Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “constraint decomposition”

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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

A simple suboptimal least-squares algorithm for attitude determination with multiple sensors

Three-axis attitude determination is equivalent to finding a coordinate transformation matrix which transforms a set of reference vectors fixed in inertial space to a set of measurement vectors fixed in the spacecraft. The attitude determination problem can be expressed as a constrained optimization problem. The constraint is that a coordinate transformation matrix must be proper, real, and orthogonal. A transformation matrix can be thought of as optimal in the least-squares sense if it maps the measurement vectors to the reference vectors with minimal 2-norm errors and meets the above constraint. This constrained optimization problem is known as Wahba's problem. Several algorithms which solve Wahba's problem exactly have been developed and used. These algorithms, while steadily improving, are all rather complicated. Furthermore, they involve such numerically unstable or sensitive operations as matrix determinant, matrix adjoint, and Newton-Raphson iterations. This paper describes an algorithm which minimizes Wahba's loss function, but without the constraint. When the constraint is ignored, the problem can be solved by a straightforward, numerically stable least-squares algorithm such as QR decomposition. Even though the algorithm does not explicitly take the constraint into account, it still yields a nearly orthogonal matrix for most practical cases; orthogonality only becomes corrupted when the sensor measurements are very noisy, on the same order of magnitude as the attitude rotations. The algorithm can be simplified if the attitude rotations are small enough so that the approximation sin(theta) approximately equals theta holds. We then compare the computational requirements for several well-known algorithms. For the general large-angle case, the QR least-squares algorithm is competitive with all other know algorithms and faster than most. If attitude rotations are small, the least-squares algorithm can be modified to run faster, and this modified algorithm is faster than all but a similarly specialized version of the QUEST algorithm. We also introduce a novel measurement averaging technique which reduces the n-measurement case to the two measurement case for our particular application, a star tracker and earth sensor mounted on an earth-pointed geosynchronous communications satellite. Using this technique, many n-measurement problems reduce to less than or equal to 3 measurements; this reduces the amount of required calculation without significant degradation in accuracy. Finally, we present the results of some tests which compare the least-squares algorithm with the QUEST and FOAM algorithms in the two-measurement case. For our example case, all three algorithms performed with similar accuracy.

Brozenec, Thomas F.↗
DOE OSTI2022

Constraints on ion velocity distributions from fusion product spectroscopy

Abstract Recent inertial confinement fusion experiments have shown primary fusion spectral moments which are incompatible with a Maxwellian velocity distribution description. These results show that an ion kinetic description of the reacting ions is necessary. We develop a theoretical classification of non-Maxwellian ion velocity distributions using the spectral moments. At the mesoscopic level, a monoenergetic decomposition of the velocity distribution reveals there are constraints on the space of spectral moments accessible by isotropic distributions. General expressions for the directionally dependent spectral moments of anisotropic distributions are derived. At the macroscopic level, a distribution of fluid element velocities modifies the spectral moments in a constrained manner. Experimental observations can be compared to these constraints to identify the character and isotropy of the underlying reactant ion velocity distribution and determine if the plasma is hydrodynamic or kinetic.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Discriminating Accretion States via Rotational Symmetry in Simulated Polarimetric Images of M87

In 2017 April, the Event Horizon Telescope observed the shadow of the supermassive black hole at the core of the elliptical galaxy Messier 87. While the original image was constructed from measurements of the total intensity, full polarimetric data were also collected, and linear polarimetric images are expected in the near future. We propose a modal image decomposition of the linear polarization field into basis functions with varying azimuthal dependence of the electric vector position angle. We apply this decomposition to images of ray traced general relativistic magnetohydrodynamics simulations of the Messier 87 accretion disk. Furthermore, for simulated images that are physically consistent with previous observations, the magnitude of the coefficient associated with rotational symmetry, β2, is a useful discriminator between accretion states. We find that at 20 μas resolution, $| {\beta }_{2}| $ is greater than 0.2 only for models of disks with horizon-scale magnetic pressures large enough to disrupt steady accretion. We also find that images with a more radially directed electric vector position angle correspond to models with higher black hole spin. Our analysis demonstrates the utility of the proposed decomposition as a diagnostic framework to improve constraints on theoretical models.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Octet and decuplet baryon σ terms and mass decompositions

