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At least 685 records · Page 38

Accelerated Training for Large Feedforward Neural Networks

In this paper we introduce a new training algorithm, the scaled variable metric (SVM) method. Our approach attempts to increase the convergence rate of the modified variable metric method. It is also combined with the RBackprop algorithm, which computes the product of the matrix of second derivatives (Hessian) with an arbitrary vector. The RBackprop method allows us to avoid computationally expensive, direct line searches. In addition, it can be utilized in the new, 'predictive' updating technique of the inverse Hessian approximation. We have used directional slope testing to adjust the step size and found that this strategy works exceptionally well in conjunction with the Rbackprop algorithm. Some supplementary, but nevertheless important enhancements to the basic training scheme such as improved setting of a scaling factor for the variable metric update and computationally more efficient procedure for updating the inverse Hessian approximation are presented as well. We summarize by comparing the SVM method with four first- and second- order optimization algorithms including a very effective implementation of the Levenberg-Marquardt method. Our tests indicate promising computational speed gains of the new training technique, particularly for large feedforward networks, i.e., for problems where the training process may be the most laborious.

Stepniewski, Slawomir W.↗

Precipitation and Latent Heating Distributions from Satellite Passive Microwave Radiometry: Method and Uncertainties - Part 1

A revised Bayesian algorithm for estimating surface rain rate, convective rain proportion, and latent heating/drying profiles from satellite-borne passive microwave radiometer observations over ocean backgrounds is described. The algorithm searches a large database of cloud-radiative model simulations to find cloud profiles that are radiatively consistent with a given set of microwave radiance measurements. The properties of these radiatively consistent profiles are then composited to obtain best estimates of the observed properties. The revised algorithm is supported by an expanded and more physically consistent database of cloud-radiative model simulations. The algorithm also features a better quantification of the convective and non-convective contributions to total rainfall, a new geographic database, and an improved representation of background radiances in rain-free regions. Bias and random error estimates are derived from applications of the algorithm to synthetic radiance data, based upon a subset of cloud resolving model simulations, and from the Bayesian formulation itself. Synthetic rain rate and latent heating estimates exhibit a trend of high (low) bias for low (high) retrieved values. The Bayesian estimates of random error are propagated to represent errors at coarser time and space resolutions, based upon applications of the algorithm to TRMM Microwave Imager (TMI) data. Errors in instantaneous rain rate estimates at 0.5 deg resolution range from approximately 50% at 1 mm/h to 20% at 14 mm/h. These errors represent about 70-90% of the mean random deviation between collocated passive microwave and spaceborne radar rain rate estimates. The cumulative algorithm error in TMI estimates at monthly, 2.5 deg resolution is relatively small (less than 6% at 5 mm/day) compared to the random error due to infrequent satellite temporal sampling (8-35% at the same rain rate).

Olson, William S.↗

Sparse Solutions for Single Class SVMs: A Bi-Criterion Approach

In this paper we propose an innovative learning algorithm - a variation of One-class nu Support Vector Machines (SVMs) learning algorithm to produce sparser solutions with much reduced computational complexities. The proposed technique returns an approximate solution, nearly as good as the solution set obtained by the classical approach, by minimizing the original risk function along with a regularization term. We introduce a bi-criterion optimization that helps guide the search towards the optimal set in much reduced time. The outcome of the proposed learning technique was compared with the benchmark one-class Support Vector machines algorithm which more often leads to solutions with redundant support vectors. Through out the analysis, the problem size for both optimization routines was kept consistent. We have tested the proposed algorithm on a variety of data sources under different conditions to demonstrate the effectiveness. In all cases the proposed algorithm closely preserves the accuracy of standard one-class nu SVMs while reducing both training time and test time by several factors.

Das, Santanu↗

Precipitation and Latent Heating Distributions from Satellite Passive Microwave Radiometry: Improved Method and Uncertainties - Part 1

