SEARCH · Engineering Papers

Results for “combinatorial”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8

All sources NASA NTRS DOE OSTI

NASA NTRS1998

Optical Sensor/Actuator Locations for Active Structural Acoustic Control

Researchers at NASA Langley Research Center have extensive experience using active structural acoustic control (ASAC) for aircraft interior noise reduction. One aspect of ASAC involves the selection of optimum locations for microphone sensors and force actuators. This paper explains the importance of sensor/actuator selection, reviews optimization techniques, and summarizes experimental and numerical results. Three combinatorial optimization problems are described. Two involve the determination of the number and position of piezoelectric actuators, and the other involves the determination of the number and location of the sensors. For each case, a solution method is suggested, and typical results are examined. The first case, a simplified problem with simulated data, is used to illustrate the method. The second and third cases are more representative of the potential of the method and use measured data. The three case studies and laboratory test results establish the usefulness of the numerical methods.

Piezoelectric actuators↗

NASA NTRS1999

Optimization Strategies for Sensor and Actuator Placement

This paper provides a survey of actuator and sensor placement problems from a wide range of engineering disciplines and a variety of applications. Combinatorial optimization methods are recommended as a means for identifying sets of actuators and sensors that maximize performance. Several sample applications from NASA Langley Research Center, such as active structural acoustic control, are covered in detail. Laboratory and flight tests of these applications indicate that actuator and sensor placement methods are effective and important. Lessons learned in solving these optimization problems can guide future research.

Padula, Sharon L.↗

NASA NTRS1997

The Topology of Symmetric Tensor Fields

Combinatorial topology, also known as "rubber sheet geometry", has extensive applications in geometry and analysis, many of which result from connections with the theory of differential equations. A link between topology and differential equations is vector fields. Recent developments in scientific visualization have shown that vector fields also play an important role in the analysis of second-order tensor fields. A second-order tensor field can be transformed into its eigensystem, namely, eigenvalues and their associated eigenvectors without loss of information content. Eigenvectors behave in a similar fashion to ordinary vectors with even simpler topological structures due to their sign indeterminacy. Incorporating information about eigenvectors and eigenvalues in a display technique known as hyperstreamlines reveals the structure of a tensor field. The simplify and often complex tensor field and to capture its important features, the tensor is decomposed into an isotopic tensor and a deviator. A tensor field and its deviator share the same set of eigenvectors, and therefore they have a similar topological structure. A a deviator determines the properties of a tensor field, while the isotopic part provides a uniform bias. Degenerate points are basic constituents of tensor fields. In 2-D tensor fields, there are only two types of degenerate points; while in 3-D, the degenerate points can be characterized in a Q'-R' plane. Compressible and incompressible flows share similar topological feature due to the similarity of their deviators. In the case of the deformation tensor, the singularities of its deviator represent the area of vortex core in the field. In turbulent flows, the similarities and differences of the topology of the deformation and the Reynolds stress tensors reveal that the basic addie-viscosity assuptions have their validity in turbulence modeling under certain conditions.

Levin, Yingmei↗

NASA NTRS1997

The Problem of Size in Robust Design

To facilitate the effective solution of multidisciplinary, multiobjective complex design problems, a departure from the traditional parametric design analysis and single objective optimization approaches is necessary in the preliminary stages of design. A necessary tradeoff becomes one of efficiency vs. accuracy as approximate models are sought to allow fast analysis and effective exploration of a preliminary design space. In this paper we apply a general robust design approach for efficient and comprehensive preliminary design to a large complex system: a high speed civil transport (HSCT) aircraft. Specifically, we investigate the HSCT wing configuration design, incorporating life cycle economic uncertainties to identify economically robust solutions. The approach is built on the foundation of statistical experimentation and modeling techniques and robust design principles, and is specialized through incorporation of the compromise Decision Support Problem for multiobjective design. For large problems however, as in the HSCT example, this robust design approach developed for efficient and comprehensive design breaks down with the problem of size - combinatorial explosion in experimentation and model building with number of variables -and both efficiency and accuracy are sacrificed. Our focus in this paper is on identifying and discussing the implications and open issues associated with the problem of size for the preliminary design of large complex systems.

