Cyber-attack on synchrophasor data has become a widely explored area. However, GPS-spoofing and FDIA attacks require different responsive actions. State-estimation based attack detection method works similar way for both types of attacks. It implies that using state-estimation based detection alone doesn’t give the control center enough information about the attack type. This scenario is specifically more critical for those attack detection methods which consider GPS-spoofing attack as another FDIA with falsified phase angle data. Since identifying correct attack type is paramount, we have attempted to develop an algorithm to distinguish these two attacks. Previous researchers exploited low-rank approximation of Hankel Matrix to differentiate between FDIA and physical events. We have demonstrated that, together with angle unwrapping algorithm, low-rank approximation of Hankel Matrix can help us separating GPS-spoofing attack with FDIA. The proposed method is verified with simulation result. It has been demonstrated that the GSA with 3 second time-shift creates a low-rank approximation error 700% higher than that of normal condition, whereas FDIA doesn’t produce any significant change in low-rank approximation error from that of normal condition. Finally, we have proposed a real-time method for successful identification of event, FDIA and GSA. / M.S. / Cyber-attack on synchrophasor data has become a widely explored area. However, GPS-spoofing and FDIA attacks require different responsive actions. State-estimation based attack detection method works similar way for both types of attacks. It implies that using state-estimation based detection alone doesn’t give the control center enough information about the attack type. This scenario is specifically more critical for those attack detection methods which consider GPS-spoofing attack as another FDIA with falsified phase angle data. Since identifying correct attack type is paramount, we have attempted to develop an algorithm to distinguish these two attacks. Previous researchers exploited low-rank approximation of Hankel Matrix to differentiate between FDIA and physical events. We have demonstrated that, together with angle unwrapping algorithm, low-rank approximation of Hankel Matrix can help us separating GPS-spoofing attack with FDIA. The simulation result verifies the next chapter discusses our proposed algorithm on GPS-spoofing attack detection and its ability to distinguish this type of attack from conventional FDIA. The proposed method is verified with simulation result. It has been demonstrated that the GSA with 3 second time-shift creates a low-rank approximation error 700% higher than that of normal condition, whereas FDIA doesn’t produce any significant change in low-rank approximation error from that of normal condition. Finally, we have proposed a real-time method for successful identification of event, FDIA and GSA.

No / This paper presents a new approach to estimate the unknown frequencies of the constituent sinusoids in a noiseless signal. The signal comprising of unknown number of sinusoids of unknown amplitudes and unknown phases is measured in the time domain. The Hankel matrix of measured samples is used as a basis for further analysis in the Pisarenko harmonic decomposition. A new constraint, the Existence Factor (EF), has been introduced in the methodology based on the relationship between the frequencies of the unknown sinusoids and the eigenspace of Hankel matrix of signal's samples. The accuracy of the method has been tested through multiple simulations on different signals with an unknown number of sinusoidal components. Results showed that the proposed method has efficiently estimated all the unknown frequencies.

We aim at expanding the horizon of existing research on cyberattacks against the time-syncrhonized devices such as PMUs and PDCs, along with corresponding countermeasures. We develop a PMU-PDC cybersecurity testbed at Virginia Tech Power and Energy Center (PEC) lab. The testbed is able to simulate real-world GPS-spoofing attack (GSA) and false data injection attack (FDIA) scenarios. Moreover, the testbed can incorporates cyberattack detection algorithm in pseudo real-time. After that, we propose three stealthy attack scenarios that exploit the vulnerabilities of time-synchronization for both PMU and PDC. The next part of this dissertation is the enhancement of Hankel-matrix based bad data detection model. The existing general Hankel-matrix based bad data detection model provide satisfactory performance. However, it fails in differentiating GPS-spoofing attack from FDIA. We propose an enhanced phase angle Hankel-matrix model that can conclusively identify GPS-spoofing attack. Furthermore, we reduce the computational burden for Hankel-matrix based bad data and cyberattack detection models. Finally, we verify the effectiveness of our enhanced Hankel-matrix model for proposed stealthy attack scenarios. / Doctor of Philosophy / Modern power systems incorporate numerous smart metering devices and communication channels to provide better resiliency against hazardous situations. One such metering device is Phasor Measurement Device (PMU), what provides GPS time-synchronized measurements to the system operator. The time-synchronized measurements are critical in ensuring the cyber and physical security of grids. However, like other smart devices, PMUs are susceptible to conventional cyberattacks. In addition to conventional cyberattacks, PMUs are also vulnerable to attacks against its time-synchronization. In this work, we dig deep into the realm of cyberattacks against time-synchronization of PMUs. We propose novel stealthy attacks against PMU time synchronization. Furthermore, we enhance existing attack detection model to conclusively identify such stealthy attacks and implemented the model in cybersecurity testbed that we developed at Virginia Tech.

