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At least 415 records · Page 23

Vector-Ordering Filter Procedure for Data Reduction

The vector-ordering filter (VOF) technique involves a procedure for sampling a large population of data vectors to select a subset of data vectors that fully characterize the state space of the large population. The VOF technique enables a large reduction of the volume of data that must be handled in the automated monitoring system and method discussed in the two immediately preceding articles. In so doing, the VOF technique enables the development of data-driven mathematical models of a monitored asset from sets of data that would otherwise exceed the memory capacities of conventional engineering computers. Data-driven mathematical models have been shown to offer high fidelity for purposes of control and monitoring of assets. In practice, a collection of asset-operating observations is acquired with the intention that the collection contain observations characteristic of the full dynamic range of operation of the asset. Often, such a collection contains an extremely large number of observations, many of which are redundant. The VOF technique fills the need for a means to extract, from the original collection of observational data, a reduced data matrix that excludes redundant data while maintaining the full statistical character and dynamic range of the original data. The reduced data matrix can then be used as the input data for development of a mathematical model of the monitored asset, or as training data for a neural-network substitute for an explicit mathematical model of the asset. Alternatively, the reduced data matrix can, itself, be used directly as a mathematical model of the monitored asset, as is commonly done in multivariate state-estimation techniques. The original data are collected from the asset over a range of operating states and are put in matrix form. Each column vector in the original data matrix represents the signal values acquired at a particular operational state of the asset. Thus, the number of columns of the original data matrix equals the number of observed states and the number of rows in this matrix equals the number of signals acquired at each observation. In the VOF technique, one extracts the reduced data matrix from the original data matrix through the selection of a representative subset of the column (state) vectors.

Bickford, Randall L.↗

The solar radiation pressure on the Mariner 9 Mars orbiter.

The refined mathematical model of the force created by the light pressure of the sun has been used to compute the solar radiation pressure force acting on the Mariner 9 (Mariner Mars 1971) spacecraft, taking into account the reflectivity characteristics of all its components. The results have been compared with values obtained from Mariner 9 observations during the cruise phase and are found to be in agreement within 0.1% of the values.

Georgevic, R. M.↗

The solar radiation pressure on the Mariner 9 Mars orbiter

The refined mathematical model of the force created by the light pressure of the sun has been used to compute the solar radiation pressure force acting on the Mariner 9 (Mariner Mars 1971) spacecraft, taking into account the reflectivity characteristics of all its components. The results have been compared with values obtained from Mariner 9 observations during the cruise phase and are found to be in agreement within 0.1% of the values.

Georgevic, R. M.↗

Optimum lattice arrangement developed from a rigorous analytical basis

The spanwise vortex-lattice arrangement is mathematically established by lattice solutions of the slender wing which are shown to be analogous to the chordwise vortex-lattice thin wing solution. Solutions for any number N of panels wing theory lift and induced drag and thin wing theory lift and moment are predicted exactly. As N approaches infinity, the slender wing elliptic spanwise loading and thin wing cotangent chordwise loading are predicted, which proves there is mathematical convergence of the vortex-lattice method to the exact answer. Based on this planform spanwise lattice arrangement, an A-vortex-lattice spanwise system is developed for an arbitrary aspect ratio A. This A-lattice has the optimum characteristic of predicting lift accurately for any value of N.

Deyoung, J.↗

Pitch angle diffusion in the Jovian magnetodisc

Using a linear approximation to the field variation and a mathematical technique for distorting the orbit integration into the complex gyrophase plane, a formula is derived for the nonadiabatic change in magnetic moment. This change varies as the cosine of the particle gyrophase at the equator, so that if a particle traverses the equator several times with different values of this gyrophase, it suffers randomly correlated values for the nonadiabatic change in magnetic moment. The algebraic formula for this nonadiabatic change is found to be in excellent agreement with previous numerical computations. The phase space density, averaged over several bounce periods, is found to satisfy a diffusion equation in pitch angle. The diffusion coefficient is dependent on particle energy, pitch angle, and the field line along which the particles are moving.

