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At least 541 records · Page 30

Optimal control of first order distributed systems

The problem of characterizing optimal controls for a class of distributed-parameter systems is considered. The system dynamics are characterized mathematically by a finite number of coupled partial differential equations involving first-order time and space derivatives of the state variables, which are constrained at the boundary by a finite number of algebraic relations. Multiple control inputs, extending over the entire spatial region occupied by the system ("distributed controls') are to be designed so that the response of the system is optimal. A major example involving boundary control of an unstable low-density plasma is developed from physical laws.

Johnson, T. L.↗

Enhanced Multiobjective Optimization Technique for Comprehensive Aerospace Design

A multidisciplinary design optimization procedure which couples formal multiobjectives based techniques and complex analysis procedures (such as computational fluid dynamics (CFD) codes) developed. The procedure has been demonstrated on a specific high speed flow application involving aerodynamics and acoustics (sonic boom minimization). In order to account for multiple design objectives arising from complex performance requirements, multiobjective formulation techniques are used to formulate the optimization problem. Techniques to enhance the existing Kreisselmeier-Steinhauser (K-S) function multiobjective formulation approach have been developed. The K-S function procedure used in the proposed work transforms a constrained multiple objective functions problem into an unconstrained problem which then is solved using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. Weight factors are introduced during the transformation process to each objective function. This enhanced procedure will provide the designer the capability to emphasize specific design objectives during the optimization process. The demonstration of the procedure utilizes a computational Fluid dynamics (CFD) code which solves the three-dimensional parabolized Navier-Stokes (PNS) equations for the flow field along with an appropriate sonic boom evaluation procedure thus introducing both aerodynamic performance as well as sonic boom as the design objectives to be optimized simultaneously. Sensitivity analysis is performed using a discrete differentiation approach. An approximation technique has been used within the optimizer to improve the overall computational efficiency of the procedure in order to make it suitable for design applications in an industrial setting.

Chattopadhyay, Aditi↗

Integrated Control Using the SOFFT Control Structure

The need for integrated/constrained control systems has become clearer as advanced aircraft introduced new coupled subsystems such as new propulsion subsystems with thrust vectoring and new aerodynamic designs. In this study, we develop an integrated control design methodology which accomodates constraints among subsystem variables while using the Stochastic Optimal Feedforward/Feedback Control Technique (SOFFT) thus maintaining all the advantages of the SOFFT approach. The Integrated SOFFT Control methodology uses a centralized feedforward control and a constrained feedback control law. The control thus takes advantage of the known coupling among the subsystems while maintaining the identity of subsystems for validation purposes and the simplicity of the feedback law to understand the system response in complicated nonlinear scenarios. The Variable-Gain Output Feedback Control methodology (including constant gain output feedback) is extended to accommodate equality constraints. A gain computation algorithm is developed. The designer can set the cross-gains between two variables or subsystems to zero or another value and optimize the remaining gains subject to the constraint. An integrated control law is designed for a modified F-15 SMTD aircraft model with coupled airframe and propulsion subsystems using the Integrated SOFFT Control methodology to produce a set of desired flying qualities.

Halyo, Nesim↗

STARBASE: Database software for the automated plate scanner

The Automated Plate Scanner (APS) of the University of Minnesota, a unique high speed 'flying spot' laser scanner, is currently being used to scan and digitize the 936 O and E plate pairs of the first epoch Palomar Sky Survey. The resultant database will be used to produce a catalog of approximately a billion stars and several million galaxies. The authors describe the ongoing development of a dedicated APS database management system which will be made available to the astronomical community via INTERNET. A specialized DBMS called STARBASE has been written to provide fast access to the hundreds of millions of images collected by the APS. This system provides an initial reduction mode for parameterizing APS images and classifying image types using a novel set of neural network image classifiers. A second analysis mode, which will be that commonly used by the general user, provides for searches of the database which may be constrained by any combination of physical and positional parameters. Through the use of pointer hash trees, the system has been optimized for extremely fast positional searches using either right ascension and declination on the sky or linear X and Y positions on the POSS field. In addition to fast data retrieval, the system provides a graphical interface for displaying scatter plots or histograms of the collected data. In addition, a specialized image display system is being developed to allow the user to view densitometric data for all objects classified as extended by the neural network system. Finally, STARBASE has a flexible programmable interface which allows other programs to access information in the database. This allows users to write applications suited to their particular needs to process APS data.

