Implementation of computer software techniques to human factors task data handling problems Final report, 21 Jun. - 30 Jun. 1967
Implementation of computer software techniques for human factors task data handling systems
Meyer, G. R.↗
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Separable physics-informed DeepONet: Breaking the curse of dimensionality in physics-informed machine learning
The deep operator network (DeepONet) has shown remarkable potential in solving partial differential equations (PDEs) by mapping between infinite-dimensional function spaces using labeled datasets. However, in scenarios lacking labeled data, the physics-informed DeepONet (PI-DeepONet) approach, which utilizes the residual loss of the governing PDE to optimize the network parameters, faces significant computational challenges, particularly due to the curse of dimensionality. This limitation has hindered its application to high-dimensional problems, making even standard 3D spatial with 1D temporal problems computationally prohibitive. Additionally, the computational requirement increases exponentially with the discretization density of the domain. Here, to address these challenges and enhance scalability for high-dimensional PDEs, we introduce the Separable physics-informed DeepONet (Sep-PI-DeepONet). This framework employs a factorization technique, utilizing sub-networks for individual one-dimensional coordinates, thereby reducing the number of forward passes and the size of the Jacobian matrix required for gradient computations. By incorporating forward-mode automatic differentiation (AD), we further optimize computational efficiency, achieving linear scaling of computational cost with discretization density and dimensionality, making our approach highly suitable for high-dimensional PDEs. We demonstrate the effectiveness of Sep-PI-DeepONet through three benchmark PDE models: the viscous Burgers’ equation, Biot’s consolidation theory, and a parameterized heat equation. Our framework maintains accuracy comparable to the conventional PI-DeepONet while reducing training time by two orders of magnitude. Notably, for the heat equation solved as a 4D problem, the conventional PI-DeepONet was computationally infeasible (estimated 289.35 h), while the Sep-PI-DeepONet completed training in just 2.5 h. These results underscore the potential of Sep-PI-DeepONet in efficiently solving complex, high-dimensional PDEs, marking a significant advancement in physics-informed machine learning.
Neural operator↗
Survey of information concerning large diameter deep hole drilling
Data are presented, covering drilling techniques, factors affecting penetration rates, cost estimation, and system improvement. Various drill bits are also discussed.
Source record↗
Time-fixed rendezvous by impulse factoring with an intermediate timing constraint
A method is presented for factoring a two-impulse orbital transfer into a three- or four-impulse transfer which solves the rendezvous problem and satisfies an intermediate timing constraint. Both the time of rendezvous and the intermediate time of a alinement are formulated as any element of a finite sequence of times. These times are integer multiples of a constant plus an additive constant. The rendezvous condition is an equality constraint, whereas the intermediate alinement is an inequality constraint. The two timing constraints are satisfied by factoring the impulses into collinear parts that vectorially sum to the original impulse and by varying the resultant period differences and the number of revolutions in each orbit. Five different types of solutions arise by considering factoring either or both of the two impulses into two or three parts with a limit for four total impulses. The impulse-factoring technique may be applied to any two-impulse transfer which has distinct orbital periods.
Green, R. N.↗
Implicit approximate-factorization schemes for the low-frequency transonic equation
Two- and three-level implicit finite-difference algorithms for the low-frequency transonic small disturbance-equation are constructed using approximate factorization techniques. The schemes are unconditionally stable for the model linear problem. For nonlinear mixed flows, the schemes maintain stability by the use of conservatively switched difference operators for which stability is maintained only if shock propagation is restricted to be less than one spatial grid point per time step. The shock-capturing properties of the schemes were studied for various shock motions that might be encountered in problems of engineering interest. Computed results for a model airfoil problem that produces a flow field similar to that about a helicopter rotor in forward flight show the development of a shock wave and its subsequent propagation upstream off the front of the airfoil.
