Spectral Estimation Research Articles

High-resolution frequency domain decomposition for modal analysis of bridges using train-induced free-vibrations

Modal parameters are structural inherent characteristics that can be applied for revealing performance of railway bridges. Free vibration signals generated by a passage of train are commonly utilized to estimate the modal parameters of railway bridges due to their higher signal-to-noise ratios compared to random vibrations caused by ambient loads. However, since free vibration signals rapidly decay over time, the available free-vibration data is typically short-time. When using the fast Fourier transform-based spectral estimation method for modal identification from short-time vibration data, a phenomenon known as spectral leakage occurs, leading to miss-identification of some structural modes. In this study, the classical frequency domain decomposition (FDD) is improved for modal identification of railway bridges, in which the higher resolution auto-power spectral density (PSD) and cross-PSD functions are calculated through the autoregressive (AR) model-based method. The AR model-based method improves both the smoothness and resolution of the PSD functions compared to the fast Fourier transform technique. These AR model-based PSD functions are then employed in the FDD process to facilitate frequency and mode shape identification while avoiding spurious noise modes. The proposed eigenvalue fitting technique is subsequently utilized to estimate damping ratios. Numerical simulation data as well as vibration data from an actual bridge are analyzed to validate the proposed method, with a comparison made to the Welch’s PSD-based method. The results demonstrate that the modified FDD approach enables more effective identification of structural modes, even in the presence of closely-spaced modes.

Hyperspectral estimation model of soil organic matter content based on principal gradient grey information

PurposeIn order to explore a new estimation approach of hyperspectral estimation, this paper aims to establish a hyperspectral estimation model of soil organic matter content with the principal gradient grey information based on the grey information theory.Design/methodology/approachFirstly, the estimation factors are selected by transforming the spectral data. The eigenvalue matrix of the modelling samples is converted into grey information matrix by using the method of increasing information and taking large, and the principal gradient grey information of modelling samples is calculated by using the method of pro-information interpolation and straight-line interpolation, respectively, and the hyperspectral estimation model of soil organic matter content is established. Then, the positive and inverse grey relational degree are used to identify the principal gradient information quantity of the test samples corresponding to the known patterns, and the cubic polynomial method is used to optimize the principal gradient information quantity for improving estimation accuracy. Finally, the established model is used to estimate the soil organic matter content of Zhangqiu and Jiyang District of Jinan City, Shandong Province.FindingsThe results show that the model has the higher estimation accuracy, among the average relative error of 23 test samples is 5.7524%, and the determination coefficient is 0.9002. Compared with the commonly used methods such as multiple linear regression, support vector machine and BP neural network, the hyperspectral estimation accuracy of soil organic matter content is significantly improved. The application example shows that the estimation model proposed in this paper is feasible and effective.Practical implicationsThe estimation model in this paper not only fully excavates and utilizes the internal grey information of known samples with “insufficient and incomplete information”, but also effectively overcomes the randomness and grey uncertainty in the spectral estimation. The research results not only enrich the grey system theory and methods, but also provide a new approach for hyperspectral estimation of soil properties such as soil organic matter content, water content and so on.Originality/valueThe paper succeeds in realizing both a new hyperspectral estimation model of soil organic matter content based on the principal gradient grey information and effectively dealing with the randomness and grey uncertainty in spectral estimation.

Type parameter estimation of 2D‐GTD model based on ADMM approach

AbstractThe type parameter helps in scattering mechanism analysis and scattering centre identification. However, current approximate solution methods based on spectral estimation are noise‐sensitive and exhibit low accuracy. In this letter, a high‐precision approach for the type parameter based on the alternating direction method of multipliers (ADMM) is proposed. Logarithmic transformation is used to separate the type parameter and the amplitude from the coupling term, and initially obtain the closed‐form solution of the type parameter. Then, the regularization term of l2‐norm is used for denoising. Finally, a joint optimization model based on ADMM is constructed to effectively estimate the type parameter. Simulation results confirm the high accuracy of the proposed approach.

