The Similarity Structure Function Lagrangian CFD and the Finite Scale Theory
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97 MATHEMATICS AND COMPUTING↗
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Application of Systems Engineering Principles and Techniques in Biological Big Data Analytics: A Review
In the past few decades, we have witnessed tremendous advancements in biology, life sciences and healthcare. These advancements are due in no small part to the big data made available by various high-throughput technologies, the ever-advancing computing power, and the algorithmic advancements in machine learning. Specifically, big data analytics such as statistical and machine learning has become an essential tool in these rapidly developing fields. As a result, the subject has drawn increased attention and many review papers have been published in just the past few years on the subject. Different from all existing reviews, this work focuses on the application of systems, engineering principles and techniques in addressing some of the common challenges in big data analytics for biological, biomedical and healthcare applications. Specifically, this review focuses on the following three key areas in biological big data analytics where systems engineering principles and techniques have been playing important roles: the principle of parsimony in addressing overfitting, the dynamic analysis of biological data, and the role of domain knowledge in biological data analytics.
dynamic analysis↗
A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modeling
Numerical solvers of partial differential equations (PDEs) have been widely employed for simulating physical systems. However, the computational cost remains a major bottleneck in various scientific and engineering applications, which has motivated the development of reduced-order models (ROMs). Recently, machine-learning-based ROMs have gained significant popularity and are promising for addressing some limitations of traditional ROM methods, especially for advection dominated systems. In this chapter, we focus on a particular framework known as Latent Space Dynamics Identification (LaSDI), which transforms the high-fidelity data, governed by a PDE, to simpler and low-dimensional latent-space data, governed by ordinary differential equations (ODEs). These ODEs can be learned and subsequently interpolated to make ROM predictions. Each building block of LaSDI can be easily modulated depending on the application, which makes the LaSDI framework highly flexible. In particular, we present strategies to enforce the laws of thermodynamics into LaSDI models (tLaSDI), enhance robustness in the presence of noise through the weak form (WLaSDI), select high-fidelity training data efficiently through active learning (gLaSDI, GPLaSDI), and quantify the ROM prediction uncertainty through Gaussian processes (GPLaSDI). We demonstrate the performance of different LaSDI approaches on Burgers equation, a non-linear heat conduction problem, and a plasma physics problem, showing that LaSDI algorithms can achieve relative errors of less than a few percent and up to thousands of times speed-ups.
Computational Engineering, Finance, and Science (c↗
Caerbannog Point Clouds
The Caerbannog Point Clouds provide point-sampled 3D models occluded in clouds of points. We synthesized the 3D point clouds from polygonal models, point-sampling the models and surrounding them in a point cloud such that the shape of the model is occluded in any 2D projection. We obscure our model-of-interest by repeatedly surrounding it with an amorphous cloud of points, giving the overall point cloud a structure of organic nature, like that of shrubbery. In a user study, participants were significantly better at identifying the models when visualized as 3D scatterplots under rotation than in axis-aligned 2D scatterplots. We provide three point-clouds, both occluded and unoccluded: the Stanford bunny, Utah Teapot, and OSG Cow.
97 MATHEMATICS AND COMPUTING↗
Advancements in structural dynamic technology resulting from Saturn 5 programs, volume 1
Saturn 5 dynamic structural analysis by dynamic testing of scale replica models, mathematical models, and tests of full scale vehicle
Grimes, P. J.↗
Solar activity prediction
A statistical study of formulas for predicting the sunspot number several years in advance is reported. By using a data lineup with cycle maxima coinciding, and by using multiple and nonlinear predictors, a new formula which gives better error estimates than former formulas derived from the work of McNish and Lincoln is obtained. A statistical analysis is conducted to determine which of several mathematical expressions best describes the relationship between 10.7 cm solar flux and Zurich sunspot numbers. Attention is given to the autocorrelation of the observations, and confidence intervals for the derived relationships are presented. The accuracy of predicting a value of 10.7 cm solar flux from a predicted sunspot number is dicussed.
Slutz, R. J.↗
Digital simulation of continuous error models with application to an instrument landing system error
A digital simulation of the continuous error of the localized beam of a conventional instrument landing system is discussed. The digital simulation was developed during the analysis of space shuttle navigation capabilities. A discrete mathematical model for use on a digital computer is described. The model generates an output random sequence which is equivalent, for simulation purposes, to the desired random process. The model is a system of difference equations driven by a zero-mean Gaussian random sequence.
