Search NASA⌕ Search

SEARCH · Search NASA

Results for “MATHEMATICS - CALCUS, OPERATIONAL”

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.

At least 523 records · Page 29

Space shuttle main engine hardware simulation

The Huntsville Simulation Laboratory (HSL) provides a simulation facility to test and verify the space shuttle main engine (SSME) avionics and software system using a maximum complement of flight type hardware. The HSL permits evaluations and analyses of the SSME avionics hardware, software, control system, and mathematical models. The laboratory has performed a wide spectrum of tests and verified operational procedures to ensure system component compatibility under all operating conditions. It is a test bed for integration of hardware/software/hydraulics. The HSL is and has been an invaluable tool in the design and development of the SSME.

Vick, H. G.↗

Digital Signal Combining for Conference Calling

Signals combined with minimal noise by use of sums in read-only memories. Signals from subscribers A and B digitized, transmitted, and combined by addressing ROM. Combining operation electronic equivalent of looking up value of function of two variables in mathematical table. Combined digitized signal transmitted, converted to analog form, and delivered to subscriber C. System intended especially for combining number of separate audio signals into one signal for retransmission, as in telephone conference calling.

Byrne, F.↗

Designing Accelerated Tests Of Electromigration

Method for design of accelerated tests of electromigration (as in microscopic conductors in integrated circuits) based partly on simplified mathematical model of electromigration and partly on error analysis. Objective to determine quickly operating life of tested components under normal operating conditions by extrapolation from lifetime measurements at operating stresses greater than normal. Involves compromise between reducing testing time by increasing stresses and reducing uncertainty in extrapolated lifetime by decreasing stresses.

Buehler, Martin G.↗

Verification Of Tooling For Robotic Welding

Computer simulations, robotic inspections, and visual inspections performed to detect discrepancies. Method for verification of tooling for robotic welding involves combination of computer simulations and visual inspections. Verification process ensures accuracy of mathematical model representing tooling in off-line programming system that numerically simulates operation of robotic welding system. Process helps prevent damaging collisions between welding equipment and workpiece, ensures tooling positioned and oriented properly with respect to workpiece, and/or determines whether tooling to be modified or adjusted to achieve foregoing objectives.

Osterloh, Mark R.↗

Flutter control of incompressible flow turbomachine blade rows by splitter blades

Splitter blades as a passive flutter control technique is investigated by developing a mathematical model to predict the stability of an aerodynamically loaded splittered-rotor operating in an incompressible flow field. The splitter blades, positioned circumferentially in the flow passage between two principal blades, introduce aerodynamic and/or combined aerodynamic-structural detuning into the rotor. The two-dimensional oscillating cascade unsteady aerodynamics, including steady loading effects, are determined by developing a complete first-order unsteady aerodynamic analysis together with an unsteady aerodynamic influence coefficient technique. The torsion mode flutter of both uniformly spaced tuned rotors and detuned rotors are predicted by incorporating the unsteady aerodyamic influence coefficients into a single-degree-of-freedom aeroelastic model. This model is then utilized to demonstrate that incorporating splitters into unstable rotor configurations results in stable splittered-rotor configurations.

Chiang, Hsiao-Wei D.↗

An evidential reasoning extension to quantitative model-based failure diagnosis

The detection and diagnosis of failures in physical systems characterized by continuous-time operation are studied. A quantitative diagnostic methodology has been developed that utilizes the mathematical model of the physical system. On the basis of the latter, diagnostic models are derived each of which comprises a set of orthogonal parity equations. To improve the robustness of the algorithm, several models may be used in parallel, providing potentially incomplete and/or conflicting inferences. Dempster's rule of combination is used to integrate evidence from the different models. The basic probability measures are assigned utilizing quantitative information extracted from the mathematical model and from online computation performed therewith.

Gertler, Janos J.↗

A User's Guide for the Differential Reduced Ejector/Mixer Analysis "DREA" Program

A system of analytical and numerical two-dimensional mixer/ejector nozzle models that require minimal empirical input has been developed and programmed for use in conceptual and preliminary design. This report contains a user's guide describing the operation of the computer code, DREA (Differential Reduced Ejector/mixer Analysis), that contains these mathematical models. This program is currently being adopted by the Propulsion Systems Analysis Office at the NASA Glenn Research Center. A brief summary of the DREA method is provided, followed by detailed descriptions of the program input and output files. Sample cases demonstrating the application of the program are presented.

