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Results for “Mathematical optimization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
NASA NTRS1990

Optimization of rotor blades for combined structural, dynamic, and aerodynamic properties

Optimal helicopter blade design with computer-based mathematical programming has received more and more attention in recent years. Most of the research has focused on optimum dynamic characteristics of rotor blades to reduce vehicle vibration. There is also work on optimization of aerodynamic performance and on composite structural design. This research has greatly increased our understanding of helicopter optimum design in each of these aspects. Helicopter design is an inherently multidisciplinary process involving strong interactions among various disciplines which can appropriately include aerodynamics; dynamics, both flight dynamics and structural dynamics; aeroelasticity: vibrations and stability; and even acoustics. Therefore, the helicopter design process must satisfy manifold requirements related to the aforementioned diverse disciplines. In our present work, we attempt to combine several of these important effects in a unified manner. First, we design a blade with optimum aerodynamic performance by proper layout of blade planform and spanwise twist. Second, the blade is designed to have natural frequencies that are placed away from integer multiples of the rotor speed for a good dynamic characteristics. Third, the structure is made as light as possible with sufficient rotational inertia to allow for autorotational landing, with safe stress margins and flight fatigue life at each cross-section, and with aeroelastical stability and low vibrations. Finally, a unified optimization refines the solution.

He, Cheng-Jian↗
DOE OSTI2024

Component-to-Optimization Workflow Demonstration

This report aims to demonstrate workflow-generating algorithms for optimizing dispatch across a broad range of Integrated Energy System applications using the Framework for Optimization of Resources and Economics (FORCE) tool suite. The optimization is performed at two different time scales. In the coarse time scale, the optimization focuses on a class of energy sources and consumers and aims to find the optimal combinations and flows of energy based on real-time price data information. In the fine time scale, the optimization focuses on a specific thermal energy delivery system and aims to find the optimal setpoints of components in order to meet the energy demands from coarse-time-scale optimizations. In this demonstration, the coarse-scale optimization is implemented using the newly developed Dispatch Optimization Variable Engine (DOVE), while the fine-scale optimization used Optimization of Real-Time Capacity Allocation (ORCA).

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2026

Algorithm-guided experimentation for autonomous AI systems in self-driving laboratories

This presentation summarizes our work in the PrOMMiS project on benchmarking of data-driven optimization algorithms and their applications in self-driving laboratories. This work supports the broader project goal of accelerating the identification of promising separation methods and operating conditions for critical minerals separation processes. We present a systematic benchmarking study of 42 data-driven optimization algorithms on a broad collection of 502 test problems. The results identify BAM, GLCCLUSTER, and MULTIMIN as the most effective optimization solvers, with BAM showing the highest overall performance and solving more than 80% of the benchmark problems. The study also shows that no single solver consistently outperforms the others across all problem types, indicating that our future laboratory applications may benefit from using a small set of strong solvers rather than relying on a single method. The presentation also illustrates an in-silico chemical reactor case study showing that data-driven optimization methods can guide autonomous experimentation in a self-driving laboratory and identify optimal operating conditions within a small number of experiments. Overall, the results provide a basis for selecting efficient optimization methods and demonstrate the practical use of data-driven optimization in self-driving laboratory workflows.

36 MATERIALS SCIENCE↗
NASA NTRS2013

Mixed Integer Programming and Heuristic Scheduling for Space Communication

Optimal planning and scheduling for a communication network was created where the nodes within the network are communicating at the highest possible rates while meeting the mission requirements and operational constraints. The planning and scheduling problem was formulated in the framework of Mixed Integer Programming (MIP) to introduce a special penalty function to convert the MIP problem into a continuous optimization problem, and to solve the constrained optimization problem using heuristic optimization. The communication network consists of space and ground assets with the link dynamics between any two assets varying with respect to time, distance, and telecom configurations. One asset could be communicating with another at very high data rates at one time, and at other times, communication is impossible, as the asset could be inaccessible from the network due to planetary occultation. Based on the network's geometric dynamics and link capabilities, the start time, end time, and link configuration of each view period are selected to maximize the communication efficiency within the network. Mathematical formulations for the constrained mixed integer optimization problem were derived, and efficient analytical and numerical techniques were developed to find the optimal solution. By setting up the problem using MIP, the search space for the optimization problem is reduced significantly, thereby speeding up the solution process. The ratio of the dimension of the traditional method over the proposed formulation is approximately an order N (single) to 2*N (arraying), where N is the number of receiving antennas of a node. By introducing a special penalty function, the MIP problem with non-differentiable cost function and nonlinear constraints can be converted into a continuous variable problem, whose solution is possible.