A revised Bayesian algorithm for estimating surface rain rate, convective rain proportion, and latent heating profiles from satellite-borne passive microwave radiometer observations over ocean backgrounds is described. The algorithm searches a large database of cloud-radiative model simulations to find cloud profiles that are radiatively consistent with a given set of microwave radiance measurements. The properties of these radiatively consistent profiles are then composited to obtain best estimates of the observed properties. The revised algorithm is supported by an expanded and more physically consistent database of cloud-radiative model simulations. The algorithm also features a better quantification of the convective and nonconvective contributions to total rainfall, a new geographic database, and an improved representation of background radiances in rain-free regions. Bias and random error estimates are derived from applications of the algorithm to synthetic radiance data, based upon a subset of cloud-resolving model simulations, and from the Bayesian formulation itself. Synthetic rain-rate and latent heating estimates exhibit a trend of high (low) bias for low (high) retrieved values. The Bayesian estimates of random error are propagated to represent errors at coarser time and space resolutions, based upon applications of the algorithm to TRMM Microwave Imager (TMI) data. Errors in TMI instantaneous rain-rate estimates at 0.5 -resolution range from approximately 50% at 1 mm/h to 20% at 14 mm/h. Errors in collocated spaceborne radar rain-rate estimates are roughly 50%-80% of the TMI errors at this resolution. The estimated algorithm random error in TMI rain rates at monthly, 2.5deg resolution is relatively small (less than 6% at 5 mm day.1) in comparison with the random error resulting from infrequent satellite temporal sampling (8%-35% at the same rain rate). Percentage errors resulting from sampling decrease with increasing rain rate, and sampling errors in latent heating rates follow the same trend. Averaging over 3 months reduces sampling errors in rain rates to 6%-15% at 5 mm day.1, with proportionate reductions in latent heating sampling errors.

Olson, William S.↗

User's manual for a fuel-conservative descent planning algorithm implemented on a small programmable calculator

A simplified flight management descent algorithm was developed and programmed on a small programmable calculator. It was designed to aid the pilot in planning and executing a fuel conservative descent to arrive at a metering fix at a time designated by the air traffic control system. The algorithm may also be used for planning fuel conservative descents when time is not a consideration. The descent path was calculated for a constant Mach/airspeed schedule from linear approximations of airplane performance with considerations given for gross weight, wind, and nonstandard temperature effects. An explanation and examples of how the algorithm is used, as well as a detailed flow chart and listing of the algorithm are contained.

Vicroy, D. D.↗

Peak Seeking Control for Reduced Fuel Consumption with Preliminary Flight Test Results

The Environmentally Responsible Aviation project seeks to accomplish the simultaneous reduction of fuel burn, noise, and emissions. A project at NASA Dryden Flight Research Center is contributing to ERAs goals by exploring the practical application of real-time trim configuration optimization for enhanced performance and reduced fuel consumption. This peak-seeking control approach is based on Newton-Raphson algorithm using a time-varying Kalman filter to estimate the gradient of the performance function. In real-time operation, deflection of symmetric ailerons, trailing-edge flaps, and leading-edge flaps of a modified F-18 are directly optimized, and the horizontal stabilators and angle of attack are indirectly optimized. Preliminary results from three research flights are presented herein. The optimization system found a trim configuration that required approximately 3.5% less fuel flow than the baseline trim at the given flight condition. The algorithm consistently rediscovered the solution from several initial conditions. These preliminary results show the algorithm has good performance and is expected to show similar results at other flight conditions and aircraft configurations.

Brown, Nelson↗

On the integration of reinforcement learning and approximate reasoning for control

The author discusses the importance of strengthening the knowledge representation characteristic of reinforcement learning techniques using methods such as approximate reasoning. The ARIC (approximate reasoning-based intelligent control) architecture is an example of such a hybrid approach in which the fuzzy control rules are modified (fine-tuned) using reinforcement learning. ARIC also demonstrates that it is possible to start with an approximately correct control knowledge base and learn to refine this knowledge through further experience. On the other hand, techniques such as the TD (temporal difference) algorithm and Q-learning establish stronger theoretical foundations for their use in adaptive control and also in stability analysis of hybrid reinforcement learning and approximate reasoning-based controllers.

