Rapid optimization of multiple-burn rocket flights, 8 March 1968 - 8 March 1969
Iterative solution of boundary value problem for rapid optimization of multiple-burn rocket flights
Brown, K. R.↗
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Highly Scalable Matching Pursuit Signal Decomposition Algorithm
Matching Pursuit Decomposition (MPD) is a powerful iterative algorithm for signal decomposition and feature extraction. MPD decomposes any signal into linear combinations of its dictionary elements or atoms . A best fit atom from an arbitrarily defined dictionary is determined through cross-correlation. The selected atom is subtracted from the signal and this procedure is repeated on the residual in the subsequent iterations until a stopping criterion is met. The reconstructed signal reveals the waveform structure of the original signal. However, a sufficiently large dictionary is required for an accurate reconstruction; this in return increases the computational burden of the algorithm, thus limiting its applicability and level of adoption. The purpose of this research is to improve the scalability and performance of the classical MPD algorithm. Correlation thresholds were defined to prune insignificant atoms from the dictionary. The Coarse-Fine Grids and Multiple Atom Extraction techniques were proposed to decrease the computational burden of the algorithm. The Coarse-Fine Grids method enabled the approximation and refinement of the parameters for the best fit atom. The ability to extract multiple atoms within a single iteration enhanced the effectiveness and efficiency of each iteration. These improvements were implemented to produce an improved Matching Pursuit Decomposition algorithm entitled MPD++. Disparate signal decomposition applications may require a particular emphasis of accuracy or computational efficiency. The prominence of the key signal features required for the proper signal classification dictates the level of accuracy necessary in the decomposition. The MPD++ algorithm may be easily adapted to accommodate the imposed requirements. Certain feature extraction applications may require rapid signal decomposition. The full potential of MPD++ may be utilized to produce incredible performance gains while extracting only slightly less energy than the standard algorithm. When the utmost accuracy must be achieved, the modified algorithm extracts atoms more conservatively but still exhibits computational gains over classical MPD. The MPD++ algorithm was demonstrated using an over-complete dictionary on real life data. Computational times were reduced by factors of 1.9 and 44 for the emphases of accuracy and performance, respectively. The modified algorithm extracted similar amounts of energy compared to classical MPD. The degree of the improvement in computational time depends on the complexity of the data, the initialization parameters, and the breadth of the dictionary. The results of the research confirm that the three modifications successfully improved the scalability and computational efficiency of the MPD algorithm. Correlation Thresholding decreased the time complexity by reducing the dictionary size. Multiple Atom Extraction also reduced the time complexity by decreasing the number of iterations required for a stopping criterion to be reached. The Course-Fine Grids technique enabled complicated atoms with numerous variable parameters to be effectively represented in the dictionary. Due to the nature of the three proposed modifications, they are capable of being stacked and have cumulative effects on the reduction of the time complexity.
Christensen, Daniel↗
Numerical Simulation of Turbulent MHD Flows Using an Iterative PNS Algorithm
A new parabolized Navier-Stokes (PNS) algorithm has been developed to efficiently compute magnetohydrodynamic (MHD) flows in the low magnetic Reynolds number regime. In this regime, the electrical conductivity is low and the induced magnetic field is negligible compared to the applied magnetic field. The MHD effects are modeled by introducing source terms into the PNS equation which can then be solved in a very efficient manner. To account for upstream (elliptic) effects, the flowfields are computed using multiple streamwise sweeps with an iterated PNS algorithm. Turbulence has been included by modifying the Baldwin-Lomax turbulence model to account for MHD effects. The new algorithm has been used to compute both laminar and turbulent, supersonic, MHD flows over flat plates and supersonic viscous flows in a rectangular MHD accelerator. The present results are in excellent agreement with previous complete Navier-Stokes calculations.
