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At least 73 records · Page 4

Optimizing Probability of Detection Point Estimate Demonstration

Probability of detection (POD) analysis is used in assessing reliably detectable flaw size in nondestructive evaluation (NDE). MIL-HDBK-18231and associated mh18232POD software gives most common methods of POD analysis. Real flaws such as cracks and crack-like flaws are desired to be detected using these NDE methods. A reliably detectable crack size is required for safe life analysis of fracture critical parts. The paper provides discussion on optimizing probability of detection (POD) demonstration experiments using Point Estimate Method. POD Point estimate method is used by NASA for qualifying special NDE procedures. The point estimate method uses binomial distribution for probability density. Normally, a set of 29 flaws of same size within some tolerance are used in the demonstration. The optimization is performed to provide acceptable value for probability of passing demonstration (PPD) and achieving acceptable value for probability of false (POF) calls while keeping the flaw sizes in the set as small as possible.

Koshti, Ajay M.↗

Optimal Control Problems with Switching Points

The main idea of this report is to give an overview of the problems and difficulties that arise in solving optimal control problems with switching points. A brief discussion of existing optimality conditions is given and a numerical approach for solving the multipoint boundary value problems associated with the first-order necessary conditions of optimal control is presented. Two real-life aerospace optimization problems are treated explicitly. These are altitude maximization for a sounding rocket (Goddard Problem) in the presence of a dynamic pressure limit, and range maximization for a supersonic aircraft flying in the vertical, also in the presence of a dynamic pressure limit. In the second problem singular control appears along arcs with active dynamic pressure limit, which in the context of optimal control, represents a first-order state inequality constraint. An extension of the Generalized Legendre-Clebsch Condition to the case of singular control along state/control constrained arcs is presented and is applied to the aircraft range maximization problem stated above. A contribution to the field of Jacobi Necessary Conditions is made by giving a new proof for the non-optimality of conjugate paths in the Accessory Minimum Problem. Because of its simple and explicit character, the new proof may provide the basis for an extension of Jacobi's Necessary Condition to the case of the trajectories with interior point constraints. Finally, the result that touch points cannot occur for first-order state inequality constraints is extended to the case of vector valued control functions.

Seywald, Hans↗

Two Point Exponential Approximation Method for structural optimization of problems with frequency constraints

The point exponential approximation method was introduced by Fadel et al. (Fadel, 1990), and tested on structural optimization problems with stress and displacement constraints. The reports in earlier papers were promising, and the method, which consists of correcting Taylor series approximations using previous design history, is tested in this paper on optimization problems with frequency constraints. The aim of the research is to verify the robustness and speed of convergence of the two point exponential approximation method when highly non-linear constraints are used.

Fadel, G. M.↗

Electromagnetic analysis for large reflector antennas

A comparison is made between the measured E and H plane patterns of the 35 GHz offset paraboloidal reflector and the calculated patterns for the same reflector using the 200 points to describe the surface. The accuracy of the computer prediction is quite good considering that the only description of the surface was the coordinates of a finite number of points on the reflector. The results indicate the possibility of acceptable accuracy in the prediction of electromagnetic performance for arbitrarily distorted reflectors using the coordinates of a practical number of measured points. An optimization of the number and distribution of points, and experimental verification for a distorted reflector are planned.

Bailey, M. C.↗

Fuel-optimal maneuvers of a spacecraft relative to a point in circular orbit

Fuel optimal maneuvers of spacecraft relative to a body in circular orbit are investigated using a point mass model in which the magnitude of the thrust vector is bounded. All nonsingular optimal maneuvers consist of intervals of full thrust and coast and are found to contain at most seven such intervals in one period. Only four boundary conditions where singular solutions occur are possible. Computer simulation of optimal flight path shapes and switching functions are found for various boundary conditions. Emphasis is placed on the problem of soft rendezvous with a body in circular orbit.

Carter, T. E.↗

High-Performance Reaction Wheel Optimization for Fine-Pointing Space Platforms: Minimizing Induced Vibration Effects on Jitter Performance plus Lessons Learned from Hubble Space Telescope for Current and Future Spacecraft Applications

