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Matched asymptotic expansion method applied to ordinary and optimal trajectory problems in hypervelocity flight dynamics
The subject of magnetohydrodynamic simulations in the 1980's, magnetic turbulence has reemerged as a favored explanation for the production of fast magnetic reconnection. Recent three-dimensional simulations reveal the formation of secondary islands that serve to shorten the current sheet and increase the accelerating electric field, while both simulations and observations witness electron holes whose collapse energizes electrons. However, little work has been done to investigate the presence of turbulent magnetic and electric field spectra in association with in situ reconnection observations in space. In this study we address this deficiency by analyzing the wavelength spectra of two reconnection events established by multiple spacecraft observations in previous publications. We apply a k-filtering analysis to determine the wave vectors. To optimize the quality of the k-filtering analysis and minimize aliasing, we select multi-spacecraft observations having optimal spacecraft tetrahedral geometry and dimensions that resolve wavelengths within the ion diffusion region. We have chosen one dayside and one nightside reconnection event each observed by the Cluster spacecraft. Spatial correlation between the reconnecting current sheet and a turbulent magnetic spectrum supports an association between turbulence and reconnection in space. The k-filtering method, a wavelet time-frequency spectrum, and a polarization analysis serve to identify wave modes associated with the turbulence. A calculation of the reconnection electric field based on the normal component of the reconnecting magnetic field provides an estimate of the reconnection rate.
A variable-complexity strategy of combining simple and detailed analysis methods is presented for the design optimization of a high-speed civil transport (HSCT) wing. Two sets of results are shown: the aerodynamic design of the wing using algebraic weight equations for structural considerations, and optimization results of the internal wing structure for a fixed wing configuration. We show example results indicating that using simple analysis methods alone for the calculation of a critical constraint can allow an optimizer to exploit weaknesses in the analysis. The structural optimization results provide a valuable check for the weight equations used in the aerodynamic design. In addition, these results confirm the need for using simple, algebraic models in conjunction with more detailed analysis methods. A strategy of interlaced aerodynanic-structural design is proposed.
Space Station Freedom is designed to be an Earth-orbiting, multidiscipline research and development (R&D) facility capable of evolution to accomodate a variety of potential uses. One evolution scenario is growth to an enhanced R&D facility. In support of the Space Station Freedom Program Preliminary Design Review (PDR), the NASA Langley Research Center Space Station Office is analyzing growth requirements and evaluating configurations for this R&D utilization. This paper presents a summary of FY1989 study results including time-phased growth plans, R&D growth issues and configurations, and recommendations for the program baseline design which will facilitate evolutionary R&D growth. This study consisted of three major areas of concentration: mission requirements analysis; Space Station Freedom systems growth analysis; and growth accomodations and trades. Mission requirements analysis was performed to develop a realistic mission model of post-Phase 1 R&D missions. A systems-level analysis was performed to project incremental growth requirements of Space Station Freedom needed to support these R&D missions. Identification of growth requirements and specific growth elements led to the need for special accomodations analyses and trades. These studies included identification of hooks and scars on the baseline design, determination of an optimal module growth pattern, analysis of the dual keel length, and determination of an optimal locaton for the customer servicing facility. Results of this study show that Space Station Freedom must be capable of evolving to a dual keel, eight pressurized module configuration (two growth habs and two growth labs); providing 275 kW power (for experimenters and station housekeeping); accomodating a crew of 24; and supporting other growth structures and special facilities to meet projected R&D mission requirements.
Some basic methods used in reliability analysis are problematic because they produce incorrect and overoptimistic predictions. Initially gratifying forecasts are often invalidated by testing and operational experience. The problematic methods in reliability analysis include estimating the system failure rate as the sum of component failure rates, assuming that reliability growth continues indefinitely during testing, overestimating the benefits of redundancy, and using the fault tolerance count instead of a detailed reliability analysis. Reliability analysis can produce more optimism than accuracy. This bug may now be a feature. The optimistic bias inevitable in project planning should be corrected by realistic reliability analysis that reflects relevant experience. That the repeated poor performance of reliability analysis is found to be surprising suggests willful blindness. Rigorous methods and impartial critical review are necessary to improve reliability analysis.
Some basic methods used in reliability analysis are problematic because they produce incorrect and overoptimistic predictions. Initially gratifying forecasts are often invalidated by testing and operational experience. The problematic methods in reliability analysis include estimating the system failure rate as the sum of component failure rates, assuming that reliability growth continues indefinitely during testing, overestimating the benefits of redundancy, and using the fault tolerance count instead of a detailed reliability analysis. Reliability analysis can produce more optimism than accuracy. This bug may now be a feature. The optimistic bias inevitable in project planning should be corrected by realistic reliability analysis that reflects relevant experience. That the repeated poor performance of reliability analysis is found to be surprising suggests willful blindness. Rigorous methods and impartial critical review are necessary to improve reliability analysis.