Kato, Hiromasa↗
Determination of vertical ozone distributions by spacecraft measurements using a limb-scan technique
The principle of a new inversion technique which uses multiple wavelength-solar UV radiation satellite measurements for determining vertical ozone profiles is described, and examples of computer simulations for 280, 300, 320, and 340 nm are discussed. Weighting functions corresponding to the sensitivity of the limb radiance to the relative ozone density at each altitude are the basis for the inversion equation, which is then solved by an iteration technique. The use of multiple wavelengths can provide more information of higher accuracy over a wider height range than those profiles recovered at a single wavelength. It is indicated that an effective range of altitude of approximately 20-70 km with a vertical resolution of 1-2 km is feasible for determining ozone profiles with an inferred profile error about three to four times larger than the measurement error within that altitude region. Ozone profile accuracy of the highest altitude region may be improved using wavelengths down to 260 nm, and inferred ozone profiles above 70 km are possible, but with a larger error.
Aruga, T.↗
Multiple zeros of polynomials
Analysis of four iterative methods for approximating zeros of polynomial expressions using digital computer
Wood, C. A.↗
The use of coherence functions to determine dynamic excitation sources on launch vehicle payloads
The problem of determining the relative contribution of simultaneous acoustic and mechanical inputs to the response of structures under combined dynamic loads was studied. An analytical technique developed by Bendat for calculating ordinary, partial, and multiple coherence functions, using an iterative nonmatrix approach was applied to data obtained from laboratory tests on a complex structural assembly. Testing was performed in an acoustically 'live' room. Up to three random inputs, having similar spectral content and varying degrees of mutual coherence, and a single output were used. Stationary and nonstationary inputs were used. It was concluded that the technique provided an effective method of identifying sources of dynamic excitation and evaluating their relative contributions to the measured output at structural resonances, for stationary random inputs. An attempt to apply the technique to nonstationary inputs did not yield consistent results.
Barrett, S.↗
Numerical Simulation of 3-D Supersonic Viscous Flow in an Experimental MHD Channel
The 3-D supersonic viscous flow in an experimental MHD channel has been numerically simulated. The experimental MHD channel is currently in operation at NASA Ames Research Center. The channel contains a nozzle section, a center section, and an accelerator section where magnetic and electric fields can be imposed on the flow. In recent tests, velocity increases of up to 40% have been achieved in the accelerator section. The flow in the channel is numerically computed using a new 3-D parabolized Navier-Stokes (PNS) algorithm that has been developed to efficiently compute MHD flows in the low magnetic Reynolds number regime. The MHD effects are modeled by introducing source terms into the PNS equations which can then be solved in a very e5uent manner. To account for upstream (elliptic) effects, the flowfield can be computed using multiple streamwise sweeps with an iterated PNS algorithm. The new algorithm has been used to compute two test cases that match the experimental conditions. In both cases, magnetic and electric fields are applied to the flow. The computed results are in good agreement with the available experimental data.
Kato, Hiromasa↗
CAISSON: Interconnect Network Simulator
Cray response to HPCS initiative. Model future petaflop computer interconnect. Parallel discrete event simulation techniques for large scale network simulation. Built on WarpIV engine. Run on laptop and Altix 3000. Can be sized up to 1000 simulated nodes per host node. Good parallel scaling characteristics. Flexible: multiple injectors, arbitration strategies, queue iterators, network topologies.
network simulation↗
3D-MAT Multi-rate Thermal Expansion and Restrained Thermal Growth
In an effort to characterize 3D Multifunctional Ablative Thermal Protection System (3D-MAT), a quartz fiber / cyanate ester composite for NASA’s Orion Multipurpose Crew Vehicle, Southern Research carried out multiple test efforts. Southern Research evaluated the coefficient of free thermal expansion at multiple heating rates in the X, Y and Z directions. To further understand the results, we further evaluated the material via Restrained Thermal Growth (RTG) in the X direction. The RTG test series involved testing via multiple procedures, resulting in an iterative process and a final conclusion.