Ambient Seismic Noise Tomography Within the Floridan Aquifer System, Santa Fe River‐Sink Rise, Florida, US

Ambient Seismic Noise Tomography Within the Floridan Aquifer System, Santa Fe River‐Sink Rise, Florida, US

Iterative Adaptive Based Multi-Polarimetric SAR Tomography of the Forested Areas

Synthetic aperture radar tomography (TomoSAR) is an extension of synthetic aperture radar (SAR) imaging. It introduces the synthetic aperture principle into the elevation direction to achieve three-dimensional (3-D) reconstruction of the observed target. Compressive sensing (CS) is a favorable technology for sparse elevation recovery. However, for the non-sparse elevation distribution of the forested areas, if CS is selected to reconstruct it, it is necessary to utilize some orthogonal bases to first represent the elevation reflectivity sparsely. The iterative adaptive approach (IAA) is a non-parametric algorithm that enables super-resolution reconstruction with minimal snapshots, eliminates the need for hyperparameter optimization, and requires fewer iterations. This paper introduces IAA to tomographicinversion of the forested areas and proposes a novel multi-polarimetric-channel joint 3-D imaging method. The proposed method relies on the characteristics of the consistent support of the elevation distribution of different polarimetric channels and uses the L2-norm to constrain the IAA-based 3-D reconstruction of each polarimetric channel. Compared with typical spectral estimation (SE)-based algorithms, the proposed method suppresses the elevation sidelobes and ambiguity and, hence, improves the quality of the recovered 3-D image. Compared with the wavelet-based CS algorithm, it reduces computational cost and avoids the influence of orthogonal basis selection. In addition, in comparison to the IAA, it demonstrates greater accuracy in identifying the support of the elevation distribution in forested areas. Experimental results based on BioSAR 2008 data are used to validate the proposed method.

Spectral Density Estimation for a Class of Spectrally Correlated Processes

We study the estimation problem of the spectral density function for harmonizable non‐stationary processes. More precisely, we consider spectrally correlated processes whose spectral measure has the support contained in the union of unknown lines with possibly non‐unit slopes. We propose the frequency‐smoothed periodogram along the estimated support line as an estimator of the spectral density function. We show the mean‐square consistency of the proposed estimator. Additionally, we discuss the estimation of the support line in a specific model with its applications in locating a moving source. Finally, we present simulations confirming the proven results.

Asymptotic normality of spectral means of Hilbert space valued random processes

A variety of statistics for functional time series allows for a representation as weighted average of corresponding periodogram operators over the frequency domain. We study consistency and asymptotic normality of such spectral mean estimators under mild assumptions. We show that weak convergence of these estimators can be deduced from the (joint) weak convergence of the sample autocovariance operators. The latter is established for a large class of weakly dependent functional time series, which admit expansions as Bernoulli shifts and the weak dependence is quantified by the condition of L4-m-approximability.

Fully automated operational modal identification based on scale-space peak picking algorithm and power spectral density estimation

Modal analysis is a fundamental and essential research direction in the field of structural engineering. The ultimate goal is to determine the modal parameters of the structures. However, the existing modal analysis algorithms often require a large number of parameter adjustments and manual intervention during operation, which cannot be fully automated. In order to realize the automatic identification of modal parameters, the automatic operational modal identification method (AOMI) is proposed based on the interpolated power spectral density estimation (IPSE). To achieve more precise spectrum analysis in the low-frequency band, IPSE is employed to perform Fourier transform on the original frequency domain segment with optimized frequency resolution. This enhances the sharpness of the obtained spectrum in the low-frequency range, making peak frequencies more discernible. Subsequently, the scale-space peak picking algorithm is used to automatically obtain the peak of the power spectral density (PSD), thus enabling the automatic identification of the natural frequency. Finally, the frequency domain decomposition method (FDD) is used to identify modal parameters based on the natural frequencies. The effectiveness of AOMI is verified through the modal identification of the old steel truss bridge and the three layer framework. Under the environmental excitation, the frequencies identified by the IPSE method is close to that of FDD, Bayesian fast fourier transform (FFT) and covariance driven stochastic subspace identification (SSI-COV). Furthermore, the PSD obtained through IPSE has sharper peak than that of FDD and the Welch’s method. The damping ratio identification accuracy and modal assurance criterion (MAC) are satisfactory in AOMI, which can improve the automatic performance.

