Frequency Estimation Research Articles

An accurate interpolation-based iterative frequency estimator of 2D multi-frequency sinusoids

ABSTRACT There are many domains in which frequency estimation of two-dimensional (2D) multi-frequency sinusoids is of great concern. In this paper, based on 2D spectrum interpolation, an accurate and efficient method is proposed to estimate 2D multi-frequency in noise. The method estimates the order of the signal by adopting a coarse-fine strategy that effectively corrects frequency leakage and suppresses interference between frequency components. To obtain the coarse estimation, 2D spectrum interpolation and 2D discrete Fourier transform (2D-DFT) are adopted after the order of sinusoids has been estimated. The fine estimation, with subtraction strategies converting sinusoids into 2D single-frequency sinusoids, suppresses interference from other frequency components. Next, 2D spectrum interpolation is used to obtain an accurate frequency estimate, whose accuracy is further improved through iteration. Simulation results demonstrate that the proposed method is capable of achieving the Cramer-Rao lower bound (CRLB) and outperforms other recently proposed frequency domain methods for 2D multi-frequency sinusoids.

Analyzing the Impact of Multiple Foundation Stiffness Correlation on the Natural Frequency of Offshore wind turbines

The analysis of wind turbine behavior should avoid unplanned resonance, as it can increase fatigue damage. It is essential to rigorously evaluate the natural frequency of wind turbines in the initial design stage. This estimation can be done through two steps, the first one is the computing of the fixed base natural frequency of the wind turbine. The second is the estimation of the foundation stiffness effect. This paper examines the error margin of four correlations of foundation stiffness namely Randolph, Davies and Budhu, DNV, and Higgins in the estimation of the natural frequency of wind turbines. The fixed base natural frequency was estimated in this paper using a special-purpose finite element computer program called TurbiSoft through beam and volume elements. A reference 5.0 MW offshore wind turbine and 9 other turbines from different wind farms have been analyzed. For the fixed base natural frequency, obtained results demonstrate the reliability of the finite element program TurbiSoft through an error margin between 1-4% for the reference 5.0 MW offshore wind turbine. For the natural frequency of the whole system, the estimated error marking was between 9-20% which is an important value.This significant error is attributed to the low accuracy of these four correlation formulas for predicting the foundation flexibility contribution. The results from the four correlation formulas used are quite similar, with a difference in the error margin of less than 1%. However, the largest error margins are observed with the Higgins formula, which has been originally developed for short monopiles, even though the analyzed monopiles can be considered short, with monopile slenderness ratios less than 8.

Synchronous decomposition match-reassigning transform and its application in planetary gearbox fault diagnosis

Abstract Under time-varying operating conditions, the instantaneous frequency (IF) of the vibration signal of the planetary gearbox exhibits non-stationary time-varying closely spaced characteristics as well as non-proportional and non-synchronous characteristics, making it difficult for traditional time-frequency analysis (TFA) methods to accurately identify its fault features and obtain accurate time-frequency representations (TFR). To address this challenge, this paper proposes a TFA method based on Synchronous Decomposition Match-Reassigning Transform (SDMRT). Firstly, the successive variational mode decomposition (SVMD) is used to adaptively separate non-synchronous frequency components in the original vibration signal. Then, the chirp rate (CR) describing the signal harmonic structure is used to synchronously match each frequency component, obtaining the TFR corresponding to each component. Next, all TFRs are merged to obtain a complete TFA result. Finally, Finally, the energy spread is re-aggregated to the ridge of the IF using the reassignment principle, resulting in a new frequency estimation operator called the Synchronous Decomposition Match-Reassigning Operator (SDMRO). SDMRT can adaptively separate non-proportional and non-synchronous IFs and achieve precise matching of time-varying closely spaced IFs, thereby completing the TFR of the vibration signal generated by the planetary gearbox. By analyzing simulated signals and measured vibration signals from planetary gearboxes, the method proposed in this paper is significantly superior to other TFA methods, thereby validating the effectiveness and superiority of SDMRT.

