Results for “Complex functions” — Page 8

NASA NTRS2006

Functional brain imaging of a complex navigation task following one night of total sleep deprivation

Study Objectives: To assess the cerebral effects associated with sleep deprivation in a simulation of a complex, real-world, high-risk task. Design and Interventions: A two-week, repeated measures, cross-over experimental protocol, with counterbalanced orders of normal sleep (NS) and total sleep deprivation (TSD). Setting: Each subject underwent functional magnetic resonance imaging (fMRI) while performing a dual-joystick, 3D sensorimotor navigation task (simulated orbital docking). Scanning was performed twice per subject, once following a night of normal sleep (NS), and once following a single night of total sleep deprivation (TSD). Five runs (eight 24s docking trials each) were performed during each scanning session. Participants: Six healthy, young, right-handed volunteers (2 women; mean age 20) participated. Measurements and Results: Behavioral performance on multiple measures was comparable in the two sleep conditions. Neuroimaging results within sleep conditions revealed similar locations of peak activity for NS and TSD, including left sensorimotor cortex, left precuneus (BA 7), and right visual areas (BA 18/19). However, cerebral activation following TSD was substantially larger and exhibited higher amplitude modulations from baseline. When directly comparing NS and TSD, most regions exhibited TSD>NS activity, including multiple prefrontal cortical areas (BA 8/9,44/45,47), lateral parieto-occipital areas (BA 19/39, 40), superior temporal cortex (BA 22), and bilateral thalamus and amygdala. Only left parietal cortex (BA 7) demonstrated NS>TSD activity. Conclusions: The large network of cerebral differences between the two conditions, even with comparable behavioral performance, suggests the possibility of detecting TSD-induced stress via functional brain imaging techniques on complex tasks before stress-induced failures.

Strangman, Gary↗

NASA NTRSDate not supplied

Physics Informed Neural Nets for Systems Health Management

To facilitate and solve the prediction problem, awareness of the current health state of the system is key, since it is necessary to perform condition-based predictions. To accurately predict the future state of any system, it is required to possess knowledge of its current health state and future operational conditions. Development in data-driven algorithms in regression of complex nonlinear functions and classification tasks have generated a growing interest in artificial intelligence for industrial applications. Complex multi-physics models as well as digital twins, once purely built on physics and corresponding simplified lumped parameter iterations, can now benefit from machine learning algorithms to mitigate the lack of understanding of some complex behavior. The research work presents application of physics-informed neural nets application to a representative electric powertrain for unmanned aerial vehicles. The model is composed of physics-derived and empirical equations, integrated with connected networks that are strategically placed within the model to substitute equations that are subject to large uncertainty. Polynomial fit driven by heuristics or empirical observations can be substituted by more flexible networks that can minimize the error between model predictions and observations without being restricted to a predefined functional form. This modeling strategy allows training of networks deep inside the model and unknown parameters in a single learning stage.

Physics Informed↗

NASA NTRS1992

Nonlinear functional approximation with networks using adaptive neurons

A novel mathematical framework for the rapid learning of nonlinear mappings and topological transformations is presented. It is based on allowing the neuron's parameters to adapt as a function of learning. This fully recurrent adaptive neuron model (ANM) has been successfully applied to complex nonlinear function approximation problems such as the highly degenerate inverse kinematics problem in robotics.

Tawel, Raoul↗

NASA NTRSDate not supplied

Hybrid Model Based Approaches for Systems Health Management and Prognostics

To facilitate and solve the prediction problem, awareness of the current health state of the system is key, since it is necessary to perform condition-based predictions. To accurately predict the future state of any system, it is required to possess knowledge of its current health state and future operational conditions. Latest achievements of data-driven algorithms in regression of complex nonlinear functions and classification tasks have generated a growing interest in artificial intelligence for industrial applications. Complex multi-physics models as well as digital twins, once purely built on physics and corresponding simplified lumped parameter iterations, can now benefit from machine learning algorithms to mitigate the lack of understanding of some complex behavior. Given models of the current and future system behavior, a general approach of model-based prognostics can solve the prediction problem and further decision making. In principle, data driven approaches can replace expensive experimental test-setups as well as reduce the number of simulations needed to explore, e.g., the parametric space of a multi-parameter model. Nonetheless, the limitations of pure data-driven methods came to light rather quickly, at least for some industries. In many industrial applications, data acquisition is costly, and the volume of data that can be collected does not satisfy the requirements for an effective model training and cross-validation. Therefore, some recent works in the area of machine learning is focusing on blending physics with data-driven algorithms, thus mitigating the drawbacks of the two approaches and emphasizing respective advantages. Partial physical knowledge of the problem can aid the learning process by “guiding” the algorithm towards efficient solutions that satisfy the physics driving the system behavior. The result is a hybrid modeling approach combining physical knowledge as well data driven methods to develop a unified hybrid approach. A hybrid framework for fusing information from physics-based performance models along with deep learning algorithms for prognostics of complex safety critical systems is presented. In this framework, physics-based performance models infer unobservable model parameters related to the system's components health solving a calibration problem in the deep learning approach.

