Matrix Pencil Method Research Articles

Investigation of Compression and Reconstruction Methods for Solar Radiation Spectra above, within, and below the Sea Ice in Polar Environments

AbstractTo reduce the amount of data transmitted, while retaining essential information on the original signal after reconstruction, this study investigated three different compression and reconstruction methods for the solar irradiance signals at different levels of the Arctic sea ice. To achieve this, characteristics of solar irradiance at different depths of the Arctic sea ice were analyzed; the solar irradiance profile was measured using a fiber optic spectrometer system at several ice packs from 11 to 25 August 2018, during the ninth Chinese National Arctic Research Expedition. Based on these measurements, three potential methods—fast Fourier transform (FFT), discrete wavelet transform (DWT), and Prony’s method—were selected and applied for the compression and reconstruction of a group of 12 measurements from one profile. The results indicated that the FFT method was generally superior to the DWT method considering the corrected reconstruction rate Rc, under the same compression ratio C. The FFT method had the highest Rc for signals with higher roughness, whereas Prony’s method was more suitable for smoother signals. To ensure that Rc was at least 80% and C was as large as possible, the compression and reconstruction method proposed in this study included the FFT method (C = 6.4) for the signals rougher than 1.5 and Prony’s method employing the matrix pencil method (C = 8) for the smoother signals. The proposed method was successfully verified using an independent group of solar irradiance measurements from another profile in the Arctic sea ice.

A Resolution-Enhanced Sliding Matrix Pencil Method for Evaluation of Harmonics Distortion in Shipboard Microgrids

Due to the rapid adoption of power electronics technology in shipboard microgrids (SMGs) in recent years, harmonic contamination has become now a crucial topic for these power systems. In order to sustain the safety of the electrical power systems, standards for power quality have imposed strict limits on the harmonic distortion allowed. In these standards, the application of the fast Fourier transform (FFT) with a window size of 10/12 cycles is often recommended for the harmonic evaluation. This method is not practical for SMGs due to large variations in load and frequency in a short duration. To address this issue, this article proposes a signal periodicity-independent algorithm to estimate the current harmonic distortion of SMGs by solving an eigenvalue problem with a short transient response. The proposed algorithm, which is based on a resolution-enhanced sliding matrix pencil method (SMPM), is distinguished by its frequency independency feature, and as a result of this, feature system frequency variations and the existence of interharmonics do not affect its accuracy. The evaluation of the proposed method is carried out under the MATLAB software and is experimentally verified via analyzing the electrical power system current of a container ship.

Synthesis of Sparse Planar Arrays With Multiple Patterns by the Generalized Matrix Enhancement and Matrix Pencil

In recent years, the matrix enhancement and matrix pencil method (MEMP) as well as the forward-backward MEMP (FBMEMP) have been successfully applied to reduce the number of antenna elements in the single-pattern planar arrays. This article aims to extend the MEMP and FBMEMP to the synthesis of sparse planar arrays with multiple patterns. The generalized MEMP (GMEMP) first constructs an enhanced matrix for each target pattern according to their data samples, respectively, and then these enhanced matrices are used to form a composite Hankel block matrix. After that, two sets of poles corresponding to two sets of reconstructed location coordinates can be extracted from the principal eigenvectors of the composite Hankel block matrix by the matrix pencil method. The randomized singular value decomposition and Hankel matrix decomposition method are used to accelerate the above extraction process. Then, we make use of improved matching algorithm to pair the two sets of position coordinates to obtain 2-D coordinates. Finally, we use the least-square method to obtain the excitations of sparse planar array elements, which makes the reconstruction process of multiple patterns more stable and accurate. Apart from the above, the GMEMP is also extended to the synthesis of multiple shaped-beam patterns using the generalized forward-backward matrix enhancement and matrix pencil method (GFBMEMP). A series of representative numerical examples show that the proposed methods can reduce the number of elements in the planar arrays efficiently while maintaining the accuracy of all the patterns to be synthesized.

