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This paper examines various first order approximation methods commonly used in structural optimization. It considers several attempts at improving the approximation by using previous analytical results and introduces an adaptation of a first order approximation method using an exponent adjusted to better fit the constraints and reduce the overall number of iterations needed to attain the optimum.
This paper examines various first order approximation methods commonly used in structural optimization. It considers several attempts at improving the approximation by using previous analytical results and introduces an adaptation of a first order approximation method using an exponent adjusted to better fit the constraints and reduce the overall number of iterations needed to attain the optimum.
A new approach to reconstruct the 3D surface of the object space from digital images is described. All the object points obtained by an automatic orientation procedure lead to a first approximation of the surface. Edges are computed for one image and matched to the other image by grey level correlation or least-squares matching through the scale space. To every discrete step in the scale space there exists the digital stereopair (image pyramid), the corresponding surface digital elevation model (DEM), and the warped images. The warped images in this discrete scale space representation correspond to digital orthophotos obtained from the DEMs that result from matching the image pyramid. The warped images will be used on every successive level in the image pyramid in order to reduce the foreshortening problems associated with any area-based matching method.
An efficient high speed aircraft design must achieve a high lift to drag ratio at transonic and supersonic speeds. In 1952 Dr. R. T. Jones proved that for any flight Mach number minimum drag at a fixed lift is achieved by an elliptic wing planform with an appropriate oblique sweep angle. Since then, wind tunnel tests and numerical flow models have confirmed that the compressibility drag of oblique wing aircraft is lower than similar symmetrical sweep designs. At oblique sweep angles above thirty degrees the highly asymmetric planform gives rise to aerodynamic and inertia couplings which affect stability and degrade the aircraft's handling qualities. In the case of the NASA-Rockwell Oblique Wing Research Aircraft, attempts to improve the handling qualities by implementing a stability augmentation system have produced unsatisfactory results because of an inherent lack of controllability in the proposed design. The present work focuses on improving the handling qualities of oblique wing aircraft by including aerodynamic configuration parameters as variables in the control system synthesis to provide additional degrees of freedom with which to further decouple the aircraft's response. Handling qualities are measured using a quadratic cost function identical to that considered in optimal control problems, but the controller architecture is not restricted to full state feedback. An optimization procedure is used to simultaneously solve for the aircraft configuration and control gains which maximize a handling qualities measure, while meeting imposed constraints on trim. In some designs wing flexibility is also modeled and reduced order controllers are implemented. Oblique wing aircraft synthesized by this integrated design method show significant improvement in handling qualities when compared to the originally proposed closed loop aircraft. The integrated design synthesis method is then extended to show how handling qualities may be traded for other types of mission performance (drag, weight, etc.). Examples are presented which show how performance can be maximized while maintaining a desired level of handling quality.
Finding the sources of sound in large nonlinear fields via direct simulation currently requires excessive computational cost. This paper describes a simple technique for efficiently solving the multidimensional nonlinear Euler equations that significantly reduces this cost and demonstrates a useful approach for validating high order nonlinear methods. Up to 15th order accuracy in space and time methods were compared and it is shown that an algorithm with a fixed design accuracy approaches its maximal utility and then its usefulness exponentially decays unless higher accuracy is used. It is concluded that at least a 7th order method is required to efficiently propagate a harmonic wave using the nonlinear Euler equations to a distance of 5 wavelengths while maintaining an overall error tolerance that is low enough to capture both the mean flow and the acoustics.
Volumetric forces resulting from local density variations and gravitational acceleration cause buoyancy induced convective motion in melts and solutions. Solutal buoyancy is a result of concentration differences in an otherwise isothermal fluid. If the fluid also exhibits variations in magnetic susceptibility with concentration then convection control by external magnetic fields can be hypothesized. Magnetic control of thermal buoyancy induced convection in ferrofluids (dispersions of ferromagnetic particles in a carrier fluid) and paramagnetic fluids have been demonstrated. Here we show the nature of magnetic control of solutal buoyancy driven convection of a paramagnetic fluid, an aqueous solution of Manganese Chloride hydrate. We predict the critical magnetic field required for balancing gravitational solutal buoyancy driven convection and validate it through a simple experiment. We demonstrate that gravity driven flow can be completely reversed by a magnetic field but the exact cancellation of the flow is not possible. This is because the phenomenon is unstable. The technique can be applied to crystal growth processes in order to reduce convection and to heat exchanger devices for enhancing convection. The method can also be applied to impose a desired g-level in reduced gravity applications.
