Publications

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The problem of missing data is ubiquitous in domains such as biomedical signal processing, network traffic analysis, bibliometrics, social network analysis, chemometrics, computer vision, and communication networks|all domains in which data collection is subject to occasional errors. Moreover, these data sets can be quite large and have more than two axes of variation, e.g., sender, receiver, time. Many applications in those domains aim to capture the underlying latent structure of the data; in other words, they need to factorize data sets with missing entries. If we cannot address the problem of missing data, many important data sets will be discarded or improperly analyzed. Therefore, we need a robust and scalable approach for factorizing multi-way arrays (i.e., tensors) in the presence of missing data. We focus on one of the most well-known tensor factorizations, CANDECOMP/PARAFAC (CP), and formulate the CP model as a weighted least squares problem that models only the known entries. We develop an algorithm called CP-WOPT (CP Weighted OPTimization) using a first-order optimization approach to solve the weighted least squares problem. Based on extensive numerical experiments, our algorithm is shown to successfully factor tensors with noise and up to 70% missing data. Moreover, our approach is significantly faster than the leading alternative and scales to larger problems. To show the real-world usefulness of CP-WOPT, we illustrate its applicability on a novel EEG (electroencephalogram) application where missing data is frequently encountered due to disconnections of electrodes.

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Wind loading from turbulence and gusts can cause damage in horizontal axis wind turbines. These unsteady loads and the resulting damage initiation and propagation are difficult to predict. Unsteady loads enter at the rotor and are transmitted to the drivetrain. The current generation of wind turbine has drivetrain-mounted vibration and bearing temperature sensors, a nacelle-mounted inertial measurement unit, and a nacelle-mounted anemometer and wind vane. Some advanced wind turbines are also equipped with strain measurements at the root of the rotor. This paper analyzes additional measurements in a rotor blade to investigate the complexity of these unsteady loads. By identifying the spatial distribution, amplitude, and frequency bandwidth of these loads, design improvements could be facilitated to reduce uncertainties in reliability predictions. In addition, dynamic load estimates could be used in the future to control high-bandwidth aerodynamic actuators distributed along the rotor blade to reduce the saturation of slower pitch actuators currently used for wind turbine blades. Local acceleration measurements are made along a rotor blade to infer operational rotor states including deflection and dynamic modal contributions. Previous work has demonstrated that acceleration measurements can be experimentally acquired on an operating wind turbine. Simulations on simplified rotor blades have also been used to demonstrate that mean blade loading can be estimated based on deflection estimates. To successfully apply accelerometers in wind turbine applications for load identification, the spectral and spatial characteristics of each excitation source must be understood so that the total acceleration measurement can be decomposed into contributions from each source. To demonstrate the decomposition of acceleration measurements in conjunction with load estimation methods, a flexible body model has been created with MSC.ADAMS{copyright} The benefit of using a simulation model as opposed to a physical experiment to examine the merits of acceleration-based load identification methods is that models of the structural dynamics and aerodynamics enable one to compare estimates of the deflection and loading with actual values. Realistic wind conditions are applied to the wind turbine and used to estimate the operational displacement and acceleration of the rotor. The per-revolution harmonics dominate the displacement and acceleration response. Turbulent wind produces broadband excitation that includes both the harmonics and modal vibrations, such as the tower modes. Power Spectral Density estimates of the acceleration along the span of the rotor blades indicate that the edge modes may be coupled to the second harmonic.

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We examine several conducting spheres moving through a magnetic field gradient. An analytical approximation is derived and an experiment is conducted to verify the analytical solution. The experiment is simulated as well to produce a numerical result. Both the low and high magnetic Reynolds number regimes are studied. Deformation of the sphere is noted in the high Reynolds number case. It is suggested that this deformation effect could be useful for designing or enhancing present protection systems against space debris.

Meaningful computational investigations of many solid mechanics problems require accurate characterization of material behavior through failure. A recent approach to fracture modeling has combined the partition of unity finite element method (PUFEM) with cohesive zone models. Extension of the PUFEM to address crack propagation is often referred to as the extended finite element method (XFEM). In the PUFEM, the displacement field is enriched to improve the local approximation. Most XFEM studies have used simplified enrichment functions (e.g., generalized Heaviside functions) to represent the strong discontinuity but have lacked an analytical basis to represent the displacement gradients in the vicinity of the cohesive crack. As such, the mesh had to be sufficiently fine for the FEM basis functions to capture these gradients.In this study enrichment functions based upon two analytical investigations of the cohesive crack problem are examined. These functions have the potential of representing displacement gradients in the vicinity of the cohesive crack with a relatively coarse mesh and allow the crack to incrementally advance across each element. Key aspects of the corresponding numerical formulation are summarized. Analysis results for simple model problems are presented to evaluate if quasi-static crack propagation can be accurately followed with the proposed formulation. A standard finite element solution with interface elements is used to provide the accurate reference solution, so the model problems are limited to a straight, mode I crack in plane stress. Except for the cohesive zone, the material model for the problems is homogenous, isotropic linear elasticity. The effects of mesh refinement, mesh orientation, and enrichment schemes that enrich a larger region around the cohesive crack are considered in the study. Propagation of the cohesive zone tip and crack tip, time variation of the cohesive zone length, and crack profiles are presented. The analysis results indicate that the enrichment functions based upon the asymptotic solutions can accurately track the cohesive crack propagation independent of mesh orientation. Example problems incorporating enrichment functions for mode II kinematics are also presented. The results yield acceptable crack paths compared with experimental studies. The applicability of the enrichment functions to problems with anisotropy, large strains, and inelasticity is the subject of ongoing studies. Preliminary results for a contrived orthotropic elastic material reflect a decrease in accuracy with increased orthotropy but do not preclude their application to this class of problems.

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Even after decades of research, Li-ion cells still lack thermal stability. A number of approaches, including adding fire retardants or fluoro compounds to the electrolyte to mitigate fire, have been investigated. These additives improved the thermal stability of the cells (only marginally) but not enough for use in transportation applications. Recent investigations indicate that hydrofluoro-ethers are promising as nonflammable additives1. We describe here the results of our studies on electrolytes containing the hydrofluoro-ethers in cells fabricated at Sandia. In particular, we are investigating two solvents as nonflammable additives. These are: (1) 2-trifluoromethyl-3-methoxyperfluoropentane {l_brace}TMMP{r_brace} and (2) 2-trifluoro-2-fluoro-3-difluoropropoxy-3-difluoro-4-fluoro-5-trifluoropentane {l_brace}TPTP{r_brace}. These electrolytes not only have good thermal stability compared to the conventional electrolytes but respectable ionic conductivity. Sandia made 18650 cells successfully completed the formational cycle. The impedance behavior is typical of Li-ion cells.

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