VEXPA: Validated EXPonential Analysis through regular sub-sampling

We present a procedure that adds a number of desirable features to standard exponential analysis algorithms, among which output reliability, a divide-and-conquer approach, the automatic detection of the exponential model order, robustness against some outliers, and the possibility to parallelize the analysis. The key enabler for these features is the introduction of uniform sub-Nyquist sampling through decimation of the dense signal data. We actually make use of possible aliasing effects to recondition the problem statement rather than that we avoid aliasing.In Section 2 the standard exponential analysis is described, including a sensitivity analysis. In Section 3 the ingredients for the new approach are collected, of which good use is made in Section 4 where we essentially bring everything together in what we call VEXPA.Some numerical examples of the new procedure illustrate in Section 5 that the additional features are indeed realized and that VEXPA is a valuable add-on to any stand-alone exponential analysis. While returning a lot of additional output, it maintains a favourable comparison to the CRLB of the underlying method, for which we here choose a matrix pencil method. Moreover, the output reliability of VEXPA is similar to that of atomic norm minimization, whereas its computational complexity is far less.

Adaptive Third-Zone Distance Protection Scheme for Power System Critical Conditions

An adaptive third-zone distance protection scheme is necessary to distinguish between faults and system stressed conditions such as power swing, voltage instability, and load encroachment. Fast and reliable detection of third-zone three-phase fault during these conditions is still a challenging issue. To address this issue and to restrict the cascaded outages, a matrix pencil method (MPM) based supervised detection index (SDI) is developed by utilizing instantaneous current. Using MPM technique the signal is reconstructed. Next, the error between the reconstructed and the original signal is estimated and the mean of the estimated error is then calculated. The absolute maximum value of mean is considered as a detection index in the proposed work. The main objective of the proposed algorithm is to provide precise detection and discrimination of third-zone three-phase fault from stressed operating conditions through an adaptive threshold. Effectiveness of the proposed algorithm is illustrated by simulation studies carried out on the IEEE 39-bus test system and 400 kV Indian Eastern Regional Grid (IERG) using PSCAD/EMTDC software. The results demonstrate that the supervised algorithm can improve power system security during critical operating conditions.

Application of short‐time matrix pencil method for high‐frequency damage detection in structural system

Structural health monitoring (SHM) has been becoming a key element of monitoring and maintenance in modern and smart cities with critical infrastructures. Within the past decade, SHM approaches are widely used in bridges, roads, skyscrapers, critical facilities, and buildings to enhance the public safety and cost efficiencies of infrastructure maintenance under extreme events, such as earthquakes. Several advanced wave-based methods, such as sliding discrete Fourier transform, discrete wavelet transform (DWT), and Hilbert transform were broadly used to detect different failure modes of systems. One of the most important deficiencies associated with the state-of-the-art approaches is their high level of sensitivity to the sampling frequency, measurement noise, and damage-induced pulse parameters. To fill this technical gap, for the first time, this paper proposes a high-frequency damage detection approach based on the short-time matrix pencil method (STMPM) that has been used in electrical engineering lately. The advantage of STMPM compared with the similar approaches is using the complex frequencies that are not used before in damage detection applications. In this study, pounding between two adjacent buildings is considered as a case study of high-frequency damage scenario. The proposed STMPM-based detection technique is compared with DWT with commonly used mother wavelets. According to the simulation results, the STMPM-based detection is more robust compared with DWT-based techniques and has lower sensitivity to the noise parameters and sampling rate.

Lamb wave mode decomposition and reconstruction based on the viscoelastic propagation model

The accurate information of Lamb wave packets, such as amplitude, time of flight, and waveform, are essential for damage detection and evaluation. Due to the dispersive, multimodal, and attenuative characteristics of Lamb waves propagating in viscoelastic media, the desired mode component is difficult to be extracted from response signals. To address this issue, a technique based on the viscoelastic propagation model of Lamb waves is proposed in this article. Different from the conventional frequency–wavenumber domain filtering, the proposed technique achieves mode extraction by estimating the parameters of the viscoelastic propagation model, that is, complex amplitude am(r, ω) and effective complex wavenumber ξm(ω). Benefiting from that, it enables to decompose and reconstruct the desired mode from spatial–temporal measurement data. First, the frequency-dependent effective complex wavenumbers are extracted using the matrix pencil method, where the real parts represent the dispersion and the imaginary parts represent the effective attenuation. After that, the complex amplitudes are obtained by solving linear least-square equations. Finally, the complex amplitude, effective complex wavenumber, and frequency range of the desired mode are picked out to reconstruct the mode component in the time domain. The finite element simulation and experimental results verify the effectiveness of our technique. Furthermore, the performance of the proposed technique in noisy circumstances is analyzed through synthetic signals, which shows a small reconstruction error and a good convergence.