A novel bearing weak fault diagnosis method based on rank constrained low-rank and sparse decomposition

Abstract Addressing the challenge of diagnosing incipient bearing faults amidst significant noise, a novel diagnostic approach is introduced, leveraging a Rank Constrained Low-Rank and Sparse Decomposition (RCLRSD) model tailored for weak fault detection in bearings. Initially, we raised the Autocorrelation Function of the Square Envelope in Frequency Domain (AFSEFD) as an innovative method for the estimation of fault frequencies. Subsequently, we constructed a two-dimensional observation matrix, which is formulated independently of predefined assumptions. Then, we examine the configuration and distribution patterns of bearing fault signals, uncovering the low-rank nature of fault characteristics within a designated two-dimensional transform domain. Moreover, we found the noise signal to exhibit sparsity and an approximate Gaussian distribution. Based on this, a rank-constrained low-rank sparse decomposition model is established, and rank-constrained low-rank regular constraints for feature information and sparse regular constraints and Gaussian constraints for interference signals are constructed respectively. Ultimately, we employed the Gray Wolf Optimization (GWO) algorithm to refine the model parameters, and we deduced the model's solver via the Alternating Direction Method of Multipliers (ADMM). The proposed RCLRSD model decomposes bearing fault data into three constituents: low-rank, sparse, and Gaussian components, effectively addressing the challenge of extracting weak fault signatures from bearings. The weak feature extraction capability of the RCLRSD model is verified using a multi-interference simulation model and experimental data of bearing failures under strong noise conditions; the generalization of the model is verified by the classification effect of the Support Vector Machine (SVM) under two bearing failure datasets. Comparison with various algorithms confirms the superiority of the proposed algorithm.

Slidingan analysis of analytical signal of non-contact photoplethysmography for assessing heart rate

The paper proposes a method for studying the variability of the subject’s heart rate based on the intellectual analysis of the pulse wave measured with remote photoplethysmography. The logically related stages of the formation of quadrature components based on the Hilbert transform of biomedical signals’ dynamics are presented. Within the framework of modern methods of intellectual analysis of non-stationary time series, realizations of adaptive estimates of instantaneous frequencies and periods of the heartbeat basic tone are obtained.

Enhancing power quality in distributed generation systems using three-phase shunt active power filter

The current paper presents a new reference current generation algorithm for shunt active power filter (SAPF) combined with distributed generation systems using the instantaneous power theory (IPT) which is organized in two main blocks. The first is the synchronization technique; we propose a new quasi open loop technique that combines a Decoupled double self-tuning filter (DDSTF) and a single-phase frequency locked loop (FLL). The DDSTF is a new technique that extracts and separates the positive and negative sequence voltage under highly unbalanced and distorted conditions with no need to the symmetrical component and/or signals delay. The FLL achieve the grid frequency adaptation. Unlike the existing frequency estimators, this technique is motivated by its simplicity and the immunity to the voltage signal amplitude and phase variation or disturbance, which is a great advantage. The second is an ADALINE in power space to separate the fundamental harmonic from the distortion harmonics of the measured currents. The effectiveness of the proposed OLS technique in their application to the SAPF is validated by simulation.

Approaches for Behavior Intensity Estimation in Groups of Heterogeneous Individuals: Precision and Applicability for Data with Uncertainty

In socially oriented areas, there arises the problem of assessing the cumulative characteristics of behavior, such as intensity, that are realized in groups of individuals. All individuals vary in their behavior and the available data is limited and may be associated with significant uncertainty: only a few episodes may be known and only a few individualsi the group may be observed. Mathematical models of behavior are used for estimation of key characteristics of the behavior. One of them is based on the gamma–Poisson point process, that reflects the heterogeneity of individuals in a form of a mixing distribution. This general model allows to formulate several methods of frequency estimation: the Cox regression, estimation of the copula parameter, and a posteriori inference in Bayesian belief networks. The aim of the paper is to assess their determine the precision of these methods based on the Kantorovich–Rubinstein distance between estimates and the true distribution of the desired parameter. The analysis of assumptions of those methods allows to formulate rules, that allow to chose the appropriate method in various sutuations of data availability. It has been shown that the copula-based approach provides the most accurate estimates and has the mild assumptions for the number of observed objects, but it cannot take into account external factors that may influence the behavior. Among methods that can take into account process covariants, estimates based on a posteriori inference in hybrid Bayesian belief networks have the highest precision. The paper considers a method for quantification of a hybrid BBNs with the approximation of mixtures of truncated exponents, that is data-demanding at the stage of calculating a priori estimates. However, it is noted that there are other approaches to setting hybrid BSDs in which a priori estimates can be set completely expertly.