DeChant, Lawrence J.↗

Practical Techniques for Modeling Gas Turbine Engine Performance

The cost and risk associated with the design and operation of gas turbine engine systems has led to an increasing dependence on mathematical models. In this paper, the fundamentals of engine simulation will be reviewed, an example performance analysis will be performed, and relationships useful for engine control system development will be highlighted. The focus will be on thermodynamic modeling utilizing techniques common in industry, such as: the Brayton cycle, component performance maps, map scaling, and design point criteria generation. In general, these topics will be viewed from the standpoint of an example turbojet engine model; however, demonstrated concepts may be adapted to other gas turbine systems, such as gas generators, marine engines, or high bypass aircraft engines. The purpose of this paper is to provide an example of gas turbine model generation and system performance analysis for educational uses, such as curriculum creation or student reference.

aerothermodynamics↗

Practical Techniques for Modeling Gas Turbine Engine Performance

The cost and risk associated with the design and operation of gas turbine engine systems has led to an increasing dependence on mathematical models. In this paper, the fundamentals of engine simulation will be reviewed, an example performance analysis will be performed, and relationships useful for engine control system development will be highlighted. The focus will be on thermodynamic modeling utilizing techniques common in industry, such as: the Brayton cycle, component performance maps, map scaling, and design point criteria generation. In general, these topics will be viewed from the standpoint of an example turbojet engine model; however, demonstrated concepts may be adapted to other gas turbine systems, such as gas generators, marine engines, or high bypass aircraft engines. The purpose of this paper is to provide an example of gas turbine model generation and system performance analysis for educational uses, such as curriculum creation or student reference.

aerothermodynamics↗

Operation and Maintenance of PV Systems: Data Science, Analysis, and Standards

This effort improves the effectiveness and reduce uncertainty in O&M cost through four primary objectives/tasks: 1) institutionalize standards for reliability and availability reporting for large PV power plants; 2) bridge systemic O&M knowledge gaps around important topics affecting O&M; 3) characterize systemic failure modes and patterns and accelerate O&M experiential learning cycles using field data; and 4) establish a baseline understanding of UPVS O&M cost drivers. Key results of this effort include publication of IEC standards, published topical papers on O&M topics, training, and characterize field data for climate- and service-related patterns (additional details below). Integrating these results serves to reduce performance risk and facilitate improvement in the way solar projects are operated and maintained. Results are well received and two publications are among the most successful SETO publications at NREL ("Model of Operation and Maintenance Costs for Photovoltaic Systems with over 40,000 downloads and "Best Practices in Operation and Maintenance of PV Systems, 3rd Ed." with over 90,000 downloads).

14 SOLAR ENERGY↗

A comprehensive and fair comparison of two neural operators (with practical extensions) based on $\mathrm{FAIR}$ data

Neural operators can learn nonlinear mappings between function spaces and offer a new simulation paradigm for real-time prediction of complex dynamics for realistic diverse applications as well as for system identification in science and engineering. Herein, we investigate the performance of two neural operators, which have shown promising results so far, and we develop new practical extensions that will make them more accurate and robust and importantly more suitable for industrial-complexity applications. The first neural operator, DeepONet, was published in 2019 (Lu et al., 2019), and its original architecture was based on the universal approximation theorem of Chen & Chen (1995). The second one, named Fourier Neural Operator or FNO, was published in 2020, and it is based on parameterizing the integral kernel in the Fourier space. DeepONet is represented by a summation of products of neural networks (NNs), corresponding to the branch NN for the input function and the trunk NN for the output function; both NNs are general architectures, e.g., the branch NN can be replaced with a CNN or a ResNet. According to Kovachki et al. (2021), FNO in its continuous form can be viewed conceptually as a DeepONet with a specific architecture of the branch NN and a trunk NN represented by a trigonometric basis. In order to compare FNO with DeepONet computationally for realistic setups, we develop several extensions of FNO that can deal with complex geometric domains as well as mappings where the input and output function spaces are of different dimensions. We also develop an extended DeepONet with special features that provide inductive bias and accelerate training, and we present a faster implementation of DeepONet with cost comparable to the computational cost of FNO, which is based on the Fast Fourier Transform. Here we consider 16 different benchmarks to demonstrate the relative performance of the two neural operators, including instability wave analysis in hypersonic boundary layers, prediction of the vorticity field of a flapping airfoil, porous media simulations in complex-geometry domains, etc. We follow the guiding principles of FAIR (Findability, Accessibility, Interoperability, and Reusability) for scientific data management and stewardship. The performance of DeepONet and FNO is comparable for relatively simple settings, but for complex geometries the performance of FNO deteriorates greatly. We also compare theoretically the two neural operators and obtain similar error estimates for DeepONet and FNO under the same regularity assumptions.