Odewahn, S. C.↗

Weighting Statistical Inputs for Data Used to Support Effective Decision Making During Severe Emergency Weather and Environmental Events

National Aeronautical and Space Administration (NASA) weather and atmospheric environmental organizations are insatiable consumers of geophysical, hydrometeorological and solar weather statistics. The expanding array of internet-worked sensors producing targeted physical measurements has generated an almost factorial explosion of near real-time inputs to topical statistical datasets. Normalizing and value-based parsing of such statistical datasets in support of time-constrained weather and environmental alerts and warnings is essential, even with dedicated high-performance computational capabilities. What are the optimal indicators for advanced decision making? How do we recognize the line between sufficient statistical sampling and excessive, mission destructive sampling ? How do we assure that the normalization and parsing process, when interpolated through numerical models, yields accurate and actionable alerts and warnings? This presentation will address the integrated means and methods to achieve desired outputs for NASA and consumers of its data.

Gardner, Adrian↗

Adaptive nonlinear optimization of the signal-to-noise ratio of an array subject to a constraint.

Investigation of a stochastic projected gradient algorithm which can be used to find a constrained optimum point for a concave or convex objective function subject to nonlinear constraints. When the constraint consists of only one linear equation, convergence to the constrained optimum value is proven, and bounds are obtained for the rate of convergence of the algorithm to the constrained optimum value. This algorithm is then applied to the nonlinear problem of automatically making an array of detectors form a beam in a desired direction in space when unknown interfering noise is present so as to maximize the signal-to-noise ratio subject to a constraint on the supergain ratio.

Winkler, L. P.↗

Concurrent material-fabrication optimization of metal-matrix laminates under thermo-mechanical loading

A methodology is developed to tailor fabrication and material parameters of metal-matrix laminates for maximum loading capacity under thermomechanical loads. The stresses during the thermomechanical response are minimized subject to failure constrains and bounds on the laminate properties. The thermomechanical response of the laminate is simulated using nonlinear composite mechanics. Evaluations of the method on a graphite/copper symmetric cross-ply laminate were performed. The cross-ply laminate required different optimum fabrication procedures than a unidirectional composite. Also, the consideration of the thermomechanical cycle had a significant effect on the predicted optimal process.

Saravanos, D. A.↗

Cosmic-structure constraints from a one-degree microwave-background anisotropy experiment

A recent anisotropy experiment with a 30-arcmin beam is close to optimal for testing models in which cosmic structure arose from inflation-generated Gaussian density perturbations. Using a Bayesian analysis to constrain the amplitude of the perturbation spectrum, it is shown that adiabatic hot-dark-matter models are convincingly ruled out and cold-dark-matter models have anisotropies near the derived limits. Theories with broken scale invariance such as isocurvature baryon models are strongly constrained, as are models with extra power crafted to give significant large-scale structures and flows.

Bond, J. R.↗

Analytical solutions to constrained hypersonic flight trajectories

The flight trajectory of aerospace vehicles subject to a class of path constraints is considered. The constrained dynamics is shown to be a natural two-time-scale system. Asymptotic analytical solutions are obtained. Problems of trajectory optimization and guidance can be dramatically simplified with these solutions. Applications in trajectory design for an aerospace plane strongly support the theoretical development.

Lu, Ping↗

Analytical solutions to constrained hypersonic flight trajectories

The flight trajectory of aerospace vehicles subject to a class of path constraints is considered. The constrained dynamics is shown to be a natural two-time-scale system. Asymptotic analytical solutions are obtained. Problems of trajectory optimization and guidance can be dramatically simplified with these solutions. Applications in trajectory design for an aerospace plane strongly support the theoretical development.