Photonic-Assisted Multi-Antenna Frequency-Spatial Compressed Sensing Array for Joint Frequency and DOA Estimation

Photonic-Assisted Multi-Antenna Frequency-Spatial Compressed Sensing Array for Joint Frequency and DOA Estimation

Joint Wideband Spectrum Sensing and Carrier Frequency Estimation in the Multi-Path Propagation Environment Based on Sub-Nyquist Sampling

We consider the wideband spectrum sensing within a multi-path propagation environment, where a multi-antenna base station (BS) is tasked with identifying the frequency positions of multiple narrowband transmissions distributed across a broad range of frequencies. To tackle this, we propose a sub-Nyquist sampling structure that incorporates a phased array system. Specifically, each antenna is connected to two separate sampling channels, i.e., one for direct sampling and another for delayed sampling, with the latter incorporating a specified time delay factor. The cross-correlation matrices associated with the samples, which are characterized by different time lags, are calculated. These matrices are represented in tensor form, and the factor matrices are extracted through CANDECOMP/PARAFAC (CP) decomposition. By these factor matrices, the carrier frequencies and the power spectra of the far-field signals of interest are estimated. Numerical simulations are conducted to evaluate the performance of the proposed method, and the results reveal the feasibility and effectiveness of the approach, demonstrating its potential for accurate and efficient wideband spectrum sensing in complex multi-path propagation environments.

Implementation of preamble based GFDM prototype for robust 5G systems

AbstractGeneralized frequency division multiplexing (GFDM) is a flexible block‐structured multi‐carrier scheme recently proposed for next‐generation wireless communication systems. There are various approaches suggested for its analysis and implementation via simulations but testing in real‐time environments is not heavily investigated. This paper carries out the real‐time implementation of the GFDM system utilizing software‐defined radio (SDR) by emphasizing mainly channel estimation and synchronization. Symbol timing, frequency offset, and channel estimate algorithms are applied using a windowed preamble with two identical halves to satisfy low egress noise requirements. Time and frequency estimation is evaluated in terms of residual offsets along with symbol error rate over frequency selective channels. This algorithm is extended to a preamble composed of multiple identical parts. This facilitates a large frequency estimation range at the cost of complexity. For practical validation of the above concepts, the National Instruments (NI) universal software radio peripheral (USRP) 2953R is employed as hardware and it is interfaced with LabVIEW.

Carrier frequency and incidence estimation of deficiency of adenosine deaminase 2 in the Chinese population based on massive exome sequencing data

Deficiency of adenosine deaminase 2 (DADA2) is an autosomal recessive autoinflammatory disease characterised by early onset stroke, recurrent fever, and diverse vascular pathologies, caused by loss-of-function homozygous or compound heterozygous variants of ADA2. This research aimed to determine the carrier frequency and expected incidence of DADA2 in China, using massive exome sequencing (ES) data. A total of 50 likely pathogenic/pathogenic variants (LP/PVs) were identified among 69,413 Chinese individuals, including 20 novel and rare variants (<0.0022 % allele frequency), expanding the known spectrum of PVs in ADA2. The overall carrier frequency in the Chinese population was 1.05 % (732/69,413) and the estimated incidence of DADA2 was approximately one in 92,251 individuals. The present study provides an accurate estimation of the prevalence of DADA2 in China, supporting genetic counseling, early diagnosis treatment, and prognostic evaluation.

Estimation of carrier frequencies of autosomal and X-linked recessive genetic conditions based on gnomAD v4.0 data in different ancestries.

Monogenic rare diseases contribute significantly to infant deaths and pediatric hospitalizations and cause burden to the patients and their families. The American College of Medical Genetics and Genomics recommended in 2021 that carrier screening of autosomal recessive and X-linked conditions with a carrier frequency of ≥ 1/200 and a severe or moderate phenotype should be offered when planning or during pregnancy. In November 2023 gnomAD v4.0 was released. It contains in total 807,162 individuals, being nearly 5x larger than previous versions, that have been used to estimate gene carrier frequencies (GCF). We utilized gnomAD v4.0 (GRCh38) to calculate the GCFs for available genetic ancestry groups for variants having pathogenic or likely pathogenic classification (>80% of submissions) in ClinVar. We calculated GCF separately for exomes and genomes, and combined data, and at-risk couple frequencies (ACF) per genetic ancestry group RESULTS: In total, 324 genes had a GCF ≥ 1/200 in at least one ancestry subgroup. The number of genes with GCF ≥ 1/200 varied greatly between subgroups. ACFs were more similar, Ashkenazi Jewish having the highest ACF of 6.11%. Improved understanding of carrier risks and updated carrier screening content would allow patients to make more informed reproductive decisions.