Jay D Feldman↗
Multiple zeros of polynomials
For polynomials of higher degree, iterative numerical methods must be used. Four iterative methods are presented for approximating the zeros of a polynomial using a digital computer. Newton's method and Muller's method are two well known iterative methods which are presented. They extract the zeros of a polynomial by generating a sequence of approximations converging to each zero. However, both of these methods are very unstable when used on a polynomial which has multiple zeros. That is, either they fail to converge to some or all of the zeros, or they converge to very bad approximations of the polynomial's zeros. This material introduces two new methods, the greatest common divisor (G.C.D.) method and the repeated greatest common divisor (repeated G.C.D.) method, which are superior methods for numerically approximating the zeros of a polynomial having multiple zeros. These methods were programmed in FORTRAN 4 and comparisons in time and accuracy are given.
Wood, C. A.↗
Performance of direct and iterative algorithms on an optical systolic processor
The frequency-multiplexed optical linear algebra processor (OLAP) is treated in detail with attention to its performance in the solution of systems of linear algebraic equations (LAEs). General guidelines suitable for most OLAPs, including digital-optical processors, are advanced concerning system and component error source models, guidelines for appropriate use of direct and iterative algorithms, the dominant error sources, and the effect of multiple simultaneous error sources. Specific results are advanced on the quantitative performance of both direct and iterative algorithms in the solution of systems of LAEs and in the solution of nonlinear matrix equations. Acoustic attenuation is found to dominate iterative algorithms and detector noise to dominate direct algorithms. The effect of multiple spatial errors is found to be additive. A theoretical expression for the amount of acoustic attenuation allowed is advanced and verified. Simulations and experimental data are included.
Ghosh, A. K.↗
Designing reduced-order linear multivariable controllers using experimentally derived plant data
An iterative numerical algorithm for simultaneously improving multiple performance and stability robustness criteria for multivariable feedback systems is developed. The unsatisfied design criteria are improved by updating the free parameters of an initial, stabilizing controller's state-space matrices. Analytical expressions for the gradients of the design criteria are employed to determine a parameter correction that improves all of the feasible, unsatisfied design criteria at each iteration. A controller design is performed using the algorithm with experimentally derived data from a large space structure test facility. Experimental results of the controller's performance at the facility are presented.
Frazier, W. G.↗
Adaptive Multi-Sensor Localization Information Fusion for Autonomous Urban Air Mobility Operations
An adaptive method is developed to iteratively fuse the information provided by multiple sensors to enable autonomous urban air mobility type operations. First, noisy and bias corrupted IMU readings are processed as soon as they arrive using kinematic equations represented in the vehicle's body frame. To correct the systems drift resulting from the integration, an information content measure is introduced to decide on the environment. For the cluttered environment the information provided by environmental sensors is counted as reliable and the drift correction as accurate. For the open space, the GPS data is counted as reliable, and the drift correction is done based on the GPS readings. The measurement noise effects are minimize using Iterated Extended Kalman Filter framework. The algorithm is implemented in the in-house developed FlightDeckz simulation environment using an IMU model, simulated video recorded from a camera mounted on the vehicle (for the purpose of this study, outside scenery was generated with XPlane), which flies in an urban environment, and GPS data generated from the environment's digital map.
Onboard Perception↗
A General Algorithm for Reusing Krylov Subspace Information. I. Unsteady Navier-Stokes
A general algorithm is developed that reuses available information to accelerate the iterative convergence of linear systems with multiple right-hand sides A x = b (sup i), which are commonly encountered in steady or unsteady simulations of nonlinear equations. The algorithm is based on the classical GMRES algorithm with eigenvector enrichment but also includes a Galerkin projection preprocessing step and several novel Krylov subspace reuse strategies. The new approach is applied to a set of test problems, including an unsteady turbulent airfoil, and is shown in some cases to provide significant improvement in computational efficiency relative to baseline approaches.
