Hybrid computer techniques for determining probability distribution.
Hybrid computer calculation of instantaneous and peak amplitude probability distribution of random signal
COMPUTER METHOD↗
SEARCH · Engineering Papers
Results for “Randomized methods”
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.
Computational methods of robust controller design for aerodynamic flutter suppression
The development of Riccati iteration, a tool for the design and analysis of linear control systems is examined. First, Riccati iteration is applied to the problem of pole placement and order reduction in two-time scale control systems. Order reduction, yielding a good approximation to the original system, is demonstrated using a 16th order linear model of a turbofan engine. Next, a numerical method for solving the Riccati equation is presented and demonstrated for a set of eighth order random examples. A literature review of robust controller design methods follows which includes a number of methods for reducing the trajectory and performance index sensitivity in linear regulators. Lastly, robust controller design for large parameter variations is discussed.
Anderson, L. R.↗
On coherent oscillations of a string.
Vibrations of an elastic string when the separation between the ends varies randomly are studied. The emphasis is on the evolution of the coherent, or ordered, oscillations of the string. Using a perturbation technique borrowed from quantum field theory and the modified Kryloff-Bogoliuboff method, the 'multiple scattering' effect of the random separation between the ends on the linear and nonlinear coherent oscillations are investigated. It is found that due to the random interactions the coherent fundamental oscillation as well as the harmonies are damped. Their frequencies are also modified.
Liu, C. H.↗
First-principles residual resistivity using a locally self-consistent multiple scattering method
The locally self-consistent multiple scattering (LSMS) method can perform efficient first-principles calculations of systems with a large number of atoms. Here, in this paper, we combine the Kubo-Greenwood equation with LSMS, enabling us to calculate the first-principles residual resistivity of large systems. This has been implemented in the open-source code LSMS . We apply this method to selected pure elements and binary random alloys. The results compare well with experiment, and with values obtained from a first-principles effective medium technique (the Korringa-Kohn-Rostoker coherent potential approximation). We discuss future applications of this method to complex systems where other methods are not applicable.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Buckling of cylindrical shells with random imperfections
Buckling of long cylindrical shells with random imperfections subjected to axial loads is treated using the method of truncated hierarchy. A system of homogeneous variational equations is set up to examine the existence of bifurcation in the neighborhood of the equilibrium state. These equations are linear and involve stationary random coefficients. The truncated-hierarchy method is applied, and characteristic equations are obtained. Various exponential cosine correlation functions associated with asymmetric imperfections are examined numerically. Qualitatively, the results obtained are as anticipated.
Fersht, R. S.↗
Recognition and characterization of hierarchical interstellar structure. II - Structure tree statistics
A new method of image analysis is described, in which images partitioned into 'clouds' are represented by simplified skeleton images, called structure trees, that preserve the spatial relations of the component clouds while disregarding information concerning their sizes and shapes. The method can be used to discriminate between images of projected hierarchical (multiply nested) and random three-dimensional simulated collections of clouds constructed on the basis of observed interstellar properties, and even intermediate systems formed by combining random and hierarchical simulations. For a given structure type, the method can distinguish between different subclasses of models with different parameters and reliably estimate their hierarchical parameters: average number of children per parent, scale reduction factor per level of hierarchy, density contrast, and number of resolved levels. An application to a column density image of the Taurus complex constructed from IRAS data is given. Moderately strong evidence for a hierarchical structural component is found, and parameters of the hierarchy, as well as the average volume filling factor and mass efficiency of fragmentation per level of hierarchy, are estimated. The existence of nested structure contradicts models in which large molecular clouds are supposed to fragment, in a single stage, into roughly stellar-mass cores.
