Prony Method Research Articles

Learning physics by data for the motion of a sphere falling in a non-Newtonian fluid

In this paper, we will introduce a mathematical model of nonlinear jerk equation of velocity v=η1η2v″+1v″+η3v″ to simulate the nonuniform oscillations of the motion of a falling sphere in the non-Newtonian fluid. This differential/algebraic equation is established only by learning the experimental data with the generalized Prony method and sparse optimization method. From the numerical results, our model successfully simulates the sustaining oscillations and abrupt increase during the sedimentation of a sphere through a non-Newtonian fluid. It presents the behavior of a chaotic system which is highly sensitive to initial conditions. More statistical and physical discussions about the dynamical features of the model are provided as well. Our model can be interpreted as a nonlinear elastic system, and includes both the uniform and nonuniform oscillatory motion of the falling sphere.

Robust Data Filtering for Estimating Electromechanical Modes of Oscillation via the Multichannel Prony Method

This paper develops a robust estimator of correlation as a data preprocessing stage to the Prony method that is able to suppress white impulsive noise. The method consists of the following steps. First, the bus voltage magnitudes and phase angles are combined to build a set of complex-valued measurements. Second, the outliers of the complex-valued data samples, which are induced by impulsive noise, are identified and suppressed using the iteratively reweighted phase–phase correlator; the latter is a robust estimator of correlation for complex-valued Gaussian processes, which has been extended here to handle outliers in both magnitude and phase angle of voltage phasor measurements. Finally, the classical Prony method is applied on the robustly estimated voltage phase angles. The good performance of the proposed method is demonstrated through simulations carried out on the two-area four-machine system, on the simplified WECC 179-bus system, as well as on real PMU data. Simulation results show that the method is very fast to compute and is compatible with real-time application requirements.

Straightforward impedance eduction method for non-grazing incidence wave with multiple modes

The control of modern aeroengine noise poses great challenge to the design of acoustic liners, due to the existence of multiple higher-order modes over a very wide frequency range in acoustic nacelles. In order to meet the pressing demand, the straightforward impedance eduction method is further developed such that it can be applied to more general acoustic environment where there are both plane mode and higher-order modes incident upon a test liner. A novelty of the present method is using a diagonally mounted microphone array on the opposite wall of the test liner in a flow duct, thus the measured wall sound pressure simultaneously contains the information of the modes in both the axial and transverse directions. Then, the employment of Prony's method enables the realization of the full modal decomposition to the acoustic field in the flow duct. Numerical experiments simulating acoustic fields with a finite element model are conducted to investigate and validate the feasibility of the present method for both a small-scale and a large-scale flow ducts. Two ceramic tubular liners and a perforated liner are tested as specimens, whose impedance values to be educed are known a priori by means of existing impedance models. Random perturbation is added into the acoustic field data to simulate realistic noisy acoustic environments. The results show that the present method can educe the imposed impedance with a good accuracy when the liner specimens are subjected to the sound field composing of multiple incident modes including several transverse modes in both ducts. The frequency scope of the impedance eduction is considerably extended when compared with the methods restricted by the assumption of plane incident mode, with the upper frequency reaching up to 6.0 kHz and 5.0 kHz for the ducts, respectively. A parametric study indicates that the accuracy of impedance eduction can be promoted by increasing the signal-to-noise ratio and the number of microphones.

Wave forecast and its application to the optimal control of offshore floating wind turbine for load mitigation

Abstract Control algorithms play an important role in energy capture and load mitigation for offshore floating wind turbines (OFWTs). One of the advanced and effective control techniques is the feedforward or model predictive control approach, which requires the forecast of incoming environment conditions. For OFWTs, wave loading is one of the dominant sources to excite structural responses. This study is thus motivated to develop forecasting algorithms for wave elevations and wave excitation forces with the purpose of applying feedforward controllers on OFWTs. Two forecasting algorithms, the approximate Prony Method based on ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) and SVM (Support Vector Machine) regression, are developed and validated using wave records from tank tests. Utilizing the forecasted wave elevations and wave excitation forces, a feedforward LQR controller is designed to mitigate structural loads of an OFWT system.

