The linearity evaluation of a dc voltage to pulse-width converter
Linearity and temperature stability of linear analog dc voltage-to-pulse width converter
PULSE WIDTH↗
SEARCH · Engineering Papers
Results for “linearization”
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.
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Design of piecewise-linear switching functions for relay control systems.
Piecewise linear switching functions design for suboptimal regulation of linear plants with relay controller in regard to transient response performance criterion
TRANSIENT RESPONSE↗
Comparison of two weighted integration models for the cueing task: linear and likelihood
In a task in which the observer must detect a signal at two locations, presenting a precue that predicts the location of a signal leads to improved performance with a valid cue (signal location matches the cue), compared to an invalid cue (signal location does not match the cue). The cue validity effect has often been explained with a limited capacity attentional mechanism improving the perceptual quality at the cued location. Alternatively, the cueing effect can also be explained by unlimited capacity models that assume a weighted combination of noisy responses across the two locations. We compare two weighted integration models, a linear model and a sum of weighted likelihoods model based on a Bayesian observer. While qualitatively these models are similar, quantitatively they predict different cue validity effects as the signal-to-noise ratios (SNR) increase. To test these models, 3 observers performed in a cued discrimination task of Gaussian targets with an 80% valid precue across a broad range of SNR's. Analysis of a limited capacity attentional switching model was also included and rejected. The sum of weighted likelihoods model best described the psychophysical results, suggesting that human observers approximate a weighted combination of likelihoods, and not a weighted linear combination.
NASA Program Biomedical Research and Countermeasur↗
Retrieval of Spatio-temporal Distributions of Particle Parameters from Multiwavelength Lidar Measurements Using the Linear Estimation Technique and Comparison with AERONET
The results of the application of the linear estimation technique to multiwavelength Raman lidar measurements performed during the summer of 2011 in Greenbelt, MD, USA, are presented. We demonstrate that multiwavelength lidars are capable not only of providing vertical profiles of particle properties but also of revealing the spatio-temporal evolution of aerosol features. The nighttime 3 Beta + 1 alpha lidar measurements on 21 and 22 July were inverted to spatio-temporal distributions of particle microphysical parameters, such as volume, number density, effective radius and the complex refractive index. The particle volume and number density show strong variation during the night, while the effective radius remains approximately constant. The real part of the refractive index demonstrates a slight decreasing tendency in a region of enhanced extinction coefficient. The linear estimation retrievals are stable and provide time series of particle parameters as a function of height at 4 min resolution. AERONET observations are compared with multiwavelength lidar retrievals showing good agreement.
AERONET↗
Linear Covariance Analysis For Proximity Operations Around Asteroid 2008 EV5
The NASA initiative to collect an asteroid, the Asteroid Robotic Redirect Mission (ARRM), is currently investigating the option of retrieving a boulder from an asteroid, demonstrating planetary defense with an enhanced gravity tractor technique, and returning it to a lunar orbit. Techniques for accomplishing this are being investigated by the Satellite Servicing Capabilities Office (SSCO) at NASA GSFC in collaboration with JPL, NASA JSC, LaRC, and Draper Laboratory, Inc. Two critical phases of the mission are the descent to the boulder and the Enhanced Gravity Tractor demonstration. A linear covariance analysis is done for these phases to assess the feasibility of these concepts with the proposed design of the sensor and actuator suite of the Asteroid Redirect Vehicle (ARV). The sensor suite for this analysis includes a wide field of view camera, LiDAR, and an IMU. The proposed asteroid of interest is currently the C-type asteroid 2008 EV5, a carbonaceous chondrite that is of high interest to the scientific community. This paper presents an overview of the linear covariance analysis techniques and simulation tool, provides sensor and actuator models, and addresses the feasibility of descending to the surface of the asteroid within allocated requirements as well as the possibility of maintaining a halo orbit to demonstrate the Enhanced Gravity Tractor technique.
