Spectrum Estimation Research Articles

Harmonic-wavelet approach for response spectrum estimation of vehicle and bridge systems with uncertain parameters subjected to stochastic excitation

Vehicle and bridge systems (VBSs) are subjected to stochastic excitations. Significant research effort has been devoted to the stochastic response analysis of VBSs. In most previous studies, VBSs have been treated as deterministic systems with certain parameters. However, the real VBSs always have uncertain parameters, such as the mass and spring stiffness of the vehicles and elastic modulus of the bridge material, which significantly affect the response power spectrum (RPS) estimation. Moreover, the equations of motion of the VBSs are essentially second-order differential equations with time-dependent and random coefficient matrices, and the excitation-response spectral relation cannot be directly described using the frequency response functions. These properties render the available methods unsuitable for the RPS estimation of the VBSs when both structural uncertainty and stochastic excitations are considered. In the present study, a harmonic-wavelet approach is proposed to estimate the time-varying RPSs of the VBSs with random parameters. The second-order differential equations of motion of VBSs with random parameters are first transformed into linear algebraic equations with random coefficient matrices using a harmonic-wavelet analysis technique; then, the excitation-response spectral relation of VBSs is derived based on these linear algebraic equations. Finally, the RPSs of VBSs with uncertain parameters are solved using the perturbation technique. The accuracy of the proposed method was verified by comparing it with the Monte Carlo method using a numerical example of railway VBS. The numerical simulation results show that the parameter uncertainties significantly affect the RPSs of the VBSs and increase the amplitude of the time-varying RPSs. The uncertainty of vehicle stiffness was the most sensitive factor for vehicle RPSs, and the bridge elastic modulus was the most sensitive factor for the bridge RPSs.

A High-Precision Baseline Calibration Method Based on Estimation of Azimuth Fringe Frequency with THz Interferometry SAR

In this study, repeat-pass synthetic aperture radar interferometry (repeat-pass THz InSAR) is first extended to the terahertz band, and it has tremendous potential in the application of high-resolution three-dimensional (3D) imaging due to its shorter wavelength, larger bandwidth, and greater sensitivity to elevation variation. The super-resolution and high sensitivity of THz InSAR pose greater demands on the baseline calibration for high-precision digital elevation model (DEM) generation. To meet the elevation accuracy requirement of THz InSAR, we propose a baseline calibration method relying on the estimation of the azimuth fringe frequency (EAFF) of the interferometric phase. Initially, a model for non-parallel sampling path errors within the squint SAR repeat-pass interferometry was established, and then, we conducted the theoretical analysis of the phase errors induced by the non-parallel errors. Following this, using a reference DEM, the relationship between the fringe frequency of the error phase and the bias in the repeat-path positioning was established. This allowed the estimation of the position errors to be transformed into the frequency spectrum estimation based on the FFT, which would mitigate the impact of unknown SAR sampling positions. Ultimately, we investigated the accuracy of the proposed EAFF calibration method, and the simulation showed that it can achieve the theoretical accuracy when the correlation coefficient exceeds 0.3. Furthermore, we configured the repeat-pass THz InSAR system with the 0.3 THz stepped-frequency radar. Compared to the conventional calibration based on ground control points (GCPs), the 3D reconstruction of both a knife and a terrain model, calibrated using the proposed EAFF algorithm, demonstrated that the elevation accuracy can achieve millimeter-level precision across the entire image swath. The above results also proved the great potential of THz InSAR in high-precision 3D imaging and remote sensing.

Spectrum Estimation and Optimal Secondary User Selection in Cognitive Radio Networks

Spectrum Estimation and Optimal Secondary User Selection in Cognitive Radio Networks

Optimal Frequency-domain Analysis for Spacecraft Time Series: Introducing the Missing-data Multitaper Power Spectrum Estimator

While the Lomb–Scargle periodogram is foundational to astronomy, it has a significant shortcoming: the variance in the estimated power spectrum does not decrease as more data are acquired. Statisticians have a 60 yr history of developing variance-suppressing power spectrum estimators, but most are not used in astronomy because they are formulated for time series with uniform observing cadence and without seasonal or daily gaps. Here we demonstrate how to apply the missing-data multitaper power spectrum estimator to spacecraft data with uniform time intervals between observations but missing data during thruster fires or momentum dumps. The F-test for harmonic components may be applied to multitaper power spectrum estimates to identify statistically significant oscillations that would not rise above a white noise–based false alarm probability. Multitapering improves the dynamic range of the power spectrum estimate and suppresses spectral window artifacts. We show that the multitaper–F-test combination applied to Kepler observations of KIC 6102338 detects differential rotation without requiring iterative sinusoid fitting and subtraction. Significant signals reside at harmonics of both fundamental rotation frequencies and suggest an antisolar rotation profile. Next we use the missing-data multitaper power spectrum estimator to identify the oscillation modes responsible for the complex “scallop-shell” shape of the K2 light curve of EPIC 203354381. We argue that multitaper power spectrum estimators should be used for all time series with regular observing cadence.

