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At least 127 records · Page 7

Mathematical Model of a Regenerative Fuel Cell for System Optimization

This thesis developed a system-level optimization model of a regenerative fuel cell (RFC) system for long-duration, off-world energy storage applications. Prior RFC design studies have typically been limited to reduced parameter sets and simplified constraints due to computational limitations relative to the number of relevant degrees of freedom. As a result, important nonlinear interactions between subsystems have not been fully captured. This work began to address that gap by developing a higher-fidelity, nonlinear optimization framework that incorporates a broader set of design variables and coupled constraints, enabling a multidimensional model that captures the coupled behavior of RFC subsystems and demonstrates the feasibility of applying optimization to such systems. An expanded system-level optimization approach was established that captures interactions between electrochemical performance, structural requirements, and storage design. This enabled a more comprehensive evaluation of trade-offs than conventional formulations. The model integrates four coupled subsystems: a fuel cell, an electrolyzer, reactant gas, and high-pressure storage tanks, and was formulated to accommodate a wide range of mission parameters, including operational time and required output power. It incorporates constraints on available solar array power, reactant mass balance between production and consumption, and pressure-dependent storage requirements. To enable reliable convergence, the optimization problem was reformulated to reduce dimensionality and improve numerical stability, with subsystem models organized for efficient evaluation. Problem dimensionality was reduced by consolidating lower-level design variables into higher-level representative quantities, and subsystem behavior was evaluated within the optimization loop. A multi-start initialization strategy was employed to mitigate sensitivity to local minima and improve solution quality, while nonlinear relationships were solved using robust numerical methods. The results showed that convergence was achieved across a range of required output power values. Specific energy reached a maximum at a critical mission power level, where the electrolyzer power matched the available solar input and operated near its voltage and current density limits. Beyond this point, further increases in required power resulted in less mass-efficient operation, increasing total system mass and reducing overall performance. The developed model represents an advancement in RFC system-level optimization by enabling analysis of a broader and more tightly coupled design space than previous considerations. While convergence behavior and computational cost remain challenges, the methods introduced improve solvability and allow inclusion of additional design variables with minimal loss of physical fidelity. However, the numerical results should not be interpreted as definitive design recommendations, as the model includes simplifying assumptions and omits several higher-order effects. Future work should extend this framework by incorporating additional subsystems and loss mechanisms, such as thermal management, parasitic power consumption, and reactant losses, to improve fidelity and ensure more representative design conclusions.

Electrochemistry

Risk Analysis for Resource Planning Optimization

This paper describes a systems engineering approach to resource planning by integrating mathematical modeling and constrained optimization, empirical simulation, and theoretical analysis techniques to generate an optimal task plan in the presence of uncertainties.

optimization

Tuning Parameters in Heuristics by Using Design of Experiments Methods

With the growing complexity of today's large scale problems, it has become more difficult to find optimal solutions by using exact mathematical methods. The need to find near-optimal solutions in an acceptable time frame requires heuristic approaches. In many cases, however, most heuristics have several parameters that need to be "tuned" before they can reach good results. The problem then turns into "finding best parameter setting" for the heuristics to solve the problems efficiently and timely. One-Factor-At-a-Time (OFAT) approach for parameter tuning neglects the interactions between parameters. Design of Experiments (DOE) tools can be instead employed to tune the parameters more effectively. In this paper, we seek the best parameter setting for a Genetic Algorithm (GA) to solve the single machine total weighted tardiness problem in which n jobs must be scheduled on a single machine without preemption, and the objective is to minimize the total weighted tardiness. Benchmark instances for the problem are available in the literature. To fine tune the GA parameters in the most efficient way, we compare multiple DOE models including 2-level (2k ) full factorial design, orthogonal array design, central composite design, D-optimal design and signal-to-noise (SIN) ratios. In each DOE method, a mathematical model is created using regression analysis, and solved to obtain the best parameter setting. After verification runs using the tuned parameter setting, the preliminary results for optimal solutions of multiple instances were found efficiently.

Arin, Arif

Wing shape optimization for maximum cross-country speed, with mathematical programming

A computer program was developed to calculate numerically the speed and circling polars of an aircraft when the lift and drag characteristics of the wing airfoils are known. The planform of the wing is described by variables which are optimized so that the cross-country speed of the glider is maximum for the particular type of thermal model. Two thermal models are compared and shown that with a greater wing area than now normally used the performance can be increased.

Helwig, G.