Lee, Charles H.↗
NASA NTRS1984

Composite laminate optimization program suitable for microcomputers

The design of a composite panel requires some way of finding the minimum thickness laminate which will withstand the load requirements without failure. The mathematical complexity of this problem dictates the use of nonlinear optimization techniques. Specialized laminate optimization programs were developed which are compact and efficient enough to run on microcomputers. Only stresses at a point and inplane loads and deflections are considered. The programs are simple to use and require no knowledge of optimization. Techniques are developed which find minimum thickness laminates with either ply ratios or ply angles as design variables. A method is presented for finding the optimum orientation for the axis of symmetry of an orthotropic laminate. The orthotropic laminate program uses an approximate failure theory, which speed up computations dramatically.

Flanagan, G. V.↗
NASA NTRS1995

Multiobjective optimization of hybrid regenerative life support technologies. Topic D: Technology Assessment

We developed simple mathematical models for many of the technologies constituting the water reclamation system in a space station. These models were employed for subsystem optimization and for the evaluation of the performance of individual water reclamation technologies, by quantifying their operational 'cost' as a linear function of weight, volume, and power consumption. Then we performed preliminary investigations on the performance improvements attainable by simple hybrid systems involving parallel combinations of technologies. We are developing a software tool for synthesizing a hybrid water recovery system (WRS) for long term space missions. As conceptual framework, we are employing the state space approach. Given a number of available technologies and the mission specifications, the state space approach would help design flowsheets featuring optimal process configurations, including those that feature stream connections in parallel, series, or recycles. We visualize this software tool to function as follows: given the mission duration, the crew size, water quality specifications, and the cost coefficients, the software will synthesize a water recovery system for the space station. It should require minimal user intervention. The following tasks need to be solved for achieving this goal: (1) formulate a problem statement that will be used to evaluate the advantages of a hybrid WRS over a single technology WBS; (2) model several WRS technologies that can be employed in the space station; (3) propose a recycling network design methodology (since the WRS synthesis task is a recycling network design problem, it is essential to employ a systematic method in synthesizing this network); (4) develop a software implementation for this design methodology, design a hybrid system using this software, and compare the resulting WRS with a base-case WRS; and (5) create a user-friendly interface for this software tool.

Manousiouthakis, Vasilios↗
NASA NTRS1990

Optimal pipelining

An effort is made to characterize the tradeoffs and overheads limiting the speedup potential theoretically projected for pipeline-incorporating computer architectures, using a mathematical model of the roles played by the various parameters. Pipeline optimization proceeds by a partitioning of the pipeline into an optimum number of segments so that maximization of throughput is obtained. Inferences are drawn from the model, and potential improvements to it are identified. Substantial agreement is obtained with Kunkel and Smith's (1986) CRAY-1S simulations of pipelining.

Dubey, Pradeep K.↗
NASA NTRS1981

Optimal searches for asteroids

Optimal searches for a fixed object are discussed, and the rigorous analytical results of discrete search theory are presented. The totally optimal, the uniformly optimal, the locally optimal, and the fastest searches are shown to be identical under not too restrictive assumptions. The mathematical formalism is illustrated by an Earth-approaching asteroid search and optimal searches for such objects are explicitly constructed. The approximation that Earth-approaching asteroids are fixed is equivalent to having a very high ( equiv 100 sq degs/hour) search rate. Generalizations to other types of astronomical search are briefly mentioned.

Taff, L. G.↗
NASA NTRS1984

Optimal searches for asteroids

Optimal searches for a fixed object are discussed, and the rigorous analytical results of discrete search theory are presented. The totally optimal, the uniformly optimal, the locally optimal, and the fastest searches are shown to be identical under not too restrictive assumptions. The mathematical formalism is illustrated by an earth-approaching asteroid search and optimal searches for such objects are explicitly constructed. The approximation that earth-approaching asteroids are fixed is equivalent to having a very high (equiv 100 sq degs/hour) search rate. Generalizations to other types of astronomical search are briefly mentioned. Previously announced in STAR as N83-34657

Taff, L. G.↗
NASA NTRS1989

Theory of the optimally coupled Q-switched laser

The general equations describing Q-switched laser operation are transcendental in nature and require numerical solutions, which greatly complicates the optimization of real devices. Here, it is shown that, using the mathematical technique of Lagrange multipliers, one can derive simple analytic expressions for all of the key parameters of the optimally coupled laser, i.e., one which uses an optimum reflector to obtain maximum laser efficiency for a given pump level. These parameters can all be expressed as functions of a single dimensionless variable z, defined as the ratio of the unsaturated small-signal gain to the dissipative (nonuseful) optical loss, multiplied by a few simple constants. Laser design tradeoff studies and performance projections can be accomplished quickly with the help of several graphs and a simple hand calculator. Sample calculations for a high-gain Nd:YAG and a low-gain alexandrite laser are presented as illustrations of the technique.

