We investigate the use of nonconvex approaches to rank minimization problems, an alternative to widely-used convex approaches such as nuclear norm minimization. Nonconvex approaches better capture the structure of the problem and may therefore lead to better solutions. It is envisioned that our analysis of the methods we develop will show that they can be successfully applied to a broad range of problems in compressed sensing, low-rank matrix theory, and low-rank tensor analysis.
One particular application of particular interest is in power systems. Data scarcity has been a major issue for power system monitoring. The current Supervisory Control and Data Acquisition (SCADA) systems typically provide measurements every 2-4 seconds, offering only a steady state view into the power system behavior. Thanks to the American Recovery and Reinvestment Act of 2009, a large number of phasor measurement units (PMUs) have now been installed and constantly provide huge volumes of data about power system operating conditions and energy demand. To date, two thousand multi-channel PMUs are installed in North America, with an average total cost per PMU as high as $40-180K. PMUs can directly measure bus voltage phasors and line current phasors at synchronized time instants. With data rates of 30 or 60 samples per second, these PMUs produce terabytes of data daily, offering dynamic visibility into the power system.
A few recent works proposed detection methods for cyber data attacks, and those methods are specific to particular attack patterns across time. We are developing identification methods for attack patterns that cannot be caught by existing methods. We are also developing a general method that identifies multiple attack patterns simultaneously.
Meng Wang, ECSE, RPI
Joe Chow, ECSE, RPI
Current graduate research assistants:
- April Sagan
Past graduate research assistants:
- Xin Shen
A Penalty Method for Rank Minimization Problems in Symmetric Matrices, Xin Shen and John E. Mitchell. DOI: 10.1007/s10589-018-0010-6. Computational Optimization and Applications, 71(2), pages 353-380, 2018.