Lu, Ping↗

A Globally Convergent Augmented Lagrangian Pattern Search Algorithm for Optimization with General Constraints and Simple Bounds

We give a pattern search adaptation of an augmented Lagrangian method due to Conn, Gould, and Toint. The algorithm proceeds by successive bound constrained minimization of an augmented Lagrangian. In the pattern search adaptation we solve this subproblem approximately using a bound constrained pattern search method. The stopping criterion proposed by Conn, Gould, and Toint for the solution of this subproblem requires explicit knowledge of derivatives. Such information is presumed absent in pattern search methods; however, we show how we can replace this with a stopping criterion based on the pattern size in a way that preserves the convergence properties of the original algorithm. In this way we proceed by successive, inexact, bound constrained minimization without knowing exactly how inexact the minimization is. So far as we know, this is the first provably convergent direct search method for general nonlinear programming.

Lewis, Robert Michael↗

Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Final Maps and Results

We present the final nine-year maps and basic results from the Wilkinson Microwave Anisotropy Probe (WMAP) mission. The full nine-year analysis of the time-ordered data provides updated characterizations and calibrations of the experiment. We also provide new nine-year full sky temperature maps that were processed to reduce the asymmetry of the effective beams. Temperature and polarization sky maps are examined to separate cosmic microwave background (CMB) anisotropy from foreground emission, and both types of signals are analyzed in detail.We provide new point source catalogs as well as new diffuse and point source foreground masks. An updated template-removal process is used for cosmological analysis; new foreground fits are performed, and new foreground reduced are presented.We nowimplement an optimal C(exp -1)1 weighting to compute the temperature angular power spectrum. The WMAP mission has resulted in a highly constrained Lambda-CDM cosmological model with precise and accurate parameters in agreement with a host of other cosmological measurements. When WMAP data are combined with finer scale CMB, baryon acoustic oscillation, and Hubble constant measurements, we find that big bang nucleosynthesis is well supported and there is no compelling evidence for a non-standard number of neutrino species (N(sub eff) = 3.84 +/- 0.40). The model fit also implies that the age of the universe is (sub 0) = 13.772 +/- 0.059 Gyr, and the fit Hubble constant is H(sub 0) = 69.32 +/- 0.80 km/s/ Mpc. Inflation is also supported: the fluctuations are adiabatic, with Gaussian random phases; the detection of a deviation of the scalar spectral index from unity, reported earlier by the WMAP team, now has high statistical significance (n(sub s) = 0.9608+/-0.0080); and the universe is close to flat/Euclidean (Omega = −0.0027+0.0039/−0.0038). Overall, the WMAP mission has resulted in a reduction of the cosmological parameter volume by a factor of 68,000 for the standard six-parameter Lambda-CDM model, based on CMB data alone. For a model including tensors, the allowed seven-parameter volume has been reduced by a factor 117,000. Other cosmological observations are in accord with the CMB predictions, and the combined data reduces the cosmological parameter volume even further.With no significant anomalies and an adequate goodness of fit, the inflationary flat Lambda-CDM model and its precise and accurate parameters rooted in WMAP data stands as the standard model of cosmology.

dark matter↗

Optical and Mechanical Designs of the Multi-band SWIR Receiver for the Lunar Flashlight CubeSat Mission

Mapping and quantifying lunar water ice addresses one of NASA’s Strategic Knowledge Gaps to understand the lunar resource potential for future human exploration of the Moon. Lunar Flashlight is an innovative NASA CubeSat mission dedicated to mapping water ice in the permanently-shadowed and occasionally-sunlit regions in the vicinity of the lunar South Pole. Lunar Flashlight will acquire these measurements from lunar orbit using a multi-band laser reflectometer composed of an optical receiver aligned with four lasers emitting different wavelengths in the shortwave infrared spectral region between 1 µm and 2 µm. The receiver measures the laser radiance reflected from the lunar surface in each spectral band and continuum/absorption reflectance band ratios are then analyzed to quantify water ice concentration in the illuminated spot. The receiver utilizes a 70×70-mm, aluminum, off-axis paraboloidal mirror with a focal length of 70 mm, which collects the incoming light onto a single, 2 mm diameter InGaAs detector with a cutoff wavelength of 2.4 µm. We present the optical and mechanical designs of the receiver, including its optimization for rejection of solar stray-light from outside its intended field of view. This highly mass- and volume-constrained instrument payload will demonstrate several firsts, including being one of the first instruments onboard a CubeSat performing science measurements beyond low Earth orbit and the first planetary mission to use multi-band active reflectometry from orbit.