Ballhaus, W. F.↗
Implicit finite difference simulation of flow about arbitrary geometries with application to airfoils
Finite difference procedures are used to solve either the Euler equations or the 'thin layer' Navier-Stokes equations subject to arbitrary boundary conditions. An automatic grid generation program is employed, and because an implicit finite difference algorithm for the flow equations is used, time steps are not severely limited when grid points are finely distributed. Computational efficiency and compatibility to vectorized computer processors is maintained by use of approximate factorization techniques. Computed results for both inviscid and viscous flow about airfoils are described and compared to various known solutions.
Steger, J. L.↗
Conservative implicit schemes for the full potential equation applied to transonic flows
Implicit approximate factorization techniques (AF) were investigated for the solution of matrix equations resulting from finite difference approximations to the full potential equation in conservation form. For transonic flows, an artificial viscosity, required to maintain stability in supersonic regions, was introduced by an upwind bias of the density. Two implicit AF procedures are presented and their convergence performance is compared with that of the standard transonic solution procedure, successive line overrelaxation (SLOR). Subcritical and supercritical test cases are considered. The results indicate that the AF schemes are substantially faster than SLOR.
Holst, T. L.↗
On implicit finite-difference simulations of three-dimensional flow
An implicit finite-difference procedure for unsteady three-dimensional flow capable of handling arbitrary geometry through the use of general coordinate transformations is described. Viscous effects are optionally incorporated with a 'thin layer' approximation of the Navier-Stokes equations. An implicit approximate factorization technique is employed so that the small grid sizes required for spatial accuracy and viscous resolution do not impose stringent stability limitations. Results obtained from the program include transonic inviscid and laminar-turbulent solutions about simple body configurations. Comparisons with existing theories and experiments are made. Numerical accuracy and the effect of three-dimensional coordinate singularities are also discussed.
Pulliam, T. H.↗
Fast, conservative schemes for the full potential equation applied to transonic flows
Implicit approximate factorization techniques (AF) are investigated for the solution of matrix equations resulting from finite-difference approximations to the full potential equation in conservation form. For transonic flows, an artificial viscosity, required to maintain stability in supersonic regions, is introduced by an upwind bias of the density. Two implicit AF procedures are presented, and their convergence performance is compared with that of the standard transonic solution procedure: successive line overrelaxation (SLOR). Subcritical and supercritical test cases are considered. Results indicate a substantial improvement in convergence rate for AF schemes relative to SLOR.
Holst, T. L.↗
Safety analysis for complex systems
Operational risk assessment considers hardware, environment, and human factors. Technique starts with division of postulated mission into segments which are further subdivided into separate operational steps. Consequences of steps, nonoccurrence, premature operation, out-of-sequence operation, and inadvertent execution are examined at subevent, event, and phase levels. Hazards are identified and treated individually. Analysis is well suited to application in energy and transportation fields.
Onesty, J. P.↗
Calibration procedures for measurement of reflectance factor in remote sensing field research
A means by which measurements of the optical properties of crops and soils can be knowledgeably compared from site to site and instrument to instrument is presented in detail. The definition of bidirectional reflectance factor is reviewed and discussed. Procedures for field implementation are illustrated and discussed. Spectral and goniometric properties of laboratory and field reference surfaces and typical environmental subjects serve as a basis for analysis of uncertainties introduced by differing illumination conditions. Results of a comparison of the performance of three spectrometer systems are presented and discussed. It is concluded that intelligent use of the bidirectional reflectance factor technique is an accurate and practical means to obtain the spectral, optical properties of crops and soils needed for advancements in agricultural remote sensing.
Robinson, B. F.↗
A conservative implicit finite difference algorithm for the unsteady transonic full potential equation
An implicit finite difference procedure is developed to solve the unsteady full potential equation in conservation law form. Computational efficiency is maintained by use of approximate factorization techniques. The numerical algorithm is first order in time and second order in space. A circulation model and difference equations are developed for lifting airfoils in unsteady flow; however, thin airfoil body boundary conditions have been used with stretching functions to simplify the development of the numerical algorithm.
