets for response surfaces in engineering optimization

Engineering optimization problems involve minimizing some function subject to constraints. In areas such as aircraft optimization, the constraint equations may be from numerous disciplines such as transfer of information between these disciplines and the optimization algorithm. They are also suited to problems which may require numerous re-optimizations such as in multi-objective function optimization or to problems where the design space contains numerous local minima, thus requiring repeated optimizations from different initial designs. Their use has been limited, however, by the fact that development of response surfaces randomly selected or preselected points in the design space. Thus, they have been thought to be inefficient compared to algorithms to the optimum solution. A development has taken place in the last several years which may effect the desirability of using response surfaces. It may be possible that artificial neural nets are more efficient in developing response surfaces than polynomial approximations which have been used in the past. This development is the concern of the work.

Carpenter, William C.↗

Optimal Experimental Design With Fast Neural Network Surrogate Models

Designing optimal experiments minimizes the uncertainty of results and maximizes the efficient use of resources. Herein, machine learning surrogate models and the approximate coordinate exchange (ACE) algorithm are used to determine optimum experimental designs over large or arbitrarily restrictive design spaces. Optimal experimental design is particularly salient in materials science where experiments are expensive and material properties must often be inferred indirectly. The proposed framework is demonstrated by finding optimal experiments with which the hidden constituent properties of composite materials can be most efficiently inferred from observable experimental outcomes. The optimum experimental design is given by an information-theoretic criteria, which maximizes the conditional mutual information between the hidden properties and the expected experimental outcomes. To perform tractable optimization a neural network is trained as a surrogate model to mimic a physics based simulation, which can calculate the expected experimental outcome based on a candidate experimental design and sampled constituent properties. The ACE algorithm is used to optimize over large design spaces with many tests and controlled parameters where an exhaustive search would be intractable even with the surrogate model. Using this approach, optimal experimental designs that are consistent with those produced by heuristic knowledge and established best practices are found; then optimal designs in larger design spaces where heuristic knowledge is unavailable are examined.

machine learning↗

A Quantum Annealing Computer Team Addresses Climate Change Predictability

The near confluence of the successful launch of the Orbiting Carbon Observatory2 on July 2, 2014 and the acceptance on August 20, 2015 by Google, NASA Ames Research Center and USRA of a 1152 qubit D-Wave 2X Quantum Annealing Computer (QAC), offered an exceptional opportunity to explore the potential of this technology to address the scientific prediction of global annual carbon uptake by land surface processes. At UMBC,we have collected and processed 20 months of global Level 2 light CO2 data as well as fluorescence data. In addition we have collected ARM data at 2sites in the US and Ameriflux data at more than 20 stations. J. Dorband has developed and implemented a multi-hidden layer Boltzmann Machine (BM) algorithm on the QAC. Employing the BM, we are calculating CO2 fluxes by training collocated OCO-2 level 2 CO2 data with ARM ground station tower data to infer to infer measured CO2 flux data. We generate CO2 fluxes with a regression analysis using these BM derived weights on the level 2 CO2 data for three Ameriflux sites distinct from the ARM stations. P. Gentine has negotiated for the access of K34 Ameriflux data in the Amazon and is applying a neural net to infer the CO2 fluxes. N. Talik validated the accuracy of the BM performance on the QAC against a restricted BM implementation on the IBM Softlayer Cloud with the Nvidia co-processors utilizing the same data sets. G. Nearing and K. Harrison have extended the GSFC LIS model with the NCAR Noah photosynthetic parameterization and have run a 10 year global prediction of the net ecosystem exchange. C. Pellisier is preparing a BM implementation of the Kalman filter data assimilation of CO2 fluxes. At UMBC, R. Prouty is conducting OSSE experiments with the LISNoah model on the IBM iDataPlex to simulate the impact of CO2 fluxes to improve the prediction of global annual carbon uptake. J. LeMoigne and D. Simpson have developed a neural net image registration system that will be used for MODIS ENVI and will be converted to a BM algorithm implementation on the QAC. The first integer adder has been implemented on the D-Wave 2X by A. Shehab that will perform HAAR wavelets for image compression of MODIS scenes. Finally, based on the next generations of QACs, we are preparing a 5-year performance road map on the scalability of the current QAC algorithms.

