Boundary value problems associated with optimization theory
Trajectory physics optimization for boundary value problem solution
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Trajectory physics optimization for boundary value problem solution
Design-Build-Test approaches for developing spaceflight hardware are prohibitively time and cost intensive and often lead to suboptimal mechanism designs. Approaches that couple machine learning and high-fidelity physics simulation could eliminate the need for hardware prototyping and dramatically accelerate the engineering design cycle, ultimately reducing cost. This work presents a modular NASA-developed toolchain to optimize hardware mechanisms in a virtual environment using numerical optimization and multi-body physics simulation. The toolchain enables multi-objective optimization, generates parametric CAD files that can be further post-processed by an end user, and can be expanded to optimize full systems and non-mechanical parameters such as feedback control variables. We demonstrate the toolchain through an independently verifiable design problem that optimizes wheel radius to achieve a desired linear velocity in a rigid-body physics environment when the wheel rotates at a constant angular speed, and then post-process the parametric CAD file of the optimal design generated by the tool before ultimately manufacturing it via 3D printing. We end with a discussion of how the toolchain can incorporate other analysis tools, including finite element analysis, computational fluid dynamics, and granular media simulations.
The invention is an apparatus and method of biofeedback training for attaining a physiological state optimally consistent with the successful performance of a task, wherein the probability of successfully completing the task is made is inversely proportional to a physiological difference value, computed as the absolute value of the difference between at least one physiological signal optimally consistent with the successful performance of the task and at least one corresponding measured physiological signal of a trainee performing the task. The probability of successfully completing the task is made inversely proportional to the physiological difference value by making one or more measurable physical attributes of the environment in which the task is performed, and upon which completion of the task depends, vary in inverse proportion to the physiological difference value.
This slide presentation reviews some of the exercises and exercise equipment that have been developed to assist in maintaining the astronauts' physical fitness, especially on long space missions.
Detailed data are presented on phenolic-glass and phenolic-asbestos compounds which compare the effect of compression molding without degas to the effects of four variations of compression molding. These variations were designed to improve elimination of entrapped volatiles and the volatile products of the condensate reaction associated with the cure of phenolic resins. The utilization of conventional methods of degas plus degas by vacuum and directional heat flow methods are involved. Detailed data are also presented on these same compounds, comparing the effect of changes in post-bake time, and post-bake temperature for the five molding techniques.
This paper addresses the development of a nonlinear optimal control methodology for magnetostrictive actuators. At moderate to high drive levels, the output from these actuators is highly nonlinear and contains significant magnetic and magnetomechanical hysteresis. These dynamics must be accommodated by models and control laws to utilize the full capabilities of the actuators. A characterization based upon ferromagnetic mean field theory provides a model which accurately quantifies both transient and steady state actuator dynamics under a variety of operating conditions. The control method consists of a linear perturbation feedback law used in combination with an optimal open loop nonlinear control. The nonlinear control incorporates the hysteresis and nonlinearities inherent to the transducer and can be computed offline. The feedback control is constructed through linearization of the perturbed system about the optimal system and is efficient for online implementation. As demonstrated through numerical examples, the combined hybrid control is robust and can be readily implemented in linear PDE-based structural models.
Research project summaries in propulsion, guidance and control, trajectory optimization, physics and chemistry, communications, and related space sciences
In this paper, the operational Global Precipitation Measurement (GPM) mission combined radar-radiometer algorithm is thoroughly described. The operational combined algorithm is designed to reduce uncertainties in GPM Core Observatory precipitation estimates by effectively integrating complementary information from the GPM Dual-Frequency Precipitation Radar (DPR) and the GPM Microwave Imager (GMI) into an optimal, physically consistent precipitation product. Although similar in many respects to previously developed combined algorithms, the GPM combined algorithm has several unique features that are specifically designed to meet the GPM objectives of deriving, based on GPM Core Observatory information, accurate and physically consistent precipitation estimates from multiple spaceborne instruments, and ancillary environmental data from reanalyses. The algorithm features an optimal estimation framework based on a statistical formulation of the Gauss-Newton method, a parameterization for the nonuniform distribution of precipitation within the radar fields of view, a methodology to detect and account for multiple scattering in Ka-band DPR observations, and a statistical deconvolution technique that allows for an efficient sequential incorporation of radiometer information into DPR precipitation retrievals.