Merrick, R. B.↗
Diagnostics of sources of disturbances and distribution of vibrations over the width of a tape in tape-feed mechanisms
Disturbances created by certain assemblies and components of tape-feed mechanisms (TFM) and acting on a moving magnetic tape are studied. The method, based on elements of digital logic, is established by stress-strain diagrams of the longitudinal deformations and vibrations across the width of a magnetic tape. Experimental studies were carried out for determination of the functional relationships of longitudinal deformations in a section of magnetic tape to the magnitude of roller play, tension vibrations rate of movement, and elasticity of magnetic tapes. A block diagram of the measurements is shown. Appropriate digital computer algorithms and programs were proposed for statistical analysis of the data obtained. Estimates of the mathematical expectation, dispersion, intercorrelation function, energy spectral density, and distribution pattern of the random process values were calculated.
Kenstavichyus, A. B. B.↗
Earth-moon system: Dynamics and parameter estimation
A theoretical development of the equations of motion governing the earth-moon system is presented. The earth and moon were treated as finite rigid bodies and a mutual potential was utilized. The sun and remaining planets were treated as particles. Relativistic, non-rigid, and dissipative effects were not included. The translational and rotational motion of the earth and moon were derived in a fully coupled set of equations. Euler parameters were used to model the rotational motions. The mathematical model is intended for use with data analysis software to estimate physical parameters of the earth-moon system using primarily LURE type data. Two program listings are included. Program ANEAMO computes the translational/rotational motion of the earth and moon from analytical solutions. Program RIGEM numerically integrates the fully coupled motions as described above.
Breedlove, W. J., Jr.↗
NASA's advanced control law program for the F-8 Digital Fly-By-Wire aircraft
This paper briefly describes the NASA F-8 Digital Fly-By-Wire (DFBW) program and Langley Research Center's role in investigating and promoting advanced control laws for possible flight experimentation. The primary purpose of the paper is to provide background material for papers describing some of the F-8 DFBW adaptive control law studies. The paper provides a brief description of the Phase II DFBW F-8 aircraft and its control system, discusses some of the advanced control law study objectives and guidelines, and provides some mathematical models which are useful in the control analysis problem.
Elliott, J. R.↗
NASA's advanced control law program for the F-8 digital fly-by-wire aircraft
This paper briefly describes the NASA F-8 Digital Fly-By-Wire (DFBW) and Langley Research Center's role in investigating and promoting advanced control laws for possible flight experimentation and also provides a brief description of the Phase II DFBW F-8 aircraft and its control system. Some of the advanced control law study objectives and guidelines are discussed, and some mathematical models which are useful in the control analysis problem are provided.
Elliott, J. R.↗
Unsteady flow model for circulation-control airfoils
An analysis and a numerical lifting surface method are developed for predicting the unsteady airloads on two-dimensional circulation control airfoils in incompressible flow. The analysis and the computer program are validated by correlating the computed unsteady airloads with test data and also with other theoretical solutions. Additionally, a mathematical model for predicting the bending-torsion flutter of a two-dimensional airfoil (a reference section of a wing or rotor blade) and a computer program using an iterative scheme are developed. The flutter program has a provision for using the CC airfoil airloads program or the Theodorsen hard flap solution to compute the unsteady lift and moment used in the flutter equations. The adopted mathematical model and the iterative scheme are used to perform a flutter analysis of a typical CC rotor blade reference section. The program seems to work well within the basic assumption of the incompressible flow.
Rao, B. M.↗
Sun Series program for the REEDA System
Modifications made to data bases and to four programs in a series of computer programs (Sun Series) which run on the REEDA HP minicomputer system to aid NASA's solar activity predictions used in orbital life time predictions are described. These programs utilize various mathematical smoothing technique and perform statistical and graphical analysis of various solar activity data bases residing on the REEDA System.