Koch, Patrick N.↗

NASA NTRS2000

Active Structural Acoustic Control of Interior Noise on a Raytheon 1900D

An active structural acoustic control system has been demonstrated on a Raytheon Aircraft Company 1900D turboprop airliner. Both single frequency and multi-frequency control of the blade passage frequency and its harmonics was accomplished. The control algorithm was a variant of the popular filtered-x LMS implemented in the principal component domain. The control system consisted of 21 inertial actuators and 32 microphones. The actuators were mounted to the aircraft's ring frames. The microphones were distributed uniformly throughout the interior at head height, both seated and standing. Actuator locations were selected using a combinatorial search optimization algorithm. The control system achieved a 14 dB noise reduction of the blade passage frequency during single frequency tests. Multi-frequency control of the first 1st, 2nd and 3rd harmonics resulted in 10.2 dB, 3.3 dB and 1.6 dB noise reductions respectively. These results fall short of the predictions which were produced by the optimization algorithm (13.5 dB, 8.6 dB and 6.3 dB). The optimization was based on actuator transfer functions taken on the ground and it is postulated that cabin pressurization at flight altitude was a factor in this discrepancy.

Palumbo, Dan↗

NASA NTRS2000

Optimizing Sensor and Actuator Arrays for ASAC Noise Control

This paper summarizes the development of an approach to optimizing the locations for arrays of sensors and actuators in active noise control systems. A type of directed combinatorial search, called Tabu Search, is used to select an optimal configuration from a much larger set of candidate locations. The benefit of using an optimized set is demonstrated. The importance of limiting actuator forces to realistic levels when evaluating the cost function is discussed. Results of flight testing an optimized system are presented. Although the technique has been applied primarily to Active Structural Acoustic Control systems, it can be adapted for use in other active noise control implementations.

Palumbo, Dan↗

NASA NTRS2000

Biological Moleculars: Have Most of Our Problems Already Been Solved?

Evolution has resulted in biological machinery that engineers have great reason to envy and at present can only poorly mimic. This is not just a curiosity as biological systems perform many functions that are desired industrial processes. Examples include photosynthesis, chemosynthesis, energy storage, low temperature chemical conversion, reproducible manufacture of chemical compounds, etc. The bases of biological machinery are the proteins and nucleic acids that comprise living organisms. Each molecule functions as a part of a biological machine. In many cases the molecule can be properly regarded as a stand alone machine of its own. Concepts and methods for harnessing the power of biological molecules exist but are often overlooked in the industrial world. Some are old and appear crude but are quite effective, e.g. the fermentation of grains and fruits. Currently, there is a revolution in progress regarding the harnessing biological processes. These include techniques such as genetic manipulation via polymerase chain reaction, forced evolution also known as evolution in a test tube, determination of molecular structure, and combinatorial chemistry. The following is a brief discussion on how these processes are performed and how they may relate to industrial and aerospace processes.

Downey, James P.↗

NASA NTRS2000

JavaGenes: Evolving Graphs with Crossover

Genetic algorithms usually use string or tree representations. We have developed a novel crossover operator for a directed and undirected graph representation, and used this operator to evolve molecules and circuits. Unlike strings or trees, a single point in the representation cannot divide every possible graph into two parts, because graphs may contain cycles. Thus, the crossover operator is non-trivial. A steady-state, tournament selection genetic algorithm code (JavaGenes) was written to implement and test the graph crossover operator. All runs were executed by cycle-scavagging on networked workstations using the Condor batch processing system. The JavaGenes code has evolved pharmaceutical drug molecules and simple digital circuits. Results to date suggest that JavaGenes can evolve moderate sized drug molecules and very small circuits in reasonable time. The algorithm has greater difficulty with somewhat larger circuits, suggesting that directed graphs (circuits) are more difficult to evolve than undirected graphs (molecules), although necessary differences in the crossover operator may also explain the results. In principle, JavaGenes should be able to evolve other graph-representable systems, such as transportation networks, metabolic pathways, and computer networks. However, large graphs evolve significantly slower than smaller graphs, presumably because the space-of-all-graphs explodes combinatorially with graph size. Since the representation strongly affects genetic algorithm performance, adding graphs to the evolutionary programmer's bag-of-tricks should be beneficial. Also, since graph evolution operates directly on the phenotype, the genotype-phenotype translation step, common in genetic algorithm work, is eliminated.