Sharp spectral gap estimates for higher-order operators on Cartan–Hadamard manifolds

The goal of this paper is to provide sharp spectral gap estimates for problems involving higher-order operators (including both the clamped and buckling plate problems) on Cartan–Hadamard manifolds. The proofs are symmetrization-free — thus no sharp isoperimetric inequality is needed — based on two general, yet elementary functional inequalities. The spectral gap estimate for clamped plates solves a sharp asymptotic problem from [Q.-M. Cheng and H. Yang, Universal inequalities for eigenvalues of a clamped plate problem on a hyperbolic space, Proc. Amer. Math. Soc. 139(2) (2011) 461–471] concerning the behavior of higher-order eigenvalues on hyperbolic spaces, and answers a question raised in [A. Kristály, Fundamental tones of clamped plates in nonpositively curved spaces, Adv. Math. 367(39) (2020) 107113] on the validity of such sharp estimates in high-dimensional Cartan–Hadamard manifolds. As a byproduct of the general functional inequalities, various Rellich inequalities are established in the same geometric setting.

Sharp interface limit for a Navier–Stokes/Allen–Cahn system in the case of a vanishing mobility

We consider the sharp interface limit of a Navier–Stokes/Allen Cahn equation in a bounded smooth domain in two space dimensions, in the case of vanishing mobility mε=ε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_\\varepsilon =\\sqrt{\\varepsilon }$$\\end{document}, where the small parameter ε>0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon >0$$\\end{document} related to the thickness of the diffuse interface is sent to zero. For well-prepared initial data and sufficiently small times, we rigorously prove convergence to the classical two-phase Navier–Stokes system with surface tension. The idea of the proof is to use asymptotic expansions to construct an approximate solution and to estimate the difference of the exact and approximate solutions with a spectral estimate for the (at the approximate solution) linearized Allen–Cahn operator. In the calculations we use a fractional order ansatz and new ansatz terms in higher orders leading to a suitable ε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon $$\\end{document}-scaled and coupled model problem. Moreover, we apply the novel idea of introducing ε\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varepsilon $$\\end{document}-dependent coordinates.

A Weighted Adaptive Range-Averaging Technique to Improve the Precision Consistency of Polarimetric Variable Fields

Abstract The two main metrics for the performance evaluation of radar-variable estimators are the bias and standard deviation (SD) of estimates. Depending on the estimator properties, the bias may increase as the signal-to-noise ratio (SNR) decreases. The standard deviation, however, always rises as the SNR becomes smaller. For instance, if estimates are computed from 16 samples (typically used for WSR-88D surveillance scans) using a rectangular data window and the maximum unambiguous velocity is ∼9 m s−1, the standard deviation of reflectivity estimates increases 1.6 times as the SNR drops from 20 to 2 dB. But for estimates of differential reflectivity, differential phase, and copolar correlation coefficient, SDs increase ∼6.7, ∼6, and ∼54 times, respectively. Hence, this effect impacts the polarimetric variables substantially more than the spectral moments. Additionally, the polarimetric variable SD is also sensitive to the correlation between signals in horizontal and vertical channels leading to reduced data quality in the regions where the correlation coefficient is low. Such increases in the variability of estimates are observable in the fields of dual polarization variables as an increased spatial inhomogeneity (or noisiness) in the areas where radar echoes exhibit low-to-moderate SNRs and/or decreased correlation coefficient. These effects can obscure the visual identification of weather features as well as adversely impact algorithms. Herein, a novel method that applies variable smoothing in the range where the smoothing intensity depends on the SDs of estimates is presented. It applies little or no range averaging in the regions where data SDs are deemed adequate while using more aggressive smoothing in areas where data appear noisy. Significance Statement The noisiness in the fields of polarimetric variables is an issue that has plagued dual-polarization weather radars since their inception. This is because standard deviations of polarimetric variable estimates increase significantly more with the reduction in SNR than those of spectral moment estimates. A typical mitigation approach that indiscriminately averages a fixed number of estimates in the range may lead to unnecessary loss of range resolution in regions where data appearance is satisfactory. Further, such an approach can be inadequate in regions with a high variability of estimates leading to insufficient enhancement of weather feature visibility. In this study, a method that mitigates these issues is proposed.