A new approximation of Fermi-Dirac integrals of order 1/2 for degenerate semiconductor devices

There had been tremendous growth in the field of Integrated circuits (ICs) in the past fifty years. Scaling laws mandated both lateral and vertical dimensions to be reduced and a steady increase in doping densities. Most of the modern semiconductor devices have invariably heavily doped regions where Fermi-Dirac Integrals are required. Several attempts have been devoted to developing analytical approximations for Fermi-Dirac Integrals since numerical computations of Fermi-Dirac Integrals are difficult to use in semiconductor devices, although there are several highly accurate tabulated functions available. Most of these analytical expressions are not sufficiently suitable to be employed in semiconductor device applications due to their poor accuracy, the requirement of complicated calculations, and difficulties in differentiating and integrating. A new approximation has been developed for the Fermi-Dirac integrals of the order 1/2 by using Prony's method and discussed in this paper. The approximation is accurate enough (Mean Absolute Error (MAE) = 0.38%) and easy enough to be used in semiconductor device equations. The new approximation of Fermi-Dirac Integrals is applied to a more generalized Einstein Relation which is an important relation in semiconductor devices.

Signal processing methods for second harmonic generation in thin specimens

This research explores five available signal processing methods: discrete Fourier transform (DFT); least squares method; original Prony method; least squares (LS) Prony method; and known poles (KP) Prony method, to accurately analyze the harmonic content of a tone-burst signal obtained from the second harmonic generation (SHG) measurement. Accurately obtaining the correct frequency content is especially important when the number of cycles is limited by the thickness or high attenuation of a specimen. Results from both numerically generated synthetic signals and experimental data from a specimen demonstrate that the least squares and KP Prony methods provide the most consistent and accurate results for tone-burst signals with low number of cycles. The conventional DFT provides accurate harmonic amplitudes only when the effective number of cycles (neff) is eight or higher. The least squares and KP Prony methods are then applied to a set of thin binary Fe-1.0% Cu alloy specimens where the changes in the nonlinearity parameter, β, as a function of heat treatment time is determined. The β parameters processed with these two methods produce trends that make better physical sense than processing with the original Prony method.

Calm Multi-Baryon Operators

There are many outstanding problems in nuclear physics which require input and guidance from lattice QCD calculations of few baryons systems. However, these calculations suffer from an exponentially bad signal-to-noise problem which has prevented a controlled extrapolation to the physical point. The variational method has been applied very successfully to two-meson systems, allowing for the extraction of the two-meson states very early in Euclidean time through the use of improved single hadron operators. The sheer numerical cost of using the same techniques in two-baryon systems has so far been prohibitive. We present an alternate strategy which offers some of the same advantages as the variational method while being significantly less numerically expensive. We first use the Matrix Prony method to form an optimal linear combination of single baryon interpolating fields generated from the same source and different sink interpolating fields. Very early in Euclidean time this optimal linear combination is numerically free of excited state contamination, so we coin it a calm baryon. This calm baryon operator is then used in the construction of the two-baryon correlation functions.To test this method, we perform calculations on the WM/JLab iso-clover gauge configurations at the SU(3) flavor symmetric point with mπ~ 800 MeV — the same configurations we have previously used for the calculation of two-nucleon correlation functions. We observe the calm baryon significantly removes the excited state contamination from the two-nucleon correlation function to as early a time as the single-nucleon is improved, provided non-local (displaced nucleon) sources are used. For the local two-nucleon correlation function (where both nucleons are created from the same space-time location) there is still improvement, but there is significant excited state contamination in the region the single calm baryon displays no excited state contamination.

Application of the AAK theory and Prony‐like Methods for sparse approximation of exponential sums

AbstractWe derive a new method for optimal ℓ2‐approximation of discrete signals on ℓ2(ℕ0) whose entries can be represented as an exponential sum of finite length. Our approach employs Prony's method in a first step to recover the exponential sum that is determined by the signal. In the second step we use the theory of Adamjan, Arov and Krein (AAK) to derive an algorithm for computing a shorter exponential sum that approximates the original signal in the ℓ2‐norm well. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Sparse phase retrieval of structured signals by Prony's method

AbstractThe phase retrieval problem consists in the recovery of a complex‐valued signal from the magnitudes of its Fourier transform. Restricting ourselves to the case of sparse structured signals f, which can be represented as a linear combination of N arbitrary translations of a given generator function, we show that almost all f can be recovered from 𝒪 (N2) intensity measurements |ℱ[f](ω)| up to trivial ambiguities. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Prony’s Method Under an Almost Sharp Multivariate Ingham Inequality

The parameter reconstruction problem in a sum of Dirac measures from its low frequency trigonometric moments is well understood in the univariate case and has a sharp transition of identifiability with respect to the ratio of the separation distance of the parameters and the order of moments. Towards a similar statement in the multivariate case, we present an Ingham inequality which improves the previously best known dimension-dependent constant from square-root growth to a logarithmic one. Secondly, we refine an argument that an Ingham inequality implies identifiability in multivariate Prony methods to the case of commonly used max-degree by a short linear algebra argument, closely related to a flat extension principle and the stagnation of a generalized Hilbert function.