Berenji, Hamid R.↗

Space Shuttle Main Engine performance analysis

For a number of years, NASA has relied primarily upon periodically updated versions of Rocketdyne's power balance model (PBM) to provide space shuttle main engine (SSME) steady-state performance prediction. A recent computational study indicated that PBM predictions do not satisfy fundamental energy conservation principles. More recently, SSME test results provided by the Technology Test Bed (TTB) program have indicated significant discrepancies between PBM flow and temperature predictions and TTB observations. Results of these investigations have diminished confidence in the predictions provided by PBM, and motivated the development of new computational tools for supporting SSME performance analysis. A multivariate least squares regression algorithm was developed and implemented during this effort in order to efficiently characterize TTB data. This procedure, called the 'gains model,' was used to approximate the variation of SSME performance parameters such as flow rate, pressure, temperature, speed, and assorted hardware characteristics in terms of six assumed independent influences. These six influences were engine power level, mixture ratio, fuel inlet pressure and temperature, and oxidizer inlet pressure and temperature. A BFGS optimization algorithm provided the base procedure for determining regression coefficients for both linear and full quadratic approximations of parameter variation. Statistical information relative to data deviation from regression derived relations was also computed. A new strategy for integrating test data with theoretical performance prediction was also investigated. The current integration procedure employed by PBM treats test data as pristine and adjusts hardware characteristics in a heuristic manner to achieve engine balance. Within PBM, this integration procedure is called 'data reduction.' By contrast, the new data integration procedure, termed 'reconciliation,' uses mathematical optimization techniques, and requires both measurement and balance uncertainty estimates. The reconciler attempts to select operational parameters that minimize the difference between theoretical prediction and observation. Selected values are further constrained to fall within measurement uncertainty limits and to satisfy fundamental physical relations (mass conservation, energy conservation, pressure drop relations, etc.) within uncertainty estimates for all SSME subsystems. The parameter selection problem described above is a traditional nonlinear programming problem. The reconciler employs a mixed penalty method to determine optimum values of SSME operating parameters associated with this problem formulation.

Santi, L. Michael↗

A globally well-posed finite element algorithm for aerodynamics applications

A finite element CFD algorithm is developed for Euler and Navier-Stokes aerodynamic applications. For the linear basis, the resultant approximation is at least second-order-accurate in time and space for synergistic use of three procedures: (1) a Taylor weak statement, which provides for derivation of companion conservation law systems with embedded dispersion-error control mechanisms; (2) a stiffly stable second-order-accurate implicit Rosenbrock-Runge-Kutta temporal algorithm; and (3) a matrix tensor product factorization that permits efficient numerical linear algebra handling of the terminal large-matrix statement. Thorough analyses are presented regarding well-posed boundary conditions for inviscid and viscous flow specifications. Numerical solutions are generated and compared for critical evaluation of quasi-one- and two-dimensional Euler and Navier-Stokes benchmark test problems.

Iannelli, G. S.↗

Ross Sea Polynyas: Response of Ice Concentration Retrievals to Large Areas of Thin Ice

For a 3-month period between May and July of 2005, we examine the response of the Advanced Microwave Scanning Radiometer (AMSR-E) Enhanced NASA Team 2 (NT2) and AMSR-E Bootstrap (ABA) ice concentration algorithms to large areas of thin ice of the Ross Sea polynyas. Coincident Envisat Synthetic Aperture Radar (SAR) coverage of the region during this period offers a detailed look at the development of the polynyas within several hundred kilometers of the ice front. The high-resolution imagery and derived ice motion fields show bands of polynya ice, covering up to approximately 105 km(sup 2) of the Ross Sea, that are associated with wind-forced advection. In this study, ice thickness from AMSR-E 36 GHz polarization information serves as the basis for examination of the response. The quality of the thickness of newly formed sea ice (<10 cm) from AMSR-E is first assessed with thickness estimates derived from ice surface temperatures from the Moderate Resolution Imaging Spectroradiometer (MODIS) instrument. The effect of large areas of thin ice in lowering the ice concentration estimates from both NT2/ABA approaches is clearly demonstrated. Results show relatively robust relationships between retrieved ice concentrations and thin ice thickness estimates that differ between the two algorithms. These relationships define the approximate spatial coincidence of ice concentration and thickness isopleths. Using the 83% (ABA) and 91% (NT2) isopleths as polynya boundaries, we show that the computed coverage compares well with that using the estimated 10-cm thickness contour. The thin ice response characterized here suggests that in regions with polynyas, the retrieval results could be used to provide useful geophysical information, namely thickness and coverage.

algorithms↗

Compression of ephemerides

An algorithm is proposed for generating sequences of Chebyshev series which are the best approximations of an astronomical ephemeris in the sense of Chebyshev over large intervals of time. The criterion for a polynomial approximation of a function to be the best polynomial approximation of the function is that the error function present certain rippling characteristics as described by Remez (1957). General features of the program in PL/1 are described.