An analysis of the “Fast” noise measurements of the dynamic VVER processes

Studies of maneuverable modes of VVER to confirm the possibility of participation of nuclear power plants in the mode of daily carrying capacity have been conducted for quite a long time. Tests at various nuclear power plants with VVER-1000 (Zaporizhzhia NPP in 1998, Khmelnitsky NPP in 2005, Tianwan NPP in 2007) have shown the practical possibility of NPP participation in the daily schedule of carrying capacity, however, the commissioning of nuclear power plants with VVER-1200 requires similar work on all new units with VVER-1200: NVAES-2, LNPP-2 Belarusian NPP. The article presents some aspects of the use of noise control methods for analyzing the condition of equipment and the core. Since the emergence of the technology of noise analysis of signals from VVER reactor installations, researchers have formulated several criteria for obtaining results of appropriate quality. The fundamental requirement for conducting noise experiments was the registration of data in stationary modes of operation of power units, since any non-stationarity made significant changes in spectral estimates, which ultimately complicated the work and “distorted” the results obtained. This requirement was included in the operating instructions of various diagnostic systems using noise signal analysis methods (the SUS system, manufactured by Siemens). For a long period of time, the current situation suited both developers of various diagnostic systems and NPP personnel operating them at power units. On the one hand, this was due to the imperfection of the technical means used (low speed of analog-to-digital converters, limited storage capacity, bulky equipment, etc.), on the other hand, the use of domestic NPP power units only in the base load mode without tracking daily power fluctuations in the power system. The standard archives of the upper block level system, the in-reactor control system and additionally produced multi-channel “fast” measurements with a frequency of 1 kHz for the analysis of maneuverable mode 95-55-95% of the VVER-1200 reactor plant were analyzed. Global disturbances of the core have been detected after one step of the regulatory body of the control and protection system, which attenuates within one second if the next step of the control and protection system has not occurred during this time. Such fast neutron processes can be controlled only by neutron-noise measurements with an upper frequency of at least 20 Hz.

Spectral density estimation for random processes with stationary increments

AbstractSpectral density analysis plays an important role in studying a stationary random process on a real line. In this paper, we extend this discussion for the random process with stationary increments. We investigate the properties of the method of moments structure function estimation, and propose a nonparametric spectral density function estimator. Our numerical results show that the proposed spectral density estimator performs comparable with the parametric counterpart when the underlying process is assumed to be band‐limited. Additionally, this method is applied to analyze US Housing Starts Data, where the hidden periodicities are detected, providing consistent conclusions with previous economic studies.

Large-Area Thickness Measurement of Transparent Films Based on a Multichannel Spectral Interference Sensor

Thickness measurement of thin films is essential for quality control in the manufacturing process of the semiconductor and display industries. Real-time monitoring of film thickness during production is an urgent technical problem to be solved. In this study, a method for large-area thickness measurement of transparent films based on a multichannel spectral interference sensor is proposed. The sensor simultaneously acquires multichannel spectral interference signals through a combination of fan-out fiber optic bundles, detection probes, and an imaging spectrometer. The spectral data are calibrated and transformed into the wavenumber dimension, and then the power spectral density estimation method is used to demodulate the data frequency to swiftly derive the film thickness. The thickness measurement capacity of the proposed system is successfully validated on two standard film samples with a relative deviation of less than 0.38% and a relative standard deviation of less than 0.044%. The total spectral acquisition and calculation time for a single multichannel measurement was approximately 7.5 ms. The experimental results on polyimide films show that the measurement efficiency of the system is at least 4 times higher than that of the traditional system, indicating the potential of the multichannel spectral interference sensor for online monitoring in film production.