Science Data Processing↗

Bioinspired Engineering of Exploration Systems (BEES) - its Impact on Future Missions

This paper describes an overview of our "Bioinspired Engineering of Exploration Systems for Mars" ( "BEES for Mars") project. The BEES approach distills selected biologically inspired strategies utilizing motion cues/optic flow, bioinspired pattern recognition, biological visual and neural control systems, bioinspired sensing and communication techniques, and birds of prey inspired search and track algorithmic systems. Unique capabilities so enabled, provide potential solutions to future autonomous robotic space and planetary mission applications. With the first series of tests performed in September 2003, August 2004 and September 2004, we have demonstrated the BEES technologies at the El Mirage Dry Lakebed site in the Mojave Desert using Delta Wing experimental prototypes. We call these test flyers the "BEES flyer", since we are developing them as dedicated test platform for the newly developed bioinspired sensors, processors and algorithmic strategies. The Delta Wing offers a robust airframe that can sustain high G launches and offers ease of compact stowability and packaging along with scaling to small size and low ReynOld's number performance for a potential Mars deployment. Our approach to developing light weight, low power autonomous flight systems using concepts distilled from biology promises to enable new applications, of dual use to NASA and DoD needs. Small in size (0.5 -5 Kg) BEES Flyers are demonstrating capabilities for autonomous flight and sensor operability in Mars analog conditions. The BEES project team spans JPL, NASA Ames, Australian National University (ANU), Brigham Young University(BYU), DC Berkeiey, Analogic Computers Inc. and other institutions. The highlights from our recent flight demonstrations exhibiting new Mission enabling capabilities are described. Further, this paper describes two classes of potential new missions for Mars exploration: (1) the long range exploration missions, and (2) observation missions, for real time imaging of critical ephemeral phenomena, that can be enabled by use of BEES flyers. For example, such flyers can serve as a powerful black-box for critical descent and landing data and enablers for improved science missions complementing and supplementing the existing assets like landers and rovers by providing valuable exploration and quick extended low-altitude aerial coverage of the sites of interest by imaging them and distributing instruments to them. Imaging done by orbiters allows broad surface coverage at limited spatial resolution. Low altitude air-borne exploration of Mars offers a means for imaging large areas, perhaps up to several hundred kilometers, quickly and efficiently, providing a close-up birds-eye view of the planetary terrain and close-up approach to constrained difficult areas like canyons and craters. A novel approach to low-mass yet highly capable flyers is enabled by small aircraft equipped using sensors and processors and algorithms developed using BEES technology. This project is focused towards showing the direct impact of blending the best of artificial intelligence attributes and bioinspiration to create a leap beyond existing capability for our future Missions.

navigation↗

An Ensemble of Bayesian Neural Networks for Exoplanetary Atmospheric Retrieval

Machine learning (ML) is now used in many areas of astrophysics, from detecting exoplanets in Kepler transit signals to removing telescope systematics. Recent work demonstrated the potential of using ML algorithms for atmospheric retrieval by implementing a random forest (RF) to perform retrievals in seconds that are consistent with the traditional, computationally expensive nested-sampling retrieval method. We expand upon their approach by presenting a new ML model, plan-net, based on an ensemble of Bayesian neural networks (BNNs) that yields more accurate inferences than the RF for the same data set of synthetic transmission spectra. We demonstrate that an ensemble provides greater accuracy and more robust uncertainties than a single model. In addition to being the first to use BNNs for atmospheric retrieval, we also introduce a new loss function for BNNs that learns correlations between the model outputs. Importantly, we show that designing ML models to explicitly incorporate domain-specific knowledge both improves performance and provides additional insight by inferring the covariance of the retrieved atmospheric parameters. We apply plan-net to the Hubble Space Telescope Wide Field Camera 3 transmission spectrum for WASP-12b and retrieve an isothermal temperature and water abundance consistent with the literature. We highlight that our method is flexible and can be expanded to higher resolution spectra and a larger number of atmospheric parameters.

Adam D. Cobb↗

A Globally Optimal Particle Tracking Technique for Stereo Imaging Velocimetry Experiments

An important phase of any Stereo Imaging Velocimetry experiment is particle tracking. Particle tracking seeks to identify and characterize the motion of individual particles entrained in a fluid or air experiment. We analyze a cylindrical chamber filled with water and seeded with density-matched particles. In every four-frame sequence, we identify a particle track by assigning a unique track label for each camera image. The conventional approach to particle tracking is to use an exhaustive tree-search method utilizing greedy algorithms to reduce search times. However, these types of algorithms are not optimal due to a cascade effect of incorrect decisions upon adjacent tracks. We examine the use of a guided evolutionary neural net with simulated annealing to arrive at a globally optimal assignment of tracks. The net is guided both by the minimization of the search space through the use of prior limiting assumptions about valid tracks and by a strategy which seeks to avoid high-energy intermediate states which can trap the net in a local minimum. A stochastic search algorithm is used in place of back-propagation of error to further reduce the chance of being trapped in an energy well. Global optimization is achieved by minimizing an objective function, which includes both track smoothness and particle-image utilization parameters. In this paper we describe our model and present our experimental results. We compare our results with a nonoptimizing, predictive tracker and obtain an average increase in valid track yield of 27 percent