Globus, Al↗

NASA NTRS2000

From Livingstone to SMV: Formal Verification for Autonomous Spacecrafts

To fulfill the needs of its deep space exploration program, NASA is actively supporting research and development in autonomy software. However, the reliable and cost-effective development and validation of autonomy systems poses a tough challenge. Traditional scenario-based testing methods fall short because of the combinatorial explosion of possible situations to be analyzed, and formal verification techniques typically require a tedious, manual modelling by formal method experts. This paper presents the application of formal verification techniques in the development of autonomous controllers based on Livingstone, a model-based health-monitoring system that can detect and diagnose anomalies and suggest possible recovery actions. We present a translator that converts the models used by Livingstone into specifications that can be verified with the SMV model checker. The translation frees the Livingstone developer from the tedious conversion of his design to SMV, and isolates him from the technical details of the SMV program. We describe different aspects of the translation and briefly discuss its application to several NASA domains.

Pecheur, Charles↗

NASA NTRS2001

Carbon Nanotubes by CVD and Applications

Carbon nanotube (CNT) exhibits extraordinary mechanical and unique electronic properties and offers significant potential for structural, sensor, and nanoelectronics applications. An overview of CNT, growth methods, properties and applications is provided. Single-wall, and multi-wall CNTs have been grown by chemical vapor deposition. Catalyst development and optimization has been accomplished using combinatorial optimization methods. CNT has also been grown from the tips of silicon cantilevers for use in atomic force microscopy.

Cassell, Alan↗

NASA NTRS1997

When Gravity Fails: Local Search Topology

Local search algorithms for combinatorial search problems frequently encounter a sequence of states in which it is impossible to improve the value of the objective function; moves through these regions, called {\em plateau moves), dominate the time spent in local search. We analyze and characterize {\em plateaus) for three different classes of randomly generated Boolean Satisfiability problems. We identify several interesting features of plateaus that impact the performance of local search algorithms. We show that local minima tend to be small but occasionally may be very large. We also show that local minima can be escaped without unsatisfying a large number of clauses, but that systematically searching for an escape route may be computationally expensive if the local minimum is large. We show that plateaus with exits, called benches, tend to be much larger than minima, and that some benches have very few exit states which local search can use to escape. We show that the solutions (i.e. global minima) of randomly generated problem instances form clusters, which behave similarly to local minima. We revisit several enhancements of local search algorithms and explain their performance in light of our results. Finally we discuss strategies for creating the next generation of local search algorithms.

Frank, Jeremy↗

NASA NTRS1998

Self-Avoiding Walks over Adaptive Triangular Grids

In this paper, we present a new approach to constructing a "self-avoiding" walk through a triangular mesh. Unlike the popular approach of visiting mesh elements using space-filling curves which is based on a geometric embedding, our approach is combinatorial in the sense that it uses the mesh connectivity only. We present an algorithm for constructing a self-avoiding walk which can be applied to any unstructured triangular mesh. The complexity of the algorithm is O(n x log(n)), where n is the number of triangles in the mesh. We show that for hierarchical adaptive meshes, the algorithm can be easily parallelized by taking advantage of the regularity of the refinement rules. The proposed approach should be very useful in the run-time partitioning and load balancing of adaptive unstructured grids.

Heber, Gerd↗

NASA NTRS2002

Number Partitioning via Quantum Adiabatic Computation

We study both analytically and numerically the complexity of the adiabatic quantum evolution algorithm applied to random instances of combinatorial optimization problems. We use as an example the NP-complete set partition problem and obtain an asymptotic expression for the minimal gap separating the ground and exited states of a system during the execution of the algorithm. We show that for computationally hard problem instances the size of the minimal gap scales exponentially with the problem size. This result is in qualitative agreement with the direct numerical simulation of the algorithm for small instances of the set partition problem. We describe the statistical properties of the optimization problem that are responsible for the exponential behavior of the algorithm.

Smelyanskiy, Vadim N.↗

NASA NTRS1999

Self-Avoiding Walks Over Adaptive Triangular Grids

Space-filling curves is a popular approach based on a geometric embedding for linearizing computational meshes. We present a new O(n log n) combinatorial algorithm for constructing a self avoiding walk through a two dimensional mesh containing n triangles. We show that for hierarchical adaptive meshes, the algorithm can be locally adapted and easily parallelized by taking advantage of the regularity of the refinement rules. The proposed approach should be very useful in the runtime partitioning and load balancing of adaptive unstructured grids.