Fault Diagnosis Method for Marine Electric Propulsion Systems Based on Zero-Crossing Tacholess Order Tracking

In marine electric propulsion systems (MEPS) driven by variable-frequency drives, motor current signals often exhibit complex modulation components, ambiguous spectra, and severe noise interference, rendering it challenging to extract fault-related modulation components. To address this issue, we propose a zero-crossing tacholess order tracking method based on motor current signals. This method utilizes zero-crossing estimation of the instantaneous frequency to perform angular resampling of stator current signals and demodulates the envelope spectrum to extract fault characteristic spectra, enabling the diagnosis of mechanical faults in MEPS. Given the synchronization of the synchronous motor speed with the inverter fundamental frequency, this method estimates instantaneous frequencies in the time domain without requiring integration or time–frequency representation, which is simple and computationally efficient. Data validation on a small-scale marine electric propulsion test platform demonstrates that the proposed method exhibits good robustness under variable-speed conditions and effectively detects imbalance faults caused by propeller breakages and gear faults resulting from bevel gear tooth defects. Therefore, the proposed method can be applied to diagnose faults in downstream mechanical equipment driven by motors.

Porous N-Doped Carbon-encapsulated Iron as Novel Catalyst Architecture for the Electrocatalytic Hydrogenation of Benzaldehyde.

Carbon porous materials containing nitrogen functionalities and encapsulated iron-based active sites have been suggested as electrocatalysts for energy conversion, however their applications to the hydrogenation of organic substrates via electrocatalytic hydrogenation (ECH) remain unexplored. Herein, we report on a Fe@C:N material synthesized with an adapted annealing procedure and tested as electrocatalyst for the hydrogenation of benzaldehyde. Using different concentrations of the organic, and electrolysis coupled to gas chromatography experiments, we demonstrate that it is possible to use such architectures for the ECH of unsaturated organics. Potential control experiments show that ECH faradaic efficiencies >70 % are possible in acid electrolytes, while maintaining selectivity for the alcohol over the pinacol dimerization product. Estimates of product formation rates and turnover frequency (TOF) values suggest that these carbon-encapsulated architectures can achieve competitive performance in acid electrolytes relative to both base and precious metal electrodes.

Electrophysiological signature of interoceptive attention: a spectral and source localization analysis.

The ability to attend to and consciously process interoceptive signals is deemed critical for the development of minimal self, adaptive self-regulation and affective experience, and optimal expression of both instrumental and executive cognitive functions. Yet, notwithstanding the richness of theoretical proposals concerning inferential accounts of interoception, empirical evidence is still scarce. Building on such premises, this study was designed to investigate the electrophysiological signature of cognitive processes leading to aware coding of interoceptive signals via EEG source localization. Thirty-six healthy participants completed an interoceptive accuracy task, i.e., the Heartbeat Counting Task (HCT), while we collected task-related and resting state electrophysiological activity. eLORETA modelling and statistical nonparametric mapping were used to estimate intracortical current density and link such estimates to participants' performance at the task. Source analysis highlighted higher current density estimates for alpha frequencies during HCT with respect to rest, with the primary cortical generator in the right parahippocampal gyrus. Also, a set of medial cortical structures-primarily represented by the cingulate gyrus-showed significant relation between task-related changes in current density estimates for beta oscillations and HCT scores. Findings suggest the informativity of EEG task-related measures of neural activation when used to assess interoceptive skills, as well as of the potential of metrics and analysis based on source localization in the quest to improve our understanding of interoceptive accuracy and neurofunctional correlates of related active inferences.

Diffusion Augmented Complex Inverse Square Root for Adaptive Frequency Estimation over Distributed Networks

Using adaptive filtering to estimate the frequency of power systems has become a popular trend. In recent years, however, few studies have been performed on adaptive frequency estimations in non-stationary noise environments. In this paper, we propose the distributed complex inverse square root algorithm and distributed augmented complex inverse square root algorithm for the frequency estimation of power systems based on the widely linear model and the inverse square root cost function, where the function can restrain both positive and negative large errors, based on its symmetry. Moreover, the wireless sensor networks support monitoring and adaptation for the frequency estimation in the distributed networks, and the proposed approach can ensure good robustness of the balanced or unbalanced three-phase power system with the help of a local complex-value voltage signal generated by Clark’s transformation. In addition, the bound of step size is driven by the global vectors, and that low computation complexity do not hinder those performances. The results of several experiments demonstrate that our algorithms can effectively estimate the frequency in impulsive noise environments.

Detection and Estimation of Diffuse Signal Components Using the Periodogram

One basic limitation of using the periodogram as a frequency estimator is that any of its significant peaks may result from a diffuse (or spread) frequency component rather than a pure one. Diffuse components are common in applications such as channel estimation, in which a given periodogram peak reveals the presence of a complex multipath distribution (unresolvable propagation paths or diffuse scattering, for example). We present a method to detect the presence of a diffuse component in a given peak based on analyzing the projection of the data vector onto the span of the signature’s derivatives up to a given order. Fundamentally, a diffuse component is detected if the energy in the derivatives’ subspace is too high at the peak’s frequency, and its spread is estimated as the ratio between this last energy and the peak’s energy. The method is based on exploiting the signature’s Vandermonde structure through the properties of discrete Chebyshev polynomials. We also present an efficient numerical procedure for computing the data component in the derivatives’ span based on barycentric interpolation. The paper contains a numerical assessment of the proposed estimator and detector.