Super-resolution of near-colliding point sources

AbstractWe consider the problem of stable recovery of sparse signals of the form $$\begin{equation*}F(x)=\sum_{j=1}^d a_j\delta(x-x_j),\quad x_j\in\mathbb{R},\;a_j\in\mathbb{C}, \end{equation*}$$from their spectral measurements, known in a bandwidth $\varOmega $ with absolute error not exceeding $\epsilon>0$. We consider the case when at most $p\leqslant d$ nodes $\{x_j\}$ of $F$ form a cluster whose extent is smaller than the Rayleigh limit ${1\over \varOmega }$, while the rest of the nodes is well separated. Provided that $\epsilon \lessapprox \operatorname{SRF}^{-2p+1}$, where $\operatorname{SRF}=(\varOmega \varDelta )^{-1}$ and $\varDelta $ is the minimal separation between the nodes, we show that the minimax error rate for reconstruction of the cluster nodes is of order ${1\over \varOmega }\operatorname{SRF}^{2p-1}\epsilon $, while for recovering the corresponding amplitudes $\{a_j\}$ the rate is of the order $\operatorname{SRF}^{2p-1}\epsilon $. Moreover, the corresponding minimax rates for the recovery of the non-clustered nodes and amplitudes are ${\epsilon \over \varOmega }$ and $\epsilon $, respectively. These results suggest that stable super-resolution is possible in much more general situations than previously thought. Our numerical experiments show that the well-known matrix pencil method achieves the above accuracy bounds.

Improved Active Interference Canceling Algorithms for Real-Time Protection of 2nd/3rd Level Facilities in Electronic Warfare Environment

In an electronic warfare environment, important equipment or facilities of the friendlies are placed in protective facilities to protect against external Electronic Attacks (EA). No matter how well shielded the facility is, some external electromagnetic waves may penetrate through various paths such as power lines or fans, and the electromagnetic waves may be fatal to certain devices due to the structural resonance of the protective facilities. This paper introduced a real-time electromagnetic canceling technique that removes the resonance field inside the protection facility caused by the intended electronic attack from the enemy. The method makes it possible to cancel the process much faster than the conventional ones that have applied the Matrix Pencil Method (MPM). This is because the internal resonant field can be predicted in a closed-form under the assumption that the external electromagnetic wave is a complex exponential function. Longer exposure to Intended Electromagnetic Interference (IEMI) could be fatal for some devices. Therefore, it is imperative to attenuate the noise within a short time, and a method of reducing internal noise in real-time is beneficial for Electronic Protection (EP). The proposed method could be applied as a new technique to protect important protection facilities, rather than the more traditional method called wrapping using the Faraday cage effect.

Data processing in NMR relaxometry using the matrix pencil

The matrix pencil method (MPM) is explored for stable, reproducible data processing in nuclear magnetic resonance (NMR) relaxometry. Data from one-dimensional and two-dimensional relaxometry experiments designed to measure transverse relaxation T2, longitudinal relaxation T1, diffusion coefficient D values, and their correlations in a standard olive oil/water mixture serve as a platform available to any NMR spectroscopist to compare the performance of the MPM to the benchmark inverse Laplace transform (ILT). The data from two practical examples, including the drying of a solvent polymer system and the enzymatic digestion of polysialic acid, were also explored with the MPM and ILT. In the cases considered here, the MPM appears to outperform the ILT in terms of resolution and stability in the determination of fundamental constants for complex materials and mixtures.

Multi-kernel Unmixing and Super-Resolution Using the Modified Matrix Pencil Method

Consider L groups of point sources or spike trains, with the lth group represented by $$x_l(t)$$. For a function $$g:\mathbb {R}\rightarrow \mathbb {R}$$, let $$g_l(t) = g(t/\mu _l)$$ denote a point spread function with scale $$\mu _l > 0$$, and with $$\mu _1< \cdots < \mu _L$$. With $$y(t) = \sum _{l=1}^{L} (g_l \star x_l)(t)$$, our goal is to recover the source parameters given samples of y, or given the Fourier samples of y. This problem is a generalization of the usual super-resolution setup wherein $$L = 1$$; we call this the multi-kernel unmixing super-resolution problem. Assuming access to Fourier samples of y, we derive an algorithm for this problem for estimating the source parameters of each group, along with precise non-asymptotic guarantees. Our approach involves estimating the group parameters sequentially in the order of increasing scale parameters, i.e., from group 1 to L. In particular, the estimation process at stage $$1 \le l \le L$$ involves (i) carefully sampling the tail of the Fourier transform of y, (ii) a deflation step wherein we subtract the contribution of the groups processed thus far from the obtained Fourier samples, and (iii) applying Moitra’s modified Matrix Pencil method on a deconvolved version of the samples in (ii).