In this paper, a unique system level spacecraft design optimization will be presented. A Genetic Algorithm is used to design the global pattern of the reinforcing structure, while a gradient routine is used to adequately stiffen the sub-structure. The system level structural design includes determining the optimal physical location (and number) of reinforcing beams of a lunar pallet lander deck structure. Design of the substructure includes determining placement of secondary stiffeners and the number of rivets required for assembly.. In this optimization, several considerations are taken into account. The primary objective was to raise the primary natural frequencies of the structure such that the Pallet Lander primary structure does not significantly couple with the launch vehicle. A secondary objective is to determine how to properly stiffen the reinforcing beams so that the beam web resists the shear buckling load imparted by the spacecraft components mounted to the pallet lander deck during launch and landing. A third objective is that the calculated stress does not exceed the allowable strength of the material. These design requirements must be met while, minimizing the overall mass of the spacecraft. The final paper will discuss how the optimization was implemented as well as the results. While driven by optimization algorithms, the primary purpose of this effort was to demonstrate the capability of genetic algorithms to enable design automation in the preliminary design cycle. By developing a routine that can automatically generate designs through the use of Finite Element Analysis, considerable design efficiencies, both in time and overall product, can be obtained over more traditional brute force design methods.
Estimates of surface precipitation and the associated vertical latent heating structure can be retrieved from space-borne passive microwave sensors such as the TRMM Microwave Imager (TMI) and Special Sensor Microwave/Imager (SSM/I). Studies have shown that assimilation of microwave rain rates can improve the quality of global analysis and forecast. Numerical weather prediction (NWP) centers are beginning to make operational use of these data. In the next few years, there will be a gradual increase in microwave rain products available from operational and research satellites, culminating to a target constellation of 9 satellites to provide global rain measurements every 3 hours with the proposed Global Precipitation Measurement (GPM) mission to be launched around 2007. Realizing the full potential of these observations in data assimilation will require continued advances in retrieval algorithms, assimilation techniques, and model physics. I present results from two research efforts at NASA GSFC. The first is on the assimilation of tropical precipitation using temperature/moisture tendency corrections within a continuous variational assimilation framework to improve analyses and forecasts produced by the Goddard Earth Observing System (GEOS) global data assimilation system. Results show that assimilation of TMI and SSM/I rain rates improves not only precipitation and moisture, but also the related clouds, radiation energy fluxes, and large-scale circulations in GEOS analyses. The improved analyses also yield better short-range forecasts, quantitative precipitation forecast (QPF) threat scores, and storm track predictions. The second part consists of results from exploratory experiments on variational assimilation of convective and stratiform latent heating profiles within the general framework of model parameter estimation as a way to identify systematic model errors and optimize physical paremeterization schemes in global forecast and climate models.
The development of pure phase 123 and Bi-based 2223 superconductors has been optimized. The pre-heat processing appears to be a very important parameter in achieving optimal physical properties. The synthesis of pure phases in the Bi-based system involves effects due to oxygen partial pressure, time, and temperature. Orientation/melt-sintering effects include the extreme c-axis orientation of Yttrium 123 and Bismuth 2223, 2212, and 2201 phases. This orientation is conductive to increasing critical currents. A procedure was established to substitute Sr for Ba in Y-123 single crystals.
Measurement of multiple biologic and non-biologic signals can be exploited for the task of monitoring the physiological status of individuals - either as patients during and following illness or injury or as those engaged in operational activities. Assessing physiological status is accomplished by measuring vital signs and wellness measures that support clinical decision-making for physical optimization, illness/injury prevention and treatment, recovery progression, and general delivery of care, or monitoring an operator's moment-to-moment personal "readiness" state. Physiological measures are beneficial for monitoring the medical state of vehicle operators, for example, through the detection of incapacitation in the realm of transportation safety. Measuring physiological signals or control inputs can also be beneficial for monitoring operator state to optimize human-autonomy-teaming performance for safety and efficiency. Similarly, monitoring a health care provider during the performance of medical procedures could provide valuable feedback on optimizing human-robot interactions and human teaming with autonomous systems. In this sense, the provider can be seen as a "Medical Operator" in the same way other "operators" drive, aviate, or control vehicles by performing manual, attention-demanding tasks during safety-critical activities.