Tracking system study

A digital computer program was generated which mathematically describes an optimal estimator-controller technique as applied to the control of antenna tracking systems used by NASA. Simulation studies utilizing this program were conducted using the IBM 360/91 computer. The basic ideas of applying optimal estimator-controller techniques to antenna tracking systems are discussed. A survey of existing tracking methods is given along with shortcomings and inherent errors. It is explained how these errors can be considerably reduced if optimal estimation and control are used. The modified programs generated in this project are described and the simulation results are summarized. The new algorithms for direct synthesis and stabilization of the systems including nonlinearities, are presented.

Dennis, A. R.

Preliminary design of composite wings for buckling, strength and displacement constraints

An unstiffened panel buckling constraint for balanced, symmetric laminated composites is included on the global design level in a mathematical programming structural optimization procedure for designing wing structures. Constraints are introduced by penalty functions, and Newton's method based on approximate second derivatives of the penalty terms is used as the search algorithm to obtain minimum-mass designs. Constraint approximations used during the optimization process contribute to the computational efficiency of the procedure. A criterion is developed that identifies the appropriate conservative form of the constraint approximations that are used with the optimization procedure. Minimum-mass design results are obtained for a multispar high-aspect-ratio wing subjected to material strength, minimum-gage, displacement, panel buckling and twist constraints. The material systems considered for the examples are all graphite-epoxy, graphite-epoxy with boron-epoxy spar caps, and all aluminum. The composite material designs are shown to have an advantage over the aluminum designs since they can often satisfy additional constraints with only small mass increases.

Starnes, J. H., Jr.

Resizing structures for minimum weight

Approximation concepts and dual-method algorithms are combined in method of minimum-weight design for structures. Approximation Concepts Code for Efficient Structural Synthesis (ACCESS3) program is powerful research tool in which mathematical programming and optimality criteria are coalesced in efficient structural weight-minimization method.

Fleury, C.

Transformation Aids Crop Analysis From Spectral Data

Crop analysis aided by mathematical transformation that optimizes perspective of six-dimensional, six-band, spectral data taken from spacecraft or aircraft. Transformation applied to any temperatureclimate vegetated scene, providing direct view of regions of data concentration resulting from band correlations and fundamental reflectance properties of scene classes. Almost all of data variability captured in three spectral features, thus reducing by factor of 2 number of spectral features carried, incurring minimal loss of important information. Three-dimensional representation with two principal planes retains about 95 percent of six-dimensional spectral data used to distinguish among scenes containing green plants and bare soil with varying degrees of moisture.

Crist, E. P.

Filter distortion effects on telemetry signal-to-noise ratio

The effect of filtering on the Signal-to-Noise Ratio (SNR) of a coherently demodulated band-limited signal is determined in the presence of worse-case amplitude ripple. The problem is formulated mathematically as an optimization problem in the L2-Hilbert space. The form of the worst-cast amplitude ripple is specified, and the degradation in the SNR is derived in a closed form expression. It is shown that when the maximum passband amplitude ripple is 2 delta (peak to peak), the SNR is degraded by at most (1 - delta squared), even when the ripple is unknown or uncompensated. For example, an SNR loss of less than 0.01 dB due to amplitude ripple can be assured by keeping the amplitude ripple to under 0.42 dB.

Sadr, R.

Locating damaged members in a truss structure using modal test data - A demonstration experiment

An experiment is designed to demonstrate and verify the performance of the on-orbit assessment approach for large flexible space truss structures. The on-orbit assessment approach can be accomplished, in principle, with dynamic response information, structural identification methods, and model correlation techniques which produce an adjusted mathematical model. An optimal update of the structure model is formed using the response data, then examined to locate damaged members. The experiment uses a laboratory scale model truss structure which exhibits characteristics expected for large space truss structures. Vibration experiments are performed to generate response data for the damaged truss. The damage location approach is described, as well as analytical work performed in support of the vibration tests, the measured response of the test article, and some preliminary results.