Hybrid Modeling↗

NASA NTRSDate not supplied

Systems Health Management and Prognostics Approaches for Electric Aircrafts

As more and more electric vehicles emerge in our daily operation progressively, a very critical challenge lies in the prediction of remaining driving flying time/distance for the flying vehicles. This information is important, particularly in the case of auto vehicles, because such vehicles can become self-aware, autonomously compute its own capabilities, and identify how to best plan and successfully complete vehicular missions safely. In case of electric aircrafts, computing the remaining flying time is also safety-critical, since an aircraft that runs out of power (battery charge) while in the air will eventually lose control leading to catastrophe. To facilitate and solve the prediction problem, awareness of the current health state of the system is key, since it is necessary to perform condition-based predictions. To accurately predict the future state of any system, it is required to possess knowledge of its current health state and future operational conditions. Latest achievements of data-driven algorithms in regression of complex nonlinear functions and classification tasks have generated a growing interest in artificial intelligence for industrial applications. Complex multi-physics models as well as digital twins, once purely built on physics and corresponding simplified lumped parameter iterations, can now benefit from machine learning algorithms to mitigate the lack of understanding of some complex behavior. Given models of the current and future system behavior, a general approach of model-based prognostics can solve the prediction problem and further decision-making. A systematic prediction framework is implemented to identify all possible sources of uncertainty, quantify each of them individually, and mathematically estimate their combined effect on the system-level quantity of interest, in this case, the remaining flying time/distance of the unmanned aircraft. Note - This presentation contains all previously published information.

Systems Health Managent↗

NASA NTRSDate not supplied

Hybrid Approaches to Systems Health Management and Prognostics

To facilitate and solve the prediction problem, awareness of the current health state of the system is key, since it is necessary to perform condition-based predictions. To accurately predict the future state of any system, it is required to possess knowledge of its current health state and future operational conditions. Latest achievements of data-driven algorithms in regression of complex nonlinear functions and classification tasks have generated a growing interest in artificial intelligence for industrial applications. Complex multi-physics models as well as digital twins, once purely built on physics and corresponding simplified lumped parameter iterations, can now benefit from machine learning algorithms to mitigate the lack of understanding of some complex behavior. Given models of the current and future system behavior, a general approach of model-based prognostics can solve the prediction problem and further decision making. In principle, data driven approaches can replace expensive experimental test-setups as well as reduce the number of simulations needed to explore, e.g., the parametric space of a multi-parameter model. Nonetheless, the limitations of pure data-driven methods came to light rather quickly, at least for some industries. In many industrial applications, data acquisition is costly, and the volume of data that can be collected does not satisfy the requirements for an effective model training and cross-validation. Therefore, some recent works in the area of machine learning is focusing on blending physics with data-driven algorithms, thus mitigating the drawbacks of the two approaches and emphasizing respective advantages. Partial physical knowledge of the problem can aid the learning process by “guiding” the algorithm towards efficient solutions that satisfy the physics driving the system behavior. The result is a hybrid modeling approach combining physical knowledge as well data driven methods to develop a unified hybrid approach. A hybrid framework for fusing information from physics-based performance models along with deep learning algorithms for prognostics of complex safety critical systems is presented. In this framework, physics-based performance models infer unobservable model parameters related to the system's components health solving a calibration problem in the deep learning approach.

