Cybernetics and space biology
Cybernetics applied to space biology and medicine through use of mathematical models, biological controls, and statistical dynamics
BIOLOGICAL MODEL↗
SEARCH · Search NASA
Results for “Applied Mathematics”
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Analytical methods for bacterial kinetics studies
Methods utilize mathematical equations and models and specialized computer techniques. Techniques apply to food production, complex chemicals production, and polluted water purification.
Edwards, V. E.↗
Tracking system study
A digital computer program was generated which mathematically describes an optimal estimator-controller technique as applied to the control of antenna tracking systems used by NASA. Simulation studies utilizing this program were conducted using the IBM 360/91 computer. The basic ideas of applying optimal estimator-controller techniques to antenna tracking systems are discussed. A survey of existing tracking methods is given along with shortcomings and inherent errors. It is explained how these errors can be considerably reduced if optimal estimation and control are used. The modified programs generated in this project are described and the simulation results are summarized. The new algorithms for direct synthesis and stabilization of the systems including nonlinearities, are presented.
Dennis, A. R.↗
A three-dimensional, time-dependent model of Mobile Bay
A three-dimensional, time-variant mathematical model for momentum and mass transport in estuaries was developed and its solution implemented on a digital computer. The mathematical model is based on state and conservation equations applied to turbulent flow of a two-component, incompressible fluid having a free surface. Thus, bouyancy effects caused by density differences between the fresh and salt water, inertia from thare river and tidal currents, and differences in hydrostatic head are taken into account. The conservation equations, which are partial differential equations, are solved numerically by an explicit, one-step finite difference scheme and the solutions displayed numerically and graphically. To test the validity of the model, a specific estuary for which scaled model and experimental field data are available, Mobile Bay, was simulated. Comparisons of velocity, salinity and water level data show that the model is valid and a viable means of simulating the hydrodynamics and mass transport in non-idealized estuaries.
Pitts, F. H.↗
Reliability-based optimization under random vibration environment
A methodology of formulating the optimum design problem for structural systems with random parameters and subjected to random vibration as a mathematical programming problem is presented. The proposed method is applied to the optimum design of a cantilever beam with a tip mass and a truss structure supporting a water tank. The excitations are assumed to be Gaussian processes and the geometric and material properties are taken to be normally distributed random variables. The probabilistic constraints are specified for individual failure modes since it is easier to specify the reliability level for each failure mode keeping in view the consequences of failure in that particular mode. The time parameter appearing in the random vibration based constraints is eliminated by replacing the probabilities of failure by suitable upper bounds. The numerical results demonstrate the feasibility and effectiveness of applying the reliability-based design concepts to structures with random parameters and operating in random vibration environment.
Rao, S. S.↗
Development and application of a time-history analysis for rotorcraft dynamics based on a component approach
A time history analysis for rotorcraft dynamics based on dynamical substructures, and nonstructural mathematical and aerodynamic components is described. The analysis is applied to predict helicopter ground resonance and response to rotor damage. Other applications illustrate the stability and steady vibratory response of stopped and gimballed rotors, representative of new technology. Desirable attributes expected from modern codes are realized, although the analysis does not employ a complete set of techniques identified for advanced software. The analysis is able to handle a comprehensive set of steady state and stability problems with a small library of components.
Sopher, R.↗
Formally verifying Ada programs which use real number types
Formal verification is applied to programs which use real number arithmetic operations (mathematical programs). Formal verification of a program P consists of creating a mathematical model of F, stating the desired properties of P in a formal logical language, and proving that the mathematical model has the desired properties using a formal proof calculus. The development and verification of the mathematical model are discussed.
Sutherland, David↗
Numbers Of Degrees Of Freedom Of Allan-Variance Estimators
Report discusses formulas for estimation of Allan variances. Presents algorithms for closed-form approximations of numbers of degrees of freedom characterizing results obtained when various estimators applied to five power-law components of classical mathematical model of clock noise.