In terminal airspace, integrating arrivals and departures with shared waypoints provides the potential of improving operational efficiency by allowing direct routes when possible. Incorporating stochastic evaluation as a post-analysis process of deterministic optimization, and imposing a safety buffer in deterministic optimization, are two ways to learn and alleviate the impact of uncertainty and to avoid unexpected outcomes. This work presents a third and direct way to take uncertainty into consideration during the optimization. The impact of uncertainty was incorporated into cost evaluations when searching for the optimal solutions. The controller intervention count was computed using a heuristic model and served as another stochastic cost besides total delay. Costs under uncertainty were evaluated using Monte Carlo simulations. The Pareto fronts that contain a set of solutions were identified and the trade-off between delays and controller intervention count was shown. Solutions that shared similar delays but had different intervention counts were investigated. The results showed that optimization under uncertainty could identify compromise solutions on Pareto fonts, which is better than deterministic optimization with extra safety buffers. It helps decision-makers reduce controller intervention while achieving low delays.
This paper presents a technical approach to improve the confidence in the systems analysis process by integrating Uncertainty Quantification (UQ) techniques within a Model-Based Systems Analysis and Engineering (MBSA&E) framework. The MBSA&E architecture uses system models and multidisciplinary analytical solutions as central artifacts for system design and analysis. The integration of UQ enables engineers to assess and mitigate uncertainties associated with a system model, design parameters, and constraint inputs, leading to more complete design studies and further informed decision-making processes. The proposed approach leverages the strengths of MBSA&E and extends it with a UQ methodology to quantify uncertainties in the input parameters and to trace the uncertainties as they propagate throughout the system model. To demonstrate the effectiveness of an integrated MBSA&E-UQ approach, a case study involving a simplified analysis of a Transonic Truss-Braced Wing (TTBW) concept vehicle is performed. This integration enables a more comprehensive evaluation of system performance and behavior under uncertainty and a more robust approach for system design and analysis. Lastly, the paper addresses the challenges and considerations associated with integrating UQ into an MBSA&E framework.
This paper presents a technical approach to improve the confidence in the systems analysis process by integrating Uncertainty Quantification (UQ) techniques within a Model-Based Systems Analysis and Engineering (MBSA&E) framework. The MBSA&E architecture uses system models and multidisciplinary analytical solutions as central artifacts for system design and analysis. The integration of UQ enables engineers to assess and mitigate uncertainties associated with a system model, design parameters, and constraint inputs, leading to more complete design studies and further informed decision-making processes. The proposed approach leverages the strengths of MBSA&E and extends it with a UQ methodology to quantify uncertainties in the input parameters and to trace the uncertainties as they propagate throughout the system model. To demonstrate the effectiveness of an integrated MBSA&E-UQ approach, a case study involving a simplified analysis of a Transonic Truss-Braced Wing (TTBW) concept vehicle is performed. This integration enables a more comprehensive evaluation of system performance and behavior under uncertainty and a more robust approach for system design and analysis. Lastly, the paper addresses the challenges and considerations associated with integrating UQ into an MBSA&E framework.
The optimal solution time that minimizes the sum of the two applied impulses necessary to rendezvous is obtained analytically for the Clohessy-Wiltshire equations with a linear gravity model assumption. A plume impingement inequality constraint on the solution is examined, and an optimal policy is developed. Numerical tests are conducted to verify the analysis and to illustrate the optimal solution algorithm.
An analytic approach is used to obtain the optimal solution time that minimizes the sum of the two applied impulses necessary to rendezvous for the Clohessy-Wiltshire equations. A plume impingement inequality constraint on the solution is examined, and an optimal policy is developed. Numerical tests are conducted to verify the analysis and to illustrate the optimal solution algorithm.
The paper deals with a NASA-sponsored, computer-based program Modeling and Analysis of Power Processing Systems (MAPPS). Three major MAPPS subprograms, Design Optimization, Control Design, and Performance Analysis are considered. The program makes it possible to reduce the design, analysis, and development time, and thus the cost, in achieving the required performance for power processing equipment and systems.
Contents include the following: Dual opposed convertors. High efficiency. Low mass space power. One-dimensional analysis. Fast computation. Design optimizations are easily done. Need for multidimensional modeling. Axisymmetric simulation. Flow characteristics. Low mach number. Laminar, transitional, and turbulent flow. Conjugate heat transfer. Third order analysis. Recent whole engine modeling. Regenerator geometry. Turbulence modeling. Flat head heater not 1-D. Empirical coefficients needed. Experiment design. Flow distribution. Sensor placement. Calibration. Validation.