Efficient anomaly classification for spacecraft reaction wheels

Attitude Determination and Control Subsystem (ADCS) in spacecraft is one of the vital systems for low-earth-orbit spacecraft in which the pointing accuracy is a highly recommended factor to satisfy its mission requirements. When any malfunction takes place at attitude actuator, the spacecraft will not satisfy the required mission objectives. It is required to identify specific faults for attitude actuators in a manner that helps to optimally recover this type of anomaly. An efficient anomaly detection and identification technique is a suitable way to identify such anomaly. This research introduces an accurate and high-performance methodology for fault detection and identification for spacecraft reaction wheels (RW) as (ADCS) actuator. Proposed approach is to differentiate among signatures of possible anomalies that may be occurred at RW like under-voltage, over-voltage, current losses, temperature decrease, and temperature increase. “Prony method,” as a feature extraction technique, is used to discriminate between normal system behavior and anomalies based on the three-axis spacecraft RW operation. A feed-forward neural network with back-propagation algorithm is used for anomaly identification. Prony order assessment is also carried out to obtain the proper order of poles and zeros to minimize the processing time required for identification. The results verify that the proposed anomaly identification is successfully accomplished with high degree of confidence and with minimal execution time. Research approach leads to generic methodology for anomaly identification process among all spacecraft subsystem anomalies.

Spectral analysis of gravitational waves from binary neutron star merger remnants

In this work we analyze the gravitational wave signal from hypermassive neutron stars formed after the merger of binary neutron star systems, focusing on its spectral features. The gravitational wave signals are extracted from numerical relativity simulations of models already considered by De Pietri et al. [Phys. Rev. D 93, 064047 (2016)], Maione et al. [Classical Quantum Gravity 33, 175009 (2016)], and Feo et al. [Classical Quantum Gravity 34, 034001 (2017)], and allow us to study the effect of the total baryonic mass of such systems (from $2.4{M}_{\ensuremath{\bigodot}}$ to $3{M}_{\ensuremath{\bigodot}}$), the mass ratio (up to $q=0.77$), and the neutron star equation of state, in both equal and highly unequal mass binaries. We use the peaks we find in the gravitational spectrum as an independent test of already published hypotheses of their physical origin and empirical relations linking them with the characteristics of the merging neutron stars. In particular, we highlight the effects of the mass ratio, which in the past was often neglected. We also analyze the temporal evolution of the emission frequencies. Finally, we introduce a modern variant of Prony's method to analyze the gravitational wave postmerger emission as a sum of complex exponentials, trying to overcome some drawbacks of both Fourier spectra and least-squares fitting. Overall, the spectral properties of the postmerger signal observed in our simulation are in agreement with those proposed by other groups. More specifically, we find that the analysis of Bauswein and Stergioulas [Phys. Rev. D 91, 124056 (2015)] is particularly effective for binaries with very low masses or with a small mass ratio and that the mechanical toy model of Takami et al. [Phys. Rev. D 91, 064001 (2015)] provides a comprehensive and accurate description of the early stages of the postmerger.

Improvement of Power Systems Stability Using a New Learning Algorithm Based on Lyapunov Theory for Neural Network

In this paper, a new learning algorithm based on Lyapunov stability theory for neural networks is used to improve the power system stability. During the online control process, the identification of system is not necessary, because of learning ability of the proposed controller. One of the proposed controller features is robustness to different operating conditions and disturbances. Moreover, the Prony method is used to obtain the exponential damping of power system oscillations in this paper. The test power systems are a two-area four-machine power system and IEEE 39-bus power system. The simulation results show that the oscillations are satisfactorily damped out by the proposed approach. The proposed approach is effective to mitigate power system oscillations and improve the stability.

Analysis of low frequency oscillations in power system using EMO ESPRIT

Identification of poorly damped low frequency oscillations present in the densely interconnected power system is of paramount importance to maintain its stable operation. Estimation of signal parameters via rotational invariance technique (ESPRIT) is a parametric method used for analysing such signals even under noisy conditions. However, this method requires precise information about the number of modes present in the signal. Hence, this work uses a combination of Exact Model Order (EMO) algorithm and ESPRIT for analysing these low frequency oscillations. The performance of the proposed method is tested using various synthetic signals with different levels of noise and PMU reporting rates. Further, the robustness of the proposed method towards noise resistance is compared with modified Prony, TLS-ESPRIT and ARMA methods. Finally, the proposed method is tested using real time probing test data obtained from Western Electricity Coordinating Council (WECC) network. Results reveal that the proposed method is accurate, precise and outperforms the other methods.