McDowell, Mark↗

Fault Diagnosis of Power Components with Reliability Assessment in Extraterrestrial Microgrids

This research investigates the possible failures caused by aging and other environmental and external factors that could significantly impact the performance of extraterrestrial power systems. Additionally, it presents a reliability assessment model for the space microgrid based on fault tree analysis (FTA). The reliability assessment model developed in this paper represents a tool that can be used by engineers to harden the system design for operational and economic benefits. To improve the reliability of the system, this work provides a broad review of the different fault detection and diagnosis (FDD) algorithms used for power microgrids and space applications. Using data sets from the Habitat Simulator developed through the NASA-funded Resilient Extraterrestrial Habitat Institute, this paper compares the applicability and accuracy of the different FDD methods. The primary FDD approach proposed and assessed in this work is based on the Markov reliability model. It predicts and detects future faults in the space microgrids by using past data samples and categorizing them into different classes. Data-driven-based models such as artificial neural networks are also investigated, tested, and evaluated using simulation data sets. According to the simulation results and the broad FDD algorithm comparison, this study provides the crew or maintenance engineers with a clear methodology to detect and localize power system failures.

Leila Chebbo↗

Modeling the spatiotemporal organization of velocity storage in the vestibuloocular reflex by optokinetic studies

1. A generalized three-dimensional state space model of visual vestibular interaction was developed. Matrix and dynamical system operators associated with inputs from the semicircular canals, otolith velocity estimator, and the visual system have been incorporated into the model, which focus on their relationship to the velocity storage integrator. 2. A relationship was postulated between the eigenvalues and the direction of the eigenvectors of the system matrix and the orientation of the spatial vertical. It was assumed that the system matrix for a tilted position was a composition of two linear transformations of the system matrix for the upright position. One transformation modifies the eigenvalues of the system matrix, whereas another rotates the eigenvectors of the system matrix. The pitch and roll eigenvectors rotate with the head, whereas the yaw axis eigenvector remains approximately spatially invariant. 3. Based on the three-dimensional model, a computational procedure was formulated to identify the eigenvalues and eigenvectors of the system matrix with the use of a modification of the marquardt algorithm. With the use of data obtained from a monkey, it was shown that the three-dimensional behavior of velocity storage cannot be predicted solely in terms of its time constants, i.e., the inverse of its eigenvalues. With the use of the same eigenvalues the data could either be fit or not fit, depending on the eigenvector directions. Therefore, it is necessary to specify eigenvector directions when characterizing velocity storage in three dimensions. 4. Parameters found with the use of the Marquardt algorithm were incorporated into the model. Diagonal matrices in a head coordinate frame were introduced for coupling the visual system to the integrator and to the direct optokinetic pathway. Simulations of optokinetic nystagmus (OKN) and optokinetic after-nystagmus (OKAN) were run. The model predicted the behavior of yaw and pitch OKN and OKAN when the animal is upright. It also predicted the cross-coupling in the side down position. The trajectories in velocity space were also accurately simulated. 5. One of the predictions of the model is that when the stimulus direction is along an eigenvector, the trajectory in velocity space is a straight line. Using the "spectral width" of the residuals from a straight line sequence during OKAN, we developed a methodology to estimate how close the OKAN decay was to an eigenvector trajectory. 6. Thus we have developed a model-based approach for studying and interpreting the response characteristics of velocity storage in three dimensions.(ABSTRACT TRUNCATED AT 400 WORDS).

Non-NASA Center↗

High-performance computing for flight vehicles; Proceedings of the Symposium, Washington, Dec. 7-9, 1992

The present conference discusses high-performance computing systems for flight vehicles, large-scale simulations on high-performance flight computers and software, multidisciplinary and design/optimization applications of computers, computational electromagnetics and acoustics, the simulation of aircraft powerplant turbomachinery and reacting flows, and flow calculations on parallel machines. Also discussed are direct flow simulation Monte Carlo methods, structural mechanics sensitivity and fracture calculations on parallel machines, grid-generation and advanced algorithms for CFD, advanced solid-mechanics and structures applications, and advancements in flow visualization technology and neural networks.

Noor, Ahmed K.↗