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NASA NTRS1999

The Behavior of Filters and Smoothers for Strongly Nonlinear Dynamics

The Kalman filter is the optimal filter in the presence of known Gaussian error statistics and linear dynamics. Filter extension to nonlinear dynamics is non trivial in the sense of appropriately representing high order moments of the statistics. Monte Carlo, ensemble-based, methods have been advocated as the methodology for representing high order moments without any questionable closure assumptions (e.g., Miller 1994). Investigation along these lines has been conducted for highly idealized dynamics such as the strongly nonlinear Lorenz (1963) model as well as more realistic models of the oceans (Evensen and van Leeuwen 1996) and atmosphere (Houtekamer and Mitchell 1998). A few relevant issues in this context are related to the necessary number of ensemble members to properly represent the error statistics and, the necessary modifications in the usual filter equations to allow for correct update of the ensemble members (Burgers 1998). The ensemble technique has also been applied to the problem of smoothing for which similar questions apply. Ensemble smoother examples, however, seem to quite puzzling in that results of state estimate are worse than for their filter analogue (Evensen 1997). In this study, we use concepts in probability theory to revisit the ensemble methodology for filtering and smoothing in data assimilation. We use Lorenz (1963) model to test and compare the behavior of a variety implementations of ensemble filters. We also implement ensemble smoothers that are able to perform better than their filter counterparts. A discussion of feasibility of these techniques to large data assimilation problems will be given at the time of the conference.

Zhu, Yanqiu↗

NASA NTRS2005

Multi-Dimensional Spectral Difference Method for Unstructured Grids

A new, high-order, conservative, and efficient method for conservation laws on unstructured grids is developed. It combines the best features of structured and unstructured grid methods to attain computational efficiency and geometric flexibility; it utilizes the concept of discontinuous and high-order local representations to achieve conservation and high accuracy; and it is based on the finite-difference formulation for simplicity. Universal reconstructions are obtained by distributing unknowns in a geometrically similar manner for all unstructured cells. Placements of the unknown and flux points with various order of accuracy are given for the line, triangular and tetrahedral elements. The data structure of the new method permits an optimum use of cache memory, resulting in further computational efficiency on modern computers. A new pointer system is developed that reduces memory requirements and simplifies programming for any order of accuracy. Numerical solutions are presented and compared with the exact solutions for wave propagation problems in both two and three dimensions to demonstrate the capability of the method. Excellent agreement has been found. The method is simpler and more efficient than previous discontinuous Galerkin and spectral volume methods for unstructured grids.

Liu, Yen↗

NASA NTRS2002

Towards Arbitrary Accuracy Inviscid Surface Boundary Conditions

Inviscid nonlinear surface boundary conditions are currently limited to third order accuracy in time for non-moving surfaces and actually reduce to first order in time when the surfaces move. For steady-state calculations it may be possible to achieve higher accuracy in space, but high accuracy in time is required for efficient simulation of multiscale unsteady phenomena. A surprisingly simple technique is shown here that can be used to correct the normal pressure derivatives of the flow at a surface on a Cartesian grid so that arbitrarily high order time accuracy is achieved in idealized cases. This work demonstrates that nonlinear high order time accuracy at a solid surface is possible and desirable, but it also shows that the current practice of only correcting the pressure is inadequate.

Dyson, Rodger W.↗

NASA NTRS1974

Comparison of numerical integration techniques for orbital applications

The present work gives a brief comparison of the performance of programs for integrating differential equations for orbital applications. The evaluation criteria and the method of testing are described, and the results of the test problem set are included. Integration methods that were chosen for comparison include high-order Runge-Kutta methods; a rational extrapolation method (Bulirsch and Stoer, 1966); a variable step, variable order, multistep method (Krogh, 1969); classical multistep methods of Adams and Cowell; and modified multistep methods. The high-order Runge-Kutta methods used in the comparison include RKF 7(8) and RKF 8(9) (Fehlberg, 1968), and RKS 8-10 (Shanks, 1966).