Steger, J. L.↗
UDU/T/ covariance factorization for Kalman filtering
There has been strong motivation to produce numerically stable formulations of the Kalman filter algorithms because it has long been known that the original discrete-time Kalman formulas are numerically unreliable. Numerical instability can be avoided by propagating certain factors of the estimate error covariance matrix rather than the covariance matrix itself. This paper documents filter algorithms that correspond to the covariance factorization P = UDU(T), where U is a unit upper triangular matrix and D is diagonal. Emphasis is on computational efficiency and numerical stability, since these properties are of key importance in real-time filter applications. The history of square-root and U-D covariance filters is reviewed. Simple examples are given to illustrate the numerical inadequacy of the Kalman covariance filter algorithms; these examples show how factorization techniques can give improved computational reliability.
Thornton, C. L.↗
Solution of the transonic full potential equation in conservative form using an implicit algorithm
The paper presents numerical solutions of the full potential equation in conservative form. The iteration scheme used is a fully implicit approximate factorization technique and provides a significant improvement in convergence speed relative to standard successive line overrelaxation algorithms. The spatial differencing algorithm is centrally differenced in both subsonic and supersonic regions to maintain stability. This effectively approximates rotated differencing, thereby greatly improving the reliability of the algorithm.
Holst, T.↗
Recent developments in multi-wire fixed abrasive slicing technique (FAST)
Slicing is an important processing step for all technologies based on the use of ingots. A comparison of the economics of three slicing techniques shows that the fixed abrasive slicing technique (FAST) is superior to the internal diameter (ID) and the multiblade slurry (MBS) techniques. Factors affecting contact length are discussed, taking into account kerf width, rocking angle, ingot size, and surface speed. Aspects of blade development are also considered. A high concentration of diamonds on wire has been obtained in wire packs usd for FAST slicing. The material removal rate was found to be directly proportional to the pressure at the diamond tips.
Schmid, F.↗
Application of a fractional-step method to incompressible Navier-Stokes equation
A numerical method for computing three dimensional, time dependent incompressible flows is presented. The method is based on a fractional step, or time-splitting, scheme in conjunction with the approximate-factorization technique. The use of velocity boundary conditions for the intermediate velocity field leads to inconsistent numerical solutions. Appropriate boundary conditions for the intermediate velocity field are derived and tested. Numerical solutions for flow inside a driven cavity and over a backward-facing step are presented and compared with experimenal data and other numerical results.
Kim, J.↗
Calibration procedures for measurement of reflectance factor in remote sensing field research
A means by which measurements of the optical properties of crops and soils can be knowledgeably compared from site to site and instrument to instrument is presented in detail. The definition of bidirectional reflectance factor is reviewed and discussed. Procedures for field implementation are illustrated and discussed. Spectral and goniometric properties of laboratory and field reference surfaces are given. It is concluded that intelligent use of the bidirectional reflectance factor technique is an accurate and practical means to obtain the spectral, optical properties of crops and soils needed for advancements in agricultural remote sensing.
Robinson, B. F.↗
Predicting viscoelastic response and delayed failures in general laminated composites
Although graphite fibers behave in an essentially elastic manner, the polymeric matrix of graphite/epoxy composites is a viscoelastic material which exhibits creep and delayed failures. The creep process is quite slow at room temperature, but may be accelerated by higher temperatures, moisture absorption, and other factors. Techniques are being studied to predict long-term behavior of general laminates based on short-term observations of the unidirectional material at elevated temperatures. A preliminary numerical procedure based on lamination theory is developed for predicting creep and delayed failures in laminated composites. A modification of the Findley nonlinear power law is used to model the constitutive behavior of a lamina. An adaptation of the Tsai-Hill failure criterion is used to predict the time-dependent strength of a lamina. Predicted creep and delayed failure results are compared with typical experimental data.
Dillard, D. A.↗