Efficient estimation of directional wave buoy spectra using a reformulated Maximum Shannon Entropy Method: Analysis and comparisons for coastal wave datasets

Directional spectra are a fundamental property of waves, determining how they interact with structures and the wider marine environment. Directional spectra can be estimated (although not directly measured) by wave buoys, the ubiquitous source of in-situ wave and seastate data. The most accurate standard method for estimating the directional spectrum is the Maximum Shannon Entropy Method (MEM-II). However, in practice, speed and numerical convergence issues force engineers to routinely rely on the simpler, but less representative methods such as the Maximum Burg Entropy Method (MEM-I) or one-parameter reconstructions.By reformulating the underlying equations, we have developed a new algorithm (and associated Matlab tool) to accurately and easily generate MEM-II reconstructions, capable of producing a month’s worth of half-hourly spectra in ten minutes. A year’s worth of directional data for six UK coastal locations was analysed using this method. Spectra were compared with those from the simpler cos2s and MEM-I methods, which were seen to produce misleading results for real sea data, including large systematic errors in spectral width. The MEM-II reconstruction also offered insights into directional bimodality for both wind seas and swells.

Altitude measurement method of VHF radar based on spatial smoothing of correlation matrix

For very high frequency (VHF) phased array radar, the key problem to be solved in altitude measurement is the super-resolution spatial spectrum estimation under the condition of coherent sources. The spatial smoothing algorithm is a kind of decorrelation algorithm with excellent properties, but the decorrelation process is at the expense of the effective array aperture. Because it only uses the autocorrelation information of the subspace, its performance is significantly reduced, when the positions of the coherent sources are very close. In order to solve the above problems, this paper proposes an altitude measurement method of VHF radar based on the space smoothing of autocorrelation and cross-correlation matrix, which is used to realize the correlation and super-resolution processing of echo signals and multipath signals. The proposed method does not need to construct a weighting matrix, and can make full use of the received data, enhance the signal components in the equivalent spatial smoothing matrix, reduce the impact of noise, and improve the resolution of coherent sources. The simulation results show that the weighted spatial smoothing method proposed in this paper is correct and effective.

Joint 3D coordinate and wave-speed estimation with nonuniform planar array: Multi-leak localization in gas pipe buried in sandy soil

The acoustic-based methods enable remote detection of gas pipeline leaks and provide the leak area. However, accurate localization of buried leaks within the leak area requires further investigation. In this scenario, the unknown wave speed in soils and the computational complexity associated with three-dimensional (3D) localization in underground spaces pose challenges. Therefore, a joint estimation method based on a specially-designed nonuniform planar array is proposed to determine both the leak position and wave-speed. Specifically, a small-aperture uniform subarray is embedded into the large-aperture nonuniform array. By utilizing the small-aperture subarray, we can solve for the relationship between wave-speed and direction of arrival (DOA) of far-field waves. Subsequently, two-dimensional spectrum estimation is performed using the large-aperture array to obtain estimates for both wave-speed and near-field source distance. Finally, without resorting to 3D spectrum estimation, the 3D coordinates of the leak are determined. Experimental results conducted on buried pipes demonstrate that the proposed method effectively works across three soil types at varying burial depths. Notably high accuracy is achieved using a large-aperture array expended from the uniform L-shaped array with RMSE less than 0.1 m at SNR of 15 dB. Both experimental validations and simulations confirm that the novel approach can be successfully applied in various scenarios.

Investigation on the Utilization of Millimeter-Wave Radars for Ocean Wave Monitoring

The feasibility of using millimeter-wave radars for wave observations was investigated in this study. The radars used in this study operate at a center frequency of 77.572 GHz. To investigate the feasibility of wave observations and extract one-dimensional and two-dimensional wave spectra, arrays consisting of multiple radar units were deployed for observations in both laboratory and field environments. Based on the data measured with the millimeter-wave radars, one-dimensional wave spectra and two-dimensional wave directional spectra were evaluated using the periodogram method and the Bayesian directional spectrum estimation method (BDM), respectively. Meanwhile, wave parameters such as the significant wave height, wave period, and wave direction were also calculated. Via comparative experiments with a capacitive wave height meter in a wave tank and RADAC’s WG5-HT-CP radar in an offshore field, the viability of using millimeter-wave radars to observe water waves was validated. The results indicate that the one-dimensional wave spectra measured with the millimeter-wave radars were consistent with those measured with the mature commercial capacitive wave height meter and the WG5-HT-CP wave radar. Via wave direction measurement experiments conducted in a wave tank and offshore environment, it is evident that the wave directions retrieved with the millimeter-wave radars were in good alignment with the actual wave directions.

