Abstract Phantom scalar fields, as a viable candidate for dark energy, have been instrumental in eliminating spacetime singularities and constructing wormholes and regular black holes. We investigate the Einstein–Maxwell–phantom (EMP) framework, in which the Ellis–Bronnikov wormholes can be charged and regular black holes can be admitted. While the previous study has shown the stability of EMP wormholes under massless scalar field perturbations, we further perform a comprehensive linear analysis of the EMP spacetime through gravito-electromagnetic field perturbations in the axial sector and phantom scalar field perturbations under an approximate treatment in the polar sector. Our analyses of effective potentials and finite difference time profiles reveal the linear instability of EMP wormholes. In the black hole scenario, the quasinormal spectra of Type I black holes, where the matrix-valued direct integration method and the Prony method are used, recover those of general relativity (GR) when the scalar charge goes to zero. Finally, by introducing the concepts of generalized specific charge and mixing angle, we quantify how the relative contributions between the phantom scalar and the electromagnetic fields modify the quasinormal spectra, and we assess the prospects for detecting spectral deviations between the EMP theory and GR in gravitational wave observation.

A Bayes–Prony oscillating modal identification and hierarchical control strategy for low-frequency oscillation (LFO) of a ship microgrid (SM) is presented in this paper. The modal probabilistic estimation of the proposed algorithm replaces point estimation of the traditional Prony method and improves the robustness of modal identification. The hierarchical control strategy first performs modal identification by means of the batch least squares Prony (BLS-Prony) algorithm. The modal identification results are calibrated by the explanatory variance score (EVS), and the control process is transferred to recursive least squares Prony (RLS-Prony) real-time detection. The third layer of decision making transfers to Bayesian Prony (Bayes–Prony) identification in case of a loss of modality or failure of identification. The designed Bayes–Prony algorithm identifies the oscillatory modal of signals with a signal-to-noise ratio (SNR) equal to 2 dB. Compared to BLS-Prony and RLS-Prony, Bayes–Prony reduces the SNR convergence domain of the signal by 30 dB as the last layer of hierarchical control. Therefore, the third-layer decision commands are used as a scheduling reference for damping control in SM power plants. The proposed algorithms and strategies maximize the saving of computational resources while ensuring that the modal identification is effective. Finally, the correctness of the proposed algorithm and strategy is verified by the LFO waveforms of the experimental platform.

Performing Prony method and down sampling factor optimization for power system oscillation analysis

Accurate measurement of broadband signals is fundamental to the broadband oscillation analysis of power grids. However, the measurement process of broadband signals generally suffers from noise interference and insufficient measurement accuracy. To address these issues, this study introduces a novel broadband measurement algorithm that integrates smooth linear segmented threshold (SLST) wavelet denoising with a fusion of the improved variational mode decomposition (VMD) and Prony methods. Initially, noise reduction preprocessing is designed for broadband signals based on the smooth linear segmented threshold wavelet denoising method to reduce the interference of noise on the measurement process, and two evaluation indices are established based on Pearson’s correlation coefficient and the signal-to-noise ratio (SNR) to assess the effectiveness of noise reduction. Subsequently, mutual information entropy and energy entropy are employed to optimize the parameters of VMD to enhance measurement precision. The denoised signal is decomposed into several modes with distinct center frequencies using the parameter-optimized VMD, thereby simplifying the signal processing complexity. Concurrently, the Prony algorithm is integrated to accurately identify the parameters of each mode, extracting frequency, amplitude, and phase information to achieve precise broadband signal measurement. The simulation results confirm that the proposed algorithm effectively reduces noise interference and enhances the measurement accuracy of broadband signals.

Analysing power system oscillations is essential for maintaining electrical grid stability and reliability. To assess power system oscillations and demonstrate the actual application in a real grid system, this research compares two popular signal processing methods: Prony’s approach and the Fast Fourier Transform from Phasor Measurement Unit data in the Java Bali (Indonesia) power system interconnection. FFT gives information about the prominent frequency components by representing system oscillations in the frequency domain. Nevertheless, windowing effects and resolution limitations limit it. By fitting exponential functions to time-domain signals, Prony’s approach, on the other hand, excels at precisely estimating the frequency and damping characteristics of oscillatory modes. The accuracy, computational effectiveness, and applicability for the real-time monitoring of both approaches are assessed in this study. Simulation results on both simulated and actual power system data illustrate the benefits and drawbacks of each strategy. The results show that although FFT is helpful for rapid spectral analysis, Prony’s approach offers more thorough mode identification, which makes it especially advantageous for damping evaluations. This study ends with suggestions for choosing the best method for power system stability analysis based on application requirements.