Birmingham, T. J.↗

Simulation of UV atomic radiation for application in exhaust plume spectrometry

Quantitative analysis of exhaust plume spectral data has long been a goal of developers of advanced engine health monitoring systems which incorporate optical measurements of rocket exhaust constituents. Discussed herein is the status of present efforts to model and predict atomic radiation spectra and infer free-atom densities from emission/absorption measurements as part of the Optical Plume Anomaly Detection (OPAD) program at Marshall Space Flight Center (MSFC). A brief examination of the mathematical formalism is provided in the context of predicting radiation from the Mach disk region of the SSME exhaust flow at nominal conditions during ground level testing at MSFC. Computational results are provided for Chromium and Copper at selected transitions which indicate a strong dependence upon broadening parameter values determining the absorption-emission line shape. Representative plots of recent spectral data from the Stennis Space Center (SSC) Diagnostic Test Facility (DTF) rocket engine are presented and compared to numerical results from the present self-absorbing model; a comprehensive quantitative analysis will be reported at a later date.

Wallace, T. L.↗

Noninvasive Determination of Bone Mechanical Properties using Vibration Response: A Refined Model and Validation in vivo

Accurate non-invasive mechanical measurement of long bones is made difficult by the masking effect of surrounding soft tissues. Mechanical Response Tissue Analysis (MRTA) offers a method for separating the effects of the soft tissue and bone; however, a direct validation has been lacking. A theoretical analysis of wave propagation through the compressed tissue revealed a strong mass effect dependent on the relative accelerations of the probe and bone. The previous mathematical model of the bone and overlying tissue system was reconfigured to incorporate the theoretical finding. This newer model (six-parameter) was used to interpret results using MRTA to determine bone cross-sectional bending stiffness, EI(sub MRTA). The relationship between EI(MRTA) and theoretical EI values for padded aluminum rods was R(exp 2) = 0.999. A biological validation followed using monkey tibias. Each bone was tested in vivo with the MRTA instrument. Postmortem, the same tibias were excised and tested to failure in three-point bending to determine EI(sub 3-PT) and maximum load. Diaphyseal Bone Mineral Density (BMD) measurements were also made. The relationship between E(sub 3-PT) and in vivo EI(sub MRTA) using the six-parameter model is strong (R(exp 2) = 0.947) and better than that using the older model (R(exp 2) = 0.645). EI(MRTA) and BMD are also highly correlated (R(exp 2) = 0.853). MRTA measurements in vivo and BMD ex vivo are both good predictors of scaled maximum strength (R(exp 2) = 0.915 and R(exp 2) = 0.894, respectively). This is the first biological validation of a non-invasive mechanical measurement of bone by comparison to actual values. The MRTA technique has potential clinical value for assessing long-bone mechanical properties.

Roberts, S. G.↗

A Framework for Dynamic Constraint Reasoning Using Procedural Constraints

Many complex real-world decision and control problems contain an underlying constraint reasoning problem. This is particularly evident in a recently developed approach to planning, where almost all planning decisions are represented by constrained variables. This translates a significant part of the planning problem into a constraint network whose consistency determines the validity of the plan candidate. Since higher-level choices about control actions can add or remove variables and constraints, the underlying constraint network is invariably highly dynamic. Arbitrary domain-dependent constraints may be added to the constraint network and the constraint reasoning mechanism must be able to handle such constraints effectively. Additionally, real problems often require handling constraints over continuous variables. These requirements present a number of significant challenges for a constraint reasoning mechanism. In this paper, we introduce a general framework for handling dynamic constraint networks with real-valued variables, by using procedures to represent and effectively reason about general constraints. The framework is based on a sound theoretical foundation, and can be proven to be sound and complete under well-defined conditions. Furthermore, the framework provides hybrid reasoning capabilities, as alternative solution methods like mathematical programming can be incorporated into the framework, in the form of procedures.

