Search NASA⌕ Search

SEARCH · Search NASA

Results for “TAYLOR THEOREM”

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.

26 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1982

Volume integrals of ellipsoids associated with the inhomogeneous Helmholtz equation

Problems of wave phenomena in the fields of acoustics, electromagnetics and elasticity are often reduced to an integration of the inhomogeneous Helmholtz equation. Results are presented for volume integrals associated with the inhomogeneous Helmholtz equation, for an ellipsoidal region. By using appropriate Taylor series expansions and the multinomial theorem, these volume integrals are obtained in series form for regions r greater than r-prime and r less than r-prime, where r and r-prime are the distances from the origin to the point of observation and the source. Derivatives of these integrals are easily evaluated. When the wavenumber approaches zero the results reduce directly to the potentials of ellipsoids of variable densities.

Fu, L. S.↗
NASA NTRS1989

The art of spacecraft design: A multidisciplinary challenge

Actual design turn-around time has become shorter due to the use of optimization techniques which have been introduced into the design process. It seems that what, how and when to use these optimization techniques may be the key factor for future aircraft engineering operations. Another important aspect of this technique is that complex physical phenomena can be modeled by a simple mathematical equation. The new powerful multilevel methodology reduces time-consuming analysis significantly while maintaining the coupling effects. This simultaneous analysis method stems from the implicit function theorem and system sensitivity derivatives of input variables. Use of the Taylor's series expansion and finite differencing technique for sensitivity derivatives in each discipline makes this approach unique for screening dominant variables from nondominant variables. In this study, the current Computational Fluid Dynamics (CFD) aerodynamic and sensitivity derivative/optimization techniques are applied for a simple cone-type forebody of a high-speed vehicle configuration to understand basic aerodynamic/structure interaction in a hypersonic flight condition.

Abdi, F.↗
NASA NTRS1986

Sensitivity analysis and approximation methods for general eigenvalue problems

Optimization of dynamic systems involving complex non-hermitian matrices is often computationally expensive. Major contributors to the computational expense are the sensitivity analysis and reanalysis of a modified design. The present work seeks to alleviate this computational burden by identifying efficient sensitivity analysis and approximate reanalysis methods. For the algebraic eigenvalue problem involving non-hermitian matrices, algorithms for sensitivity analysis and approximate reanalysis are classified, compared and evaluated for efficiency and accuracy. Proper eigenvector normalization is discussed. An improved method for calculating derivatives of eigenvectors is proposed based on a more rational normalization condition and taking advantage of matrix sparsity. Important numerical aspects of this method are also discussed. To alleviate the problem of reanalysis, various approximation methods for eigenvalues are proposed and evaluated. Linear and quadratic approximations are based directly on the Taylor series. Several approximation methods are developed based on the generalized Rayleigh quotient for the eigenvalue problem. Approximation methods based on trace theorem give high accuracy without needing any derivatives. Operation counts for the computation of the approximations are given. General recommendations are made for the selection of appropriate approximation technique as a function of the matrix size, number of design variables, number of eigenvalues of interest and the number of design points at which approximation is sought.

Murthy, D. V.↗
NASA NTRS1992

The free and forced vibrations of structures using the finite dynamic element method

In addition to an extensive review of the literature on exact and corrective displacement based methods of vibration analysis, a few theorems are proven concerning the various structural matrices involved in such analyses. In particular, the consistent mass matrix and the quasi-static mass matrix are shown to be equivalent, in the sense that the terms in their respective Taylor expansions are proportional to one another, and that they both lead to the same dynamic stiffness matrix when used with the appropriate stiffness matrix.

Fergusson, Neil J.↗
NASA NTRS1978

Transverse shear stiffness of laminated anisotropic shells

Equations are derived for the transverse shear stiffness of laminated anisotropic shells. Without making assumptions for thickness distribution for either transverse shear stresses or strains, constitutive equations for the transverse shear deformation theory of anisotropic heterogeneous shells are found. The equations are based on Taylor series expansions about a generic point for stress resultants and couples, identically satisfying plate equilibrium equations. These equations are used to find statically correct expressions for in-surface stresses, transverse shear stresses, and the area density of transverse shear strain energy, in terms of transverse shear stress resultants and redundants. The application of Castigliano's theorem of least work minimizes shear strain energy with respect to the redundants. Examples are presented for several laminated walls. Good agreement is found between the results and those of exact three-dimensional elasticity solutions for the cylindrical bending of a plate.