Navigation↗
Linear Algorithms for Worst Case Identification in H infinity with Applications to Flexible Structures
This paper is concerned with linear algorithms for identification in which have been studied in [9]. It is shown that the two different linear algorithms in [9] can be unified into a single one which can be further extended to nonuniformly spaced frequency response samples with exponential convergence for the noise free case. Improved upper bounds for the corresponding identification errors are derived. Applications to the identification of lightly damped systems such as flexible structures are also considered.
linear↗
A Modified Linear-MIxing Method for Calculating Atmospheric Path Radiances of Aerosol Mixtures
The top-of-atmosphere (TOA) path radiance generated by an aerosol mixture can be synthesized by linearly adding the contributions of the individual aerosol components, weighted by their fractional optical depths. The method, known as linear mixing, is exact in the single-scattering limit.
top-of-atmosphere↗
Towards Formalization of Advanced Linear Algebra with Applications to Dynamical Systems using PVS
Linear Algebra is essential for numerous aerospace problems of interest. Formal reasoning about hybrid systems that contain variables modeled by differential equations rely on concepts from Linear Algebra such as eigenvalues, matrix decompositions, and matrix valued functions. For example, the long-term dynamics of a system of differential equations depend on the stability/instability of its equilibrium points, which often reduces to an eigenvalue problem. This talk will embark on a quest to formalize theorems and results about eigenvalues and eigenvectors using PVS. We shall start our journey with 2 x 2 complex matrices, where we will apply our PVS code to a simple example of a dynamical system. Since it can be difficult or impossible to give simple expressions of eigenvalues for larger matrices (i.e. 5 x 5 or higher), we then move towards specifying the power method for verified computation of eigenvalue approximations in PVS. This effort requires development of multivariate complex arithmetic. At the end of the day, having such additions to the PVS NASA libraries will help move towards the use of formal methods to verify concepts of control theory and system level verification.
Linear Algebra↗
Linear Regression Model for Predictive Service Provider Selection
The increasing number of satellites in orbit has led to a growing reliance on third-party service providers for data transfer between Earth and space. Traditional approaches to managing satellite communications require human intervention, which becomes more burdensome with the escalating number of satellites. This research addresses the need for an efficient and automated system to optimize service provider selection for NASA space communication. Previous research has utilized human-operated approaches for service provider management. Our study fills a gap by developing a cognitive algorithm that automates and optimizes the selection process based on various parameters, such as data volume, priority, quality of service and cost. This novel solution reduces user burden, facilitates service management, and contributes to the development of cognitive spaceflight missions, ultimately supporting NASA’s research into Cognitive Communications technology. The algorithm design consists of three major steps: modeling data, developing a Link Selection Algorithm (LSA) based on a grading system, and applying machine learning using linear regression. The LSA evaluates providers based on user-defined constraints, considering factors such as delivery time, cost, and quality of service. We define a suitability metric which allows our algorithm to make a recommendation to a user regarding which commercial service providers to select. The addition of Linear Regression predicts the future suitability value. Our main findings demonstrate that the resulting algorithm can autonomously manage connections between satellites and providers, maximizing communication channel efficiency. This research has significant implications, as it not only addresses a pressing issue in satellite communication management but also advances the field of cognitive spaceflight missions.
Linear regression↗
Evaluating Delta-V Dispersions Using Linear Covariance Techniques with Applications to Rendezvous and Docking
One of the attractive advantages of using linear covariance analysis (LinCov) is that it can accurately produce both navigation errors and trajectory dispersions in a fraction of the time comparable to the standard Monte Carlo analysis approach that is traditionally adopted. It also has the capability of generating delta-v dispersions which is perhaps the most influential performance metric since many aspects of a mission design revolve around the anticipated propellant usage. Accurately capturing this key performance criteria using linear covariance techniques has several subtle caveats raising reasonable doubts and a cautious sense of skepticism. This paper outlines multiple approaches of modeling delta-v usage in LinCov, highlights their limitations and advantages, and ultimately compares their corresponding results to the actual Monte Carlo performance. The theory is also extended to reliably account for an arbitrary thruster configuration and the resultant propellant consumptions due to both translational burns and attitude maneuvers. This provides near instant insight into the impacts of thruster layout design and different vehicle mass properties. These derived techniques are applied and verified using an NRHO rendezvous and docking scenario consistent with upcoming NASA Artemis missions for Orion.
Linear Covariance Analysis↗
Novel Solver Algorithms for Nearly Singular Linear Systems Arising in Combustion Modelling
Direct Numerical Simulations of realistic combustion devices are extremely challenging due to the wide separation of scales in the simulation, for example an internal combustion (IC) engine chamber, and the flame thickness of a high-pressure flame. The PeleLMeX solver uses adaptive mesh refinement (AMR) to evolve multi-species reacting flows in the low Mach number limit at the Exascale and relies on an embedded boundary (EB) approach to represent complex geometries. In that framework, the EB geometries often give rise to very small cut-cells along the boundary, which translate into extreme ill-conditioning of the pressure-projection, with eigenvalues that span 15-16 orders of magnitude. In this talk, we focus on the case of a typical IC piston bowl geometry for which we present on a novel approach towards solving these nearly singular linear systems with ILU-based, C-AMG smoothers on massively parallel architectures. In particular, we use scaling and equilibration algorithms to handle the non-normality of the upper triangular factors. This enables us to approximate the highly sequential triangular solve algorithm, embedded in the AMG smoothing-solve phase, with Jacobi iterations. This approximation can be written as a convergent Neumann series whose terms are composed of highly parallel sparse matrix vector multiplications. The result is an algorithm that substantially decreases setup and solve time, compared to state-of-the-art, for these challenging linear systems.
