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84 records · Page 5

Quantification of human responses

Human perception is a complex phenomenon which is difficult to quantify with instruments. For this reason, large panels of people are often used to elicit and aggregate subjective judgments. Print quality, taste, smell, sound quality of a stereo system, softness, and grading Olympic divers and skaters are some examples of situations where subjective measurements or judgments are paramount. We usually express what is in our mind through language as a medium but languages are limited in available choices of vocabularies, and as a result, our verbalizations are only approximate expressions of what we really have in mind. For lack of better methods to quantify subjective judgments, it is customary to set up a numerical scale such as 1, 2, 3, 4, 5 or 1, 2, 3, ..., 9, 10 for characterizing human responses and subjective judgments with no valid justification except that these scales are easy to understand and convenient to use. But these numerical scales are arbitrary simplifications of the complex human mind; the human mind is not restricted to such simple numerical variations. In fact, human responses and subjective judgments are psychophysical phenomena that are fuzzy entities and therefore difficult to handle by conventional mathematics and probability theory. The fuzzy mathematical approach provides a more realistic insight into understanding and quantifying human responses. This paper presents a method for quantifying human responses and subjective judgments without assuming a pattern of linear or numerical variation for human responses. In particular, quantification and evaluation of linguistic judgments was investigated.

Steinlage, R. C.↗

Bayesian Symbolic Regression: Addressing Challenges in Estimating Fractional Bayes Factors and Application to Fatigue Crack Growth Modeling

This research pioneers advancements in computational mechanics by integrating Bayesian-based uncertainty quantification into symbolic regression, specifically focusing on the critical task of accurately estimating the fractional Bayes factor for selecting arbitrary equations. In our exploration, we rigorously study two prominent methods—sequential Monte Carlo and the Laplace approximation—employed for computing the fractional Bayes factor. Our findings underscore the limitations of the Laplace approximation, revealing its diminished accuracy in nonlinear and multimodal scenarios. Specifically, the Laplace approximation is shown to underpredict fractional Bayes factor on a wide set of equations associated with a symbolic regression benchmark. This comparative analysis sheds light on the nuanced performance of these techniques, guiding researchers toward more informed choices in uncertainty quantification within symbolic regression. Furthermore, we showcase the practical utility of these enhanced symbolic regression tools through their application to a real-world problem in fatigue crack growth modeling, emphasizing their efficacy in capturing the complexities of mechanical systems.

Geoffrey Bomarito↗

High Order Discontinuous Gelerkin Methods for Convection Dominated Problems with Application to Aeroacoustics

This project is about the investigation of the development of the discontinuous Galerkin finite element methods, for general geometry and triangulations, for solving convection dominated problems, with applications to aeroacoustics. On the analysis side, we have studied the efficient and stable discontinuous Galerkin framework for small second derivative terms, for example in Navier-Stokes equations, and also for related equations such as the Hamilton-Jacobi equations. This is a truly local discontinuous formulation where derivatives are considered as new variables. On the applied side, we have implemented and tested the efficiency of different approaches numerically. Related issues in high order ENO and WENO finite difference methods and spectral methods have also been investigated. Jointly with Hu, we have presented a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the RungeKutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method. Jointly with Hu, we have constructed third and fourth order WENO schemes on two dimensional unstructured meshes (triangles) in the finite volume formulation. The third order schemes are based on a combination of linear polynomials with nonlinear weights, and the fourth order schemes are based on combination of quadratic polynomials with nonlinear weights. We have addressed several difficult issues associated with high order WENO schemes on unstructured mesh, including the choice of linear and nonlinear weights, what to do with negative weights, etc. Numerical examples are shown to demonstrate the accuracies and robustness of the methods for shock calculations. Jointly with P. Montarnal, we have used a recently developed energy relaxation theory by Coquel and Perthame and high order weighted essentially non-oscillatory (WENO) schemes to simulate the Euler equations of real gas. The main idea is an energy decomposition under the form epsilon = epsilon(sub 1) + epsilon(sub 2), where epsilon(sub 1) is associated with a simpler pressure law (gamma)-law in this paper) and the nonlinear deviation epsilon(sub 2) is convected with the flow. A relaxation process is performed for each time step to ensure that the original pressure law is satisfied. The necessary characteristic decomposition for the high order WENO schemes is performed on the characteristic fields based on the epsilon(sub l) gamma-law. The algorithm only calls for the original pressure law once per grid point per time step, without the need to compute its derivatives or any Riemann solvers. Both one and two dimensional numerical examples are shown to illustrate the effectiveness of this approach.