Cohen, G. A.↗
DOE OSTI2024

Towards Provable Security in Industrial Control Systems Via Dynamic Protocol Attestation

Industrial control systems (ICSs) increasingly rely on digital technologies vulnerable to cyber attacks. Cyber attackers can infiltrate ICSs and execute malicious actions. Individually, each action seems innocuous. But taken together, they cause the system to enter an unsafe state. These attacks have resulted in dramatic consequences such as physical damage, economic loss, and environmental catastrophes. This paper introduces a methodology that restricts actions using protocols. These protocols only allow safe actions to execute. Protocols are written in a domain specific language we have embedded in an interactive theorem prover (ITP). The ITP enables formal, machine-checked proofs to ensure protocols maintain safety properties. We use dynamic attestation to ensure ICSs conform to their protocol even if an adversary compromises a component. Since protocol conformance prevents unsafe actions, the previously mentioned cyber attacks become impossible. We demonstrate the effectiveness of our methodology using an example from the Fischertechnik Industry 4.0 platform. We measure dynamic attestation's impact on latency and throughput. Our approach is a starting point for studying how to combine formal methods and protocol design to thwart attacks intended to cripple ICSs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Magnetized liner inertial fusion platform development to assess performance scaling with drive parameters

Magnetized liner inertial fusion (MagLIF) experiments have demonstrated fusion-relevant ion temperatures up to 3.1 keV and thermonuclear production of up to 1.1 × 1013 deuterium–deuterium neutrons. This performance was enabled through platform development that provided increases in applied magnetic field, coupled preheat energy, and drive current. Advanced coil designs with internal reinforcement enabled an increase from 10 to 20 T. An improved laser pulse shape, beam smoothing, and thinner laser entrance foils increased preheat energy coupling from less than 1 to 2.3 kJ. A redesign of the final transmission line and load region increased peak load current from 16 to 20 MA. The wider range of input parameters was leveraged to study target performance trends with preheat energy, applied magnetic field, and peak load current. Ion temperature and neutron yield generally followed trends in two-dimensional clean Lasnex calculations. Stagnation performance improved with peak load current when other input parameters were also increased such that convergence was maintained. This dataset suggests that reducing convergence to less than 30 would improve predictability of target performance. Lasnex was used to identify a simulation-optimized scaling path, which suggests 10+ kJ of fusion yield is possible on the Z facility with achievable input parameters. This path also indicates >10 MJ could be generated through volume burn on a future facility with a path to high yield (>200 MJ) using cryogenic dense fuel layers. The newly developed MagLIF platform enables exploration of both this simulation optimized scaling path and a recently developed similarity-scaling path.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Resilience Measurement Framework For Post-deployment Artificial Intelligence (ai) Integrated Systems

Resilience is largely defined as the ability to adapt or recover from adverse conditions, stresses, attacks, or compromises on systems that use or are enabled by digital resources. In Artificial Intelligence Management and Research for Advanced Networked Testbed Hub (AMARANTH), resilience is measured in the amount of time it took from the beginning of a testing period for the model to reach predictions outside of the original 95% confidence interval or using the Kullback-Leibler (KL) divergence theorem, the Population Stability Index (PSI), and traditional methods such as root mean squared error (RMSE) threshold. Artificial Intelligence (AI) model drift is of significant concern when deploying AI-integrated systems into critical and/or secure environments. Drift can impact resilience of the AI-integrated system post-deployment and requires consistent maintenance and upkeep to ensure the model is accurate and precise. To quantify model drift and predict the point when a model's drift becomes unacceptable, we describe using Kullback-Leibler (KL) divergence, Population Stability Index (PSI) and/or confidence interval width estimations to determine the point of failure and time to failure of a model post-deployment. Through simple code functions, the KL-divergence, PSI, confidence interval, and root mean squared (RMSE) point of failures can be used to derive when a model needs to be maintained as well as the impact of adversarial action through statistical means.

Yockey, Patience [Idaho National Laboratory (INL),↗