Taking advantage of a novel approach to the design of the orbital transfer optimization problem and advanced non-linear programming algorithms, several optimal transfer trajectories are found for problems with and without known analytic solutions. This method treats the fixed known gravitational constants as optimization variables in order to reduce the need for an advanced initial guess. Complex periodic orbits are targeted with very simple guesses and the ability to find optimal transfers in spite of these bad guesses is successfully demonstrated. Impulsive transfers are considered for orbits in both the 2-body frame as well as the circular restricted three-body problem (CRTBP). The results with this new approach demonstrate the potential for increasing robustness for all types of orbit transfer problems.
Introduction: The probability of bone fracture during and after spaceflight is quantified to aid in mission planning, to determine required astronaut fitness standards and training requirements and to inform countermeasure research and design. Probability is quantified with a probabilistic modeling approach where distributions of model parameter values, instead of single deterministic values, capture the parameter variability within the astronaut population and fracture predictions are probability distributions with a mean value and an associated uncertainty. Because of this uncertainty, the model in its current state cannot discern an effect of countermeasures on fracture probability, for example between use and non-use of bisphosphonates or between spaceflight exercise performed with the Advanced Resistive Exercise Device (ARED) or on devices prior to installation of ARED on the International Space Station. This is thought to be due to the inability to measure key contributors to bone strength, for example, geometry and volumetric distributions of bone mass, with areal bone mineral density (BMD) measurement techniques. To further the applicability of model, we performed a parameter sensitivity study aimed at identifying those parameter uncertainties that most effect the model forecasts in order to determine what areas of the model needed enhancements for reducing uncertainty. Methods: The bone fracture risk model (BFxRM), originally published in (Nelson et al) is a probabilistic model that can assess the risk of astronaut bone fracture. This is accomplished by utilizing biomechanical models to assess the applied loads; utilizing models of spaceflight BMD loss in at-risk skeletal locations; quantifying bone strength through a relationship between areal BMD and bone failure load; and relating fracture risk index (FRI), the ratio of applied load to bone strength, to fracture probability. There are many factors associated with these calculations including environmental factors, factors associated with the fall event, mass and anthropometric values of the astronaut, BMD characteristics, characteristics of the relationship between BMD and bone strength and bone fracture characteristics. The uncertainty in these factors is captured through the use of parameter distributions and the fracture predictions are probability distributions with a mean value and an associated uncertainty. To determine parameter sensitivity, a correlation coefficient is found between the sample set of each model parameter and the calculated fracture probabilities. Each parameters contribution to the variance is found by squaring the correlation coefficients, dividing by the sum of the squared correlation coefficients, and multiplying by 100. Results: Sensitivity analyses of BFxRM simulations of preflight, 0 days post-flight and 365 days post-flight falls onto the hip revealed a subset of the twelve factors within the model which cause the most variation in the fracture predictions. These factors include the spring constant used in the hip biomechanical model, the midpoint FRI parameter within the equation used to convert FRI to fracture probability and preflight BMD values. Future work: Plans are underway to update the BFxRM by incorporating bone strength information from finite element models (FEM) into the bone strength portion of the BFxRM. Also, FEM bone strength information along with fracture outcome data will be incorporated into the FRI to fracture probability.
NASA Glenn Research Center has tested the BLI2DTF propulsor including the fan rotor. BLI2DTF stands for Boundary Layer Ingesting Inlet/Distortion-Tolerant Fan. A comparison of the vibratory response between analysis results and experimental wind tunnel test results yielded reasonable agreement, yet some differences were noted. Blade mistuning effects have been identified as a potential cause for these differences. A tuned forced response analysis in a turbomachinery engine rotor system assumes that all of the blades are identical, so that the natural frequencies of individual blades are the same. In contrast to this assumption, the wind tunnel tests of the BLI2DTF rotor system revealed that the individual blade response frequencies varied. These variations in individual blade frequencies may be attributed to blade mistuning due to potential differences in the structural and material properties of individual blades. For an understanding of these variations, it is necessary to analyze the influence of blade mistuning on the BLI2DTF rotor system, which will provide a more precise assessment of its vibratory stresses and high cycle fatigue life. The purpose of the study was to investigate the influence of blade mistuning on the dynamic characteristics of this rotor system. At the same fan operation condition, a comparative forced response analysis was performed for both tuned and mistuned BLI2DTF rotor systems. A comparison of the results from these analyses found that the mistuning effects on the present BLI2DTF rotor system are notable. As a result, fan blade mistuning is to be considered a contributor to the levels of vibratory dynamic stresses observed during the wind tunnel experiment.