Shu, Chi-Wang↗

Viscous compressible flow direct and inverse computation and illustrations

An algorithm for laminar and turbulent viscous compressible two dimensional flows is presented. For the application of precise boundary conditions over an arbitrary body surface, a body-fitted coordinate system is used in the physical plane. A thin-layer approximation of tne Navier-Stokes equations is introduced to keep the viscous terms relatively simple. The flow field computation is performed in the transformed plane. A factorized, implicit scheme is used to facilitate the computation. Sample calculations, for Couette flow, developing pipe flow, an isolated airflow, two dimensional compressor cascade flow, and segmental compressor blade design are presented. To a certain extent, the effective use of the direct solver depends on the user's skill in setting up the gridwork, the time step size and the choice of the artificial viscosity. The design feature of the algorithm, an iterative scheme to correct geometry for a specified surface pressure distribution, works well for subsonic flows. A more elaborate correction scheme is required in treating transonic flows where local shock waves may be involved.

Yang, T. T.↗

Quantitative PLIF Imaging in High-Pressure Combustion

This is the final report for a research project aimed at developing planar laser-induced fluorescence (PLIF) techniques for quantitative 2-D species imaging in fuel-lean, high-pressure combustion gases, relevant to modem aircraft gas turbine combustors. The program involved both theory and experiment. The theoretical activity led to spectroscopic models that allow calculation of the laser-induced fluorescence produced in OH, NO and 02 for arbitrary excitation wavelength, pressure, temperature, gas mixture and laser linewidth. These spectroscopic models incorporate new information on line- broadening, energy transfer and electronic quench rates. Extensive calculations have been made with these models in order to identify optimum excitation strategies, particularly for detecting low levels (ppm) of NO in the presence of large 02 mole fractions (10% is typical for the fuel-lean combustion of interest). A promising new measurement concept has emerged from these calculations, namely that excitation at specific wavelengths, together with detection of fluorescence in multiple spectral bands, promises to enable simultaneous detection of both NO (at ppm levels) and 02 or possibly NO, 02 and temperature. Calculations have been made to evaluate the expected performance of such a diagnostic for a variety of conditions and choices of excitation and detection wavelengths. The experimental effort began with assembly of a new high-pressure combustor to provide controlled high-temperature and high-pressure combustion products. The non-premixed burner enables access to postflame gases at high temperatures (to 2000 K) and high pressures (to 13 atm), and a range of fuel-air equivalence ratios. The chamber also allowed use of a sampling probe, for chemiluminescent detection of NO/NO2, and thermocouples for measurement of gas temperature. Experiments were conducted to confirm the spectroscopic models for OH, NO and 02.

Hanson, R. K.↗

An Algorithm for Statistical Audibility Prediction (SAP) of an Arbitrary Signal in the Presence of Noise

A method for predicting the audibility of an arbitrary time-varying noise (signal) in the presence of masking noise has been developed. The statistical audibility prediction (SAP) method relies on the specific loudness, or loudness perceived through the individual auditory filters, for accurate statistical estimation of audibility vs. time. More recent development has focused on derivation and inclusion of frequency-dependent correction factors in SAP’s model to account for the ability to hear signals below the level of the masking noise. Audibility prediction vs. time is intuitive since it captures changes in audibility with time as it occurs, which is critical for the study of human response to noise. Concurrently time-frequency prediction of audibility may also provide valuable information about the root cause(s) for audibility useful for the design and operation of sources of noise. Empirical data, gathered under a three-alternative forced-choice (3AFC) test paradigm for low-frequency sound, has been used to examine the accuracy of SAP.

audibility↗

Canonical forms for nonlinear systems

Necessary and sufficient conditions for transforming a nonlinear system to a controllable linear system have been established, and this theory has been applied to the automatic flight control of aircraft. These transformations show that the nonlinearities in a system are often not intrinsic, but are the result of unfortunate choices of coordinates in both state and control variables. Given a nonlinear system (that may not be transformable to a linear system), we construct a canonical form in which much of the nonlinearity is removed from the system. If a system is not transformable to a linear one, then the obstructions to the transformation are obvious in canonical form. If the system can be transformed (it is called a linear equivalent), then the canonical form is a usual one for a controllable linear system. Thus our theory of canonical forms generalizes the earlier transformation (to linear systems) results. Our canonical form is not unique, except up to solutions of certain partial differential equations we discuss. In fact, the important aspect of this paper is the constructive procedure we introduce to reach the canonical form. As is the case in many areas of mathematics, it is often easier to work with the canonical form than in arbitrary coordinate variables.