Heber, Gerd↗

NASA NTRS2002

Dynamics of Quantum Adiabatic Evolution Algorithm for Number Partitioning

We have developed a general technique to study the dynamics of the quantum adiabatic evolution algorithm applied to random combinatorial optimization problems in the asymptotic limit of large problem size n. We use as an example the NP-complete Number Partitioning problem and map the algorithm dynamics to that of an auxiliary quantum spin glass system with the slowly varying Hamiltonian. We use a Green function method to obtain the adiabatic eigenstates and the minimum exitation gap, gmin = O(n2(sup -n/2)), corresponding to the exponential complexity of the algorithm for Number Partitioning. The key element of the analysis is the conditional energy distribution computed for the set of all spin configurations generated from a given (ancestor) configuration by simultaneous flipping of a fixed number of spins. For the problem in question this distribution is shown to depend on the ancestor spin configuration only via a certain parameter related to the energy of the configuration. As the result, the algorithm dynamics can be described in terms of one-dimensional quantum diffusion in the energy space. This effect provides a general limitation of a quantum adiabatic computation in random optimization problems. Analytical results are in agreement with the numerical simulation of the algorithm.

Smelyanskiy, Vadius↗

NASA NTRS2003

On the Critical Behaviour, Crossover Point and Complexity of the Exact Cover Problem

Research into quantum algorithms for NP-complete problems has rekindled interest in the detailed study a broad class of combinatorial problems. A recent paper applied the quantum adiabatic evolution algorithm to the Exact Cover problem for 3-sets (EC3), and provided an empirical evidence that the algorithm was polynomial. In this paper we provide a detailed study of the characteristics of the exact cover problem. We present the annealing approximation applied to EC3, which gives an over-estimate of the phase transition point. We also identify empirically the phase transition point. We also study the complexity of two classical algorithms on this problem: Davis-Putnam and Simulated Annealing. For these algorithms, EC3 is significantly easier than 3-SAT.

Morris, Robin D.↗

NASA NTRS2003

Flame Spray Strain Gages with Improved Durability and Lifetimes

The focus of this APP research program was to improve the bond coats used in the fabrication of flame sprayed instrumentation. Typically. a bond coat is applied to a superalloy surface prior to the application of a thin dielectric coating onto which instrumentation is placed. After affixing the instrumentation, a much thicker ceramic topcoat is typically applied to protect the instrumentation from harsh environments. The fatigue life of NiCoCrAlY coated superalloys was extended beyond current state-of-the-art by relatively simple and cost effective means. Heat treatment in reduced oxygen partial pressures at 1750 to 1800 F effectively doubled the fatigue life of NiCoCrAlY coated substrates relative to as-sprayed substrates and when used in conjunction with platinum diffusion barriers yielded a four fold increase in the fatigue life of NiCoCrAlY coated substrates. Further improvements in the fatigue life of thermally sprayed coatings were made by employing intermediate coatings, which minimized thermal expansion differences between the bond coat and top coat. Combinatorial chemistry experiments yielded an optimum composition for an intermediate TCE matching coating that showed considerable promise in extending the fatigue life of thermal spray instrumentation. The intermediate coating had two functions: to reduce the surface roughness of the peaks and valleys associated with the as-sprayed NiCoCrAlY bond coat, and to produce a thin layer of a mixture of Al2O3 and NiCoCrAlY that exhibited an intermediate TCE. The optimal composition of the intermediate coating consisted of 60 wt% Al2O3 and 40 wt% NiCoCrAlY, as determined by energy dispersive analysis of x-rays (EDS). Intermediate coatings having this composition were prepared by physical vapor deposition and the resulting coating systems are being evaluated in our test facility.

Fralick, Gustave↗

NASA NTRS2001

The Effect of Cytidine on the Structure and Function of an RNA Ligase Ribozyme

A cytidine-free ribozyme with RNA ligase activity was obtained by in vitro evolution, starting from a pool of random- sequence RNAs that contained only guanosine, adenosine, and uridine. This ribozyme contains 74 nt and catalyzes formation of a 3',5' -phosphodiester linkage with a catalytic rate of 0.016/min. The RNA adopts a simple secondary structure based on a three-way junction motif, with ligation occurring at the end of a stem region located several nucleotides away from the junction. Cytidine was introduced to the cytidine-free ribozyme in a combinatorial fashion and additional rounds of in vitro evolution were carried out to allow the molecule to adapt to this added component. The resulting cytidine-containing ribozyme formed a 3',5' linkage with a catalytic rate of 0.32/min. The improved rate of the cytidine-containing ribozyme was the result of 12 mutations, including seven added cytidines, that remodeled the internal bulge loops located adjacent to the three-way junction and stabilized the peripheral stem regions.

Rogers, Jeff↗