Systems Health Management↗

NASA NTRS2022

Hybrid Model Based Approaches for Systems Health Management and Prognostics

This is a previously approved and published presentation. To accurately predict the future state of any system, it is required to possess knowledge of its current health state and future operational conditions. Present achievements of data-driven algorithms in regression of complex nonlinear functions and classification tasks have generated a growing interest in artificial intelligence for industrial applications. Complex multi-physics models as well as digital twins, once purely built on physics and corresponding simplified lumped parameter iterations, can now benefit from machine learning algorithms to mitigate the lack of understanding of some complex behavior. Given models of the current and future system behavior, a general approach of model-based prognostics can solve the prediction problem and further decision-making. In principle, data-driven approaches can replace expensive experimental test-setups as well as reduce the number of simulations needed to explore, e.g., the parametric space of a multi-parameter model. Nonetheless, the limitations of pure data-driven methods came to light rather quickly, at least for some industries. In many industrial applications, data acquisition is costly, and the volume of data that can be collected does not satisfy the requirements for effective model training and cross-validation. Therefore, some recent works in the area of machine learning is focusing on blending physics with data-driven algorithms, thus mitigating the drawbacks of the two approaches and emphasizing respective advantages. Partial physical knowledge of the problem can aid the learning process by “guiding” the algorithm towards efficient solutions that satisfy the physics driving the system behavior. The result is a hybrid modeling approach combining physical knowledge as well data-driven methods to develop a unified hybrid approach. A hybrid framework for fusing information from physics-based performance models along with deep learning algorithms for prognostics of complex safety-critical systems is presented. In this framework, physics-based performance models infer unobservable model parameters related to the system's components health solving a calibration problem in the deep learning approach.

Prognostics↗

NASA NTRSDate not supplied

Health Monitoring and Prognostics for Electric Aircrafts

As more and more electric vehicles emerge in our daily operation progressively, a very critical challenge lies in the prediction of remaining driving flying time/distance for the flying vehicles. This information is important, particularly in the case of auto vehicles, because such vehicles can become self-aware, autonomously compute its own capabilities, and identify how to best plan and successfully complete vehicular missions safely. In case of electric aircrafts, computing the remaining flying time is also safety-critical, since an aircraft that runs out of power (battery charge) while in the air will eventually lose control leading to catastrophe. To facilitate and solve the prediction problem, awareness of the current health state of the system is key, since it is necessary to perform condition-based predictions. To accurately predict the future state of any system, it is required to possess knowledge of its current health state and future operational conditions. Latest achievements of data-driven algorithms in regression of complex nonlinear functions and classification tasks have generated a growing interest in artificial intelligence for industrial applications. Complex multi-physics models as well as digital twins, once purely built on physics and corresponding simplified lumped parameter iterations, can now benefit from machine learning algorithms to mitigate the lack of understanding of some complex behavior. Given models of the current and future system behavior, a general approach of model-based prognostics can solve the prediction problem and further decision-making. A systematic prediction framework is implemented to identify all possible sources of uncertainty, quantify each of them individually, and mathematically estimate their combined effect on the system-level quantity of interest, in this case, the remaining flying time/distance of the unmanned aircraft. Note - This presentation contains all previously approved and published information.

Systems Health Managent↗

NASA NTRS1993

Cognitive engineering models in space systems

NASA space systems, including mission operations on the ground and in space, are complex, dynamic, predominantly automated systems in which the human operator is a supervisory controller. Models of cognitive functions in complex systems are needed to describe human performance and form the theoretical basis of operator workstation design, including displays, controls, and decision aids. Currently, there several candidate modeling methodologies. They include the Rasmussen abstraction/aggregation hierarchy and decision ladder, the goal-means network, the problem behavior graph, and the operator function model. The research conducted under the sponsorship of this grant focuses on the extension of the theoretical structure of the operator function model and its application to NASA Johnson mission operations and space station applications. The initial portion of this research consists of two parts. The first is a series of technical exchanges between NASA Johnson and Georgia Tech researchers. The purpose is to identify candidate applications for the current operator function model; prospects include mission operations and the Data Management System Testbed. The second portion will address extensions of the operator function model to tailor it to the specific needs of Johnson applications. At this point, we have accomplished two things. During a series of conversations with JSC researchers, we have defined the technical goal of the research supported by this grant to be the structural definition of the operator function model and its computer implementation, OFMspert. Both the OFM and OFMspert have matured to the point that they require infrastructure to facilitate use by researchers not involved in the evolution of the tools. The second accomplishment this year was the identification of the Payload Deployment and Retrieval System (PDRS) as a candidate system for the case study. In conjunction with government and contractor personnel in the Human-Computer Interaction Lab, the PDRS was identified as the most accessible system for the demonstration. Pursuant to this a PDRS simulation was obtained from the HCIL and an initial knowledge engineering effort was conducted to understand the operator's tasks in the PDRS application. The preliminary results of the knowledge engineering effort and an initial formulation of an operator function model (OFM) are contained in the appendices.