Smith, Suzanne Weaver

Recent experience with multidisciplinary analysis and optimization in advanced aircraft design

The task of modern aircraft design has always been complicated due to the number of intertwined technical factors from the various engineering disciplines. Furthermore, this complexity has been rapidly increasing by the development of such technologies as aeroelasticity tailored materials and structures, active control systems, integrated propulsion/airframe controls, thrust vectoring, and so on. Successful designs that achieve maximum advantage from these new technologies require a thorough understanding of the physical phenomena and the interactions among these phenomena. A study commissioned by the Aeronautical Sciences and Evaluation Board of the National Research Council has gone so far as to identify technology integration as a new discipline from which many future aeronautical advancements will arise. Regardless of whether one considers integration as a new discipline or not, it is clear to all engineers involved in aircraft design and analysis that better methods are required. In the past, designers conducted parametric studies in which a relatively small number of principal characteristics were varied to determine the effect on design requirements which were themselves often diverse and contradictory. Once a design was chosen, it then passed through the various engineers' disciplines whose principal task was to make the chosen design workable. Working in a limited design space, the discipline expert sometimes improved the concept, but more often than not, the result was in the form of a penalty to make the original concept workable. If an insurmountable problem was encountered, the process began over. Most design systems that attempt to account for disciplinary interactions have large empirical elements and reliance on past experience is a poor guide in obtaining maximum utilizations of new technologies. Further compounding the difficulty of design is that as the aeronautical sciences have matured, the discipline specialist's area of research has generally narrowed as more sophisticated methods are developed in the specialist's area of expertise. The results have been a decrease in the awareness of the impact of his decisions on other disciplines. This paper will outline the progress and problems encountered in the analysis, design, optimization sensitivity analysis, mathematical modeling, and configurations control and the means by which they are being solved. The breadth versus depth dilemma in analysis and design and the means for coping with that dilemma will be discussed. Finally, the all-important human aspects and the need for a new 'culture ' for doing business in an integrated, multidisciplinary design environment are discussed.

Dollyhigh, Samuel M.

Integrated design of structures, controls, and materials

In this talk we shall discuss algorithms and CAD tools for the design and analysis of structures for high performance applications using advanced composite materials. An extensive mathematical theory for optimal structural (e.g., shape) design was developed over the past thirty years. Aspects of this theory have been used in the design of components for hypersonic vehicles and thermal diffusion systems based on homogeneous materials. Enhancement of the design methods to include optimization of the microstructure of the component is a significant innovation which can lead to major enhancements in component performance. Our work is focused on the adaptation of existing theories of optimal structural design (e.g., optimal shape design) to treat the design of structures using advanced composite materials (e.g., fiber reinforced, resin matrix materials). In this talk we shall discuss models and algorithms for the design of simple structures from composite materials, focussing on a problem in thermal management. We shall also discuss methods for the integration of active structural controls into the design process.

Blankenship, G. L.

Coevolutionary Free Lunches

Recent work on the mathematical foundations of optimization has begun to uncover its rich structure. In particular, the "No Free Lunch" (NFL) theorems state that any two algorithms are equivalent when their performance is averaged across all possible problems. This highlights the need for exploiting problem-specific knowledge to achieve better than random performance. In this paper we present a general framework covering more search scenarios. In addition to the optimization scenarios addressed in the NFL results, this framework covers multi-armed bandit problems and evolution of multiple co-evolving players. As a particular instance of the latter, it covers "self-play" problems. In these problems the set of players work together to produce a champion, who then engages one or more antagonists in a subsequent multi-player game. In contrast to the traditional optimization case where the NFL results hold, we show that in self-play there are free lunches: in coevolution some algorithms have better performance than other algorithms, averaged across all possible problems. We consider the implications of these results to biology where there is no champion.

Wolpert, David H.

Mathematical Formalism for Designing Wide-Field X-Ray Telescopes: Mirror Nodal Positions and Detector Tilts

We provide a mathematical formalism for optimizing the mirror nodal positions along the optical axis and the tilt of a commonly employed detector configuration at the focus of a x-ray telescope consisting of nested mirror shells with known mirror surface prescriptions. We adopt the spatial resolution averaged over the field-of-view as the figure of merit M. A more complete description appears in our paper in these proceedings.

Elsner, R. F.

Mixed Integer Programming and Heuristic Scheduling for Space Communication Networks

We developed framework and the mathematical formulation for optimizing communication network using mixed integer programming. The design yields a system that is much smaller, in search space size, when compared to the earlier approach. Our constrained network optimization takes into account the dynamics of link performance within the network along with mission and operation requirements. A unique penalty function is introduced to transform the mixed integer programming into the more manageable problem of searching in a continuous space. The constrained optimization problem was proposed to solve in two stages: first using the heuristic Particle Swarming Optimization algorithm to get a good initial starting point, and then feeding the result into the Sequential Quadratic Programming algorithm to achieve the final optimal schedule. We demonstrate the above planning and scheduling methodology with a scenario of 20 spacecraft and 3 ground stations of a Deep Space Network site. Our approach and framework have been simple and flexible so that problems with larger number of constraints and network can be easily adapted and solved.

Mixed Integer Programming