Greenhall, Charles A.↗
Efficient Computational Model of Hysteresis
A recently developed mathematical model of the output (displacement) versus the input (applied voltage) of a piezoelectric transducer accounts for hysteresis. For the sake of computational speed, the model is kept simple by neglecting the dynamic behavior of the transducer. Hence, the model applies to static and quasistatic displacements only. A piezoelectric transducer of the type to which the model applies is used as an actuator in a computer-based control system to effect fine position adjustments. Because the response time of the rest of such a system is usually much greater than that of a piezoelectric transducer, the model remains an acceptably close approximation for the purpose of control computations, even though the dynamics are neglected. The model (see Figure 1) represents an electrically parallel, mechanically series combination of backlash elements, each having a unique deadband width and output gain. The zeroth element in the parallel combination has zero deadband width and, hence, represents a linear component of the input/output relationship. The other elements, which have nonzero deadband widths, are used to model the nonlinear components of the hysteresis loop. The deadband widths and output gains of the elements are computed from experimental displacement-versus-voltage data. The hysteresis curve calculated by use of this model is piecewise linear beyond deadband limits.
Shields, Joel↗
Considerations for the Extension of Gas Path Analysis to Electrified Aircraft Propulsion Systems
Aircraft operators rely on gas path analysis techniques for monitoring the performance and health of their gas turbine engine assets. This is accomplished by analyzing discernable shifts in measurement parameters acquired from the engine. This paper reviews the founding mathematical principles of gas path analysis, including conventional approaches applied for estimating engine performance deterioration. Considerations for extending the application of gas path analysis techniques to Electrified Aircraft Propulsion (EAP) systems is also discussed, and simulated results from their application to an EAP concept comprised of turbomachinery and electrical system hardware is provided. Results are provided comparing the parameter estimation accuracy offered by taking a whole-system approach towards the problem setup versus that offered by analyzing each subsystem individually. For the latter, the importance of having accurate direct or inferred measurements of external mechanical torque loads placed upon turbomachinery shafts is emphasized.
Electrified Aircraft Propulsion↗
Considerations for the Extension of Gas Path Analysis to Electrified Aircraft Propulsion Systems
Aircraft operators rely on gas path analysis techniques for monitoring the performance and health of their gas turbine engine assets. This is accomplished by analyzing discernable shifts in measurement parameters acquired from the engine. This paper reviews the founding mathematical principles of gas path analysis, including conventional approaches applied for estimating engine performance deterioration. Considerations for extending the application of gas path analysis techniques to Electrified Aircraft Propulsion (EAP) systems is also discussed, and simulated results from their application to an EAP concept comprised of turbomachinery and electrical system hardware is provided. Results are provided comparing the parameter estimation accuracy offered by taking a whole-system approach towards the problem setup versus that offered by analyzing each subsystem individually. For the latter, the importance of having accurate direct or inferred measurements of external mechanical torque loads placed upon turbomachinery shafts is emphasized.
Electrified Aircraft Propulsion↗
Considerations for the Extension of Gas Path Analysis to Electrified Aircraft Propulsion Systems
Aircraft operators rely on gas path analysis techniques for monitoring the performance and health of their gas turbine engine assets. This is accomplished by analyzing discernable shifts in measurement parameters acquired from the engine. This paper reviews the founding mathematical principles of gas path analysis, including conventional approaches applied for estimating engine performance deterioration. Considerations for extending the application of gas path analysis techniques to Electrified Aircraft Propulsion (EAP) systems is also discussed, and simulated results from their application to an EAP concept comprised of turbomachinery and electrical system hardware is provided. Results are provided comparing the parameter estimation accuracy offered by taking a whole-system approach towards the problem setup versus that offered by analyzing each subsystem individually. For the latter, the importance of having accurate direct or inferred measurements of external mechanical torque loads placed upon turbomachinery shafts is emphasized.
Electrified Aircraft Propulsion↗
Multi-Agent Motion Planning using Deep Learning for Space Applications
State-of-the-art motion planners cannot scale to a large number of systems. Motion planning for multiple agents is an NP (non-deterministic polynomial-time) hard problem, so the computation time increases exponentially with each addition of agents. This computational demand is a major stumbling block to the motion planner's application to future NASA missions involving the swarm of space vehicles. We applied a deep neural network to transform computationally demanding mathematical motion planning problems into deep learning-based numerical problems. We showed optimal motion trajectories can be accurately replicated using deep learning-based numerical models in several 2D and 3D systems with multiple agents. The deep learning-based numerical model demonstrates superior computational efficiency with plans generated 1000 times faster than the mathematical model counterpart.