combustion modelling↗
Sensor Anomaly Detection for Nuclear Reactor Systems Utilizing Linear Regression and K-Means Unsupervised Machine Learning
Nuclear reactors and related systems are becoming increasingly complex due to advancing technologies in next-generation power reactors. This increased complexity necessitates enhanced automation and data management capabilities. To successfully realize autonomous systems, methods must be developed to handle vast volumes of data and effectively distinguish anomalous data from noise and expected data. While impressive models utilizing digital twins and similar approaches are under development, here we propose a simplified model for analyzing fundamental methods and techniques. Initially, we created a general dataset by using initial data from PCTRAN in order to represent ideal steady-state conditions. We then inserted anomalies based on prevalent sensor anomaly types (e.g., point anomalies, linear drift, and downward deviations), along with unusual anomalies such as exponential drift and upward deviations. To detect anomalies, we developed a program that employs data partitioning and linear regression to preprocess and filter the anomalous data. A K-Means machine learning (ML) method was then applied to separate and count the data within the anomalous partition. The results from all datasets—apart from exponential growth—demonstrated positive outcomes, with each returning multiple instances of greaterthan-95% accuracy. We conducted further investigations using Idaho National Laboratory’s RAVEN software to perform a sensitivity analysis on the input variables (R 2 Tolerance, Slope Tolerance, and Window Size) and found that the output variables (Accuracy and Time) were most sensitive to the Window Size. Despite the promising results published, further development is required to effectively apply these methods to nuclear systems. Nevertheless, the strengths of this approach are evident and hold promise for future applications in the field.
21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
Design of Linear Accelerator (LINAC) tanks for proton therapy via Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) approaches
A homemade computer code for designing a Side- Coupled Linear Accelerator (SCL) is written. It integrates a simplified model of SCL tanks with the Particle Swarm Optimization (PSO) algorithm. The computer code main aim is to obtain useful guidelines for the design of Linear Accelerator (LINAC) resonant cavities. The design procedure, assisted via the aforesaid approach seems very promising, allowing future improvements towards the optimization of actual accelerating geometries. (authors)
43 PARTICLE ACCELERATORS↗
Improved Evaluation of Large Network Matrices for Linear Power Flow Within Optimization Problems: Preprint
This work discusses methods for evaluating the Power Transfer Distribution Factor (PTDF) and Line Outage Distribution Factor (LODF) matrices by employing sparse linear algebra for large-scale computing applications. These matrices are critical in many power systems applications, such as the Unit Commitment Problem (UC), pre- and post-contingency power flow analysis, and transmission expansion. These matrices are typically dense, which means they require a significant amount of time and memory to be computed for large networks. However, by analyzing the structure of the matrices and their computation method, it is possible to use reduced memory methods based on sparse matrix operations. This paper shows that sparse linear algebra algorithms are faster and require less memory and time than traditional dense approaches. Additionally, we explore the effect of matrix sparsification by eliminating trailing digits on power flow calculations.
ENERGY PLANNING, POLICY, AND ECONOMY↗
Adaptive Control for Load-Following of Boiling Water Reactors Part I: Linear Systems and Fully-Observable Dynamics
Automation control is a key strategy to improve the economic competitiveness of nuclear power plants. Not only does it help reduce operational costs, but it also extends the value proposition of these plants to nontraditional markets, including unattended operations in remote villages and space. However, the dynamics of the operating environments of nuclear reactors are subject to changes over time, and there are no widely adopted methods to ensure that the automation strategy will remain effective over the extended durations required for these applications. Adaptive control is a discipline that offers the possibility to accommodate such changes online. However, it relies on mathematical assumptions that must be respected to ensure robustness and reliability. In this work, we derive an adaptive control formulation for linear systems in which all states are observable and apply it to an instance of load-follow operation for Boiling Water Reactors. We assumed uncertainty in two factors: the temperature coefficient and the control rod worth, both of which are affected over time by the evolution of the nuclear reactor core environment. With an arbitrary penalty factor of 5, we found that the mean absolute and integral time absolute errors can be reduced by more than 90%, underscoring the strength of adaptive control. To extend the application to more challenges, different uncertainties and load-follow trajectories, as well as new formulations that include non-linearity and partial observability, are currently being developed.