Degnan, John J.↗
DOE OSTI2024

Tracking the topology of neural manifolds across populations

Neural manifolds summarize the intrinsic structure of the information encoded by a population of neurons. Advances in experimental techniques have made simultaneous recordings from multiple brain regions increasingly commonplace, raising the possibility of studying how these manifolds relate across populations. However, when the manifolds are nonlinear and possibly code for multiple unknown variables, it is challenging to extract robust and falsifiable information about their relationships. We introduce a framework, called the method of analogous cycles, for matching topological features of neural manifolds using only observed dissimilarity matrices within and between neural populations. We demonstrate via analysis of simulations and in vivo experimental data that this method can be used to correctly identify multiple shared circular coordinate systems across both stimuli and inferred neural manifolds. Conversely, the method rejects matching features that are not intrinsic to one of the systems. Further, as this method is deterministic and does not rely on dimensionality reduction or optimization methods, it is amenable to direct mathematical investigation and interpretation in terms of the underlying neural activity. We thus propose the method of analogous cycles as a suitable foundation for a theory of cross-population analysis via neural manifolds.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1973

Automated procedure for design of wing structures to satisfy strength and flutter requirements

A pilot computer program was developed for the design of minimum mass wing structures under flutter, strength, and minimum gage constraints. The wing structure is idealized by finite elements, and second-order piston theory aerodynamics is used in the flutter calculation. Mathematical programing methods are used for the optimization. Computation times during the design process are reduced by three techniques. First, iterative analysis methods used to reduce significantly reanalysis times. Second, the number of design variables is kept small by not using a one-to-one correspondence between finite elements and design variables. Third, a technique for using approximate second derivatives with Newton's method for the optimization is incorporated. The program output is compared witH previous published results. It is found that some flutter characteristics, such as the flutter speed, can display discontinous dependence on the design variables (which are the thicknesses of the structural elements). It is concluded that it is undesirable to use such quantities in the formulation of the flutter constraint.

Haftka, R. T.↗
NASA NTRS1973

Some questions of an optimum probability synthesis of dynamic metalworking machine systems

Attempts were made to develop a dynamic metal working machine tool system using probability information on external factors and independent disturbances of the parameters. The problem was optimized in two stages: (1) creation of mathematical models under conditions determined by input influences, and (2) processing the results of calculations obtained on such models. Data were obtained on the patterns of distribution of dynamic quality characteristics of the tool, vibration frequencies and amplitudes, attenuation coefficients, and duration of a transition process. These data were obtained using a digital computer, statistical test methods, or logical possibility trees.

Dobrynin, S. A.↗
NASA NTRS1975

System analysis of a piston steam engine employing the uniflow principle, a study in optimized performance

Results are reported which were obtained from a mathematical model of a generalized piston steam engine configuration employing the uniflow principal. The model accounted for the effects of clearance volume, compression work, and release volume. A simple solution is presented which characterizes optimum performance of the steam engine, based on miles per gallon. Development of the mathematical model is presented. The relationship between efficiency and miles per gallon is developed. An approach to steam car analysis and design is presented which has purpose rather than lucky hopefulness. A practical engine design is proposed which correlates to the definition of the type engine used. This engine integrates several system components into the engine structure. All conclusions relate to the classical Rankine Cycle.

Peoples, J. A.↗
NASA NTRS1978

The 14th Annual Conference on Manual Control

Human operator dynamics during actual manual control or while monitoring the automatic control systems involved in air-to-air tracking, automobile driving, the operator of undersea vehicles, and remote handling are examined. Optimal control models and the use of mathematical theory in representing man behavior in complex man machine system tasks are discussed with emphasis on eye/head tracking and scanning; perception and attention allocation; decision making; and motion simulation and effects.

Source record↗
NASA NTRS1980

ACCESS 3. Approximation concepts code for efficient structural synthesis: User's guide

A user's guide is presented for ACCESS-3, a research oriented program which combines dual methods and a collection of approximation concepts to achieve excellent efficiency in structural synthesis. The finite element method is used for structural analysis and dual algorithms of mathematical programming are applied in the design optimization procedure. This program retains all of the ACCESS-2 capabilities and the data preparation formats are fully compatible. Four distinct optimizer options were added: interior point penalty function method (NEWSUMT); second order primal projection method (PRIMAL2); second order Newton-type dual method (DUAL2); and first order gradient projection-type dual method (DUAL1). A pure discrete and mixed continuous-discrete design variable capability, and zero order approximation of the stress constraints are also included.

Fleury, C.↗
NASA NTRS1985

Development of a flutter suppression control law by use of linear quadratic Gaussian and constrained optimization design techniques

A control law to suppress symmetric flutter for a mathematical model of an aeroelastic research vehicle is developed. An implementable control law is attained by including modified linear quadratic Gaussian design techniques, controller order reduction, and gain scheduling. A complementary design approach for a flight condition wherein nongradient-based constrained optimization techniques are applied to maximize controller robustness is illustrated.

Adams, W. M.↗