A Psychoacoustic Quality Criterion for Path-Traced Sound Propagation.

In developing virtual acoustic environments, it is important to understand the relationship between the computation cost and the perceptual significance of the resultant numerical error. In this paper, we propose a quality criterion that evaluates the error significance of path-tracing-based sound propagation simulators. We present an analytical formula that estimates the error signal power spectrum. With this spectrum estimation, we can use a modified Zwicker's loudness model to calculate the relative loudness of the error signal masked by the ideal output. Our experimental results show that the proposed criterion can explain the human perception of simulation error in a variety of cases.

Fast and accurate wideband sparse spatial spectrum estimation in an underwater strong interference environment.

Wideband sparse spatial spectrum estimation is an important direction-of-arrival (DOA) estimation method that can obtain a high resolution with few snapshots and a low signal-to-noise ratio. However, in an underwater strong interference environment, the accuracy of DOA estimation may be seriously affected, and even the weak targets could be completely masked. In this paper, we propose a fast matrix filter design method based on truncated nuclear norm regularization to attenuate strong interferences while passing weak targets. The matrix filter operator and the exact covariance matrix after filtering can be obtained simultaneously by solving a convex optimization problem that contains the output power term and non-Toeplitz error propagation control term. Then the modified sparse spectrum fitting algorithm based on the matrix filter is used to estimate spatial spectrum over closely spaced wideband signals. Compared with existing methods, the proposed method achieves higher DOA estimation accuracy and lower computational time for matrix filter design. Meanwhile, the estimation accuracy of the proposed method is verified with the experimental results.

Enhanced approach to fusing automatic characteristic frequency extraction and adaptive array signals weighting for abnormal machine sound localization

In this paper, an enhanced approach for sound localization is proposed, which fuses automatic extraction of array signal characteristic frequencies and adaptive weighting. The method refines the autoregressive power spectral estimation algorithm and improves density-based spatial clustering of applications with noise algorithm for characteristic frequency extraction. Adaptive weighting technique is introduced to alleviate the problem of frequency mismatch in the localization process. The initial weight of narrowband signals is calculated and normalized using the frequency domain amplitude integration of narrowband signals, followed by adaptive threshold correction to eliminate invalid narrowband signal weights. The adaptive weight vector improves the localization method’s accuracy and interference suppression. The effectiveness and universality of the proposed method are demonstrated with test data from dry transformers and pumps, and its applicability is shown to extend to various spatial spectrum estimation algorithms and deep learning-based sound source localization techniques.

A Separation Method for Electromagnetic Radiation Sources of the Same Frequency

To separate electromagnetic interference sources with an unknown source number, a new separation method is proposed, which includes five key steps: spatial spectrum estimation, source number and direction-of-arrival estimation, mixed matrix estimation, separation matrix estimation, and source signal recovery. A pseudospatial spectrum estimation network based on a convolutional neural network is proposed to estimate the number of electromagnetic radiation sources, their direction of arrival, and the mixing matrix. A new loss function is designed as an optimization criterion for estimating the separation matrix. To ensure generalization, both simulated and measured datasets are used to train the proposed network. Experimental results demonstrate that the proposed separation method outperforms existing source separation techniques in terms of correlation coefficient, root mean square error, and running time. Importantly, it exhibits strong performance in underdetermined cases, as well as in overdetermined or determined cases.

Quantitative interpretations of potential fields: from parametric to geostructural recalculations

The relevance. Need to development of an applied algorithm for combined interpretation of heterogeneous geophysical data based on unified physical analogy, focused on solving the inverse problem of potential theory. The wave approximation of the cross-section of mining massif fits into the paradigm of dissipative structuring of nonequilibrium media acts as a special case of the above analogy. The task of the study is to adapt this algorithm to recalculations of both potential and non-potential geofields. In the list of nonpotential geofields the remote sensing data and digital terrain model are the most interesting as the data with non-regulated access. Practical significance of the research is associated with the approbation of a family of algorithms in production projects of both geological and engineering nature. The aim. To minimize the family of equivalent solutions to the inverse problem by mutual verification of heterogeneous models of the anomaly-forming source. The objects. Development of the geofields combined interpretation algorithm and recalculation of geofields in depth for tracing elements of stratification and geological fractures. The methods. Formed by software and algorithmic development, which is based on deterministic analytical representations: computation of Cauchy integral, iterative application of direct solution, spectrum estimation. The results. Reduced to the set of parametric cross-sections derived with recalculations with minimum a priori geological information with final geological consideration. The combination of visualizations of analytical continuation, singular points and results of automated fitting admits the reconstruction of geostructural model of parametric cross-section with significant reliability. Extension of standard methods of quantitative interpretation by means of wave approximations includes quasi-seismic halftone visualizations verifying the mentioned reconstructions.