Houlahan, Padraig↗
DROP DURABILITY ASSESSMENT OF ELECTRONIC ASSEMBLIES UNDER OFF-AXIS LOADING WITH SKEWED FIXTURES
This thesis studies drop durability of electronic assemblies when the acceleration vector is oriented at 45° to the out-of-plane direction of the circuit card. The off-axis drop tests are accomplished with a skewed fixture and are conducted as a proxy for multiaxial drop testing. Advanced shock testing and vibration test methods have been developed over the last few decades to better represent real-world field environments during ground-based laboratory testing. However, many of these test methods require expensive and specialized equipment not available in most laboratories. An alternative approach for approximating simultaneous loading along multiple axes on conventional equipment utilizes skewed fixtures which have seen use in off-axis random vibration and drop impact testing. These methods generally rely on the conversion of a uniaxial input load from the test equipment (using a uniaxial drop tower or shaker) into a multiaxial load when resolved in the reference frame of the test article (mounted on a skewed fixture). Skewed fixture design is presented and recommendations for conducting skewed angle drop testing are introduced based on local measurements along the skewed face of the fixture to accurately monitor the impact event. Characterization tests were performed with a skewed fixture, at simultaneous acceleration loads from 500 to 3,000 g in two (in-plane and out-of-plane) directions, while meeting standard time domain tolerances. Upon experimental characterization, drop shock durability tests were conducted on a printed circuit assembly (PCA). Mean drops-to-failure were measured and quantified with Weibull statistics. Dominant solder joint failure modes were identified via failure analysis. Prior work on inclined angle impact testing is limited, and the majority of solder joint interconnect level fatigue studies are conducted considering perpendicular loading normal the circuit card. Low-cycle fatigue curves are generated based on plastic strain and plastic work density within the solder joint. A multiscale nonlinear finite element model is used to relate board-level flexure to solder joint interconnect level plastic strain. A high strain rate solder constitutive model allows for accurate modeling of solder plasticity resulting from high-impact drop shock. Fatigue parameters are computed from the Coffin-Manson relation and Palmgren-Miner damage accumulation. This work serves to apply established low-cycle fatigue methods for conventional drop shock loading (impact normal to circuit card) to non-perpendicular loading with a skewed fixture.
Hower, Jonathan [Kansas City National Security Cam↗
Increasing the hardness of posiform planting using random QUBOs for programmable quantum annealer benchmarking
Posiform planting is a method for constructing QUBO instances with a unique planted solution that can be tailored to arbitrary connectivity graphs. In this study we investigate making posiform planted QUBOs computationally harder by fusing many smaller random Ising models, whose global minimum is computed classically, with posiform planted QUBOs. The unique ground state of the resulting QUBO is the concatenation of (exactly one of) the ground states of each smaller problem. Our method generates QUBO instances that have a unique solution, are native to the hardware graph, and have tunable computational hardness. We use our QUBOs to benchmark three D-Wave quantum annealing processors (with 563–5627 qubits), and compare them against simulated annealing and Gurobi. Surprisingly, we find that the D-Wave ground state sampling success rate is not dependent on the glued random QUBO size, and that some QUBO classes are solved at high success rates at short annealing times on the Zephyr processors.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Neuromorphic scaling advantages for energy-efficient random walk computations
Neuromorphic computing, which aims to replicate the computational structure and architecture of the brain in synthetic hardware, has typically focused on artificial intelligence applications. What is less explored is whether such brain-inspired hardware can provide value beyond cognitive tasks. Here we show that the high degree of parallelism and configurability of spiking neuromorphic architectures makes them well suited to implement random walks via discrete-time Markov chains. Overall, these random walks are useful in Monte Carlo methods, which represent a fundamental computational tool for solving a wide range of numerical computing tasks. Using IBM’s TrueNorth and Intel’s Loihi neuromorphic computing platforms, we show that our neuromorphic computing algorithm for generating random walk approximations of diffusion offers advantages in energy-efficient computation compared with conventional approaches. We also show that our neuromorphic computing algorithm can be extended to more sophisticated jump-diffusion processes that are useful in a range of applications, including financial economics, particle physics and machine learning.
97 MATHEMATICS AND COMPUTING↗
Fatigue loading history reconstruction based on the rain-flow technique
Methods are considered for reducing a non-random fatigue loading history to a concise description and then for reconstructing a time history similar to the original. In particular, three methods of reconstruction based on a rain-flow cycle counting matrix are presented. A rain-flow matrix consists of the numbers of cycles at various peak and valley combinations. Two methods are based on a two dimensional rain-flow matrix, and the third on a three dimensional rain-flow matrix. Histories reconstructed by any of these methods produce a rain-flow matrix identical to that of the original history, and as a result the resulting time history is expected to produce a fatigue life similar to that for the original. The procedures described allow lengthy loading histories to be stored in compact form.
Khosrovaneh, A. K.↗
Fatigue loading history reconstruction based on the rainflow technique
Methods are considered of reducing a non-random fatigue loading history to a concise description and then of reconstructing a time history similar to the original. In particular, three methods of reconstruction based on a rainflow cycle counting matrix are presented. A rainflow matrix consists of the numbers of cycles at various peak and valley combinations. Two methods are based on a two-dimensional rainflow matrix, and the third on a three-dimensional rainflow matrix. Histories reconstructed by any of these methods produce a rainflow matrix identical to that of the original history, and the resulting time history is expected to produce a fatigue life similar to that for the original. The procedures described allow lengthy loading histories to be stored in compact form.