22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
Fracture propagation in Indiana Limestone interpreted via linear softening cohesive fracture model
In this study, we examine the use of a linear softening cohesive fracture model (LCFM) to predict single-trace fracture growth in short-rod (SR) and notched 3-point-bend (N3PB) test configurations in Indiana Limestone. The broad goal of this work is to (a) understand the underlying assumptions of LCFM and (b) use experimental similarities and deviations from the LCFM to understand the role of loading paths of tensile fracture propagation. Cohesive fracture models are being applied in prediction of structural and subsurface fracture propagation in geomaterials. They lump the inelastic processes occurring during fracture propagation into a thin zone between elastic subdomains. LCFM assumes that the cohesive zone initially deforms elastically to a maximum tensile stress ( σ max ) and then softens linearly from the crack opening width at σ max to zero stress at a critical crack opening width w 1 . Using commercial finite element software, we developed LCFMs for the SR and N3PB configurations. After fixing σ max with results from cylinder splitting tests and finding an initial Young's modulus ( E ) with unconfined compressive strength tests, we manually calibrate E and w 1 in the SR model against an envelope of experimental data. We apply the calibrated LCFM parameters in the N3PB geometry and compare the model against an envelope of N3PB experiments. For accurate simulation of fracture propagation, simulated off-crack stresses are high enough to require inclusion of damage. Different elastic moduli are needed in tension and compression. We hypothesize that the timing and location of shear versus extensional micromechanical failures control the qualitative macroscopic force-versus-displacement response in different tests. For accurate prediction, the LCFM requires a constant style of failure, which the SR configuration maintains until very late in deformation. The N3PB configuration does not maintain this constancy. To be broadly applicable between geometries and failure styles, the LCFM would require additional physics, possibly including elastoplastic damage in the bulk material and more complicated cohesive softening models.
58 GEOSCIENCES↗
Site-Selective Catalysis of a Multifunctional Linear Molecule: The Steric Hindrance of Metal–Organic Framework Channels
The site-selective reaction of a multifunctional linear molecule requires a suitable catalyst possessing both uniform narrow channel to limit the molecule rotation and a designed active site in the channel. Recently, nanoparticles (NPs) were incorporated in metal–organic frameworks (MOFs) with the tailorable porosity and ordered nanochannel, which makes these materials (NPs/MOFs) highly promising candidates as catalytic nanoreactors in the field of heterogeneous catalysis. Inspired by a “Gondola” sailing in narrow “Venetian Canal” without sufficient space for a U-turn, a simple heterogeneous catalyst based on NPs/MOFs is developed here that exhibits site-selectivity for the oxidation of diols by restricting the random rotation of the molecule (the “Gondola”) in the limited space of the MOF channel (the narrow “Venetian Canal”), thereby protecting the middle functional group via steric hindrance. This strategy is not limited to the oxidation of diols, but can be extended to the site-selective reaction of many similar multifunctional linear molecules, such as the reduction of alkadienes.
36 MATERIALS SCIENCE↗
Birefringent Glass‐Engraved Quasi‐Linear Nanograting Metasurface Based on Self‐Organizing Process for Large Aperture High Power Laser Applications
All-glass metasurface “nanograting” structures that exhibit birefringence in the formed layer are reported. The key enabler of this work is ion beam processing at an angle sufficiently off-normal incidence, inducing self-assembly of a deposited metal layer into quasi-linear metallic features that can function as an etching mask. As a result, a fused silica metasurface, monolithic to the underlying substrate, is demonstrated at 375 nm wavelength to exhibit a phase delay angle of 30° between the principal axes. The capability of an angled etch mask replenishment process is also demonstrated for achieving deeper etch depth and for increasing the grating period, another first – to the best of the knowledge. This is the first display of a technology capable of fabricating glass-engraved near-linear grating structure with a feature-to-feature period as small as 118.6 nm. Furthermore, this technology has the potential to generate grating-like structures with periods as small as 12.4 nm, as demonstrated here with reactive ion beam processing assisted mask assembly. Furthermore, these structures are shown to have reflectivity < 0.4% across the wavelength band 350 nm – 1000 nm. Such a technology can enable laser-durable grating structures for the deep-UV and even down to soft X-ray wavelengths.
Ray, Nathan J. [Lawrence Livermore National Labora↗