Moore, H.↗

NASA NTRS1996

Computational considerations for the simulation of shock-induced sound

The numerical study of aeroacoustic problems places stringent demands on the choice of a computational algorithm, because it requires the ability to propagate disturbances of small amplitude and short wavelength. The demands are particularly high when shock waves are involved, because the chosen algorithm must also resolve discontinuities in the solution. The extent to which a high-order-accurate shock-capturing method can be relied upon for aeroacoustics applications that involve the interaction of shocks with other waves has not been previously quantified. Such a study is initiated in this work. A fourth-order-accurate essentially nonoscillatory (ENO) method is used to investigate the solutions of inviscid, compressible flows with shocks in a quasi-one-dimensional nozzle flow. The design order of accuracy is achieved in the smooth regions of a steady-state test case. However, in an unsteady test case, only first-order results are obtained downstream of a sound-shock interaction. The difficulty in obtaining a globally high-order-accurate solution in such a case with a shock-capturing method is demonstrated through the study of a simplified, linear model problem. Some of the difficult issues and ramifications for aeroacoustics simulations of flows with shocks that are raised by these results are discussed.

Casper, Jay↗

NASA NTRS1989

A real time microcomputer implementation of sensor failure detection for turbofan engines

An algorithm was developed which detects, isolates, and accommodates sensor failures using analytical redundancy. The performance of this algorithm was demonstrated on a full-scale F100 turbofan engine. The algorithm was implemented in real-time on a microprocessor-based controls computer which includes parallel processing and high order language programming. Parallel processing was used to achieve the required computational power for the real-time implementation. High order language programming was used in order to reduce the programming and maintenance costs of the algorithm implementation software. The sensor failure algorithm was combined with an existing multivariable control algorithm to give a complete control implementation with sensor analytical redundancy. The real-time microprocessor implementation of the algorithm which resulted in the successful completion of the algorithm engine demonstration, is described.

Delaat, John C.↗

NASA NTRS1990

A real time microcomputer implementation of sensor failure detection for turbofan engines

An algorithm was developed that detects, isolates, and accommodates sensor failures using analytical redundancy. The performance of this algorithm has been demonstrated on a full-scale F100 turbofan engine. The algorithm was implemented in real-time on a microprocessor-based controls computer which includes parallel processing and high order language programming. Parallel processing was used to achieve the required computational power for the real-time implementation. High order language programming was used in order to reduce the programming and maintenance costs of the algorithm implementation software. The sensor failure algorithm was combined with an existing multivariable control algorithm to give a complete control implementation with sensor analytical redundancy. The real-time microprocessor implementation of the algorithm, which resulted in the successful completion of the algorithm engine demonstration, is described.

Delaat, John C.↗

NASA NTRS1999

622-Mbps Orthogonal Frequency Division Multiplexing Modulator Developed

The Communications Technology Division at the NASA Lewis Research Center is developing advanced electronic technologies for the space communications and remote sensing systems of tomorrow. As part of the continuing effort to advance the state-of-the art in satellite communications and remote sensing systems, Lewis is developing a programmable Orthogonal Frequency Division Multiplexing (OFDM) modulator card for high-data-rate communication links. The OFDM modulator is particularly suited to high data-rate downlinks to ground terminals or direct data downlinks from near-Earth science platforms. It can support data rates up to 622 megabits per second (Mbps) and high-order modulation schemes such as 16-ary quadrature amplitude modulation (16-ary QAM) or 8- phase shift keying (8PSK). High order modulations can obtain the bandwidth efficiency over the traditional binary phase shift keying (BPSK) or quadrature phase shift keying (QPSK) modulator schemes. The OFDM modulator architecture can also be precompensated for channel disturbances and alleviate amplitude degradations caused by nonlinear transponder characteristics.