Su, R.↗

Feasibility of Decentralized Linear-Quadratic-Gaussian Control of Autonomous Distributed Spacecraft

A distributed satellite formation, modeled as an arbitrary number of fully connected nodes in a network, could be controlled using a decentralized controller framework that distributes operations in parallel over the network. For such problems, a solution that minimizes data transmission requirements, in the context of linear-quadratic-Gaussian (LQG) control theory, was given by Speyer. This approach is advantageous because it is non-hierarchical, detected failures gracefully degrade system performance, fewer local computations are required than for a centralized controller, and it is optimal with respect to the standard LQG cost function. Disadvantages of the approach are the need for a fully connected communications network, the total operations performed over all the nodes are greater than for a centralized controller, and the approach is formulated for linear time-invariant systems. To investigate the feasibility of the decentralized approach to satellite formation flying, a simple centralized LQG design for a spacecraft orbit control problem is adapted to the decentralized framework. The simple design uses a fixed reference trajectory (an equatorial, Keplerian, circular orbit), and by appropriate choice of coordinates and measurements is formulated as a linear time-invariant system.

Carpenter, J. Russell↗

Feasibility of Decentralized Linear-Quadratic-Gaussian Control of Autonomous Distributed Spacecraft

A distributed satellite formation, modeled as an arbitrary number of fully connected nodes in a network, could be controlled using a decentralized controller framework that distributes operations in parallel over the network. For such problems, a solution that minimizes data transmission requirements, in the context of linear-quadratic-Gaussian (LQG) control theory, was given by Speyer. This approach is advantageous because it is non-hierarchical, detected failures gracefully degrade system performance, fewer local computations are required than for a centralized controller, and it is optimal with respect to the standard LQG cost function. Disadvantages of the approach are the need for a fully connected communications network, the total operations performed over all the nodes are greater than for a centralized controller, and the approach is formulated for linear time-invariant systems. To investigate the feasibility of the decentralized approach to satellite formation flying, a simple centralized LQG design for a spacecraft orbit control problem is adapted to the decentralized framework. The simple design uses a fixed reference trajectory (an equatorial, Keplerian, circular orbit), and by appropriate choice of coordinates and measurements is formulated as a linear time-invariant system.

Carpenter, J. Russell↗

Image Correlation Pattern Optimization for Micro-Scale In-Situ Strain Measurements

The accuracy and precision of digital image correlation (DIC) is a function of three primary ingredients: image acquisition, image analysis, and the subject of the image. Development of the first two (i.e. image acquisition techniques and image correlation algorithms) has led to widespread use of DIC; however, fewer developments have been focused on the third ingredient. Typically, subjects of DIC images are mechanical specimens with either a natural surface pattern or a pattern applied to the surface. Research in the area of DIC patterns has primarily been aimed at identifying which surface patterns are best suited for DIC, by comparing patterns to each other. Because the easiest and most widespread methods of applying patterns have a high degree of randomness associated with them (e.g., airbrush, spray paint, particle decoration, etc.), less effort has been spent on exact construction of ideal patterns. With the development of patterning techniques such as microstamping and lithography, patterns can be applied to a specimen pixel by pixel from a patterned image. In these cases, especially because the patterns are reused many times, an optimal pattern is sought such that error introduced into DIC from the pattern is minimized. DIC consists of tracking the motion of an array of nodes from a reference image to a deformed image. Every pixel in the images has an associated intensity (grayscale) value, with discretization depending on the bit depth of the image. Because individual pixel matching by intensity value yields a non-unique scale-dependent problem, subsets around each node are used for identification. A correlation criteria is used to find the best match of a particular subset of a reference image within a deformed image. The reader is referred to references for enumerations of typical correlation criteria. As illustrated by Schreier and Sutton and Lu and Cary systematic errors can be introduced by representing the underlying deformation with under-matched shape functions. An important implication, as discussed by Sutton et al., is that in the presence of highly localized deformations (e.g., crack fronts), error can be reduced by minimizing the subset size. In other words, smaller subsets allow the more accurate resolution of localized deformations. Contrarily, the choice of optimal subset size has been widely studied and a general consensus is that larger subsets with more information content are less prone to random error. Thus, an optimal subset size balances the systematic error from under matched deformations with random error from measurement noise. The alternative approach pursued in the current work is to choose a small subset size and optimize the information content within (i.e., optimizing an applied DIC pattern), rather than finding an optimal subset size. In the literature, many pattern quality metrics have been proposed, e.g., sum of square intensity gradient (SSSIG), mean subset fluctuation, gray level co-occurrence, autocorrelation-based metrics, and speckle-based metrics. The majority of these metrics were developed to quantify the quality of common pseudo-random patterns after they have been applied, and were not created with the intent of pattern generation. As such, it is found that none of the metrics examined in this study are fit to be the objective function of a pattern generation optimization. In some cases, such as with speckle-based metrics, application to pixel by pixel patterns is ill-conditioned and requires somewhat arbitrary extensions. In other cases, such as with the SSSIG, it is shown that trivial solutions exist for the optimum of the metric which are ill-suited for DIC (such as a checkerboard pattern). In the current work, a multi-metric optimization method is proposed whereby quality is viewed as a combination of individual quality metrics. Specifically, SSSIG and two auto-correlation metrics are used which have generally competitive objectives. Thus, each metric could be viewed as a constraint imposed upon the others, thereby precluding the achievement of their trivial solutions. In this way, optimization produces a pattern which balances the benefits of multiple quality metrics. The resulting pattern, along with randomly generated patterns, is subjected to numerical deformations and analyzed with DIC software. The optimal pattern is shown to outperform randomly generated patterns.