We present a comprehensive analysis of the SU(3) octet and decuplet baryon masses and σ terms using high-precision lattice QCD data and chiral SU(3) effective theory with finite range regularization. The effects of various systematic uncertainties, including from the scale setting of the lattice data and the regularization prescriptions, are quantified. We find the pion-nucleon and strange nucleon σ terms to be σ πN = 44(3)(3) MeV and σ Ns = 50(6)(1) MeV, respectively. Furthermore, the results provide constraints on the energy-momentum tensor mass decompositions of the SU(3) octet and decuplet baryons, where we find that the trace anomaly and quark-gluon energies decrease for strange baryons due to their larger strange σ terms.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1991

Balancing antagonistic time and resource utilization constraints in over-subscribed scheduling problems

In this paper, we report work aimed at applying concepts of constraint-based problem structuring and multi-perspective scheduling to an over-subscribed scheduling problem. Previous research has demonstrated the utility of these concepts as a means for effectively balancing conflicting objectives in constraint-relaxable scheduling problems, and our goal here is to provide evidence of their similar potential in the context of HST observation scheduling. To this end, we define and experimentally assess the performance of two time-bounded heuristic scheduling strategies in balancing the tradeoff between resource setup time minimization and satisfaction of absolute time constraints. The first strategy considered is motivated by dispatch-based manufacturing scheduling research, and employs a problem decomposition that concentrates local search on minimizing resource idle time due to setup activities. The second is motivated by research in opportunistic scheduling and advocates a problem decomposition that focuses attention on the goal activities that have the tightest temporal constraints. Analysis of experimental results gives evidence of differential superiority on the part of each strategy in different problem solving circumstances. A composite strategy based on recognition of characteristics of the current problem solving state is then defined and tested to illustrate the potential benefits of constraint-based problem structuring and multi-perspective scheduling in over-subscribe scheduling problems.

Smith, Stephen F.↗
NASA NTRS1991

Control system software, simulation, and robotic applications

All essential existing capabilities needed to create a man-machine interaction dynamics and performance (MMIDAP) capability are reviewed. The multibody system dynamics software program Order N DISCOS will be used for machine and musculo-skeletal dynamics modeling. The program JACK will be used for estimating and animating whole body human response to given loading situations and motion constraints. The basic elements of performance (BEP) task decomposition methodologies associated with the Human Performance Institute database will be used for performance assessment. Techniques for resolving the statically indeterminant muscular load sharing problem will be used for a detailed understanding of potential musculotendon or ligamentous fatigue, pain, discomfort, and trauma. The envisioned capacity is to be used for mechanical system design, human performance assessment, extrapolation of man/machine interaction test data, biomedical engineering, and soft prototyping within a concurrent engineering (CE) system.

Frisch, Harold P.↗
NASA NTRS1992

Integrated controls-structures optimization of a large space structure

General-purpose control and structural codes are applied to a large detailed structural model including objective and constraint functions derived from actual design specifications. The approach is to divide the problem into a controls optimization step, a structural optimization step, and a system level coordination step. The objective is to minimize mass and power consumption with constraints on vibration characteristics, strength, and damping. This decomposition and optimization approach significantly enhances the design of a structure based on the COFS-I Mast Flight System, which is selected as a demonstration problem.