The Hubble Space Telescope (HST) applies large-diameter optics (2.5-m primary mirror) for diffraction-limited resolution spanning an extended wavelength range (approx. 100-2500 nm). Its Pointing Control System (PCS) Reaction Wheel Assemblies (RWAs), in the Support Systems Module (SSM), acquired an unprecedented set of high-sensitivity Induced Vibration (IV) data for 5 flight-certified RWAs: dwelling at set rotation rates. Focused on 4 key ratios, force and moment harmonic values (in 3 local principal directions) are extracted in the RWA operating range (0-3000 RPM). The IV test data, obtained under ambient lab conditions, are investigated in detail, evaluated, compiled, and curve-fitted; variational trends, core causes, and unforeseen anomalies are addressed. In aggregate, these values constitute a statistically-valid basis to quantify ground test-to-test variations and facilitate extrapolations to on-orbit conditions. Accumulated knowledge of bearing-rotor vibrational sources, corresponding harmonic contributions, and salient elements of IV key variability factors are discussed. An evolved methodology is presented for absolute assessments and relative comparisons of macro-level IV signal magnitude due to micro-level construction-assembly geometric details/imperfections stemming from both electrical drive and primary bearing design parameters. Based upon studies of same-size/similar-design momentum wheels' IV changes, upper estimates due to transitions from ground tests to orbital conditions are derived. Recommended HST RWA choices are discussed relative to system optimization/tradeoffs of Line-Of-Sight (LOS) vector-pointing focal-plane error driven by higher IV transmissibilities through low-damped structural dynamics that stimulate optical elements. Unique analytical disturbance results for orbital HST accelerations are described applicable to microgravity efforts. Conclusions, lessons learned, historical context/insights, and perspectives on future applications are given; these previously unpublished data and findings represents a valuable resource for fine-pointing spacecraft or space-based platforms using RWAs, Control Moment Gyros (CMGs), Momentum Wheels, or other ball-bearing-based rotational units.

Hasha, Martin D.↗

Effects of Planetary Gear Ratio on Mean Service Life

Planetary gear transmissions are compact, high-power speed reductions which use parallel load paths. The range of possible reduction ratios is bounded from below and above by limits on the relative size of the planet gears. For a single plane transmission, the planet gear has no size at a ratio of two. As the ratio increases, so does the size of the planets relative to the sizes of the sun and ring. Which ratio is best for a planetary reduction can be resolved by studying a series of optimal designs. In this series, each design is obtained by maximizing the service life for a planetary with a fixed size, gear ratio, input speed power and materials. The planetary gear reduction service life is modeled as a function of the two-parameter Weibull distributed service lives of the bearings and gears in the reduction. Planet bearing life strongly influences the optimal reduction lives which point to an optimal planetary reduction ratio in the neighborhood of four to five.

Savage, M.↗

Effects of Planetary Speed Reduction Ratio on Mean Service Life

Planetary gear transmissions are compact speed reductions which use parallel-load paths to transmit high power. The range of possible reduction ratios is bounded from below and above by limits on the relative size of the planet gears. For a single plane planetary transmission, the speed-reduction ratio must be greater than two for planet gears to exist. As the ratio increase, so does the size of the planets relative to the sizes of the sun and ring. Which ratio is best for a planetary reduction can be resolved by studying a series of optimal designs. In this series, each design is obtained by maximizing the service life for a spur-gear planetary with a fixed size, speed reduction ratio, input speed, power and materials. The planetary gear reduction service life is modeled as a function of the two-parameter Weibull distributed service lives of the ball bearings and spur gears in the reduction. Planet-bearing life strongly influences the optimal reduction lives which point to an optimal planetary reduction ratio in the neighborhood of four to five.

Savage, M.↗

Effects of Planetary Speed-Reduction Ratio on Mean Service Life

Planetary-gear transmissions are compact speed reductions which use parallel-load paths to transmit high power. The range of possible reduction ratios is bounded from below and above by limits on the relative size of the planet gears. For a single-plane planetary transmission, the speed-reduction ratio must be greater than two for planet gears to exist. As the ratio increases, so does the size of the planets relative to the sizes of the sun and ring. Which ratio is best for a planetary reduction can be resolved by studying a series of optimal designs. In this series, each design is obtained by maximizing the service life for a spur-gear planetary with a fixed size, speed-reduction ratio, input speed, power and materials. The planetary-gear reduction service life is modeled as a function of the two-parameter Weibull distributed service lives of the ball bearings and spur gears in the reduction. Planet-bearing life strongly influences the optimal reduction lives which point to an optimal planetary reduction ratio in the neighborhood of four to five.

Savage, M.↗

Implementation of Combinatorial Optimization Techniques for Automated Fiber Placement Through Thickness Defect Stack-Up Minimization

The Computer Aided Process Planning (CAPP) module was developed to facilitate and accelerate the process planning workflow for Automated Fiber Placement (AFP). CAPP assists process planners in identifying optimal starting point locations and layup strategies for each ply of a laminate. Ply optimization operates on measurement and scoring of geometry-based defects such as gaps, overlaps, angle deviation, and steering. This paper expands on the established framework for analyzing defect stack-up through thickness of a laminate. Four different combinatorial optimization algorithms are implemented and evaluated: (1) genetic algorithm, (2) differential evolution, (3) particle swarm, and (4) greedy search. The algorithms identify the optimal combination of ply-level layup strategies, by scoring potential laminates on defect stacking, using two different objective functions. A final optimization approach is also presented which trades some performance for a large gain in efficiency. These approaches are compared to a randomized combination using a complex tool surface in a virtual case study. The result is a streamlined methodology for comparing different laminate-level manufacturing strategies and minimizing the through thickness defect stack up.