A generic functional inequality and Riccati pairs: an alternative approach to Hardy-type inequalities

AbstractWe present a generic functional inequality on Riemannian manifolds, both in additive and multiplicative forms, that produces well known and genuinely new Hardy-type inequalities. For the additive version, we introduce Riccati pairs that extend Bessel pairs developed by Ghoussoub and Moradifam (Proc. Natl. Acad. Sci. USA, 2008 & Math. Ann., 2011). This concept enables us to give very short/elegant proofs of a number of celebrated functional inequalities on Riemannian manifolds with sectional curvature bounded from above by simply solving a Riccati-type ODE. Among others, we provide alternative proofs for Caccioppoli inequalities, Hardy-type inequalities and their improvements, spectral gap estimates, interpolation inequalities, and Ghoussoub-Moradifam-type weighted inequalities. Concerning the multiplicative form, we prove sharp uncertainty principles on Cartan-Hadamard manifolds, i.e., Heisenberg-Pauli-Weyl uncertainty principles, Hydrogen uncertainty principles and Caffarelli-Kohn-Nirenberg inequalities. Some sharpness and rigidity phenomena are also discussed.

Analysis of Spectral Characteristics of Cotton Leaves at Bud Stage under Different Nitrogen Application Rates

Soil salinity affects nutrient uptake by cotton. The cotton bud stage is a very important period in the process of cotton planting and directly affects the yield of cotton. The nutritional status of the bud stage directly affects the reflectance spectra of cotton canopy leaves. Therefore, it is of great significance to nondestructively monitor the nutritional status of the cotton bud stage on salinized soil via spectroscopic techniques and perform corresponding management measures to improve cotton yield. In this study, potted plants with different nitrogen application rates were set up to obtain the reflection spectral curves of cotton bud stage leaves, analyze their spectral characteristics under different nitrogen application rates, and establish spectral estimation models of chlorophyll density. The results are as follows: in the continuum removal spectrum of the cotton bud stage, the lowest point of the absorption valley near 500 nm shifted to the shortwave direction with an increasing nitrogen application rate. The mean reflectance between 765 and 880 nm was significantly different between nitrogen-stressed and nitrogen-unstressed cotton. The average reflectance of the near-infrared band, the absorption valley depths near 500 nm and 675 nm, the first derivative of the 710 nm reflectance, and the second derivatives of the 690 nm and 730 nm reflectance increased with increasing nitrogen application and chlorophyll density, and significant correlations were observed with the chlorophyll density. These parameters were modeled using support vector regression (SVR) and artificial neural network (ANN) methods, two commonly used algorithms in the field of machine learning. The determination coefficients of the three chlorophyll samples via the ANN models were 0.92, 0.77, and 0.94 for the modeling set and 0.77, 0.69, and 0.77 for the verification set. The ratio of quartile to root-mean-square error (RPIQ) of the ANN model was greater than 2.2, and the ratio of the standard error of the measured value to the standard error of the predicted (SEL/SEP) was close to 1, indicating that the chlorophyll density estimation models built based on the ANN algorithm had robust prediction ability. Our model could accurately estimate the leaf chlorophyll density in the cotton bud stage.