Nguyen, Na T.↗

NASA NTRS2016

Improving Fidelity of Launch Vehicle Liftoff Acoustic Simulations

Launch vehicles experience high acoustic loads during ignition and liftoff affected by the interaction of rocket plume generated acoustic waves with launch pad structures. Application of highly parallelized Computational Fluid Dynamics (CFD) analysis tools optimized for application on the NAS computer systems such as the Loci/CHEM program now enable simulation of time-accurate, turbulent, multi-species plume formation and interaction with launch pad geometry and capture the generation of acoustic noise at the source regions in the plume shear layers and impingement regions. These CFD solvers are robust in capturing the acoustic fluctuations, but they are too dissipative to accurately resolve the propagation of the acoustic waves throughout the launch environment domain along the vehicle. A hybrid Computational Fluid Dynamics and Computational Aero-Acoustics (CFD/CAA) modeling framework has been developed to improve such liftoff acoustic environment predictions. The framework combines the existing highly-scalable NASA production CFD code, Loci/CHEM, with a high-order accurate discontinuous Galerkin (DG) solver, Loci/THRUST, developed in the same computational framework. Loci/THRUST employs a low dissipation, high-order, unstructured DG method to accurately propagate acoustic waves away from the source regions across large distances. The DG solver is currently capable of solving up to 4th order solutions for non-linear, conservative acoustic field propagation. Higher order boundary conditions are implemented to accurately model the reflection and refraction of acoustic waves on launch pad components. The DG solver accepts generalized unstructured meshes, enabling efficient application of common mesh generation tools for CHEM and THRUST simulations. The DG solution is coupled with the CFD solution at interface boundaries placed near the CFD acoustic source regions. Both simulations are executed simultaneously with coordinated boundary condition data exchange.

Liever, Peter↗

NASA NTRSDate not supplied

An Integrated Software Architecture for Solar Cruiser Mission Design and Navigation

Solar Cruiser is a solar sailing mission, riding as a secondary payload to the Interstellar Mapping and Acceleration Probe (IMAP) mission, slated to launch in February of 2025. The Solar Cruiser vehicle will generate thrust via a complex, low-thrust solar sail. The extreme low-thrust nature of the solar sail will leave Solar Cruiser highly sensitive to external environmental effects (such as solar radiation pressure and high-order gravitational perturbations) throughout the entirety of flight. Because of this, preliminary operational optimization routines must be intricately tied to high-order predictive propagation models to ensure the greatest possible confidence in mission success. The Solar Cruiser Mission Design and Navigation (MDNav) team has designed a software tool suite, employing the latest in software containerization technology, to accomplish this task; allowing for seamless development across several users and operating systems. Combining JPL’s Monte toolkit with high-performance optimizers written by the University of Alabama, the proposed architecture allows for instant verification of optimized trajectories within the same development environment that the optimization takes place, removing the need for mission designers and navigators to switch between tools. The MDNav suite image deployment process is separated from the development and operational scripts to be used in flight, which allows for maintaining a low-footprint version control profile without unnecessary file bloating. This paper discusses the historical differences between previous iterations of the Solar Cruiser MDNav tool suite and the current iteration, planned operational interfaces of the tool with other software and subsystems, and the planned path forward in maintaining containerization services for the software throughout the lifetime of Solar Cruiser.

optimization↗

NASA NTRSDate not supplied

An Integrated Software Architecture for Solar Cruiser Mission Design and Navigation