Khosrovaneh, A. K.↗
A method for the analysis of nonlinearities in aircraft dynamic response to atmospheric turbulence
An analytical method is developed which combines the equivalent linearization technique for the analysis of the response of nonlinear dynamic systems with the amplitude modulated random process (Press model) for atmospheric turbulence. The method is initially applied to a bilinear spring system. The analysis of the response shows good agreement with exact results obtained by the Fokker-Planck equation. The method is then applied to an example of control-surface displacement limiting in an aircraft with a pitch-hold autopilot.
Sidwell, K.↗
Ab Initio Study of Stability, Local Order, and Phase Diagram For a Series of bcc-based Transition Metal Alloys
In this work, a parameter-free electronic structure approach is applied to the study of stability and chemical order in the 15 substitutional body-centered cubic (bcc)-based alloys made of the six transition metals of groups 5 (V, Nb, Ta) and 6 (Cr, Mo, W) of the periodic table. The method is based on a Green’s function description of the electronic structure of the random alloys. Configurational order is treated within the generalized perturbation method, and temperature effects are examined with a generalized mean-field approach. In contrast to the results summarized in the assessed phase diagrams, stability and ordering trends are predicted in a broad range of alloy composition for at least seven alloys, and explanation is found in their electronic structure properties. Short-range order results, thermodynamics analysis, and bcc-based phase diagrams are also presented.
36 MATERIALS SCIENCE↗
Towards robust surrogate models: Benchmarking machine learning approaches to expediting phase field simulations of brittle fracture
Data-driven approaches have the potential to make modeling complex, nonlinear physical phenomena significantly more computationally tractable. For example, computational modeling of fracture is a core challenge where machine learning techniques have the potential to provide a much needed speedup that would enable progress in areas such as multi-scale modeling and uncertainty quantification. Currently, phase field modeling (PFM) of fracture is one such approach that offers a convenient variational formulation to model crack nucleation, branching and propagation. To date, machine learning techniques have shown promise in approximating PFM simulations. While standard fracture benchmarks represent realistic scenarios frequently observed in practice, they typically do not provide sufficiently challenging tests for data-driven methods. Here, to address this gap, we introduce a challenging dataset based on PFM simulations designed to benchmark and advance ML methods for fracture modeling. This dataset includes three energy decomposition methods, two boundary conditions, and 1000 random initial crack configurations for a total of 6000 simulations. Each sample contains 100 time steps capturing the temporal evolution of the crack field. Alongside this dataset, we also implement and evaluate Physics Informed Neural Networks (PINN), Fourier Neural Operators (FNO), and UNet models as baselines, and explore the impact of ensembling strategies on prediction accuracy. With this combination of our dataset and baseline models drawn from the literature we aim to provide a standardized and challenging benchmark for evaluating machine learning approaches to solid mechanics. Our results highlight both the promise and limitations of popular current models, and demonstrate the utility of this dataset as a testbed for advancing machine learning in fracture mechanics research.
Benchmark dataset↗
Multiscale Concurrent Atomistic-Continuum (CAC) modeling of multicomponent alloys
We report strengthening in complex multicomponent systems such as solid solution alloys is controlled primarily by the dynamic interactions between dislocation lines and heterogeneously distributed solute species. Modeling of extended defect length scales in such multicomponent systems becomes prohibitively expensive, motivating the development of reduced order approaches. This work explores the application of the Concurrent Atomistic-Continuum (CAC) method to model dislocation mobility in random alloys at extended length scales. By employing recently developed average-atom interatomic potentials, the average “bulk” material response in coarse-grained regions interacts with true random solute species in the atomistic-scale domain. We demonstrate that spurious stresses in domain resolution transition regions are eliminated entirely due to the CAC formulation. Simultaneously, the key details of local stress fluctuation due to randomness in the dislocation core region are captured, and fluctuating stress smoothly decays to the long-range dislocation stress field response. Dislocation mobility calculations, for line lengths over 400 nm, are computed as a function of alloy composition in the model FeNiCr system and compared to full molecular dynamics (MD). The results capture the composition-dependent trends, while reducing degrees of freedom by nearly 40%. This approach can be readily extended to any system described by an EAM potential and facilitates the study of large-scale defect dynamics in complex solute environments to support computational alloy design.