When dealing with imperfect data and general models of dynamic systems, the best estimate is always sought in the presence of uncertainty or unknown parameters. In many cases, as the first attempt, the Extended Kalman filter (EKF) provides sufficient solutions to handling issues arising from nonlinear and non-Gaussian estimation problems. But these issues may lead unacceptable performance and even divergence. In order to accurately capture the nonlinearities of most real-world dynamic systems, advanced filtering methods have been created to reduce filter divergence while enhancing performance. Approaches, such as Gaussian sum filtering, grid based Bayesian methods and particle filters are well-known examples of advanced methods used to represent and recursively reproduce an approximation to the state probability density function (pdf). Some of these filtering methods were conceptually developed years before their widespread uses were realized. Advanced nonlinear filtering methods currently benefit from the computing advancements in computational speeds, memory, and parallel processing. Grid based methods, multiple-model approaches and Gaussian sum filtering are numerical solutions that take advantage of different state coordinates or multiple-model methods that reduced the amount of approximations used. Choosing an efficient grid is very difficult for multi-dimensional state spaces, and oftentimes expensive computations must be done at each point. For the original Gaussian sum filter, a weighted sum of Gaussian density functions approximates the pdf but suffers at the update step for the individual component weight selections. In order to improve upon the original Gaussian sum filter, Ref. [2] introduces a weight update approach at the filter propagation stage instead of the measurement update stage. This weight update is performed by minimizing the integral square difference between the true forecast pdf and its Gaussian sum approximation. By adaptively updating each component weight during the nonlinear propagation stage an approximation of the true pdf can be successfully reconstructed. Particle filtering (PF) methods have gained popularity recently for solving nonlinear estimation problems due to their straightforward approach and the processing capabilities mentioned above. The basic concept behind PF is to represent any pdf as a set of random samples. As the number of samples increases, they will theoretically converge to the exact, equivalent representation of the desired pdf. When the estimated qth moment is needed, the samples are used for its construction allowing further analysis of the pdf characteristics. However, filter performance deteriorates as the dimension of the state vector increases. To overcome this problem Ref. [5] applies a marginalization technique for PF methods, decreasing complexity of the system to one linear and another nonlinear state estimation problem. The marginalization theory was originally developed by Rao and Blackwell independently. According to Ref. [6] it improves any given estimator under every convex loss function. The improvement comes from calculating a conditional expected value, often involving integrating out a supportive statistic. In other words, Rao-Blackwellization allows for smaller but separate computations to be carried out while reaching the main objective of the estimator. In the case of improving an estimator's variance, any supporting statistic can be removed and its variance determined. Next, any other information that dependents on the supporting statistic is found along with its respective variance. A new approach is developed here by utilizing the strengths of the adaptive Gaussian sum propagation in Ref. [2] and a marginalization approach used for PF methods found in Ref. [7]. In the following sections a modified filtering approach is presented based on a special state-space model within nonlinear systems to reduce the dimensionality of the optimization problem in Ref. [2]. First, the adaptive Gaussian sum propagation is explained and then the new marginalized adaptive Gaussian sum propagation is derived. Finally, an example simulation is presented.
Krylov vectors and the concept of parameter matching are combined here to develop model-reduction algorithms for structural dynamics systems. The method is derived for a structural dynamics system described by a second-order matrix differential equation. The reduced models are shown to have a promising application in the control of flexible structures. It can eliminate control and observation spillovers while requiring only the dynamic spillover terms to be considered. A model-order reduction example and a flexible structure control example are provided to show the efficacy of the method.
Higher order numerical methods derived from polynomial spline interpolation or Hermitian differencing are applied to a separating laminar boundary layer, i.e., the Howarth problem, and the turbulent flat plate boundary layer flow. Preliminary results are presented. It is found that accuracy equal to that of conventional second order accurate finite difference methods is achieved with many fewer mesh points and with reduced computer storage and time requirements.
The advanced propeller developed for high Mach number cruise incorporates swept blades to reduce compressibility losses. In order to evaluate the induced flow-field vortex lattice methods are applied to a swept propeller blade. The blade is modeled by a radial distribution of helical horseshoe vortices with a single swept bound vortex at the quarter chord and the control point at the three-quarter chord of each radial section. The results of numerical calculations show that the power coefficient decreases as the blade is swept and the power loading distribution shifts inboard.