Jonsson, Ari K.↗

Practical and Optimal Sequential Bayesian Experimental Design for Complex Systems Incorporating Human Experimenter Preferences (Final Scientific/Technical Report)

Experiments are indispensable for developing models of complex systems. Carefully designed experiments can provide substantial savings for these expensive data-acquisition opportunities. However, designs based on heuristics are often suboptimal for systems with multiphysics, nonlinear dynamics, and uncertain and noisy environments. Optimal experimental design, while leveraging predictive models, seeks to systematically quantify and maximize the value of experiments. In this project, we focused on the design of multiple experiments, where current approaches are largely suboptimal: batch-design does not adapt to new data acquired during the experiment campaign (no feedback), and greedy/myopic design ignores future dynamics and consequences (no lookahead). We developed the mathematical framework and computational methods for sequential optimal experimental design (sOED) for complex systems. We enabled tractable model-based sOED in a rigorous manner through novel algorithms based on reinforcement learning, and investigated the effects of human experimenters on the design process. Our methods are fully Bayesian, able to quantify and update uncertainty in a principled manner. The traits aimed by our approach—mathematical rigor and optimality, human effects and uncertainty quantification, computational practicality—are crucial for elevating the standards of artificial intelligence (AI) to support decision-making in scientific domains, and contribute toward trust and realistic adoption of AI in experimental design practice.

97 MATHEMATICS AND COMPUTING↗

A qualitative study of the complete set of solutions of the differential equation of motion of a test particle in the equatorial plane of the Kerr gravitational field

A study is made of the mathematical solution of the differential equation of motion of a test particle in the equatorial plane of the Kerr gravitational field, using S (Schwarzschild-like) coordinates. A qualitative solution of this equation leads to the conclusion that there can only be 25 different types of orbits. For each value of a, the results are presented in a master diagram for which h and e are the parameters. A master diagram divides the h, e parameter space into regions such that at each point within one of these regions the types of admissible orbits are qualitatively the same. A pictorial representation of the physical orbits in the r, phi plane is also given.

Montgomery, H. E.↗

Tidal evolution in close binary systems.

Mathematical outline of the theory of tidal evolution in close binary systems of secularly constant total momentum. Following a general outline of the problem the basic expressions for the energy and momenta of close binaries consisting of components of arbitrary internal structure are established, and the maximum and minimum values of the energy (kinetic and potential) which such systems can attain for a given amount of total momentum are investigated. These results are compared with the actual facts encountered in binaries with components whose internal structure (and, therefore, rotational momenta) are known from evidence furnished by the observed rates of apsidal advance. The results show that all such systems whether of detached or semidetached type - disclose that more than 99% of their total momenta are stored in the orbital momentum. The sum of the rotational momenta of the constituent components amounts to less than 1% of the total -a situation characteristic of a state close to the minimum energy for given total momentum.

Kopal, Z.↗

A class of neutral functional differential equations.

Formulation and study of the initial value problem for neutral functional differential equations. The existence, uniqueness, and continuation of solutions to this problem are investigated, and an analysis is made of the dependence of the solutions on the initial conditions and parameters, resulting in the derivation of a continuous dependence theorem in which the fundamental mathematical principles underlying the continuous dependence problem for a very general system of nonlinear neutral functional differential equations are separated out.

Melvin, W. R.↗

The neutrino charge form-factor

Mathematical analysis and dispersion relations are used to obtain the general functional form of the neutrino charge form-factor. It is shown that if the scale for weak interactions is given by G, where G is the Fermi coupling constant, then for a large range of momentum transfer values, the form-factor may be approximated by a function that is linear in the square of the momentum transfer.