Carpenter, Mark H.↗
Modern Design of Resonant Edge-Slot Array Antennas
Resonant edge-slot (slotted-waveguide) array antennas can now be designed very accurately following a modern computational approach like that followed for some other microwave components. This modern approach makes it possible to design superior antennas at lower cost than was previously possible. Heretofore, the physical and engineering knowledge of resonant edge-slot array antennas had remained immature since they were introduced during World War II. This is because despite their mechanical simplicity, high reliability, and potential for operation with high efficiency, the electromagnetic behavior of resonant edge-slot antennas is very complex. Because engineering design formulas and curves for such antennas are not available in the open literature, designers have been forced to implement iterative processes of fabricating and testing multiple prototypes to derive design databases, each unique for a specific combination of operating frequency and set of waveguide tube dimensions. The expensive, time-consuming nature of these processes has inhibited the use of resonant edge-slot antennas. The present modern approach reduces costs by making it unnecessary to build and test multiple prototypes. As an additional benefit, this approach affords a capability to design an array of slots having different dimensions to taper the antenna illumination to reduce the amplitudes of unwanted side lobes. The heart of the modern approach is the use of the latest commercially available microwave-design software, which implements finite-element models of electromagnetic fields in and around waveguides, antenna elements, and similar components. Instead of building and testing prototypes, one builds a database and constructs design curves from the results of computational simulations for sets of design parameters. The figure shows a resonant edge-slot antenna designed following this approach. Intended for use as part of a radiometer operating at a frequency of 10.7 GHz, this antenna was fabricated from dimensions defined exclusively by results of computational simulations. The final design was found to be well optimized and to yield performance exceeding that initially required.
Gosselin, R. B.↗
Selection of Thermal Worst-Case Orbits via Modified Efficient Global Optimization
Efficient Global Optimization (EGO) was used to select orbits with worst-case hot and cold thermal environments for the Stratospheric Aerosol and Gas Experiment (SAGE) III. The SAGE III system thermal model changed substantially since the previous selection of worst-case orbits (which did not use the EGO method), so the selections were revised to ensure the worst cases are being captured. The EGO method consists of first conducting an initial set of parametric runs, generated with a space-filling Design of Experiments (DoE) method, then fitting a surrogate model to the data and searching for points of maximum Expected Improvement (EI) to conduct additional runs. The general EGO method was modified by using a multi-start optimizer to identify multiple new test points at each iteration. This modification facilitates parallel computing and decreases the burden of user interaction when the optimizer code is not integrated with the model. Thermal worst-case orbits for SAGE III were successfully identified and shown by direct comparison to be more severe than those identified in the previous selection. The EGO method is a useful tool for this application and can result in computational savings if the initial Design of Experiments (DoE) is selected appropriately.
Moeller, Timothy M.↗
NASA DEVELOP’s User-Centric Approach to Building Capacity to Use Earth Observations for Decision Making
The DEVELOP Program, part of NASA’s Applied Sciences, conducts 50-60 feasibility studies annually that center on user needs. Each project is tailored to its partner’s decision making processes with the goal of identifying and implementing opportunities for Earth observation data and information to be integrated into environmental decision making processes. These projects are conducted by a team of early career professionals through a 10-week term where the DEVELOP team rapidly iterates with partners culminating in a “recipe” for using NASA Earth observations. This presentation will introduce the DEVELOP model for user-centered design of projects, share the program's iterative approach to project execution, highlight multiple case studies, and lessons learned in the program’s model evolution.
Capacity Building↗
Newton's method: A link between continuous and discrete solutions of nonlinear problems
Newton's method for nonlinear mechanics problems replaces the governing nonlinear equations by an iterative sequence of linear equations. When the linear equations are linear differential equations, the equations are usually solved by numerical methods. The iterative sequence in Newton's method can exhibit poor convergence properties when the nonlinear problem has multiple solutions for a fixed set of parameters, unless the iterative sequences are aimed at solving for each solution separately. The theory of the linear differential operators is often a better guide for solution strategies in applying Newton's method than the theory of linear algebra associated with the numerical analogs of the differential operators. In fact, the theory for the differential operators can suggest the choice of numerical linear operators. In this paper the method of variation of parameters from the theory of linear ordinary differential equations is examined in detail in the context of Newton's method to demonstrate how it might be used as a guide for numerical solutions.
Thurston, G. A.↗