Solar Cruiser is a solar sailing mission, riding as a secondary payload to the Interstellar Mapping and Acceleration Probe (IMAP) mission, expected to launch in February of 2025. The Solar Cruiser vehicle will generate thrust via a complex, low-thrust solar sail. The extreme low-thrust nature of the solar sail will leave Solar Cruiser highly sensitive to external environmental effects (such as solar radiation pressure and high-order gravitational perturbations) throughout the entirety of flight. Because of this, preliminary & operational optimization routines must be intricately tied to high-order predictive propagation models to ensure the greatest possible confidence in mission success. The Solar Cruiser Mission Design and Navigation (MDNav) team has designed a software tool suite, employing the latest in software containerization technology, to accomplish this task, allowing for seamless development across several users and operating systems. Combining JPL’s Monte toolkit with high-performance optimizers written by researchers at the University of Alabama, the proposed architecture allows for instant verification of optimized trajectories within the same development environment that the optimization takes place, removing the need for mission designers and navigators to switch between tools. The MDNav software suite itself is separated from the development and operational scripts to be used in flight, which allows for maintaining a low-footprint version control profile – thus avoiding unnecessary file bloating. This paper discusses the historical differences between previous iterations of the Solar Cruiser MDNav tool suite and the current iteration, planned operational interfaces of the tool with other software and subsystems, and the planned path forward in maintaining containerization services for the software throughout the lifetime of Solar Cruiser.

Containerization↗

NASA NTRSDate not supplied

An Integrated Software Architecture for Solar Cruiser Mission Design and Navigation

Solar Cruiser is a solar sailing mission, riding as a secondary payload to the Interstellar Mapping and Acceleration Probe (IMAP) mission, expected to launch in February of 2025. The Solar Cruiser vehicle will generate thrust via a complex, low-thrust solar sail. The extreme low-thrust nature of the solar sail will leave Solar Cruiser highly sensitive to external environmental effects (such as solar radiation pressure and high-order gravitational perturbations) throughout the entirety of flight. Because of this, preliminary & operational optimization routines must be intricately tied to high-order predictive propagation models to ensure the greatest possible confidence in mission success. The Solar Cruiser Mission Design and Navigation (MDNav) team has designed a software tool suite, employing the latest in software containerization technology, to accomplish this task, allowing for seamless development across several users and operating systems. Combining JPL’s Monte toolkit with University of Alabama’s high-performance optimizer, ASSET, the proposed architecture allows for instant verification of optimized trajectories within the same development environment that the optimization takes place, removing the need for mission designers and navigators to switch between tools. The MDNav software suite itself is separated from the development and operational scripts to be used in flight, which allows for maintaining a low-footprint version control profile – thus avoiding unnecessary file bloating. This paper discusses the historical differences between previous iterations of the Solar Cruiser MDNav tool suite and the current iteration, planned operational interfaces of the tool with other software and subsystems, and the planned path forward in maintaining containerization services for the software throughout the lifetime of Solar Cruiser.

solar cruiser↗

NASA NTRS1996

Inhomogeneous Radiation Boundary Conditions Simulating Incoming Acoustic Waves for Computational Aeroacoustics

A set of nonhomogeneous radiation and outflow conditions which automatically generate prescribed incoming acoustic or vorticity waves and, at the same time, are transparent to outgoing sound waves produced internally in a finite computation domain is proposed. This type of boundary condition is needed for the numerical solution of many exterior aeroacoustics problems. In computational aeroacoustics, the computation scheme must be as nondispersive ans nondissipative as possible. It must also support waves with wave speeds which are nearly the same as those of the original linearized Euler equations. To meet these requirements, a high-order/large-stencil scheme is necessary The proposed nonhomogeneous radiation and outflow boundary conditions are designed primarily for use in conjunction with such high-order/large-stencil finite difference schemes.

Tam, Christopher K. W.↗

NASA NTRS1995

Subband Image Coding with Jointly Optimized Quantizers

An iterative design algorithm for the joint design of complexity- and entropy-constrained subband quantizers and associated entropy coders is proposed. Unlike conventional subband design algorithms, the proposed algorithm does not require the use of various bit allocation algorithms. Multistage residual quantizers are employed here because they provide greater control of the complexity-performance tradeoffs, and also because they allow efficient and effective high-order statistical modeling. The resulting subband coder exploits statistical dependencies within subbands, across subbands, and across stages, mainly through complexity-constrained high-order entropy coding. Experimental results demonstrate that the complexity-rate-distortion performance of the new subband coder is exceptional.