We investigate the oblique Lanczos method recently put forward in Ref. [1] for analysing Euclidean correlators in lattice field theories and show that it is analytically equivalent to the well known Prony Generalised Eigenvalue Method (PGEVM). Moreover, we discuss that the signal-to-noise problem is not alleviated by either of these two methods. Still, both methods show clear advantages when compared to the standard effective mass approach.

Dynamic harmonic estimation is important for the monitoring and control of power-electronic grids. But the high-precision dynamic harmonic estimation algorithms usually have a heavy computational burden and occupy a large memory space, making them difficult to implement in the embedded platform. Thus, the motivation of this paper lies in providing an estimator with low computational complexity and less storage space consumption. A purely real-valued fast dynamic harmonics estimator is proposed. Firstly, a purely real-valued estimation model is established based on the Taylor series expansion on the time-varying amplitude and phase angle. Secondly, the estimation filter bank is computed in the least-squares sense, and the corresponding estimation error is theoretically analyzed. Finally, the purely real-valued fast dynamic harmonics estimator is designed. The advantage includes significantly reducing the computational complexity and memory space consumption while maintaining high-precision estimation. The testing results show that the proposed estimator can achieve the highest harmonics estimation precision under dynamic conditions. The frequency error, magnitude error, and phase angle error are less than 5 × 10−2 Hz, 7 × 10−1%, and 8 × 10−2 degrees, respectively, which verifies the advantage of high-precision estimation. The proposed estimator achieves a computational speed-up of approximately 430, 396, and 330 times compared to the Prony method, ESPRIT method, and iterative Taylor Fourier transform method, respectively. The computational load rate for executing the proposed estimator on the embedded prototype using C6748 DSP for estimating 50 harmonics is approximately only 2.05%, which verifies the advantage of a low computational load rate.

A 4.75-ft-diameter dynamically scaled proprotor was tested on a semispan wing pylon in airplane mode up to high speeds of 200 kt. Aeroelastic stability data was acquired at two wind tunnels: Navy Carderock tunnel and the University of Maryland Glenn L. Martin tunnel, and for two hub configurations: gimballed and gimbal locked. The data consisted of frequency and damping of beam, chord, and torsion modes of the coupled rotor–wing-pylon system at a Froude-scale rpm of 1050. The eigenvalues were extracted with moving-block and Prony methods and were compared. The tests shed light on the nature of roots in high-speed tiltrotor flight. The key conclusions were the following: 1) the beam and chord damping for the gimballed rotor remained low, around 1–2%; 2) torsion damping was higher, around 3–6%; 3) the gimbal-locked condition increased chord and torsion damping significantly and also changed their trends with speed; 4) the model remained flutter-free up to 200 kt, which is equivalent to 458 kt in full scale; and 5) moving block and Prony are methods equally effective for extracting damping from time-series data for these test conditions.

Paper proposes an approach for improving the complex amplitude parameter estimation in the standard parametric spectral analysis methods. This approach allows to adjust the estimated complex normalized frequency values slightly aiming to improve the estimation of the amplitudes. The method was tested for a mono-frequency signal and for a signal with 4 harmonic frequency components. The test signal length was justified by testing the additive noise for attaining the appropriate probabilistic characteristics. It was shown that proposed method can improve the estimation quality via the Prony's method drastically, letting it exceed the quality of the matrix pencil method in some cases.

Improving Electrical Distance Accuracy for Cable Fault Location Based on the Prony Method

The singularity problem has always been a key focus of physicists’ research. To address this issue, Penrose proposed the cosmic censorship conjecture, with the Strong Cosmic Censorship Conjecture (SCCC) being particularly crucial. However, verifying SCCC in different scenarios still faces many challenges. This paper, set against the background of short-hair black holes, explores whether they obey SCCC when subjected to scalar field perturbations. Using the WKB method, Prony method, Lyapunov exponent, and Weak Gravity Conjecture (WGC), the behavior of a short-hair black hole under different parameter conditions was systematically analyzed. Numerical results indicate that as the charge Q of the short-hair black hole approaches its extremal value, the SCCC is violated. However, as the order k of the metric equation and the angular quantum number ℓ increase, the violation of SCCC is delayed. These results suggest that the proximity of the black hole’s charge Q to its extremal value, along with the size of the angular quantum number ℓ and the order k, play key roles in exploring the physical properties of black holes and verifying SCCC. Finally, research using the WGC shows that when the charge-to-mass ratio in a scalar field meets certain conditions, short-hair black holes can still comply with the SCCC under extreme conditions. This study not only reveals the behavior of short-hair black holes in extreme situations but also offers a new perspective for further exploration of such black holes.