Mathematical model for cost estimates and optimal control of ultrahigh vacuum system
A method to optimize the Faraday MHD generator performance under a prescribed set of electrical and magnet constraints is described. The results of generator performance calculations using this technique are presented for a very large MHD/steam plant. The differences between the maximum power and maximum net power generators are described. The sensitivity of the generator performance to the various operational parameters are presented.
Specially designed focusing of light beams has been proposed as a means of improving the performances of optical buffers based on cells containing hot atomic vapors (e.g., rubidium vapor). There is also a companion proposal to improve performance by use of incoherent optical pumping under suitable conditions. Regarding the proposal to use focusing: The utility of atomic-vapor optical buffers as optical storage and processing devices has been severely limited by nonuniform spatial distributions of intensity in optical beams, arising from absorption of the beams as they propagate in atomic-vapor cells. Such nonuniformity makes it impossible to optimize the physical conditions throughout a cell, thereby making it impossible to optimize the performance of the cell as an optical buffer. In practical terms simplified for the sake of brevity, "to optimize" as used here means to design the cell so as to maximize the group delay of an optical pulse while keeping the absorption and distortion of the pulse reasonably small. Regarding the proposal to use incoherent optical pumping: For reasons too complex to describe here, residual absorption of light is one of the main impediments to achievement of desirably long group delays in hot atomic vapors. The present proposal is directed toward suppressing residual absorption of light. The idea of improving the performance of slow-light optical buffers by use of incoherent pumping overlaps somewhat with the basic idea of Raman-based slow-light systems. However, prior studies of those systems did not quantitatively answer the question of whether the performance of an atomic vapor or other medium that exhibits electromagnetically induced transparency (EIT) with Raman gain is superior to that of a medium that exhibits EIT without Raman gain.
A technique has been described which optimizes the power out of a Faraday MHD generator operating under a prescribed set of electrical and magnetic constraints. The method does not rely on complicated numerical optimization techniques. Instead the magnetic field and the electrical loading are adjusted at each streamwise location such that the resultant generator design operates at the most limiting of the cited stress levels. The simplicity of the procedure makes it ideal for optimizing generator designs for system analysis studies of power plants. The resultant locally optimum channel designs are, however, not necessarily the global optimum designs. The results of generator performance calculations are presented for an approximately 2000 MWe size plant. The difference between the maximum power generator design and the optimal design which maximizes net MHD power are described. The sensitivity of the generator performance to the various operational parameters are also presented.
A generalized Markov chain representation of fault dynamics is presented for the case that available modeling of fault growth physics and future environmental stresses can be represented by two independent stochastic process models. A contrived but representatively challenging example will be presented and analyzed, in which uncertainty in the modeling of fault growth physics is represented by a uniformly distributed dice throwing process, and a discrete random walk is used to represent uncertain modeling of future exogenous loading demands to be placed on the system. A finite horizon dynamic programming algorithm is used to solve for an optimal control policy over a finite time window for the case that stochastic models representing physics of failure and future environmental stresses are known, and the states of both stochastic processes are observable by implemented control routines. The fundamental limitations of optimization performed in the presence of uncertain modeling information are examined by comparing the outcomes obtained from simulations of an optimizing control policy with the outcomes that would be achievable if all modeling uncertainties were removed from the system.
Wing design optimization has been studied extensively and is of continued interest as optimization tools are developed and become more accessible. In each of these studies, certain assumptions and simplifications are made to make the design problem tractable. However, it is difficult to find systematic studies in which several considerations are added or removed one at a time to study how much impact they have. In this work, we examine how certain physical considerations (viscous drag, wave drag, thrust loads, and inertial relief from structural, fuel, and engine masses), impact the aerostructural optimization results for three distinct aircraft wings. The goal is to help develop a rough idea of how important these physical considerations are. We do this using gradient-based optimization and a multidisciplinary design optimization framework, OpenMDAO. We use the open-source tool OpenAeroStruct that couples a vortex lattice method to a finite element method. We establish a baseline aerostructural design optimization problem then perform a series of optimizations, each with one physical consideration removed from the baseline case. We find that depending on the size of the aircraft and flight conditions, the importance of some of these physical considerations varies considerably whereas the importance of others do not. Specifically, the optimal designs change radically without proper viscous and wave drag considerations and smaller aircraft with more distributed propulsion are more affected by the inclusion of engine loads.