Source Spectra of Pg and Lg Waves from North Korean Nuclear Tests Estimated Using a Nonmodel-Based Approach

ABSTRACT In this article, we demonstrate that source spectra for regional seismic waves generated by an underground explosion may be uniquely extracted using a simple linear regression method between the geometrical spreading corrected displacement spectra and epicentral distances as long as the recording stations are well distributed in distances. Using this method, source spectra of Pg and Lg waves from North Korean nuclear tests conducted between 2009 and 2017 are estimated, respectively, and are compared to test the conjecture of Fisk (2006) as well as to determine the relative size between the seismic moment of Lg waves and that of compressional waves. For a specified explosion, the resultant Pg and Lg source spectra approximately have equal low-frequency source level. Based on this result, it is estimated that for the explosions seismic moment of Lg waves would be about 35% of that of compressional waves. In addition, it is shown the Fisk conjecture approximately stands, as for a specified explosion the observed Pg and Lg source spectra share the same manner of high-frequency rolloff as f−2, the source corner frequency of Lg waves is smaller than that of Pg waves by a factor of about 1/3, and the Pg source spectrum exhibits a prominent overshoot, whereas it is not obvious in corresponding Lg source spectrum. The new method for source spectra estimation may have a promising application prospect in monitoring studies. As an example, it is shown that the yield and even buried depths of the North Korean nuclear explosions may be reasonably estimated by fitting the observed Pg source spectra using an MM71- (Mueller and Murphy, 1971) and DJ91 (Denny and Johnson, 1991)-based hybrid source model suggested by Ford and Walter (2013).

Study of the Reasonable Acquisition Frequency Evaluation Method of Midspan Deflection of Medium- and Small-Span Beam Bridges

The objective of this study is to further promote and apply the structural monitoring system to medium and small bridges, given the relative delays in scientific research, technical specifications, and engineering practice for the safety monitoring of small and medium-span girder bridges, as well as the relative simplicity of the structural system of these bridges, their well-defined forces, and the relatively large proportion of live load responses during operation. These concepts are proposed based on the evaluation method of live loading (As therefore, this paper suggests the notion of sensor acquisition frequency and appropriate acquisition frequency based on the live load assessment method and the fundamental reliability theory). Based on the time-history curve depicting the midspan deflection response of the vehicle-bridge coupling system, the frequency domain analysis reveals that the power spectrum at −3 dB corresponds to the response cutoff frequency. Significantly, the cutoff frequency mentioned is double the acquisition frequency considered suitable for the study. Based on the definition of a quasi-static response, it can be deduced that the velocity of a load does not exert any influence on the quasi-static response of a bridge structure. As a result, the derivation of the components related to the midspan deflection of a bridge’s quasi-static response is presented, together with a recommended set of methodological guidelines for the extraction of finite elements. This study introduces a novel approach for determining the cutoff frequency of the structural response by utilizing the characteristics of amplitude spectrum estimation and power spectrum estimation in frequency domain analysis. The cutoff frequency of the signal is determined by analyzing the amplitude-frequency curve of the power spectrum. Subsequently, the probability density function of the original time-history curve data is estimated based on the amplitude spectrum. Finally, reliability analysis is conducted by calculating the ratio of the amplitude spectrum area of the signal obtained through a reasonable acquisition frequency to the area of the amplitude spectrum function of the original signal. This analysis verifies the reliability of the proposed method for determining the midspan deflection acquisition frequency.

