An official website of the United States government
Synchrophasor data suffer from quality issues like missing and bad data. Exploiting the low-rankness of the Hankel matrix of the synchrophasor data, this paper formulates the data recovery problem as a robust low-rank Hankel matrix completion problem and proposes a Bayesian data recovery method that estimates the posterior distribution of synchrophasor data from partial observations. In contrast to the deterministic approaches, our proposed Bayesian method provides an uncertainty index to evaluate the confidence of each estimation. To the best of our knowledge, this is the first method that provides confidence measure for synchrophasor data recovery. Numerical experiments on synthetic data and recorded synchrophasor data demonstrate that our method outperforms existing low-rank matrix completion methods.
more »
« less
This content will become publicly available on July 17, 2026
Accelerating ill-conditioned Hankel matrix recovery via structured Newton-like descent
This paper studies the robust Hankel recovery problem, which simultaneously removes the sparse outliers and fulfills missing entries from the partial observation. We propose a novel non-convex algorithm, coined Hankel structured Newton-like descent (HSNLD), to tackle the robust Hankel recovery problem. HSNLD is highly efficient with linear convergence, and its convergence rate is independent of the condition number of the underlying Hankel matrix. The recovery guarantee has been established under some mild conditions. Numerical experiments on both synthetic and real datasets show the superior performance of HSNLD against state-of-the-art algorithms.
more »
« less
- Award ID(s):
- 2304489
- PAR ID:
- 10632628
- Publisher / Repository:
- IOP Science
- Date Published:
- Journal Name:
- Inverse Problems
- Volume:
- 41
- Issue:
- 7
- ISSN:
- 0266-5611
- Page Range / eLocation ID:
- 075015
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
This work attempts to recover digital signals from a few stochastic samples in time domain. The target signal is the linear combination of one-dimensional complex sine components with R different but continuous frequencies. These frequencies control the continuous values in the domain of normalized frequency [0, 1), contrary to the previous research into compressed sensing. To recover the target signal, the problem was transformed into the completion of a low-rank structured matrix, drawing on the linear property of the Hankel matrix. Based on the completion of the structured matrix, the authors put forward a feasible-point algorithm, analyzed its convergence, and speeded up the convergence with the fast iterative shrinkage-thresholding (FIST) algorithm. The initial algorithm and the speed up strategy were proved effective through repeated numerical simulations. The research results shed new lights on the signal recovery in various fields.more » « less
-
This paper presents time-domain measurement data-based dynamic model parameter estimation for synchronous generators and inverter-based resources (IBRs). While prediction error method (PEM) is a well-known and popular method, it requires a good initial guess of parameters which should be in the domain of convergence. Recently, the system identification community has made significant progress in improving the PEM method by taking into consideration of the characteristics of the low-rank data Hankel matrix. In turn, an estimation problem can be formulated as a rank-constraint optimization problem, and further a difference of convex programming (DCP) problem. This paper adopted the data Hankel matrix fitting strategy and developed the problem formulation for the parameter estimation problems for synchronous generators and IBRs. These two examples are presented and the results are satisfying.more » « less
-
Abstract We consider the problem of recovering the superposition of $$R$$ distinct complex exponential functions from compressed non-uniform time-domain samples. Total variation (TV) minimization or atomic norm minimization was proposed in the literature to recover the $$R$$ frequencies or the missing data. However, it is known that in order for TV minimization and atomic norm minimization to recover the missing data or the frequencies, the underlying $$R$$ frequencies are required to be well separated, even when the measurements are noiseless. This paper shows that the Hankel matrix recovery approach can super-resolve the $$R$$ complex exponentials and their frequencies from compressed non-uniform measurements, regardless of how close their frequencies are to each other. We propose a new concept of orthonormal atomic norm minimization (OANM), and demonstrate that the success of Hankel matrix recovery in separation-free super-resolution comes from the fact that the nuclear norm of a Hankel matrix is an orthonormal atomic norm. More specifically, we show that, in traditional atomic norm minimization, the underlying parameter values must be well separated to achieve successful signal recovery, if the atoms are changing continuously with respect to the continuously valued parameter. In contrast, for the OANM, it is possible the OANM is successful even though the original atoms can be arbitrarily close. As a byproduct of this research, we provide one matrix-theoretic inequality of nuclear norm, and give its proof using the theory of compressed sensing.more » « less
-
Lawrence, N (Ed.)This paper addresses the end-to-end sample complexity bound for learning in closed loop the state estimator-based robust H2 controller for an unknown (possibly unstable) Linear Time Invariant (LTI) system, when given a fixed state-feedback gain. We build on the results from Ding et al. (1994) to bridge the gap between the parameterization of all state-estimators and the celebrated Youla parameterization. Refitting the expression of the relevant closed loop allows for the optimal linear observer problem given a fixed state feedback gain to be recast as a convex problem in the Youla parameter. The robust synthesis procedure is performed by considering bounded additive model uncertainty on the coprime factors of the plant, such that a min-max optimization problem is formulated for the robust H2 controller via an observer approach. The closed-loop identification scheme follows Zhang et al. (2021), where the nominal model of the true plant is identified by constructing a Hankel-like matrix from a single time-series of noisy, finite length input-output data by using the ordinary least squares algorithm from Sarkar et al. (2020). Finally, a H∞ bound on the estimated model error is provided, as the robust synthesis procedure requires bounded additive uncertainty on the coprime factors of the model. Reference Zhang et al. (2022b) is the extended version of this paper.more » « less