Kossentini, Faouzi↗

NASA NTRS1998

Spurious Numerical Oscillations in Numerical Simulation of Supersonic Flows Using Shock Capturing Schemes

The numerical simulation of transitional and turbulent processes in hypersonic boundary layers often involves a physical process of a shock-disturbance wave interaction in complex two-dimensional and three-dimensional flow fields. For such simulations, it is required that there be a high order of accuracy in capturing both the shock and the small disturbances. The purpose of this paper is to evaluate the viability of using high order shock capturing schemes to track small disturbances in a multi-dimensional steady hypersonic flow. The numerical methods that are to be studied are the Total Variation Diminishing (TVD) scheme, and Essentially Non-Oscillatory (ENO) scheme. This paper shows that the presence of numerical oscillations in the flow field solution may drastically hinder any attempt at tracking the propagation of any physical disturbances. It has been found that the numerical oscillations that exist for shock capturing methods may be significant enough to pollute a flow field containing small physical disturbances. The effects of the refinement of the grid do not reduce the oscillations, but rather they decrease the wavelength of the oscillations. It is shown that by aligning the shock with the grid, the amplitude of these spurious oscillations may be greatly reduced.

Lee, Theodore K.↗

NASA NTRS2012

Quantum Limits of Space-to-Ground Optical Communications

For a pure loss channel, the ultimate capacity can be achieved with classical coherent states (i.e., ideal laser light): (1) Capacity-achieving receiver (measurement) is yet to be determined. (2) Heterodyne detection approaches the ultimate capacity at high mean photon numbers. (3) Photon-counting approaches the ultimate capacity at low mean photon numbers. A number of current technology limits drive the achievable performance of free-space communication links. Approaching fundamental limits in the bandwidth-limited regime: (1) Heterodyne detection with high-order coherent-state modulation approaches ultimate limits. SOA improvements to laser phase noise, adaptive optics systems for atmospheric transmission would help. (2) High-order intensity modulation and photon-counting can approach heterodyne detection within approximately a factor of 2. This may have advantages over coherent detection in the presence of turbulence. Approaching fundamental limits in the photon-limited regime (1) Low-duty cycle binary coherent-state modulation (OOK, PPM) approaches ultimate limits. SOA improvements to laser extinction ratio, receiver dark noise, jitter, and blocking would help. (2) In some link geometries (near field links) number-state transmission could improve over coherent-state transmission

laser communications↗

NASA NTRS1994

Composite-Plate-Buckling Analysis Program

Composite-Plate-Buckling Analysis Program (COMPPAP) helps engineers determine buckling loads of orthotropic or isotropic irregularly shaped plates without need to perform manual calculations and extensive finite-element mathematical modeling. One-element finite-element program utilizing high-order displacement functions to perform plane-stress analysis of general plate followed by buckling calculation based on stresses found in plane-stress solution. High order of displacement functions enables user to obtain results more accurately. Written in ANSI FORTRAN 77. Two machine versions available: (MSC-22428) for computers of IBM PC 386 and higher series and for compatible computers; and UNIX (MSC-22286).

Smith, James P.↗

NASA NTRS1987

Constrained optimization techniques for active control of aeroelastic response

Active control of aeroelastic response is a complex problem in which the designer usually tries to satisfy many design criteria which are often conflicting in nature. To further complicate the design problem, the state space equations describing this type of control problem are usually of high order, involving a large number of states to represent the flexible structure and unsteady aerodynamics. Control laws based on the standard Linear - Quadratic - Gaussian method are of the same high order as the aeroelastic plant and may be difficult to implement in the flight computer. To overcome this disadvantage a new approach was developed for designing low-order optimized robust control laws. In this approach, a nonlinear programming algorithm is used to search for the values of control law design variables that minimize a performance index while satisfying several inequality constraints that describe the design criteria on the stability robustness and responses. The method is applied to a gust load alleviation problem and a stability robustness improvement problem of a drone aircraft.

Mukhopadhyay, Vivekananda↗