Poles Extraction of Underwater Targets Based on Matrix Pencil Method

The majority of the sonic frequency bands used in active sonar detection and identification are within the resonance region of the target. The poles of target are very important characteristics of the resonance region. This paper analyzes and studies the method of extracting poles by using the matrix Pencil Method. A method which can determine the number of poles of underwater target automatically is proposed. It can average the poles that are gathered to synthesize a point as an alternative pole. Then by setting up a reasonable threshold. The poles with the higher energy in the target echo is extracted as the main pole. Aiming at the problem that the main poles of the target are missing or there are false poles in some directions, the main poles extracted from multiple directions of the target are integrated to obtain the final poles of the target. Finally, to prove the feasibility of proposed novel method echo pole extraction, the experiment was conducted in underwater spherical shell and thin rod in a silencing pool.

Boundary switch on/off control approach to simultaneous identification of diffusion coefficient and initial state for one-dimensional heat equation

In this paper, we consider simultaneous reconstruction of diffusion coefficient and initial state for a one-dimensional heat equation through boundary control and measurement. The boundary measurement is proposed to make the system approximately observable, and both the coefficient and initial state are shown to be identifiable by this measurement under a boundary switch on/off control. By a Dirichlet series representation for the observation, we can transform the problem into an inverse process of reconstruction of the spectrum and coefficients for the Dirichlet series in terms of observation. This happens to be the reconstruction of spectral data for an exponential sequence with measurement error, and it enables us to develop an algorithm based on the matrix pencil method in signal analysis. A theoretical error analysis for the algorithm concerning the coefficient reconstruction is carried out for the proposed method. The numerical simulations are presented to verify the proposed algorithm.

Mapping the Physical and Dielectric Properties of Layered Soil Using Short-Time Matrix Pencil Method-Based Ground-Penetrating Radar

This paper presents the mapping of the physical and dielectric properties of layered soil by using ground-penetrating radar (GPR). Poles extracted from the GPR signals by using the short-time matrix pencil method, along with preprocessing, including filtering and antenna calibration, were employed in order to map the physical and dielectric properties of the layered soil. With the proposed system, the conjugate gradient method was also introduced to solve the time-domain inverse problem faced in the antenna calibration. Experimentations were conducted on four different days in Nakhon Ratchasima province in Thailand, which is a potential area for the occurrence of hardpan. These were done based on the hypothesis that the soil properties, such as water content and dielectric constant, should change when the experimentation day changes in spite of the experimentations in the same area. In the experimentations, soil samples were collected using a core method, and their physical and dielectric properties were measured by using a standard laboratory method and a commercial dielectric probe kit. The measured soil properties and extracted poles for each experiment and each soil layer are shown and analyzed. The results indicate that the real part of the dielectric constants, strongly related to water content, can be mapped using extracted natural frequency. In order to map the dielectric properties, i.e. the water content and dielectric constants of the layered soil, the experimental results were fitted to $2^{\mathrm {nd}}$ -order polynomial curve. The largest regression value of the fitted curve was 0.9994. The bulk density, which is a physical property of the soil, distinguishes the soil type here differentiated by different soil layers. According to the experimental results, the hardpan occurred at the second soil layer because its bulk density was higher than 1.8 g/cm 3 . The bulk density was mapped by extracted poles, including damping factors and natural frequencies.

An Efficient Approach for the Synthesis of Large Sparse Planar Array

An innovative noniterative approach based on the matrix enhancement and matrix pencil (MEMP) is proposed for the synthesis of arbitrary sparse planar arrays. In this study, the estimation of array parameters is recast as a 2-D pole extraction problem, and the number of array elements is minimized by the reduced rank processing. Subsequently, the Hankel matrix decomposition algorithm is exploited to accelerate the singular value decomposition (SVD) of the Hankel matrix constructed by the desired pattern samples, which conquers the restriction on the matrix dimension of the sampled Hankel matrix with the increasing of the number of array elements. The MEMP approach is further extended to the synthesis of shaped-beam patterns by using the forward–backward matrix enhancement and matrix pencil method (FBMEMP). A set of representative numerical experiments is provided to validate the effectiveness and advantages of the proposed method.