Pasula, S. L.↗
DOE OSTI2021

A Kinetic Monte Carlo Approach for Simulating Cascading Transmission Line Failure

In this work, cascading transmission line failures are studied through a dynamical model of the power system operating under fixed conditions. The power grid is modeled as a stochastic dynamical system where first-principles electromechanical dynamics are excited by small Gaussian disturbances in demand and generation around a specified operating point. In this context, a single line failure is interpreted in a large deviation context as a first escape event across a surface in phase space defined by line security constraints. The resulting system of stochastic differential equations admits a transverse decomposition of the drift, which leads to considerable simplification in evaluating the quasipotential (rate function) and, consequently, computation of exit rates. Tractable expressions for the rate of transmission line failure in a restricted network are derived from large deviation theory arguments and validated against numerical simulations. Extensions to realistic settings are considered, and individual line failure models are aggregated into a Markov model of cascading failure inspired by chemical kinetics. Cascades are generated by traversing a graph composed of weighted edges representing transitions to degraded network topologies. Numerical results indicate that the Markov model can produce cascades with qualitative power-law properties similar to those observed in empirical cascades.

Kinetic Monte Carlo, rare events, Cascading Failur↗
DOE OSTI2022

Stochastic scheduling of generating units with weekly energy storage: A hybrid decomposition approach

We propose a solution method for the large-scale stochastic unit commitment (SUC) problem with weekly-dispatched energy storage and significant weather-dependent stochastic generating capacity. Weekly storage facilities that mostly charge during weekends and discharge during weekdays require a weekly scheduling of generating units, which result in a large-scale optimization problem. This SUC problem is formulated as a two-stage stochastic model and we use the conditional value-at-risk as a risk measure. Using a Benders framework, the proposed solution method decomposes the problem into a mixed-integer linear master problem and linear and continuous subproblems. The master problem corresponds to the first-stage decisions throughout the week and includes all the commitment (binary) variables and their corresponding constraints. The subproblems correspond to the actual dispatch of the generating units on a weekly basis. Based on the success of column-and-constraint generation algorithms to solve robust optimization problems, we improve the low communication between the master problem and the subproblems in the standard Benders decomposition by adding primal variables and constraints from the subproblems to the master problem, which provides a better approximation of the recourse function. Furthermore, our computational experiments demonstrate the effectiveness of the proposed decomposition method using an instance of the South Carolina synthetic system with 90 generating units under 40 scenarios.

25 ENERGY STORAGE↗
NASA NTRS2003

A Graph Based Backtracking Algorithm for Solving General CSPs

Many AI tasks can be formalized as constraint satisfaction problems (CSPs), which involve finding values for variables subject to constraints. While solving a CSP is an NP-complete task in general, tractable classes of CSPs have been identified based on the structure of the underlying constraint graphs. Much effort has been spent on exploiting structural properties of the constraint graph to improve the efficiency of finding a solution. These efforts contributed to development of a class of CSP solving algorithms called decomposition algorithms. The strength of CSP decomposition is that its worst-case complexity depends on the structural properties of the constraint graph and is usually better than the worst-case complexity of search methods. Its practical application is limited, however, since it cannot be applied if the CSP is not decomposable. In this paper, we propose a graph based backtracking algorithm called omega-CDBT, which shares merits and overcomes the weaknesses of both decomposition and search approaches.

Pang, Wanlin↗
DOE OSTI2021

Imposing equilibrium on experimental 3-D stress fields using Hodge decomposition and FFT-based optimization

Here, we present a methodology to impose micromechanical constraints, i.e. stress equilibrium at grain and sub-grain scale, to an arbitrary (non-equilibrated) voxelized stress field obtained, for example, by means of synchrotron X-ray diffraction techniques. The method consists in finding the equilibrated stress field closest (in L 2 -norm sense) to the measured non-equilibrated stress field, via the solution of an optimization problem. The extraction of the divergence-free (equilibrated) part of a general (non-equilibrated) field is performed using the Hodge decomposition of a symmetric matrix field, which is the generalization of the Helmholtz decomposition of a vector field into the sum of an irrotational field and a solenoidal field. The combination of: a) the Euler–Lagrange equations that solve the optimization problem, and b) the Hodge decomposition, gives a differential expression that contains the bi-harmonic operator and two times the curl operator acting on the experimental stress field. These high-order derivatives can be efficiently performed in Fourier space. The method is applied to filter the non-equilibrated parts of a synthetic piecewise constant stress fields with a known ground truth, and stress fields in Gum Metal, a beta-Ti-based alloy measured in-situ using Diffraction Contrast Tomography (DCT). In both cases, the largest corrections were obtained near grain boundaries.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks

One of the open problems in scientific computing is the long-time integration of nonlinear stochastic partial differential equations (SPDEs), especially with arbitrary initial data. We address this problem by taking advantage of recent advances in scientific machine learning and the spectral dynamically orthogonal (DO) and borthogonal (BO) methods for representing stochastic processes. The recently introduced DO/BO methods reduce the SPDE to solving a system of deterministic PDEs and a system of stochastic ordinary differential equations. Specifically, we propose two new physics-informed neural networks (PINNs) for solving time-dependent SPDEs, namely the neural network (NN)-DO/BO methods. The proposed methods incorporate the DO/BO constraints into the loss function (along with the modal decomposition of the SPDE) with an implicit form instead of generating explicit expressions for the temporal derivatives of the DO/BO modes. Hence, the NN-DO/BO methods can overcome some of the drawbacks of the original DO/BO methods. For example, we do not need the assumption that the covariance matrix of the random coefficients is invertible as in the original DO method, and we can remove the assumption of no eigenvalue crossing as in the original BO method. Moreover, the NN-DO/BO methods can be used to solve time-dependent stochastic inverse problems with the same formulation and same computational complexity as for forward problems. Furthermore, we demonstrate the capability of the proposed methods via several numerical examples, namely: (1) A linear stochastic advection equation with deterministic initial condition: we obtain good results with the proposed methods, while the original DO/BO methods cannot be applied directly in this case. (2) Long-time integration of the stochastic Burgers' equation: we show the good performance of NN-DO/BO methods, especially the effectiveness of the NN-BO approach for such problems with many eigenvalue crossings during the whole time evolution, while the original BO method fails. (3) Nonlinear reaction diffusion equation: we consider both the forward problem and the inverse problems, including very noisy initial point values, to investigate the flexibility of the NN-DO/BO methods in handling inverse and mixed type problems. Taken together, these simulation results demonstrate that the NN-DO/BO methods can be employed to effectively quantify uncertainty propagation in a wide range of physical problems, but future work should address the efficiency issue of PINNs for forward problems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1989

Conservative treatment of boundary interfaces for overlaid grids and multi-level grid adaptations

Conservative algorithms for boundary interfaces of overlaid grids are presented. The basic method is zeroth order, and is extended to a higher order method using interpolation and subcell decomposition. The present method, strictly based on a conservative constraint, is tested with overlaid grids for various applications of unsteady and steady supersonic inviscid flows with strong shock waves. The algorithm is also applied to a multi-level grid adaptation in which the next level finer grid is overlaid on the coarse base grid with an arbitrary orientation.

Moon, Young J.↗
NASA NTRS1989

Conservative treatment of boundary interfaces for overlaid grids and multi-level grid adaptations

Conservative algorithms for boundaray interfaces of overlaid grids are presented. The basic method is zeroth order, and is extended to a higher order method using interpolation and subcell decomposition. The present method, strictly based on a conservative constraint, is tested with overlaid grids for various applications of unsteady and steady supersonic inviscid flows with strong shock waves. The algorithm is also applied to a multi-level grid adaptation in which the next level finer grid is overlaid on the coarse base grid with an arbitrary orientation.

Moon, Young J.↗
NASA NTRS1990

Arcjet load characteristics

Experiments were conducted to define the interface characteristics and constraints of 1 kW class arcjets run on simulated decomposition products of hydrazine and power processors. The impacts of power supply output current ripple on arcjet performance were assessed by variation of the ripple frequency from 100 Hz to 100 kHz with 10 percent peak-to-peak ripple amplitude at 1.2 kW. Ripple had no significant effects on thrust, specific impulse or efficiency. The impact of output ripple on thruster lifetime was not assessed. The static and dynamic impedances of the arcjet were quantified with two thrusters of nearly identical configuration. Superposition of an AC component on the DC arc current was used to characterize the dynamic impedance as a function of flow rate and DC current level. A mathematical model was formulated from these data. Both the static and dynamic impedance magnitude were found to be dependent on mass flow rate. The amplitude of the AC component was found to have little effect on the dynamic impedance. Reducing the DC level from 10 to 8 amps led to a large change in the magnitude of the dynamic impedance with no observable phase change. The impedance data compared favorably between the two thrusters.