Mickens, R. E.↗

Noninvasive Determination of Bone Mechanical Properties Using Vibration Response: A Refined Model and Validation in vivo

Accurate non-invasive mechanical measurement of long bones is made difficult by the masking effect of surrounding soft tissues. Mechanical response tissue analysis (MRTA) offers a method for separating the effects of the soft tissue and bone; however, a direct validation has been lacking. A theoretical analysis of wave propagation through the compressed tissue revealed a strong mass effect dependent on the relative accelerations of the probe and bone. The previous mathematical model of the bone and overlying tissue system was reconfigured to incorporate the theoretical finding. This newer model (six-parameter) was used to interpret results using MRTA to determine bone cross-sectional bending stiffness, EI(sub MRTA). The relationship between EI(sub MRTA) and theoretical EI values for padded aluminum rods was R(sup 2) = 0.999. A biological validation followed using monkey tibias. Each bone was tested in vivo with the MRTA instrument. Postmortem, the same tibias were excised and tested to failure in three-point bending to determine EI(sub 3-PT) and maximum load. Diaphyseal bone mineral density (BMD) measurements were also made. The relationship between EI(sub 3-PT) and in vivo EI(sub MRTA) using the six-parameter model is strong (R(sup 2) = 0.947) and better than that using the older model (R(sup 2) = 0.645). EI(sub MRTA) and BMD are also highly correlated (R(sup 2) = 0.853). MRTA measurements in vivo and BMD ex vivo are both good predictors of scaled maximum strength (R(sup 2) = 0.915 and R(sup 2) = 0.894, respectively). This is the first biological validation of a non- invasive mechanical measurement of bone by comparison to actual values. The MRTA technique has potential clinical value for assessing long-bone mechanical properties.

Roberts, S. G.↗

A matheuristic for design and dispatch of a utility-connected distributed energy system

Modeling distributed power generation systems often requires complicated mathematical expressions that present challenges for commercial optimization solvers. Here, this paper presents a matheuristic to solve a mixed-integer optimization model that informs decisions regarding the design and dispatch of a utility-connected microgrid. We deploy a genetic algorithm to search the system design space and a linear program to solve the economic dispatch problem. The model is a component of a web tool that requires solutions within a few minutes. Our method yields objective function values within 5% of an exogenously produced optimal in fewer than 30 seconds for 90% of our test cases compared to only 10% of our test cases by a traditional optimization solver in the same amount of time.

24 POWER TRANSMISSION AND DISTRIBUTION↗

The viscoelastic behavior of notched glassy polymers

In the bulk, glassy polymers exhibit a nonlinear viscoelastic response during deformation. Stress or strain induced damage (i.e. crazing, microshear banding) results in the production of nonrecoverable work and observed nonlinearity. Stress or strain dependent shift factors have been used to mathematically model the mechanical behavior of these polymers. Glassy polymers that have been notched, may exhibit very different load displacement response compared to the same material under bulk deformation. If a sharp notch is introduced into the body then loaded, the load displacement trace may appear to be single-valued in the absence of viscoelasticity and crack growth. This suggests the volume of damaged material is small compared to the overall dimensions of the specimen. The ability to produce a single-valued load-load-line displacement trace through the use of the Correspondence Principle may prove to be useful for fracture of viscoelastic materials.

Crook, R. A.↗

Critical Compressive Stress for Outstanding Flanges

A chart is presented for the values of the coefficient in the formula for the critical compressive stress at which buckling may be expected to occur in outstanding flanges. These flanges are flat rectangular plates supported along the loaded edges, supported and elastically restrained along one unloaded edge, and free along the other unloaded edge. The mathematical derivations of the formulas required for construction of the chart are given.

Lundquist, Eugene E↗

Critical Compressive Stress for Outstanding Flanges

A chart is presented for the values of the coefficient in the formula for the critical compressive stress at which buckling may be expected to occur in outstanding flanges. These flanges are flat rectangular plates supported along the Loaded edges, supported and elastically restrained along one unloaded edge, and free along the other unloaded edge. The mathematical derivations of the formulas required for the construction of the chart are given.

Lundquist, Eugene E.↗