Mitchell, Christine M.↗

NASA NTRS1991

Transition operators in acoustic-wave diffraction theory. I - General theory. II - Short-wavelength behavior, dominant singularities of Zk0 and Zk0 exp -1

A formal theory of the scattering of time-harmonic acoustic scalar waves from impenetrable, immobile obstacles is established. The time-independent formal scattering theory of nonrelativistic quantum mechanics, in particular the theory of the complete Green's function and the transition (T) operator, provides the model. The quantum-mechanical approach is modified to allow the treatment of acoustic-wave scattering with imposed boundary conditions of impedance type on the surface (delta-Omega) of an impenetrable obstacle. With k0 as the free-space wavenumber of the signal, a simplified expression is obtained for the k0-dependent T operator for a general case of homogeneous impedance boundary conditions for the acoustic wave on delta-Omega. All the nonelementary operators entering the expression for the T operator are formally simple rational algebraic functions of a certain invertible linear radiation impedance operator which maps any sufficiently well-behaved complex-valued function on delta-Omega into another such function on delta-Omega. In the subsequent study, the short-wavelength and the long-wavelength behavior of the radiation impedance operator and its inverse (the 'radiation admittance' operator) as two-point kernels on a smooth delta-Omega are studied for pairs of points that are close together.

Hahne, G. E.↗

NASA NTRS2003

Intracellular localization of a group II chaperonin indicates a membrane-related function

Chaperonins are protein complexes that are believed to function as part of a protein folding system in the cytoplasm of the cell. We observed, however, that the group II chaperonins known as rosettasomes in the hyperthermophilic archaeon Sulfolobus shibatae, are not cytoplasmic but membrane associated. This association was observed in cultures grown at 60 degrees C and 76 degrees C or heat-shocked at 85 degrees C by using immunofluorescence microscopy and in thick sections of rapidly frozen cells grown at 76 degrees C by using immunogold electron microscopy. We observed that increased abundance of rosettasomes after heat shock correlated with decreased membrane permeability at lethal temperature (92 degrees C). This change in permeability was not seen in cells heat-shocked in the presence of the amino acid analogue azetidine 2-carboxylic acid, indicating functional protein synthesis influences permeability. Azetidine experiments also indicated that observed heat-induced changes in lipid composition in S. shibatae could not account for changes in membrane permeability. Rosettasomes purified from cultures grown at 60 degrees C and 76 degrees C or heat-shocked at 85 degrees C bind to liposomes made from either the bipolar tetraether lipids of Sulfolobus or a variety of artificial lipid mixtures. The presence of rosettasomes did not significantly change the transition temperature of liposomes, as indicated by differential scanning calorimetry, or the proton permeability of liposomes, as indicated by pyranine fluorescence. We propose that these group II chaperonins function as a structural element in the natural membrane based on their intracellular location, the correlation between their functional abundance and membrane permeability, and their potential distribution on the membrane surface.

Cell Membrane/physiology/ultrastructure↗

NASA NTRS1993

VUV thin films, chapter 7

The application of thin film technology to the vacuum ultraviolet (VUV) wavelength region from 120 nm to 230 nm has not been fully exploited in the past because of absorption effects which complicate the accurate determination of the optical functions of dielectric materials. The problem therefore reduces to that of determining the real and imaginary parts of a complex optical function, namely the frequency dependent refractive index n and extinction coefficient k. We discuss techniques for the inverse retrieval of n and k for dielectric materials at VUV wavelengths from measurements of their reflectance and transmittance. Suitable substrate and film materials are identified for application in the VUV. Such applications include coatings for the fabrication of narrow and broadband filters and beamsplitters. The availability of such devices open the VUV regime to high resolution photometry, interferometry and polarimetry both for space based and laboratory applications. This chapter deals with the optics of absorbing multilayers, the determination of the optical functions for several useful materials, and the design of VUV multilayer stacks as applied to the design of narrow and broadband reflection and transmission filters and beamsplitters. Experimental techniques are discussed briefly, and several examples of the optical functions derived for selected materials are presented.

Zukic, Muamer↗

NASA NTRS2000

Evaluation of Fieldbus and OPC for Advanced Life Support

FOUNDATION(Tm) Fieldbus and OP(TM) (OLE(TM)for Process Control) technologies were integrated into an existing control system for a crop growth chamber at NASA Ames Research Center. FOUNDATION(TM) Fieldbus is a digital, bi-directional, multi-drop, serial communications network which functions essentially as a LAN for sensors. FOUNDATION(TM) Fieldbus is heterarchical, with publishers and subscribers of data performing complex control functions at low levels without centralized control and its associated overhead. OPC(TM) is a set of interfaces which replace proprietary drivers with a transparent means of exchanging data between the fieldbus and applications. The objectives were: (1) to integrate FOUNDATION(TM) Fieldbus into existing ALS hardware and determine its overall effectiveness and reliability and, (2) to quantify any savings produced by using fieldbus and OPC technologies. We encountered several problems with the FOUNDATION(TM) Fieldbus hardware chosen. Our hardware exposed 100 data for each channel of the fieldbus. The fieldbus configurator software used to program the fieldbus was simply not adequate. The fieldbus was also not inherently reliable. It lost its settings twice during our tests for unknown reasons. OPC also had issues. It did not function at all as supplied, requiring substitution of some of its components with those from other vendors. It would stop working after a fixed period of time. Certain database calls eventually lock the machine. Overall, we would not recommend FOUNDATION(TM) Fieldbus: it was too difficult to implement with little overall added value. It also seems unlikely that FOUNDATION(TM) Fieldbus will gain sufficient penetration into the laboratory instrument market to ever be cost effective for the ALS community. OPC had good reliability and performance once a stable installation was achieved. It allowed a rapid change to an alternative software strategy when our first strategy failed. It is a cost effective solution to distributed control systems development.