An optimal Routh approximant of a single-input single-output dynamic system is a reduced-order transfer function of which the denominator is obtained by the Routh approximation method while the numerator is determined by minimizing a time-response integral-squared-error (ISE) criterion. In this paper, a new elegant approach is presented for obtaining the optimal Routh approximants for linear time-invariant continuous-time systems. The approach is based on the Routh canonical expansion, which is a finite-term orthogonal series of rational basis functions, and minimization of the ISE criterion. A procedure for combining the above approach with the bilinear transformation is also presented in order to obtain the optimal bilinear Routh approximants of linear time-invariant discrete-time systems. The proposed technique is simple in formulation and is amenable to practical implementation.
As part of the NASA Hi-Rate Composite Aircraft Manufacturing (HiCAM) Project, state-of-the-art progressive damage and failure analysis (PDFA) tools developed for use with thermosets are being evaluated for use in modeling alternative material systems, like thermoplastics. Experimental low-velocity impact data of a thermoplastic material system, AS4D/PEKK-FC, is presented and includes characterization of the impact damage mechanisms as well as associated load and displacement data. Following the presentation of experimental results, two simulation approaches using the PDFA tool MAT299 in the commercial off-the-shelf finite element software LS-DYNA are employed to predict damage area and force-displacement responses of thermoplastic panels subjected to various impact energies. The first modeling method uses solid elements with a high-density mesh and a ply-by-ply modeling approach similar to previously published work for thermosets. This method has the capability of capturing individual crack development, progression, and delamination on a per ply basis. The second modeling method uses TSHELL elements that have in-plane dimensions that are an order of magnitude larger than the elements used in the solid element approach and reduces the number of elements through the thickness of the laminate. The second method produces a lower-fidelity model with reduced run times that is incapable of monitoring every delamination plane and damage within each ply. Results from both simulation methods are compared to experiment, and limitations of the methods are discussed.
As part of the NASA Hi-Rate Composite Aircraft Manufacturing (HiCAM) Project, state-of-the-art progressive damage and failure analysis (PDFA) tools developed for use with thermosets are being evaluated for use in modeling alternative material systems, like thermoplastics. Experimental low-velocity impact data of a thermoplastic material system, AS4D/PEKK-FC, is presented and includes characterization of the impact damage mechanisms as well as associated load and displacement data. Following the presentation of experimental results, two simulation approaches using the PDFA tool MAT299 in the commercial off-the-shelf finite element software LS-DYNA are employed to predict damage area and force-displacement responses of thermoplastic panels subjected to various impact energies. The first modeling method uses solid elements with a high-density mesh and a ply-by-ply modeling approach similar to previously published work for thermosets. This method has the capability of capturing individual crack development, progression, and delamination on a per ply basis. The second modeling method uses TSHELL elements that have in-plane dimensions that are an order of magnitude larger than the elements used in the solid element approach and reduces the number of elements through the thickness of the laminate. The second method produces a lower-fidelity model with reduced run times that is incapable of monitoring every delamination plane and damage within each ply. Results from both simulation methods are compared to experiment, and limitations of the methods are discussed.
An improved version of the 'GRUMFOIL' code has been developed for the computation of airfoil flows. The method employs a conservative difference scheme for the potential equation, integral methods for the boundary layer, and viscous coupling conditions that fully account for the wake and strong interaction effects at trailing edges. The improved version uses Jameson's 'MAD' scheme to accelerate convergence of the inviscid solution, an improved 2nd order artificial viscosity and far field 'TARE' correction to reduce spatial truncation errors and Carter's semi-inverse method for the viscous solution. Results are presented which demonstrate a factor of ten reduction in computing cost.
Calculations of boundary layer flows past blunt bodies at angles of incidence are presented. Using the method of integral relations together with the method of lines, the full three-dimensional boundary layer equations are reduced to a system of first-order ordinary differential equations. The streamwise shear stress function and the cross-flow velocity component are represented as suitable functions of the streamwise velocity component. The role of the zone of dependence is automatically satisfied by the choice of differencing in the method of lines. Solutions correct to the second order are obtained in the positive shear region for flow over an ellipsoid at 30-deg incidence. The results are compared with corresponding finite difference solutions.