Shankle, R. W.↗
Coolant passage heat transfer with rotation. A progress report on the computational aspects
Turbine airfoils are subjected to increasingly higher heat loads which escalate the cooling requirements in order to satisfy life goals for the component materials. If turbine efficiency is to be maintained, however, cooling requirements should be as low as possible. To keep the quantity of cooling air bounded, a more efficient internal cooling scheme must be developed. One approach is to employ airfoils with multipass cooling passages that contain devices to augment internal heat transfer while limiting pressure drop. Design experience with multipass cooling passage airfoils has shown that a surplus of cooling air must be provided as a margin of safety. This increased cooling air leads to a performance penalty. Reliable methods for predicting the internal thermal and aerodynamic performance of multipass cooling passage airfoils would reduce or eliminate the need for the safety margin of surplus cooling air. The objective of the program is to develop and verify improved analytical methods that will form the basis for design technology which will result in efficient turbine components with improved durability without sacrificing performance. The objective will be met by: (1) establishing a comprehensive experimental data base that can form the basis of an empirical design system; (2) developing computational fluid dynamic techniques; and (3) analyzing the information in the data base with both phenomenological modeling and mathematical modeling to derive a suitable design and analysis procedure.
Aceto, L. D.↗
An analysis of the productivity of a CELSS continuous algal culture system
One of the most attractive aspects of using algal cultures as plant components for a Closed Ecological Life Support Systems (CELSS) is the efficiency with which they can be grown. Although algae are not necessarily intrinsically more efficient than higher plants, the ease which they can be handled and manipulated (more like chemical reagents than plants), and the culturing techniques available, result in much higher growth rates than are usually attainable with higher plants. Furthermore, preliminary experiments have demonstrated that algal growth and physiology is not detectable altered in a microgravity environment, (1) whereas the response of higher plants to zero gravity is unknown. In order to rationally design and operate culture systems, it is necessary to understand how the macroparameters of a culture system, e.g., productivity, are related to the physiological aspects of the algal culture. A first principles analysis of culture system is discussed, and a mathematical model that describes the relationship of culture productivity to the cell concentration of light-limited culture is derived. The predicted productivity vs cell concentration curve agrees well with the experimental data obtained to test this model, indicating that this model permits an accurate prediction of culture productivity given the growth parameters of the system.
Radmer, R.↗
Asymptotic expansions in nonlinear rotordynamics
This paper is an examination of special nonlinearities of the Jeffcott equations in rotordynamics. The immediate application of this analysis is directed toward understanding the excessive vibrations recorded in the LOX pump of the SSME during hot-firing ground testing. Deadband, side force, and rubbing are three possible sources of inducing nonlinearity in the Jeffcott equations. The present analysis initially reduces these problems to the same mathematical description. A special frequency, named the nonlinear natural frequency, is defined and used to develop the solutions of the nonlinear Jeffcott equations as singular asymptotic expansions. This nonlinear natural frequency, which is the ratio of the cross-stiffness and the damping, plays a major role in determining response frequencies.
Day, William B.↗
A study of aeroelastic stability for the model support system of the National Transonic Facility
Oscillations of wind-tunnel models have been observed during testing in the National Transonic Facility. These oscillations have been the subject of an extensive investigation. As a part of this effort, a study of the aeroelastic stability of the model support structure has been performed. This structure is mathematically modelled as a wing and conventional flutter analysis is performed. The math model implemented both experimentally and numerically obtained modal characteristics. A technique for illustrating the flutter boundary for wind tunnels is demonstrated. Results indicate that the classical flutter boundary is well above the operating envelope of the facility. However, the analysis indicates a damping-dependent instability is present which is inherent in the design. One possible modification in the design has been evaluated which eliminates the predicted instability.
Strganac, Thomas W.↗
NASA'S controls-structures interaction program
A NASA program is about to start which has the objective to advance Controls-Structures Interaction (CSI) technology to a point where it can be used in spacecraft design for future missions. Because of the close interrelationships between the structure, the control hardware, and the analysis/design, a highly interdisciplinary activity is defined in which structures, dynamics, controls, computer and electronics engineers work together on a daily basis and are co-located to a large extent. Methods will be developed which allow the controls and structures analysis and design functions to use the same mathematical models. Hardware tests and applications are emphasized and will require development of concepts and test methods to carry out. Because of a variety of mission application problem classes, several time-phased, focus ground test articles are planned. They will be located at the Langley Researdh Center (LaRC), the Marshall Space Flight Center (MSFC) and at the Jet Propulsion Laboratory (JPL). It is anticipated that the ground tests will be subject to gravity and other environmental effects to the extent that orbital flights tests will be needed for verification of some technology items. The need for orbital flight experiments will be quantified based on ground test results and mission needs. Candidate on-orbit experiments will be defined and preliminary design/definition and cost studies will be carried out for one or more high-priority experiments.
Hanks, Brantley R.↗