36 MATERIALS SCIENCE↗
1-D coupled surface flow and transport equations revisited via the physics-informed neural network approach
The de Saint-Venant equation (SVE) and advection–diffusion equation (ADE) are commonly employed to solve solute transport problems in surface water. In this work, we propose a mesh-free method based on the physics-informed neural network (PINN) to solve the one dimensional (1-D) SVE, ADE, and the coupled SVE and ADE (SVE-ADE) under various initial and boundary conditions. The PINN model extends the architecture of deep neural networks (DNNs) with implementation of loss function, which are additionally subject to constraints imposed by the physical laws of SVE and ADE, along with their initial and boundary conditions. In such a manner, PINNs can be quickly steered to the true solution while obeying the physical laws. The results of PINN model are compared with the analytical and/or numerical solutions under various conditions to investigate its accuracy and efficiency in solving the SVE, ADE, and SVE-ADE. Our results indicate PINN can accurately simulate the shock wave morphology and avoid numerical dissipation in unsteady flow condition. The PINN method outweighed traditional numerical methods in several aspects, including its ability to function with small amounts of data, no grid discretization, and random selection of sampling points, etc. Additionally, the PINN method is also suitable for solving inverse problems with sparse and noisy data. With 1% noise and 2000 initial and boundary condition points (N u ), the errors of the estimated flow rate (v) and diffusion coefficient (D) are 0.003% and 0.105%, respectively, which indicate the accuracy and robustness of the proposed method. Finally, our results indicate the capability and robustness of the proposed PINN methodology for solving multi-physics problems, irrespective of the presence of sparse and noisy data in the training dataset.
54 ENVIRONMENTAL SCIENCES↗
Establishing metrics to quantify spatial similarity in spherical and red blood cell distributions
As computational power increases and systems with millions of red blood cells can be simulated, it is important to note that varying spatial distributions of cells may affect simulation outcomes. Since a single simulation may not represent the ensemble behavior, many different configurations may need to be sampled to adequately assess the entire collection of potential cell arrangements. In order to determine both the number of distributions needed and which ones to run, we must first establish methods to identify well-generated, randomly placed cell distributions and to quantify distinct cell configurations. We utilize metrics to assess (1) the presence of any underlying structure to the initial cell distribution and (2) similarity between cell configurations. We propose the use of the radial distribution function to identify long-range structure in a cell configuration and apply it to a randomly distributed and structured set of red blood cells. To quantify spatial similarity between two configurations, we make use of the Jaccard index, and characterize sets of red blood cell and sphere initializations. As an extension to our work submitted to the International Conference on Computational Science, we significantly increase our data set size from 72 to 1048 cells, include a similar set of studies using spheres, compare the effects of varying sphere size, and utilize the Jaccard index distribution to probe sets of extremely similar configurations. Our results show that the radial distribution function can be used as a metric to determine long-range structure in both distributions of spheres and RBCs. We determine that the ideal case of spheres within a cube versus bi-concave shaped cells within a cylinder affects the shape of the Jaccard index distributions, as well as the range of Jaccard values, showing that both the shape of particle and the domain may play a role. Furthermore, we also find that the distribution is able to capture very similar configurations through Jaccard index values greater than 95% when appending several nearly identical configurations into the data set.
59 BASIC BIOLOGICAL SCIENCES↗
Geometrical defect detection for additive manufacturing with machine learning models
This study proposed a scheme based on Machine Learning (ML) models to detect geometric defects of additively manufactured objects. The ML models are trained with synthetic 3D point clouds with defects and then applied to detect defects in actual production. Using synthetic 3D point clouds rather than experimental data could save a huge amount of training time and costs associated with many prints for each design. Besides distance differences of individual points between source and target point clouds, this scheme uses a new concept called “patch” to capture macro-level information about nearby points for ML training and implementation. Numerical comparisons of prediction results on experimental data with different shapes showed that the proposed scheme outperformed the existing Z-difference method in the literature. Five ML methods (Bagging of Trees, Gradient Boosting, Random Forest, K-nearest Neighbors and Linear Supported Vector Machine) were compared under various conditions, such as different point cloud densities and defect sizes. Bagging and Random Forest were found the two best models regarding predictability; and the right patch size was found to be at 20. The proposed ML-based scheme is applicable to in-situ defect detection during additive manufacturing with the aid of a proper 3D data acquisition system.
Additive manufacturing↗