Sellar, R. Glenn↗

A Functional Interpolation Approach to Compute Period Orbits in the Circular Restricted Three-body Problem

In this paper, we develop a method to solve for periodic orbits, i.e., Lyapunov and Halo orbits, using a functional interpolation scheme called the Theory of Func- tional Connections (TFC). Using this technique, a periodic constraint is analyti- cally embedded into the TFC constrained expression. By doing this, the system of differential equations governing the three-body problem is transformed into an unconstrained optimization problem where simple numerical schemes can be used to find a solution, e.g., nonlinear least-squares is used. This allows for a simpler numerical implementation with comparable accuracy and speed to the traditional differential corrector method.

Mortari, Daniele↗

Broadband Predictions of Optimized Proprotors in Axial Forward Flight

A low-fidelity toolchain was used to predict broadband self-noise trends for three proprotors in axial flight: a baseline (C24ND) and two acoustically constrained proprotors (OPT-III and COPR-3). Rotor loads were predicted with the ANOPP Propeller Analysis System (PAS) and self-noise was predicted with the semiempirical method of Brooks, Pope, and Marcolini (BPM) implemented in the ANOPP2 Self-Noise Internal Functional Module (ASNIFM). Comparisons to experimental data revealed that trends for turbulent boundary layer trailing edge (TBL-TE) noise could be modeled across several flight conditions by increasing the boundary layer thicknesses via the trip setting. Since the Mach number range of the BPM method is exceeded in these predictions, a dependence of boundary layer displacement thickness on blade station Mach number was suggested as a possible reason for needing to model thicker boundary layers, suggesting that the TBL-TE model needs to be developed further. Bluntness vortex shedding noise (BVS) predictions required tuning the trailing edge thickness and trailing edge closure angle for each flight condition to match experimental trends, demonstrating that the BVS noise model is incomplete and that BVS noise may vary with the angle of attack. This study indicates that the BPM self-noise method needs to be improved, which will lead to more accurate broadband predictions.

Broadband self-noise↗

Broadband Predictions of Optimized Proprotors in Axial Forward Flight

A low-fidelity toolchain was used to predict broadband self-noise trends for three proprotors in axial flight: a baseline (C24ND) and two acoustically constrained proprotors (OPT-III and COPR-3). Rotor loads were predicted with the ANOPP Propeller Analysis System (PAS) and self-noise was predicted with the semiempirical method of Brooks, Pope, and Marcolini (BPM) implemented in the ANOPP2 Self-Noise Internal Functional Module (ASNIFM). Comparisons to experimental data revealed that trends for turbulent boundary layer trailing edge (TBL-TE) noise could be modeled across several flight conditions by increasing the boundary layer thicknesses via the trip setting. Since the Mach number range of the BPM method is exceeded in these predictions, a dependence of boundary layer displacement thickness on blade station Mach number was suggested as a possible reason for needing to model thicker boundary layers, suggesting that the TBL-TE model needs to be developed further. Bluntness vortex shedding noise (BVS) predictions required tuning the trailing edge thickness and trailing edge closure angle for each flight condition to match experimental trends, demonstrating that the BVS noise model is incomplete and that BVS noise may vary with the angle of attack. This study indicates that the BPM self-noise method needs to be improved, which will lead to more accurate broadband predictions.