Bomarito, G. F.↗

Human Factors in Space Flight

After forty years of experience with human space flight (Table 1), the current emphasis is on the design of space vehicles, habitats, and missions to ensure mission success. What lessons have we learned that will affect the design of spacecraft for future space exploration, leading up to exploring Mars? This chapter addresses this issue in four sections: Anthropometry and Biomechanics; Environmental Factors; Habitability and Architecture; and Crew Personal Sustenance. This introductory section introduces factors unique to space flight. A unique consideration for design of a habitable volume in a space vehicle is the lack of gravity during a space flight, referred to as microgravity. This affects all aspects of life, and drives special features in the habitat, equipment, tools, and procedures. The difference in gravity during a space mission requires designing for posture and motion differences. In Earth s gravity, or even with partial gravity, orientation is not a variable because the direction in which gravity acts defines up and down. In a microgravity environment the working position is arbitrary; there is no gravity cue. Orientation is defined primarily through visual cues. The orientation within a particular crew station or work area is referred to as local vertical, and should be consistent within a module to increase crew productivity. Equipment was intentionally arranged in various orientations in one module on Skylab to assess the efficiency in use of space versus the effects of inconsistent layout. The effects of that arrangement were confusion on entering the module, time spent in re-orientation, and conflicts in crew space requirements when multiple crew members were in the module. Design of a space vehicle is constrained by the three major mission drivers: mass, volume and power. Each of these factors drives the cost of a mission. Mass and volume determine the size of the launch vehicle directly; they can limit consumables such as air, water, and propellant; and they impact crew size and the types of activities the crew performs. Power is a limiting factor for a space vehicle. All environmental features (e.g., atmosphere, temperature, lighting) require power to maintain them. Power can be generated from batteries, from fuel cells, or from solar panels. Each of these sources requires lifting mass and volume from Earth, driving mission cost. All engineering decisions directly impact the design for habitation design and usage. For instance, if fuel cells are used they produce water, which is used for drinking and food preparation. If a different power source is used water has to be carried and stored on the vehicle which then directly impacts the food system choice as well as the launch weight of the vehicle.

Woolford, Barbara J.↗

Hierarchic models for laminated plates

Structural plates and shells are three-dimensional bodies, one dimension of which happens to be much smaller than the other two. Thus, the quality of a plate or shell model must be judged on the basis of how well its exact solution approximates the corresponding three-dimensional problem. Of course, the exact solution depends not only on the choice of the model but also on the topology, material properties, loading and constraints. The desired degree of approximation depends on the analyst's goals in performing the analysis. For these reasons models have to be chosen adaptively. Hierarchic sequences of models make adaptive selection of the model which is best suited for the purposes of a particular analysis possible. The principles governing the formulation of hierarchic models for laminated plates are presented. The essential features of the hierarchic models described models are: (1) the exact solutions corresponding to the hierarchic sequence of models converge to the exact solution of the corresponding problem of elasticity for a fixed laminate thickness; and (2) the exact solution of each model converges to the same limit as the exact solution of the corresponding problem of elasticity with respect to the laminate thickness approaching zero. The formulation is based on one parameter (beta) which characterizes the hierarchic sequence of models, and a set of constants whose influence was assessed by a numerical sensitivity study. The recommended selection of these constants results in the number of fields increasing by three for each increment in the power of beta. Numerical examples analyzed with the proposed sequence of models are included and good correlation with the reference solutions was found. Results were obtained for laminated strips (plates in cylindrical bending) and for square and rectangular plates with uniform loading and with homogeneous boundary conditions. Cross-ply and angle-ply laminates were evaluated and the results compared with those of MSC/PROBE. Hierarchic models make the computation of any engineering data possible to an arbitrary level of precision within the framework of the theory of elasticity.

Actis, Ricardo Luis↗