42 ENGINEERING↗

Detection of crustal motion using spaceborne laser ranging systems

Laser ranging systems operated from space are capable of detecting motions on earth in the 2-5 cm range. Attention is given to the detection of crustal motion, specifically along the San Andreas fault, and a mathematical model is presented for a geometric mode system consisting of at least five grid and three distant (fundamental) stations to be operated with airborne and spaceborne lasers. The ground stations are designed to operate unattended, and to work in conjunction with Shuttle-based hardware to become operational in 1982. The Shuttle laser ranging system is expected to provide survey data within a period from one to two weeks, with a resurvey capability to be used as required.

Kumar, M.↗

Direct interpolative construction of the discrete Fourier transform as a matrix product operator

The quantum Fourier transform (QFT), which can be viewed as a reindexing of the discrete Fourier transform (DFT), has been shown to be compressible as a low-rank matrix product operator (MPO) or quantized tensor train (QTT) operator. However, the original proof of this fact does not furnish a construction of the MPO with a guaranteed error bound. Meanwhile, the existing practical construction of this MPO, based on the compression of a quantum circuit, is not as efficient as possible. We present a simple closed-form construction of the QFT MPO using the interpolative decomposition, with guaranteed near-optimal compression error for a given rank. This construction can speed up the application of the QFT and the DFT, respectively, in quantum circuit simulations and QTT applications. We also connect our interpolative construction to the approximate quantum Fourier transform (AQFT) by demonstrating that the AQFT can be viewed as an MPO constructed using a different interpolation scheme.

97 MATHEMATICS AND COMPUTING↗

Matrix Product (GEMM) Performance Data from GPUs

Timing data for mixed precision GEMM matrix product operations on several GPU models, including NVIDIA V100 and A100, AMD MI100 and Intel P580. Also data from machine learning model training on this data using Scikit-learn.

97 MATHEMATICS AND COMPUTING↗

Streamlining Ocean Dynamics Modeling with Fourier Neural Operators: A Multiobjective Hyperparameter and Architecture Optimization Approach

Training an effective deep learning model to learn ocean processes involves careful choices of various hyperparameters. We leverage DeepHyper’s advanced search algorithms for multiobjective optimization, streamlining the development of neural networks tailored for ocean modeling. The focus is on optimizing Fourier neural operators (FNOs), a data-driven model capable of simulating complex ocean behaviors. Selecting the correct model and tuning the hyperparameters are challenging tasks, requiring much effort to ensure model accuracy. DeepHyper allows efficient exploration of hyperparameters associated with data preprocessing, FNO architecture-related hyperparameters, and various model training strategies. We aim to obtain an optimal set of hyperparameters leading to the most performant model. Moreover, on top of the commonly used mean squared error for model training, we propose adopting the negative anomaly correlation coefficient as the additional loss term to improve model performance and investigate the potential trade-off between the two terms. The numerical experiments show that the optimal set of hyperparameters enhanced model performance in single timestepping forecasting and greatly exceeded the baseline configuration in the autoregressive rollout for long-horizon forecasting up to 30 days. Utilizing DeepHyper, we demonstrate an approach to enhance the use of FNO in ocean dynamics forecasting, offering a scalable solution with improved precision.