Broadband self-noise↗

Leading-edge slat optimization for maximum airfoil lift

A numerical procedure for determining the position (horizontal location, vertical location, and deflection) of a leading edge slat that maximizes the lift of multielement airfoils is presented. The structure of the flow field is calculated by iteratively coupling potential flow and boundary layer analysis. This aerodynamic calculation is combined with a constrained function minimization analysis to determine the position of a leading edge slat so that the suction peak on the nose of the main airfoil is minized. The slat position is constrained by the numerical procedure to ensure an attached boundary layer on the upper surface of the slat and to ensure negligible interaction between the slat wake and the boundary layer on the upper surface of the main airfoil. The highest angle attack at which this optimized slat position can maintain attached flow on the main airfoil defines the optimum slat position for maximum lift. The design method is demonstrated for an airfoil equipped with a leading-edge slat and a trailing edge, single-slotted flap. The theoretical results are compared with experimental data, obtained in the Ames 40 by 80 Foot Wind Tunnel, to verify experimentally the predicted slat position for maximum lift. The experimentally optimized slat position is in good agreement with the theoretical prediction, indicating that the theoretical procedure is a feasible design method.

Olson, L. E.↗

Augmenting Parametric Optimal Ascent Trajectory Modeling with Graph Theory

It has been well documented that decisions made in the early stages of Conceptual and Pre-Conceptual design commit up to 80% of total Life-Cycle Cost (LCC) while engineers know the least about the product they are designing [1]. Once within Preliminary and Detailed design however, making changes to the design becomes far more difficult to enact in both cost and schedule. Primarily this has been due to a lack of detailed data usually uncovered later during the Preliminary and Detailed design phases. In our current budget-constrained environment, making decisions within Conceptual and Pre-Conceptual design which minimize LCC while meeting requirements is paramount to a program's success. Within the arena of launch vehicle design, optimizing the ascent trajectory is critical for minimizing the costs present within such concerns as propellant, aerodynamic, aeroheating, and acceleration loads while meeting requirements such as payload delivered to a desired orbit. In order to optimize the vehicle design its constraints and requirements must be known, however as the design cycle proceeds it is all but inevitable that the conditions will change. Upon that change, the previously optimized trajectory may no longer be optimal, or meet design requirements. The current paradigm for adjusting to these updates is generating point solutions for every change in the design's requirements [2]. This can be a tedious, time-consuming task as changes in virtually any piece of a launch vehicle's design can have a disproportionately large effect on the ascent trajectory, as the solution space of the trajectory optimization problem is both non-linear and multimodal [3]. In addition, an industry standard tool, Program to Optimize Simulated Trajectories (POST), requires an expert analyst to produce simulated trajectories that are feasible and optimal [4]. In a previous publication the authors presented a method for combatting these challenges [5]. In order to bring more detailed information into Conceptual and Pre-Conceptual design, knowledge of the effects originating from changes to the vehicle must be calculated. In order to do this, a model capable of quantitatively describing any vehicle within the entire design space under consideration must be constructed. This model must be based upon analysis of acceptable fidelity, which in this work comes from POST. Design space interrogation can be achieved with surrogate modeling, a parametric, polynomial equation representing a tool. A surrogate model must be informed by data from the tool with enough points to represent the solution space for the chosen number of variables with an acceptable level of error. Therefore, Design Of Experiments (DOE) is used to select points within the design space to maximize information gained on the design space while minimizing number of data points required. To represent a design space with a non-trivial number of variable parameters the number of points required still represent an amount of work which would take an inordinate amount of time via the current paradigm of manual analysis, and so an automated method was developed. The best practices of expert trajectory analysts working within NASA Marshall's Advanced Concepts Office (ACO) were implemented within a tool called multiPOST. These practices include how to use the output data from a previous run of POST to inform the next, determining whether a trajectory solution is feasible from a real-world perspective, and how to handle program execution errors. The tool was then augmented with multiprocessing capability to enable analysis on multiple trajectories simultaneously, allowing throughput to scale with available computational resources. In this update to the previous work the authors discuss issues with the method and solutions.

Patrick D Dees↗