CAPP↗

Implementation of a Point Algorithm for Real-Time Convex Optimization

The primal-dual interior-point algorithm implemented in G-OPT is a relatively new and efficient way of solving convex optimization problems. Given a prescribed level of accuracy, the convergence to the optimal solution is guaranteed in a predetermined, finite number of iterations. G-OPT Version 1.0 is a flight software implementation written in C. Onboard application of the software enables autonomous, real-time guidance and control that explicitly incorporates mission constraints such as control authority (e.g. maximum thrust limits), hazard avoidance, and fuel limitations. This software can be used in planetary landing missions (Mars pinpoint landing and lunar landing), as well as in proximity operations around small celestial bodies (moons, asteroids, and comets). It also can be used in any spacecraft mission for thrust allocation in six-degrees-of-freedom control.

Acikmese, Behcet↗

Optimization of a GO2/GH2 Swirl Coaxial Injector Element

An injector optimization methodology, method i, is used to investigate optimal design points for a gaseous oxygen/gaseous hydrogen (GO2/GH2) swirl coaxial injector element. The element is optimized in terms of design variables such as fuel pressure drop, DELTA P(sub f), oxidizer pressure drop, DELTA P(sub 0) combustor length, L(sub comb), and full cone swirl angle, theta, for a given mixture ratio and chamber pressure. Dependent variables such as energy release efficiency, ERE, wall heat flux, Q(sub w) injector heat flux, Q(sub inj), relative combustor weight, W(sub rel), and relative injector cost, C(sub rel), are calculated and then correlated with the design variables. An empirical design methodology is used to generate these responses for 180 combinations of input variables. Method i is then used to generate response surfaces for each dependent variable. Desirability functions based on dependent variable constraints are created and used to facilitate development of composite response surfaces representing some, or all, of the five dependent variables in terms of the input variables. Two examples illustrating the utility and flexibility of method i are discussed in detail. First, joint response surfaces are constructed by sequentially adding dependent variables. Optimum designs are identified after addition of each variable and the effect each variable has on the design is shown. This stepwise demonstration also highlights the importance of including variables such as weight and cost early in the design process. Secondly, using the composite response surface that includes all five dependent variables, unequal weights are assigned to emphasize certain variables relative to others. Here, method i is used to enable objective trade studies on design issues such as component life and thrust to weight ratio.

Tucker, P. Kevin↗

Automated Fiber Placement Through Thickness Defect Stacking Optimization

In its 2022 commercial market outlook, Boeing forecasted an 80% increase in the global fleet through 2041 compared to 2019 pre-pandemic levels. This sharp rise in demand will drive pressure onto airframe manufacturers to ramp up production and find more efficient ways to design and manufacture airplanes. Complicating this challenge is the industry’s recent transformation from traditional metal-based airframes towards hybrid composite-metal aircraft. While composites have been used in aviation for decades, aircraft manufacturers are still struggling to design and manufacture quality parts at a high rate. Automated Fiber Placement (AFP) is one of the main manufacturing techniques used to produce large-scale composite parts. After a design has been created, a manufacturing strategy has to be developed based on the working material, part geometry, and machine capabilities. This process planning stage is essential to the AFP workflow and currently requires a high level of manual input from an experienced process planner. In an effort to automate and optimize this stage, the Computer Aided Process Planning (CAPP) module was developed. CAPP assists process planners in identifying optimal starting point location and layup strategy for each ply of a laminate. This Ply-Level Optimization (PLO) phase operates on the quantification of ply quality through predictable geometry-based defects such as gaps, overlaps, angle deviation, and steering. As you move from PLO to Laminate-Level Optimization (LLO) the design space grows exponentially, emphasizing the need for automated optimization. The work presented in this thesis expands CAPP’s functionality by comparing the planned fiber paths through the thickness of the laminate to mitigate stacked area defects and achieve an optimal laminate-level manufacturing strategy. Within CAPP, predicted gap and overlap defects are imported from Vericut Composites Programming (VCP) and then discretized to streamline the through-thickness comparison. Two objective functions are used to score different combinations of ply layup strategies based on defect stacking both globally and locally. Four combinatorial optimization algorithms were coupled with these objective functions to investigate the laminate-level manufacturing strategy design space and converge on the optimal plan. These algorithms were evaluated based on accuracy and efficiency through virtual testing on a complex tool surface. A separate LLO approach was developed to achieve near-optimal laminates in significantly less time. The end result is a software package which greatly reduces the required input from process planners, shortening the design-build cycle time and improving part quality.

AFP↗

Optimization of a GO2/GH2 Impinging Injector Element

An existing injector optimization methodology, method i, is used to investigate optimal design points for a GO2/GH2 impinging injector element. The impinging element, an F-O-F triplet, is optimized in terms of such relevant design variables as fuel pressure drop, DELTA-P(sub f), oxidizer pressure drop, DELTA-P(sub o), combustor length, L(sub comb), and impingement angle, alpha, for a given mixture ratio and chamber pressure.

Tucker, P. Kevin↗