Event Extraction with Spectrum Estimation Using Neural Networks Linear Methods

The timely extraction of event information from enormous amounts of textual data is a critical research problem. Event extraction using deep learning technology has gained academic attention as a result of the fast growth of deep learning. Event extraction requires costly, expert-level, high-quality human annotations. As a result, developing a data-efficient event extraction model that can be trained using only a few labelled samples has emerged as a key difficulty. Existing research work focuses mainly on the structured data with supervised models. The proposed work focuses on Movie Scene Event Extraction, a practical media analysis problem that seeks to extract structured events from unstructured movie screenplays. We suggest using the correlation between various argument roles in situations where different argument roles in a movie scene share similar qualities. This can be beneficial to the Movie Scene Argument Extraction (argument classification and identification) and film scene trigger extraction (Trigger recognition and classifying). In order to represent the relation between different roles in argument and their respective roles, we propose a Superior Concept of Role (SRC) as a top-level idea of a role that is based on the classic argument role, as well as an SRC-based Graph Attention System (GAT). To assess the efficacy of the model we designed, we constructed the dataset MovieSceneEvent to extract movies’ scene-related events. Additionally, we conducted tests on an existing dataset in order to compare results with different models. Results from the experiments like extraction of words, aspect keywords from the documents indicate that our model does better than other models. Furthermore, the information on the relationship between the argument roles helps improve the effectiveness of film scene extraction of events.

Non-stationary astrophysical stochastic gravitational-wave background: A new probe to the high redshift population of binary black holes

Abstract The astrophysical Stochastic Gravitational Wave Background (SGWB) originates from the mergers of compact binary objects that are otherwise undetected as individual events, along with other sources such as supernovae, magnetars, etc. The individual GW signal is time-varying over a time scale that depends on the chirp mass of the coalescing binaries. Another timescale that plays a role is the timescale at which the sources repeat, which depends on the merger rate. The combined effect of these two leads to a breakdown of the time-translation symmetry of the observed SGWB and a correlation between different frequency modes in the signal covariance matrix of the SGWB. Using an ensemble of SGWB due to binary black hole coalescence, calculated using simulations of different black hole mass distributions and merger rates, we show how the structure of the signal covariance matrix varies. This structure in the signal covariance matrix brings additional information about the sources on top of the power spectrum. We show that there is a significant improvement in the Figure of Merit by using this additional information in comparison to only power spectrum estimation for the LIGO-Virgo-KAGRA (LVK) network of detectors with the design sensitivity noise with two years of observation. The inclusion of the off-diagonal correlation in the covariance of the SGWB in the data analysis pipelines will be beneficial in the quest for the SGWB signal in LVK frequency bands as well as in lower frequencies and in getting an insight into its origin.

Multi-taper S-transform method for estimating Wigner-Ville and Loève spectra of quasi-stationary harmonizable processes

Current non-stationary load models based on the evolutionary power spectral density (EPSD) may lead to overestimation and ambiguity of structural responses. The quasi-stationary harmonizable process with its Wigner-Ville spectrum (WVS) and Loève spectrum, which do not suffer from the deficiencies of EPSD, is suitable for modeling non-stationary loads and analyzing their induced structural responses. In this study, the multi-taper S-transform (MTST) method for estimating WVS and Loève spectrum of multi-variate quasi-stationary harmonizable processes is presented. The analytical biases and variances of the WVS, Loève spectrum, and time-invariant and time-varying coherence estimators from the MTST method are provided under the assumption that the target multi-variate harmonizable process is Gaussian. Using a numerical case of a bivariate harmonizable wind speed process, the superiority and reliability of the MTST method are demonstrated through comparisons with several existing methods for the WVS and Loève spectrum estimations. Finally, the MTST method is applied to two pieces of ground motion acceleration records measured during the Turkey earthquake in 2023.

A note on spike localization for line spectrum estimation

A note on spike localization for line spectrum estimation

Inductive Matrix Completion and Root-MUSIC-Based Channel Estimation for Intelligent Reflecting Surface (IRS)-Aided Hybrid MIMO Systems

This paper studies the estimation of cascaded channels in passive intelligent reflective surface (IRS)-aided multiple-input multiple-output (MIMO) systems employing hybrid precoders and combiners. We propose a low-complexity solution that estimates the channel parameters progressively. The angles of departure (AoDs) and angles of arrival (AoAs) at the transmitter and receiver, respectively, are first estimated using inductive matrix completion (IMC) followed by root-MUSIC-based super-resolution spectrum estimation. Forward-backward spatial smoothing (FBSS) is applied to address the coherence issue. Using the estimated AoAs and AoDs, the training precoders and combiners are then optimized and the angle differences between the AoAs and AoDs at the IRS are estimated using the least squares (LS) method followed by FBSS and the root-MUSIC algorithm. Finally, the composite path gains of the cascaded channel are estimated using on-grid sparse recovery with a small-size dictionary. The simulation results suggest that the proposed estimator can achieve improved channel parameter estimation performance with lower complexity as compared to several recently reported alternatives, thanks to the exploitation of the knowledge of the array responses and low-rankness of the channel using low-complexity algorithms at all the stages.