Variations at the event horizon structure of a black hole will emit the signals of the gravitational wave echoes associated with the ringdown of the binary black hole merger. In this work, combining mass model of M87 and Einasto profile for dark matter halo, we construct one formal solution of black holes in dark matter halo, and this solution includes the regular black hole for geometric parameter a<2M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a < 2M$$\\end{document} and the wormhole for a≥2M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a \\ge 2M$$\\end{document}. Then, we test this solution under axial gravitational perturbation and calculate their quasinormal modes (QNM). Our results show that when geometric parameter a>2M\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$a>2M$$\\end{document}, a series of gravitational wave echoes appear after the QNM, and one distinctive feature of gravitational wave echoes is the double barrier. Besides, we also study the impacts of shape parameters α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document} of Einasto profile both on the QNM and gravitational wave echoes, and extract their frequencies using WKB method and Prony method. In principle, with the increasing of shape parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}, the frequencies of the QNM and gravitational wave echoes between the different shape parameters must be different. But now there is zero difference of the frequencies between shape parameter α=0.18\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha =0.18$$\\end{document} and α=0.20\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha =0.20$$\\end{document}. Zero difference is not allowed, so we give an upper limit for shape parameter α\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha $$\\end{document}, which is approximately α<0.18\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha <0.18$$\\end{document}. These signals of gravitational wave echoes in a dark matter halo may be detected in the near future, and these characteristics of gravitational wave echoes may serve as local measurements of dark matter.

Multi-method piecewise low-frequency identification

We show that the first several overtones could be calculated by the time-domain integration method for asymptotically de Sitter black holes already at the lowest multipole numbers of gravitational and electromagnetic perturbations. This is not possible for asymptotically flat black holes, for which extraction of frequencies with the Prony method is usually possible with reasonable accuracy only for the fundamental mode. The reason for much better efficiency in the de Sitter case is the absence of power-law tails: the quasinormal modes dominate the signal not only at the intermediate stage, but also at asymptotically late times.

On the accuracy of Prony's method for recovery of exponential sums with closely spaced exponents

Novel Surface Impedance Formulation via FILT and Prony Method for FDTD Analyses of Lossy Media

Iterative Time-Varying Channel Prediction Based on the Vector Prony Method

Identification of power grids low-frequency oscillations through a combined MEEMD-Prony method

A potential future challenge in the wave energy sector will involve the design and construction of massive wave power farms. That is, collections of several (> 100) wave energy converters (WEC) operating in identical environmental conditions at a distance comparable with typical water wave lengths. In this context, the WECs are likely to be influenced by each another by radiation force effects that are associated with the radiated wave field propagated by WECs operating in the surrounding wave field. These effects are commonly captured by the Cummins’ equation, where the radiation force is expressed as a convolution integral depending on the past values of the WEC response. Due to this mathematical representation, the time domain computation of the wave farm response can become computationally daunting. This article proposes one approach for computing efficiently the wave farm response in the time domain. Specifically, it demonstrates that the values of the radiation force components can be determined at each time step from their previous values by approximating the retardation function matrix elements via the Prony method. A notable advantage of this approach with respect to the ones available in the open literature is that it does not require either the storage of past response values or additional differential equations. Instead, it uses simple algebraic expressions for updating at each time instant the radiation force values. Obviously, this feature can induce significant computational efficiency in analyzing an actual wave farm facility.The reliability and efficiency of the proposed algorithm are assessed vis-à-vis direct time domain comparisons and Monte Carlo data concerning a wave farm composed by an array of U-Oscillating Water Columns. Notably, the proposed methodology can be applied to any linear or nonlinear dynamics problem governed by differential equations involving memory effects.

Abstract Most studies regarding models of tensegrity systems miss the possibility of large static deformations or provide elaborate and lengthy solutions to determine the system dynamics. Contrarily, this work presents a straightforward methodology to find the dynamic characteristics of a guyed tensegrity beam structure, allowing the application of vibration control strategies in conditions of large deformations. The methodology is based on a low-order, adaptive, nonlinear finite element model with pre-stressed components. The method is applied to numerical and experimental models of a class 2 tensegrity structure with a high length-to-width aspect ratio. Image processing and accelerometer data are combined to extract the experimental natural frequencies of the structure, which are compared to numerical results. Prony’s method is applied to estimate damping, and a numerical control strategy is employed using the dynamical model of the structure.