Smoother Semiclassical Dispersion for Density Functional Theory via D3S: Understanding and Addressing Unphysical Minima in the D3 Dispersion Correction Model.

One of the most widely used and computationally efficient models that accounts for London dispersion interactions within density functional theory (DFT) is the D3 dispersion correction model. In this work, we demonstrate that this model can induce the appearance of unphysical minima on the potential energy surface (PES) when the coordination number of atoms changes. Optimizing to these artifactual structures can lead to significant errors in determining the interaction energy between two molecules and in estimating the thermodynamic properties of the system. In several specific examples, such as Kuratowski-type H2-NiKur and H2-PdKur clusters, these local minima exhibited extremely high PES curvature, resulting in incorrect estimations of harmonic frequencies and significant overestimations of zero-point energy and enthalpy values. Although such erroneous behavior of the D3 model is relatively rare, it can occur across a wide range of chemical species, including molecules like the [Li(C6H6)]+ complex and the dispiro(acridan)-substituted pyracene (DSAP) molecule. Our analysis reveals that the root of the problem lies in the definition of the AB atomic-pair dependent C6AB coefficients in the D3 model. To address this issue, we propose a reparameterization of the D3 model by introducing a modified C6AB functional form that now depends on the specific pair of considered atoms. This new model, termed D3-Smooth (or D3S for short), is designed to smooth out the PES associated with the dispersion correction. By doing so, we demonstrate that D3S eliminates unphysical local minima while maintaining the quite satisfactory accuracy of the parent D3 method in interaction energy benchmark sets. For example, the RMS difference between using the D3(BJ) correction to B3LYP and the D3S(BJ) correction across the large MGCDB84 data set of nearly 5000 data points is only 0.12 kJ/mol. Similar results are obtained for every other D3-corrected functional tested. Consistent with this result, no significant improvement could be obtained for the B3LYP-D3S(0) correction by reoptimizing the damping function.

Estimation of frequencies and Q-factors of Earth’s low-frequency toroidal normal modes using strain data

In the study, estimations of the parameters of three low-frequency toroidal modes 0T2, 0T3, and 0T4, excited by the 13 largest earthquakes of the 21st century, were carried out. The etimations were obtained using the data from the Baksan Laser Interferometer–Strainmeter of SAI MSU. Using an adaptive spectral algorithm, estimates of the modes’ frequencies were obtained, and they were compared with the PREM model. Significant deviations in the frequency estimates of the 0T4 mode for a series of earthquakes were found, showing their possible connection with local inhomogeneities in the values of the speed of shear waves and the Earth’s density in the upper mantle. The splitting of the 0T2 mode due to Earth’s ellipticity and rotation was studied, with frequency estimates of singlets excited after catastrophic earthquakes in Sumatra, Japan, and Chile obtained. An evaluation of the Q-factors of the low-frequency toroidal modes was performed using three different methods.

Adaptive Measurement and Parameter Estimation for Low-SNR PRBC-PAM Signal Based on Adjusting Zero Value and Chaotic State Ratio

Accurately estimating the modulation parameters of pseudorandom binary code–pulse amplitude modulation (PRBC–PAM) signals damaged by strong noise poses a significant challenge in emitter identification and countermeasure. Traditionally, weak signal detection methods based on chaos theory can handle situations with low signal-to-noise ratio, but most of them are developed for simple sin/cos waveform and cannot face PRBC–PAM signals commonly used in ultra-low altitude performance equipment. To address the issue, this article proposes a novel adaptive detection and estimation method utilizing the in-depth analysis of the Duffing oscillator’s behaviour and output characteristics. Firstly, the short-time Fourier transform (STFT) is used for chaotic state identification and ternary processing. Then, two novel approaches are proposed, including the adjusting zero value (AZV) method and the chaotic state ratio (CSR) method. The proposed weak signal detection system exhibits unique capability to adaptively modify its internal periodic driving force frequency, thus altering the difference frequency to estimate the signal parameters effectively. Furthermore, the accuracy of the proposed method is substantiated in carrier frequency estimation under varying SNR conditions through extensive experiments, demonstrating that the method maintains high precision in carrier frequency estimation and a low bit error rate in both the pseudorandom sequence and carrier frequency, even at an SNR of −30 dB.