Deprit, A.↗

System design for a million channel digital spectrum analyzer /MCSA/

The system design of a wideband (8 MHz) million-channel digital spectrum analyzer for use with a SETI receiver is presented. The analyzer makes use of a digital bandpass filter bank for transforming the wideband input signal into a specified number (120) of uniform narrowband output channels by the use of a Fourier transform digital processor combined with a prototype digital weighting network (finite impulse response filter). The output is then processed separately by 120 microprocessor-based discrete Fourier transform computers, each producing 8190 output channels of approximately 8 Hz bandwidth by the use of an 8190-point prime factor algorithm.

Peterson, A.↗

Theory, computation, and application of exponential splines

A generalization of the semiclassical cubic spline known in the literature as the exponential spline is discussed. In actuality, the exponential spline represents a continuum of interpolants ranging from the cubic spline to the linear spline. A particular member of this family is uniquely specified by the choice of certain tension parameters. The theoretical underpinnings of the exponential spline are outlined. This development roughly parallels the existing theory for cubic splines. The primary extension lies in the ability of the exponential spline to preserve convexity and monotonicity present in the data. Next, the numerical computation of the exponential spline is discussed. A variety of numerical devices are employed to produce a stable and robust algorithm. An algorithm for the selection of tension parameters that will produce a shape preserving approximant is developed. A sequence of selected curve-fitting examples are presented which clearly demonstrate the advantages of exponential splines over cubic splines.

Mccartin, B. J.↗

Numerical simulation of the transonic flowfield for wing/nacelle configurations

An efficient grid-interfacing zonal algorithm has been developed for computing the three-dimensional transonic flow field about wing/nacelle multicomponent configurations. The algorithm uses the full-potential formulation and the AF2 fully-implicit approximate factorization scheme. The flow field position is computed using a component-adaptive grid approach in which separate grids are employed for the individual components in the multicomponent configuration, where each component grid is optimized for a particular geometry such as the wing or nacelle. The wing and nacelle component grids are allowed to overlap, and flow field information is transmitted from one grid to another through the overlap region using trivariate interpolation. This paper presents a discussion of the computational methods used to generate both the wing and nacelle component grids, the technique used to interface the component grids, and the method used to obtain the inviscid multicomponent flow field solution. Computed results and correlations with experiment are presented to illustrate application of the analysis.

Atta, E. H.↗

Closed-form Grammians and model reduction for flexible space structures

Analytical expression are derived for the Grammians of a model in modal coordinates for the dynamics of a flexible space structure (FSS). These exact results provide insight into the dynamics of such systems and reduce the known approximate expressions in the case of lightly damped, widely separated modes. A novel algorithm is outlined that uses these to compute a dominant reduced-order model for such a system in an efficient manner.

Williams, Trevor↗

Numerical simulation of flow over a hypersonic aircraft using an explicit upwind PNS solver

A hypersonic flow field over a generic airplane configuration is simulated by solving the Parabolized Navier-Stokes (PNS) equations. The finite difference solution of the PNS equations is calculated using a noniterative space marching, explicit, upwind scheme recently developed by the authors. Special gridding techniques are used which allowed the sharp changes in surface geometry of the airplane configuration to be modelled without smoothing of corners. Comparisons of the PNS results to a solution of the Navier-Stokes equations demonstrates a good agreement of the numerical results in approximately 1/6 of the cpu time. This paper demonstrates that the explicit upwind algorithm for solving the PNS equations is an efficient method for simulating hypersonic flow fields about complete airplane configurations and should be considered as an alternative to solving the Navier-Stokes equations for flow fields where the PNS equations are valid.

Korte, John J.↗

Dual-shaped offset reflector antenna designs from solutions of the geometrical optics first-order partial differential equations

In obtaining solutions to the first-order nonlinear partial differential equations (PDEs) for synthesizing offset dual-shaped reflectors, it is found that previously observed computational problems can be avoided if the integration of the PDEs is started from an inner projected perimeter and integrated outward rather than starting from an outer projected perimeter and integrating inward. This procedure, however, introduces a new parameter, the main reflector inner perimeter radius p(o), when given a subreflector inner angle 0(o). Furthermore, a desired outer projected perimeter (e.g., a circle) is no longer guaranteed. Stability of the integration is maintained if some of the initial parameters are determined first from an approximate solution to the PDEs. A one-, two-, or three-parameter optimization algorithm can then be used to obtain a best set of parameters yielding a close fit to the desired projected outer rim. Good low cross-polarization mapping functions are also obtained. These methods are illustrated by synthesis of a high-gain offset-shaped Cassegrainian antenna and a low-noise offset-shaped Gregorian antenna.

Galindo-Israel, V.↗