On the streamwise velocity, temperature and passive scalar fields in compressible turbulent channel flows: a viewpoint from multiphysics couplings

It is generally believed that the velocity and passive scalar fields share many similarities and differences in wall-bounded turbulence. In the present study, we conduct a series of direct numerical simulations of compressible channel flows with passive scalars and employ the two-dimensional spectral linear stochastic estimation and the correlation function as diagnostic tools to shed light on these aspects. Particular attention is paid to the relevant multiphysics couplings in the spectral domain, i.e. the velocity–temperature ( $u-T$ ), scalar–temperature ( $g-T$ ) and velocity–scalar ( $u-g$ ) couplings. These couplings are found to be utterly different at a given wall-normal position in the logarithmic and outer regions. Specifically, in the logarithmic region, the $u-T$ and $u-g$ couplings are tight at the scales that correspond to the attached eddies and the very large-scale motions (VLSMs), whereas the $g-T$ coupling is robust in the whole spectral domain. In the outer region, $u-T$ and $u-g$ couplings are only active at the scales corresponding to the VLSMs, whereas the $g-T$ coupling is diminished but still strong at all scales. Further analysis indicates that although the temperature field in the vast majority of zones in a channel can be roughly treated as a passive scalar, its physical properties gradually deviate from those of a pure passive scalar as the wall-normal height increases due to the enhancement of the acoustic mode. Furthermore, the deep involvement of the pressure field in the self-sustaining process of energy-containing motions also drives the streamwise velocity fluctuation away from a passive scalar. The current work is an extension of our previous study (Cheng & Fu, J. Fluid Mech., vol. 964, 2023, A15), and further uncovers the details of the multiphysics couplings in compressible wall turbulence.

Best practices recommendations for estimating dissipation rates from shear probes

As a part of the Scientific Committee on Oceanographic Research (SCOR) Working Group #160 “Analyzing ocean turbulence observations to quantify mixing” (ATOMIX), we have developed recommendations on best practices for estimating the rate of dissipation of kinetic energy, ε, from measurements of turbulence shear using shear probes. The recommendations provided here are platform-independent and cover the conceivable range of dissipation rates in the ocean, seas, and other natural waters. They are applicable to commonly deployed platforms that include vertical profilers, fixed and moored instruments, towed profilers, submarines, self-propelled ocean gliders, and other autonomous underwater vehicles. The procedure for preparing the shear data for spectral estimation is discussed in detail, as are the quality control metrics that should accompany each estimate of ε. The methods are illustrated using a high-quality ‘benchmark’ dataset, while potential pitfalls are demonstrated with a second dataset containing common faults.

EEG rhythmic and arrhythmic spectral components and functional connectivity at resting state may predict the development of synucleinopathies in idiopathic REM sleep behavior disorder.

Idiopathic/isolated REM-sleep behavior disorder (iRBD) often precedes the onset of synucleinopathies. Here, we investigated whether baseline resting-state EEG advanced spectral power and functional connectivity differ between iRBD patients who converted towards a synucleinopathy at follow-up and those who did not. Eighty-one participants with iRBD (66.89±6.91 years) underwent a baseline resting-state EEG recording, a neuropsychological assessment and a neurological examination. We estimated EEG power spectral density using standard analyses and derived spectral estimates of rhythmic and arrhythmic components. Global and pairwise EEG functional connectivity analyses were computed using the weighted phase-lag index (wPLI). Pixel-based permutation tests were used to compare groups. After a mean follow-up of 5.01±2.76 years, 34 patients were diagnosed with a synucleinopathy (67.81±7.34 years) and 47 remained disease-free (65.53±7.09 years). Among patients who converted, 22 were diagnosed with Parkinson's disease and 12 with dementia with Lewy bodies. As compared to patients who did not convert, patients who converted exhibited at baseline higher relative theta standard power, steeper slopes of the arrhythmic component and higher theta rhythmic power mostly in occipital regions. Furthermore, patients who converted showed higher beta global wPLI but lower alpha wPLI between left temporal and occipital regions. Analyses of resting-state EEG rhythmic and arrhythmic components and functional connectivity suggest an imbalanced excitatory-to-inhibitory activity within large-scale networks, which is associated with later development of a synucleinopathy in iRBD patients.

Spectral gap estimates for mixed p-spin models at high temperature

Spectral gap estimates for mixed p-spin models at high temperature