Boulanger, Richard P.↗

NASA NTRS1989

Shear buckling of specially orthotropic plates with centrally located cutouts

The shear loading of a composite rectangular plate with a centrally located circular cutout was analyzed in order to predict the buckling load of the plate. The first step in this analysis is to calculare the in-plane stress distribution of the plate prior to buckling. This problem can be solved using finite element methods, but a quicker and more cost efficient method is desired. The method chosen to determine the pre-buckling stresses is that of boundary collocation using complex variables. The real valued force functions are written in terms of two complex valued functions, each of which is a function of a different complex variable. The solution of the generalized biharmonic function is a superposition of functions of these two complex variables. For this analysis, the force functions are represented with a Laurent series. The constants in these series are found using boundary collocation. Two force equations for complex variables are satisfied over the plate boundaries to obtain these constants. The stresses in the plate are then known for any particular locations on the plate given the applied shear on the edges of the plate.

Klang, Eric C.↗

NASA NTRS1973

Structural optimization by methods of feasible directions.

A general design algorithm based on methods of feasible directions is presented. Zoutendijk's method of feasible directions is first presented as applied to structural design. This method is modified to improve numerical stability of the design process and is then further modified to deal efficiently with infeasible designs. The algorithm requires the analytic gradient of the objective function and the constraint functions which are active at a given stage in the design process. Gradient information is not required for nonactive constraints. Complex constraint functions may be ignored in the initial design stages because violation of these constraints is efficiently overcome later in the design process. The algorithm is demonstrated with elastic design of redundant trusses.

Vanderplaats, G. N.↗

NASA NTRS2001

Complex Correlation Kohn-T Method of Calculating Total and Elastic Cross Sections: Electron-Hydrogen Elastic Scattering - Part 1

We report on the first part of a study of electron-hydrogen scattering, using a method which allows for the ab initio calculation of total and elastic cross sections at higher energies. In its general form the method uses complex 'radial' correlation functions, in a (Kohn) T-matrix formalism. The titled method, abbreviated Complex Correlation Kohn T (CCKT) method, is reviewed, in the context of electron-hydrogen scattering, including the derivation of the equation for the (complex) scattering function, and the extraction of the scattering information from the latter. The calculation reported here is restricted to S-waves in the elastic region, where the correlation functions can be taken, without loss of generality, to be real. Phase shifts are calculated using Hylleraas-type correlation functions with up to 95 terms. Results are rigorous lower bounds; they are in general agreement with those of Schwartz, but they are more accurate and outside his error bounds at a couple of energies,

Bhatia, A. K.↗

NASA NTRS1976

Curve fitting of aeroelastic transient response data with exponential functions

The extraction of frequency, damping, amplitude, and phase information from unforced transient response data is considered. These quantities are obtained from the parameters determined by fitting the digitized time-history data in a least-squares sense with complex exponential functions. The highlights of the method are described, and the results of several test cases are presented. The effects of noise are considered both by using analytical examples with random noise and by estimating the standard deviation of the parameters from maximum-likelihood theory.

Bennett, R. M.↗

NASA NTRS1992

Cognitive engineering models in space systems

NASA space systems, including mission operations on the ground and in space, are complex, dynamic, predominantly automated systems in which the human operator is a supervisory controller. The human operator monitors and fine-tunes computer-based control systems and is responsible for ensuring safe and efficient system operation. In such systems, the potential consequences of human mistakes and errors may be very large, and low probability of such events is likely. Thus, models of cognitive functions in complex systems are needed to describe human performance and form the theoretical basis of operator workstation design, including displays, controls, and decision support aids. The operator function model represents normative operator behavior-expected operator activities given current system state. The extension of the theoretical structure of the operator function model and its application to NASA Johnson mission operations and space station applications is discussed.

Mitchell, Christine M.↗