A DORT-Uniform Diffraction Tomography Algorithm for Through-the-Wall Imaging

Strong reflections of the front wall in a through-the-wall imaging (TWI) system can challenge the detection of the scatterers behind the wall, and cause defocusing and displacement of the images. In this article, a generalized pencil-of-function (GPOF)-based wall mitigation approach is introduced and implemented along with a selective focusing algorithm for TWI. We develop and employ a wideband decomposition of the time-reversal operator (DORT) in conjunction with the uniform diffraction tomographic (UDT) imaging algorithm to image through a stratified medium. Selective focusing is achieved by tracking the singular value decomposition (SVD) of the time-reversal operator over the entire bandwidth of operation. The frequency independent phase of SVD is the main challenge in this process and has been solved by a new approach based on the decomposition formulation of UDT. The formulation of the proposed mitigation algorithm and DORT-UDT are presented along with simulated and measured results for validation. The efficacy of the method is demonstrated on a multistatic TWI system.

A Pole-Extraction Algorithm for Wall Characterization in Through-the-Wall Imaging Systems

Estimation of wall parameters is critical for focused through-the-wall imaging (TWI). In this paper, a novel algorithm based on pole extraction and wall reflection coefficients is presented to accurately estimate the essential parameters of a multi-layered wall. The generalized pencil of function (GPOF) is applied to decompose the frequency-domain received signal into a summation of ordered exponential terms and phase delays. Matching the terms with the multiple wall reflections provides equations for extracting the parameters. A frequency-domain calibration process is proposed to remove the antenna response from the measured wall response. The formulation of the proposed parameter extraction and calibration algorithms is presented along with the simulated and measured results for validation. The efficacy of the method is demonstrated on a real TWI system.

Use of Matrix-Pencil Method for Efficient Islanding Detection in Static DG and a Parallel Comparison With DWT Method

Islanding or nonislanding events in grid-connected distributed generation bring along a typical distinguishable transient signature in its frequency profile. This demarcation leads to the development of a new islanding protection approach, which is based on the estimation of frequency waveform parameter (transient's frequency) by Matrix pencil (MP) method. To demonstrate the efficacy of the proposed MP method, four critical scenarios are considered in this paper for covering all possible disturbance events. These events are also compared along with a discrete wavelet transform (DWT) based islanding detection method in simulations as well as in RT-LAB-based real-time environment. It is noteworthy to mention that the proposed MP method has been found to have a positive edge over the DWT-based method in terms of robustness and chances of misidentification.

Performance analysis of the LS Prony method for estimating parameters of damped sinusoids

The authors address the performance analysis of the least squares (LS) Prony method for estimating the natural frequencies of radar target in the study. Based on the perturbation theory and the Taylor series expansion, the authors get explicit expressions of the mean square error (MSE) of the LS solution, the MSE of the z-plane natural frequencies and the MSE of the s-plane natural frequencies. The validity of the derived expressions is demonstrated by comparing the analytic results with simulation results. For further validation of the results, simulation results of the GPOF method have been used for comparison.

Distance relaying algorithm for phasor measurement unit assisted zone‐3 relays of series compensated wind integrated system

The signals of wind integrated system are contaminated with inter-harmonic components which may result in erroneous calculations of apparent impedance seen by the distance relays. Therefore, it is indispensable to filter these signals before being used by relays. Presently, the measurements obtained from phasor measurement units (PMUs) are effectively used by distance relays for zone-3 protection. However, PMUs use discrete Fourier transform (DFT) algorithm to compute phasors which may produce incorrect results in presence of inter-harmonics. To overcome this issue, a matrix pencil method is proposed as a pre-processing filtering technique for PMU assisted distance relays. The analog input signals to PMUs are filtered by the matrix pencil algorithm to eliminate inter-harmonics present in the signals and the phasors are computed using DFT algorithm. These phasors are utilized by zone-3 distance relays to estimate the impedance trajectories. To test the effectiveness of proposed distance relaying algorithm, IEEE 14-bus system with a series compensated line is integrated with wind energy and is simulated under diverse test cases of different operating conditions. The impacts of fault resistances, type of faults and fault inception angles on the performance of proposed technique are examined and the results are compared with different signal processing techniques.