97 MATHEMATICS AND COMPUTING↗

Fourier-MIONet: Fourier-enhanced multiple-input neural operators for multiphase modeling of geological carbon sequestration

Geologic carbon sequestration (GCS) is a safety-critical technology that aims to reduce the amount of carbon dioxide in the atmosphere, which also places high demands on reliability. Multiphase flow in porous media is essential to understand CO 2 migration and pressure fields in the subsurface associated with GCS. However, numerical simulation for such problems in 4D is computationally challenging and expensive, due to the multiphysics and multiscale nature of the highly nonlinear governing partial differential equations (PDEs). It prevents us from considering multiple subsurface scenarios and conducting real-time optimization. Here, we develop a Fourier-enhanced multiple-input neural operator (Fourier-MIONet) to learn the solution operator of the problem of multiphase flow in porous media. Fourier-MIONet utilizes the recently developed framework of the multiple-input deep neural operators (MIONet) and incorporates the Fourier neural operator (FNO) in the network architecture. Once Fourier-MIONet is trained, it can predict the evolution of saturation and pressure of the multiphase flow under various reservoir conditions, such as permeability and porosity heterogeneity, anisotropy, injection configurations, and multiphase flow properties. Compared to the enhanced FNO (U-FNO), the proposed Fourier-MIONet has 90% fewer unknown parameters, and it can be trained in significantly less time (about 3.5 times faster) with much lower CPU memory (<15%) and GPU memory (<35%) requirements, to achieve similar prediction accuracy. In addition to the lower computational cost, Fourier-MIONet can be trained with only 6 snapshots of time to predict the PDE solutions for 30 years. Furthermore, we observed that Fourier-MIONet can maintain good accuracy when predicting out-of-distribution (OOD) data. The excellent generalizability of Fourier-MIONet is enabled by its adherence to the physical principle that the solution to a PDE is continuous over time. Furthermore, the developed Fourier-MIONet makes it possible to solve the long-time evolution of geological carbon sequestration in a large-scale three-dimensional space accurately and efficiently.

97 MATHEMATICS AND COMPUTING↗

Precursor Analysis Report: Industroyer2 and Wiper Malware Targeting Ukrainian Energy Provider 2022

The Industroyer2 and Wiper Malware Targeting Ukrainian Energy Provider 2022 Precursor Analysis Report leverages publicly available information about the Industroyer2 cyber attack and catalogs anomalous observables for each technique employed in the attack. This analysis is based upon the methodology of the Cybersecurity for the Operational Technology Environment (CyOTE) program. An adversary attempted to cause a blackout in Ukraine in April 2022 by using the Industroyer2 malware against a regional Ukrainian energy provider. The adversary targeted eight high-voltage electrical substations and utilized the malware in tandem with disk wipers for Windows, Linux, and Solaris operating systems in an attempt to make response and recovery efforts more difficult. The adversary reused a piece of the original Industroyer malware designed to open circuit breakers and de-energize target substations. The adversary gained initial access to the victim’s enterprise network through unknown means in February 2022 and was able to perform reconnaissance, pivot to the operations network, and reside in the system for at least 51 days. This gave the adversary a detailed understanding of the environment and allowed them to customize the Industroyer2 malware to the victim’s operations network. However, defenders detected and stopped the attack before the adversary could achieve their intended impact. Had the Industroyer2 attack been successful, it could have caused a blackout for more than two million people during the early stages of Russia’s invasion of Ukraine. Researchers and analysts identified 22 unique techniques (used in a sequence of 31 steps) utilized during the attack with a total of 297 observables using MITRE ATT&CK® for Industrial Control Systems. The CyOTE program assesses observables accompanying techniques used prior to the triggering event to identify opportunities to detect malicious activity. If observables accompanying the attack techniques are perceived and investigated prior to the triggering event, earlier comprehension of malicious activity can take place. Twenty-three of the identified techniques used during the Industroyer2 cyber attack were precursors to the triggering event. Analysis identified 224 observables associated with these precursor techniques, 122 of which were assessed to have an increased likelihood of being perceived in the 51 days preceding the triggering event. The response and comprehension time could have been reduced if the observables had been identified earlier. The information gathered in this report contributes to a library of observables tied to a repository of artifacts, data sources, and technique detection references for practitioners and developers to support the comprehension of indicators of attack. Asset owners and operators can use these products if they experience similar observables or to prepare for comparable scenarios.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