SEARCH · Search NASA
Results for “ADMM”
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.
Beyond union of subspaces: Subspace pursuit on Grassmann manifold for data representation
Discovering the underlying structure of a high-dimensional signal or big data has always been a challenging topic, and has become harder to tackle especially when the observations are exposed to arbitrary sparse perturbations. Here in this paper, built on the model of a union of subspaces (UoS) with sparse outliers and inspired by a basis pursuit strategy, we exploit the fundamental structure of a Grassmann manifold, and propose a new technique of pursuing the subspaces systematically by solving a non-convex optimization problem using the alternating direction method of multipliers. This problem as noted is further complicated by non-convex constraints on the Grassmann manifold, as well as the bilinearity in the penalty caused by the subspace bases and coefficients. Nevertheless, numerical experiments verify that the proposed algorithm, which provides elegant solutions to the sub-problems in each step, is able to de-couple the subspaces and pursue each of them under time-efficient parallel computation.
Distributed Optimization for Nonrigid Nano-Tomography
Resolution level and reconstruction quality in nano-computed tomography (nano-CT) are in part limited by the stability of microscopes, because the magnitude of mechanical vibrations during scanning becomes comparable to the imaging resolution, and the ability of the samples to resist radiation induced deformations during data acquisition. In such cases, there is no incentive in recovering the sample state at different time steps like in time-resolved reconstruction methods, but instead the goal is to retrieve a single reconstruction at the highest possible spatial resolution and without any imaging artifacts. Here we propose a distributed optimization solver for tomographic imaging of samples at the nanoscale. Our approach solves the tomography problem jointly with projection data alignment, nonrigid sample deformation correction, and regularization. Projection data consistency is regulated by dense optical flow estimated by Farneback's algorithm, leading to sharp sample reconstructions with less artifacts. Synthetic data tests show robustness of the method to Poisson and low-frequency background noise. We accelerated the solver on multi-GPU systems and validated the method on three nano-imaging experimental data sets.
Efficient Algorithms for Convolutional Sparse Representations
When applying sparse representation techniques to images, the standard approach is to independently compute the representations for a set of overlapping image patches. This method performs very well in a variety of applications, but results in a representation that is multi-valued and not optimized with respect to the entire image. Additionally, an alternative representation structure is provided by a convolutional sparse representation, in which a sparse representation of an entire image is computed by replacing the linear combination of a set of dictionary vectors by the sum of a set of convolutions with dictionary filters. The resulting representation is both single-valued and jointly optimized over the entire image. While this form of a sparse representation has been applied to a variety of problems in signal and image processing and computer vision, the computational expense of the corresponding optimization problems has restricted application to relatively small signals and images. Here, this paper presents new, efficient algorithms that substantially improve on the performance of other recent methods, contributing to the development of this type of representation as a practical tool for a wider range of problems.
Modeling Alzheimer’s Disease Progression with Fused Laplacian Sparse Group Lasso
Alzheimer’s disease (AD), the most common type of dementia, not only imposes a huge financial burden on the health care system, but also a psychological and emotional burden on patients and their families. There is furthermore an urgent need to infer trajectories of cognitive performance over time and identify biomarkers predictive of the progression. Here, we introduce the multi-task learning with fused Laplacian sparse group lasso model, which can identify biomarkers closely related to cognitive measures due to its sparsity-inducing property, and model the disease progression with a general weighted (undirected) dependency graphs among the tasks. An efficient alternative directions method of multipliers based optimization algorithm is derived to solve the proposed non-smooth objective formulation. The effectiveness of the presented model is demonstrated by its superior prediction performance over multiple state-of-the-art methods and accurate identification of compact sets of cognition-relevant imaging biomarkers that are consistent with prior medical studies.
Decomposable Formulation of Transmission Constraints for Decentralized Power Systems Optimization
One of the most complicating factors in decentralized solution methods for a broad range of power system optimization problems is the modeling of power flow equations. Existing formulations for direct current power flows either have limited scalability or are very dense and unstructured, making them unsuitable for large-scale decentralized studies. Here, in this work, we present a novel sparsified variant of the injection shift factors formulation, which has a decomposable block-diagonal structure and scales well for large systems. We also propose a decentralized solution method, based on the alternating direction multiplier method, that efficiently handles transmission line outages in N-1 security requirements. Benchmarks on multizonal security-constrained unit commitment problems show that the proposed formulation and algorithm can reliably and efficiently solve interconnection-level test systems with up to 6,515 buses with no convergence or numerical issues.
A New Distributed Optimization for Community Microgrids Scheduling
This paper proposes a distributed optimization model for community microgrids considering the building thermal dynamics and customer comfort preference. The microgrid central controller (MCC) minimizes the total cost of operating the community microgrid, including fuel cost, purchasing cost, battery degradation cost and voluntary load shedding cost based on the customers' consumption, while the building energy management systems (BEMS) minimize their electricity bills as well as the cost associated with customer discomfort due to room temperature deviation from the set point. The BEMSs and the MCC exchange information on energy consumption and prices. When the optimization converges, the distributed generation scheduling, energy storage charging/discharging and customers' consumption as well as the energy prices are determined. In particular, we integrate the detailed thermal dynamic characteristics of buildings into the proposed model. The heating, ventilation and air-conditioning (HVAC) systems can be scheduled intelligently to reduce the electricity cost while maintaining the indoor temperature in the comfort range set by customers. Numerical simulation results show the effectiveness of proposed model.
Peak Load Management in Distribution Systems Using Legacy Utility Equipment and Distributed Energy Resources
This presentation provides an overview of peak load management in distribution systems using legacy utility equipment and distributed energy resources.
Efficient Network Partitioning: Application for Decentralized State Estimation in Power Distribution Grids: Preprint
Increase in the proliferation of DERs requires real-time situational awareness for efficient grid operations. State estimation plays an important role for real time control and management of the power grid. As the sensing infrastructure grows, aggregating and handling high volumes of data at a centralized location is extremely difficult. To address this challenge, this paper first proposes a novel and efficient hierarchical spectral clustering-based network partition algorithm followed by a decentralized compressive sensing (DCS) based state estimation. The applicability of the proposed network partitioning algorithm is tested on IEEE-123 bus, IEEE-8500 node, and a 6204-node distribution network. The results shows that the proposed approach efficiently divides the network into multiple sub-networks with the minimum edge connections among the neighbors. Then, we perform DCS-based state estimation on the 6204-node distribution network after dividing the network into 18 optimal partitions. Simulation results show that DCS-based state estimation recovers the system states with high accuracy and low complexity.