Hamley, John A.↗
NASA NTRS1990

Arcjet load characteristics

Experiments were conducted to define the interface characteristics and constraints of 1 kW class arcjets run on simulated decomposition products of hydrazine and power processors. The impacts of power supply output current ripple on arcjet performance were assessed by variation of the ripple frequency from 100 Hz to 100 kHz with 10 percent peak-to-peak ripple amplitude at 1.2 kW. Ripple had no significant effects on thrust, specific impulse or efficiency. The impact of output ripple on thruster lifetime was not assessed. The static and dynamic impedances of the arcjet were quantitied with two thrusters of nearly identical configuration. Superposition of an AC component on the DC arc current was used to characterize the dynamic impedance as a function of flow rate and DC current level. A mathematical model was formulated from these data. Both the static and dynamic impedance magnitude were found to be dependent on mass flow rate. The amplitude of the AC component was found to have little effect on the dynamic impedance. Reducing the DC level from 10 to 8 amps led to a large change in the magnitude of the dynamic impedance with no observable phase change. The impedance data compared favorably between the two thrusters.

Hamley, John A.↗
NASA NTRS1993

Assimilation of solids during ascent of magmas from the Bartoy Field of the Baikal Region, Siberia

Most investigators ascribe mare basalt magma genesis to partial melting at depths of approximately 130 to greater than 400 km within the cumulate pile deposited from a lunar magma ocean. Mare basalts share with mid-ocean ridge basalts the characteristic of relative depletion in LREE and other incompatible trace elements that arises from melting within 'used' mantle, from which crust-forming elements have already been separated. Some mare basalt types do not show the classical, La-Nd depleted mare basalt REE distributions; however, some types are isotopically heterogeneous. These differences have been ascribed to assimilation, mainly AFC-style, of KREEPy highland material overlying the source region. Might such assimilation occur during magma ascent through the KREEPy material? To gain information from a terrestrial setting on possible assimilation during ascent, we have studied a suite of Quaternary nepheline-hawalites and nepheline-mugearites from the Bartoy cinder cone complex of the Baikal Rift, Siberia. The Bartoy magmas originated from greater than 80 km deep, and erupted through thick Archean crust. We find evidence for assimilation of approximately 31 wt. percent xenocrysts of garnet, aluminous clinopyroxene, kaersutite, and olivine, all presumably from the basalt source region, but no appreciable assimilation of overlying crust, consistent with isotopic constraints. Magmatic superheat made available by rapid ascent and decomposition accounts adequately for the energy of assimilation; no accompanying fractional crystallization is required or evident.

Haas, Johnson R.↗
NASA NTRS2003

Abstract-Reasoning Software for Coordinating Multiple Agents

A computer program for scheduling the activities of multiple agents that share limited resources has been incorporated into the Automated Scheduling and Planning Environment (ASPEN) software system, aspects of which have been reported in several previous NASA Tech Briefs articles. In the original intended application, the agents would be multiple spacecraft and/or robotic vehicles engaged in scientific exploration of distant planets. The program could also be used on Earth in such diverse settings as production lines and military maneuvers. This program includes a planning/scheduling subprogram of the iterative repair type that reasons about the activities of multiple agents at abstract levels in order to greatly improve the scheduling of their use of shared resources. The program summarizes the information about the constraints on, and resource requirements of, abstract activities on the basis of the constraints and requirements that pertain to their potential refinements (decomposition into less-abstract and ultimately to primitive activities). The advantage of reasoning about summary information is that time needed to find consistent schedules is exponentially smaller than the time that would be needed for reasoning about the same tasks at the primitive level.

Clement, Bradley↗