Forward and Backward Extended Prony (FBEP) Method for Power System Small-Signal Stability Analysis

The performance of the Forward and Backward Extended Prony (FBEP) method on power system small-signal stability analysis is investigated in this paper. The effectiveness of the FBEP method in identifying system eigenvalues from the output signal is validated by experiments on a test system model. Using a four-machine-two-area power system model the estimation of the dominant modes contained in oscillatory signals given by the FBEP method is compared with that given by the SVD-TLS method, Trudnowski's algorithm, and the Prony with stepwise regression method. The multi-signal analysis and sliding window analysis using the FBEP method are also studied.

Induction Motor Stator Fault Diagnosis by Rotor Slots Harmonics Tracking Using Prony Improved Approach

The short-circuit fault diagnosis is essential in order to avoid irreversible damages that could affect the stator circuit of the induction motor. For this purpose, this paper addresses a new approach based on Prony's high resolution spectral analysis method to avoid the drawbacks of the well-known method based on the power spectral density estimation by Periodogram technique. This new approach, called Root-Prony, allows a better frequency resolution even on a very short acquisition time as well as a better detection even on very small magnitudes. Moreover, and in order to reduce the computation time of this approach, this paper proposes to analyze only the band around the first rotor slot frequencies. The choice of this band allows avoiding any confusion with the frequency signatures of external phenomena which appear most often in very low frequencies. The experimental results obtained show the efficiency and the reliability of this new approach in tracking the induction motor stator winding degradation.

Data‐driven time–frequency analysis of seismic data using non‐stationary Prony method

ABSTRACTEmpirical mode decomposition aims to decompose the input signal into a small number of components named intrinsic mode functions with slowly varying amplitudes and frequencies. In spite of its simplicity and usefulness, however, empirical mode decomposition lacks solid mathematical foundation. In this paper, we describe a method to extract the intrinsic mode functions of the input signal using non‐stationary Prony method. The proposed method captures the philosophy of the empirical mode decomposition but uses a different method to compute the intrinsic mode functions. Having the intrinsic mode functions obtained, we then compute the spectrum of the input signal using Hilbert transform. Synthetic and field data validate that the proposed method can correctly compute the spectrum of the input signal and could be used in seismic data analysis to facilitate interpretation.

A Robust Prony Method Against Synchrophasor Measurement Noise and Outliers

This letter presents a novel robust prony method for power system oscillatory modes monitoring that is immune to synchrophasor measurement noise and outliers. The conventional least squares for polynomial coefficients estimation is reformulated as a structural weighted total least square (WTLS) estimation problem to mitigate the impact of measurement noise. To enhance the robustness of WTLS for handling gross measurement errors, i.e., outliers, Huber type M-estimator is advocated and solved by means of an iteratively reweighted regression algorithm. Numerical results on the simplified realistic WECC 179-bus system demonstrate the effectiveness and robustness of the proposed method.

Dynamic synchrophasor estimation by Taylor–Prony method in harmonic and non‐harmonic conditions

Dynamic phasor is suitable for analysis of non-stationary signals (such as power swings) in phasor measurement unit. In this study, dynamic phasor of the generated signals during power swing is analysed by a classical signal processing technique known as Prony. The Prony analysis is a useful technique to model a linear sum of damped complex exponential signals. In this study, a combination of the least square-based Prony analysis and Taylor expansion called as Taylor–Prony is proposed to estimate the dynamic phasor. Zeroth-order Taylor–Prony, i.e. static phasor is compared with the second-order Taylor–Prony, i.e. dynamic phasor for illustrating the dynamic phasor capability. Sinusoidal and step changes of amplitude and phase, harmonic condition, frequency tracking tests, noise infiltration and computation time are different tests which are used to validate the proposed method. First, the method is explained theoretically, and then its potential is demonstrated by simulating various numerical signals in MATLAB and measured signals during power swing from three-machine power system simulated in PSCAD. Simulation results show that the proposed method can estimate the dynamic phasor during power swing accurately. Ultimately, the proposed method is compared with six methods which have already presented to verify the capability of the proposed method.

Estimation of dominant mode parameters in power systems using correlation analysis

This paper proposes a hybrid Prony-cross-correlation real-time tracking dominant mode and parameter estimation using simulated and phasor measurement unit (PMU) data. It proposes a new method for detecting the dominant mode during the transient phenomena in electrical power systems. The performance of the proposed method has been compared to some of the existing methods for estimating the frequency and damping factor of a signal under noisy conditions, such as the Prony and EKF methods. In contrast to the traditional Prony and EKF methods for estimating the modes parameters, which require the order of the model and the initial parameters of the mode, the hybrid Prony-cross-correlation does not require any previous information. Three Brazilian systems (reduced, north and NIS) have been studied for both stationary and transient phenomena in power systems to determine the robustness and the accurate estimates even in the presence of noise in the measured signal by the proposed method.