Pasinaudojant Henkelio matricomis tiriamas elektrokardiogramos ir jos parametrų kompleksiškumas. Po to, elektrokardiogramos fragmentai aprašomi eksponenčių baigtine sume. Taip pat pasiūlytas algoritmas, kaip pasinaudojant koreliacija dvylika standartinių derivacijų pakeisti trimis laisvai pasirenkamomis. / The method how to reinstate standard ECG lead by means of correlation and by three freely chosen ECG leads is suggested in this work. Next method is to evaluate complexity, to analyze, how many components are needed to record ECG and ECG parameters. Also we try to describe ECG fragment using exponential sum.

Medicinoje duomenys dažniausiai yra analizuojami statistiniais metodais. Tačiau šiame darbe elektrokardiogramos (EKG) parametrus tirsime naudodamiesi algebriniais metodais, nes į kiekvieno žmogaus organizmą žvelgiant kaip į sudėtingą ir unikalią kompleksinę sistemą, statistinio tyrimo nepakanka. Egzistuoja specialus algoritmas, leidžiantis funkciją , aprašytą Teiloro eilute arba jos reikšmėmis, išreikšti baigtine eksponenčių suma. Šio darbo tikslas – baigtine eksponenčių suma aproksimuoti EKG parametrų funkcijos dalis, kurios turi baigtinį kompleksiškumą, bei tirti parametrų kompleksiškumo pokyčius ilgame EKG įraše. / Medical data are often analysed using statistical methods. However the aim of this work is to analyse the complexity of some electrocardiogram (ECG) parameters using algebraic mathematical methods, because if we consider a human organism a complex and individual system, the former methods are not adequate. Mainly, we analyse two parameters of ECG: the complexity of R wave amplitude and duration between R waves. The method of Hankel matrices, in which functions of the finite h-rank are written as linear combinations of exponential functions, is used.

No description available.

Spectrally sparse signals arise in many applications of signal processing. A spectrally sparse signal is a mixture of a few undamped or damped complex sinusoids. An important problem from practice is to reconstruct such a signal from partial time domain samples. Previous convex methods have the drawback that the computation and storage costs do not scale well with respect to the signal length. This common drawback restricts their applicabilities to large and high-dimensional signals. The reconstruction of a spectrally sparse signal from partial samples can be formulated as a low-rank Hankel matrix completion problem. We develop two fast and provable non-convex solvers, FIHT and PGD. FIHT is based on Riemannian optimization while PGD is based on Burer-Monteiro factorization with projected gradient descent. Suppose the underlying spectrally sparse signal is of model order r and length n. We prove that O(r^2log^2(n)) and O(r^2log(n)) random samples are sufficient for FIHT and PGD respectively to achieve exact recovery with overwhelming probability. Every iteration, the computation and storage costs of both methods are linear with respect to signal length n. Therefore they are suitable for handling spectrally sparse signals of large size, which may be prohibited for previous convex methods. Extensive numerical experiments verify their recovery abilities as well as computation efficiency, and also show that the algorithms are robust to noise and mis-specification of the model order. Comparing the two solvers, FIHT is faster for easier problems while PGD has a better recovery ability.

Consider the D-optimal designs for the dth-degree polynomial regression model with a bounded and positive weight function on a compact interval. As the degree of the model goes to infinity, we show that the D-optimal design converges weakly to the arcsin distribution. If the weight function is equal to 1, we derive the formulae of the values of the D-criterion for five classes of designs including (i) uniform density design; (ii) arcsin density design; (iii) J_{1/2,1/2} density design; (iv) arcsin support design and (v) uniform support design. The comparison of D-efficiencies among these designs are investigated; besides, the asymptotic expansions and limits of their D-efficiencies are also given. It shows that the D-efficiency of the arcsin support design is the highest among the first four designs.

For noiseless sampled data, we describe the close connections between Prony--like methods, namely the classical Prony method, the matrix pencil method and the ESPRIT method. Further we present a new efficient algorithm of matrix pencil factorization based on QR decomposition of a rectangular Hankel matrix. The algorithms of parameter estimation are also applied to sparse Fourier approximation and nonlinear approximation.

For noiseless sampled data, we describe the close connections between Prony--like methods, namely the classical Prony method, the matrix pencil method and the ESPRIT method. Further we present a new efficient algorithm of matrix pencil factorization based on QR decomposition of a rectangular Hankel matrix. The algorithms of parameter estimation are also applied to sparse Fourier approximation and nonlinear approximation.