Madani, Ramtin↗
SuperHERO (Super - High Energy Replicated Optics) Balloon Mission Concept
The SuperHERO hard-x-ray telescope is a proposed high-angular resolution successor to Marshall Space Flight Center’s (MSFC) successful High Energy Replicated Optic (HERO) and the HERO to Explore the Sun (HEROES) balloon missions. By utilizing recent advancements in MSFC’s replicated full shell, NiCo x-ray optic technology, SuperHERO will achieve its technical goal of demonstrating better than 10 arcseconds (arcsecs) angular resolution in half-power diameter (HPD) on a balloon platform. This represents a 6-fold improvement to the current state-of-the-art resolution for hard-x-ray, astrophysical telescopes and will allow for the observation of the high-energy-universe in unprecedented spatial detail. The SuperHERO balloon observatory will consist of seven coaligned, identical telescopes with a total focal length of 12-meters. Each telescope will pair a Mirror Module Assembly (MMA) comprised of NiCo shell optics matched to a CdTe Double-sided Strip Detector (CdTe-DSD) plane provided by iMAGINE-X Inc. and Kavli Institute for the Physics and Mathematics of the Universe (Kavli-IPMU). Iridium coating applied directly to each shell will boost reflectivity into the hard-x-ray regime. Employing additional high-heritage technology, SuperHERO will have an open-truss carbon-composite gondola similarly used on the XL-Calibur balloon mission and will use the Wallops Arc-Second Pointer (WASP) system for attitude control
NickThomas↗
Transforming the Bootstrap: Using Transformers to Compute Scattering Amplitudes in Planar N = 4 Super Yang-Mills Theory
We pursue the use of deep learning methods to improve state-of-the-art computations in theoretical high-energy physics. Planar N = 4 Super Yang-Mills theory is a close cousin to the theory that describes Higgs boson production at the Large Hadron Collider; its scattering amplitudes are large mathematical expressions containing integer coefficients. In this paper, we apply Transformers to predict these coefficients. The problem can be formulated in a language-like representation amenable to standard cross-entropy training objectives. We design two related experiments and show that the model achieves high accuracy (> 98%) on both tasks. Our work shows that Transformers can be applied successfully to problems in theoretical physics that require exact solutions.
Lance, Dixon↗
Mathematical models of human operators in simple two-axis manual control systems.
Continuous parameter optimization techniques applied to synthesis of model of human operators in simple two-axis manual control system
MATHEMATICAL MODEL↗
A generalized procedure for constructing an upwind-based TVD scheme
A generalized formulation for constructing second- and higher-order accurate TVD (total variation diminishing) schemes is presented. A given scheme is made TVD by limiting antidiffusive flux differences with some nonlinear functions, so-called limiters. The general idea of the formulation and its mathematical proof of Harten's TVD conditions is shown by applying the Lax-Wendroff method to a scalar nonlinear equation and constant-coefficient system of conservation laws. For the system of equations, several definitions are derived for the argument used in the limiter function and present their performance to numerical experiments. Then the formulation is formally extended to the nonlinear system of equations. It is demonstrated that use of the present procedure allows easy conversion of existing central or upwind, and second- or higher-order differencing schemes so as to preserve monotonicity and to yield physically admissible solutions. The formulation is simple mathematically as well as numerically; neither matrix-vector multiplication nor Riemann solver is required. Roughly twice as much computational effort is needed as compared to conventional scheme. Although the notion of TVD is based on the initial value problem, application to the steady Euler equations of the formulation is also made. Numerical examples including various ranges of problems show both time- and spatial-accuracy in comparison with exact solutions.
Liou, Meng-Sing↗
Kalman filtering applied to real-time monitoring of apogee maneuvers
Part of the Space Mathematics Division in CNES, the Flight Dynamics Center provides attitude and orbit determinations and maneuvers during the Launch and Early Operation Phase (LEOP) of geostationary satellites. Orbit determination is based on a Kalman filter method; when the 2 GHz CNES/NASA network is used, Doppler measurements are available and allow orbit determination during the apogee maneuvers. This method was used for TELE-X and TDF 2 LEOP (3-axis controlled satellites) and also for TELECOM 2 and HISPASAT (spun satellites): it enables us to follow the evolution of the maneuver and gives out a quite accurate estimation of the reached orbit. In this paper, we briefly describe the dynamic models of the orbit evolution in both cases, '3-axis' and 'inertial' thrust. Then, we present the results obtained for each case. Afterwards, we present some cases to show the robustness of the filter.
Deboer, Frederic↗