An inviscid transonic code capable of designing an axisymmetric body in a uniform or nonuniform flow was developed. The design was achieved by direct optimiation by coupling an analysis code with an optimizer. Design examples were provided for axisymmetric bodies with fineness ratios of 8.33 and 5 at different Mach numbers. It was shown that by reducing the nose radius and increasing the afterbody thickness of initial shapes obtained from symmetric NACA four-digit airfoil contours, wave drag could be reduced by 29 percent for a body of fineness ratio 8.33 in a nonuniform transonic flow of M = 0.98 to 0.995. The reduction was 41 percent for a body of fineness ratio 5 in a uniform transonic flow of M = 0.925 and 65 percent for the same body but in a nonuniform transonic flow of M = 0.90 to 0.95.
The optimal control policy for the aeroglide portion of the minimum fuel, orbital plane change problem for maneuvering entry vehicles is reduced to the solution of a turning point problem for the bank angle control. For this problem a turning point occurs at the minimum altitude of the flight, when the flight path angle equals zero. The turning point separates the bank angle control into two outer solutions that are valid away from the turning point. In a neighborhood of the turning point, where the bank angle changes rapidly, an inner solution is developed and matched with the two outer solutions. An asymptotic analysis of the turning point problem is given, and an analytic example is provided to illustrate the construction of the bank angle control.
To facilitate the effective solution of multidisciplinary, multiobjective complex design problems, a departure from the traditional parametric design analysis and single objective optimization approaches is necessary in the preliminary stages of design. A necessary tradeoff becomes one of efficiency vs. accuracy as approximate models are sought to allow fast analysis and effective exploration of a preliminary design space. In this paper we apply a general robust design approach for efficient and comprehensive preliminary design to a large complex system: a high speed civil transport (HSCT) aircraft. Specifically, we investigate the HSCT wing configuration design, incorporating life cycle economic uncertainties to identify economically robust solutions. The approach is built on the foundation of statistical experimentation and modeling techniques and robust design principles, and is specialized through incorporation of the compromise Decision Support Problem for multiobjective design. For large problems however, as in the HSCT example, this robust design approach developed for efficient and comprehensive design breaks down with the problem of size - combinatorial explosion in experimentation and model building with number of variables -and both efficiency and accuracy are sacrificed. Our focus in this paper is on identifying and discussing the implications and open issues associated with the problem of size for the preliminary design of large complex systems.
Recent advances in parallel methods and algorithms integrated into large-scale codes are presented. Consideration is given to problem decomposition (substructuring), efficient matrix solution algorithms for shared memory architectures, dynamic and transient analysis algorithms for shared memory architectures, and algorithms for distributed and massively parallel architectures. Particular attention is given to partitioning of unstructured problems for parallel processing, parallel-vector computation for linear-structural analysis and nonlinear unconstraint optimization problems, a parallel-vector equation solver for unsymmetric matrices on supercomputers, parallel nonlinear finite element dynamic response, multigrid algorithms for solving structural mechanics problems on supercomputers, structural analysis on massively parallel computers, explicit finite element methods with contact-impact on SIMD computers, and the impact of mapping and sparsity on parallelized finite element method modules.
We have developed transition-edge sensor (TES) microcalorimeter arrays with high count-rate capability and high energy resolution to carry out x-ray imaging spectroscopy observations of various astronomical sources and the Sun. We have studied the dependence of the energy resolution and throughput (fraction of processed pulses) on the count rate for such microcalorimeters with two different transition temperatures T(sub c). Devices with both transition temperatures were fabricated within a single microcalorimeter array directly on top of a solid substrate where the thermal conductance of the microcalorimeter is dependent upon the thermal boundary resistance between the TES sensor and the dielectric substrate beneath. Because the thermal boundary resistance is highly temperature dependent, the two types of device with different T(sub c)(sup s) had very different thermal decay times, approximately one order of magnitude different. In our earlier report, we achieved energy resolutions of 1.6 and 2.eV at 6 keV from lower and higher T(sub c) devices, respectively, using a standard analysis method based on optimal filtering in the low flux limit. We have now measured the same devices at elevated x-ray fluxes ranging from 50 Hz to 1000 Hz per pixel. In the high flux limit, however, the standard optimal filtering scheme nearly breaks down because of x-ray pile-up. To achieve the highest possible energy resolution for a fixed throughput, we have developed an analysis scheme based on the socalled event grade method. Using the new analysis scheme, we achieved 5.0 eV FWHM with 96 Percent throughput for 6 keV x-rays of 1025 Hz per pixel with the higher T(sub c) (faster) device, and 5.8 eV FWHM with 97 Percent throughput with the lower T(sub c) (slower) device at 722 Hz.