Accurate Frequency Estimation Research Articles

The Effect of Sample Size on the Interpolation Algorithm of Frequency Estimation

Fast and accurate frequency estimation is essential in various engineering applications, including control systems, communications, and resonance sensing systems. This study investigates the effect of sample size on the interpolation algorithm of frequency estimation. In order to enhance the accuracy of frequency estimation and performance, we describe a novel method that provides a number of approaches for calculating and defending the sample size for of the window function designs, whereas, the correct choice of the type and the size of the window function makes it possible to reduce the error. Computer simulation using Matlab / Simulink environment is performed to investigate the proposed procedure's performance and feasibility. This study performs the comparison of the interpolation algorithm of frequency estimation strategies that can be applied to improve the accuracy of the frequency estimation. Simulation results shown that the proposed strategy with the Parzen and Flat-top gave remarkable change in the maximum error of frequency estimation. They perform better than the conventional windows at a sample size equal to 64 samples, where the maximum error of frequency estimation is 2.13e-2, and 2.15e-2 for Parzen and Flat-top windows, respectively. Moreover, the efficiency and performance of the Nuttall window also perform better than other windows, where the maximum error is 7.76×10-5 at a sample size equal to 8192. The analysis of simulation result showed that when using the proposed strategy to improve the accuracy of the frequency estimation, it is first essential to evaluate what is the maximum number of samples that can be obtained, how many spectral lines should be used in the calculations, and only after that choose a suitable window.

Time-frequency reassignment of blade tip timing signal

The health condition of a rotor blade can be assessed by its dynamic frequency with respect the rotational speed, which can be derived from the time–frequency analysis of the blade vibration signal. Blade tip timing (BTT), as a non-contact measurement technique, provides an alternative to traditional contact strain measurement methods. However, the vibration signal measured by BTT is usually undersampled, which limits the application of conventional time–frequency analysis methods. BTT sparse time–frequency methods utilize the sparsity to reconstruct undersampled BTT signals. Nevertheless, BTT sparse time–frequency representation suffers from poor concentration and inaccurate estimation of the dynamic frequency, especially in the case of fast varying speed and limited BTT sensors. In this paper, a BTT time–frequency reassignment method is proposed to enhance the concentration of the BTT time–frequency spectrum and improve the accuracy of dynamic frequency estimation. Firstly, BTT time–frequency reassignment utilizes the blade natural frequency, obtained from the Campbell diagram, as prior information. The blade dynamic frequency with respect to the rotational speed is estimated by combining the prior frequency with the measured frequency in the Bayesian framework. Subsequently, weights are assigned to both the time–frequency coefficients and the posterior frequency. The time–frequency coefficients are relocated around the posterior frequency according to the weights. The advantages of BTT time–frequency reassignment are demonstrated through a simulation, a laboratory test and a full-scale aeroengine test. Both simulation and experimental results demonstrate that BTT time–frequency reassignment enhances the concentration of the BTT time–frequency spectrum and improves the accuracy of the estimated dynamic frequency when limited BTT sensors are available. The influence of the prior frequency is discussed to evaluate the robustness of BTT time–frequency reassignment. In the full-scale aeroengine test, the reliability of BTT time–frequency reassignment is verified under the fast varying speed.

Fastmixture generates fast and accurate estimates of global ancestry proportions and ancestral allele frequencies

fastmixture generates fast and accurate estimates of global ancestry proportions and ancestral allele frequencies

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.

Quantitative suppression of unsteady powerline noise in transient electromagnetic surveys: Adjustment of base-frequency and optimal choice of stacking-times.

Powerline noise is a severe interference source in urban or mine transient electromagnetic (TEM) surveys. TEM systems generally adopt the synchronous detection scheme to suppress the powerline noise. However, when the powerline frequency fluctuates differing from its nominal value (50/60Hz), the considerable powerline noise residue still remains even after synchronous detection. To overcome this problem, this paper proposes the quantitative suppression method for powerline noise taking into account the instability of powerline frequency. The method is based on the adjustment of base-frequency and optimal choice of stacking-times. We represent mathematically the sufficient condition for powerline noise suppression by synchronous detection. It consists of two equations, one with respect to base-frequency and other with respect to stacking-times. The base-frequency is adjusted according to powerline frequency estimate. We first derive the mathematical relationship between frequency estimation accuracy, residual noise amplitude, and stacking-times. Based on it, we develop an efficient algorithm to determine the optimal stacking-times. The algorithm takes as an input the powerline noise estimates and the noise tolerance limit. The tolerance limit is set to a certain value desired by the user, such as 10, 4, and 1 µV. By adjusting base-frequency and determining optimal stacking-times, the powerline noise residue after synchronous detection is reduced to below the desired tolerance limit. We verify the effectiveness of the proposed method for both simulated and actual noise. Experimental results show that the method achieves quantitative suppression of unsteady powerline noise without any damage of effective signal and prevents the measurement time loss due to excessive stacking.

Dynamic time warping based instantaneous frequency estimation for rotating machineries under non-stationary operating conditions

Abstract For tacho-less order tracking, it is crucial to achieve an accurate estimation of instantaneous phase and frequency under non-stationary conditions for fault diagnosis of mechanical systems. Therefore, an instantaneous frequency estimation method based on dynamic time warping for rotating machinery was proposed. Firstly, a mono-component signal is obtained by variational mode decomposition of multi-harmonic vibration signal generated in practical engineering. Then, a stationary reference signal is constructed by the mean frequency of the vibration signal, which is obtained by the signal spectrum. Aligning the vibration signal with the reference signal to obtain the rough phase estimation and warping path. Finally, a polynomial model is constructed to calculate the analytic expression of the smooth warping path to obtain the instantaneous frequency result. The simulation and experiment present that the dynamic time warping-based method can estimate the instantaneous frequency of the signal under non-stationary conditions. Compared with the classical Hilbert transform method, the proposed dynamic time-warping algorithm has stronger noise resistance.

A cross-comparison of different extreme value modeling techniques for traffic conflict-based crash risk estimation

Extreme Value Theory (EVT) models have recently gained increasing popularity for crash risk estimation using traffic conflict data. Extreme value modeling consists of two fundamental approaches: the block maxima approach and the peak-over-threshold approach, each with several variants. However, a comprehensive comparison of these two approaches and their variants in crash risk estimation is lacking. This study bridges this gap by comparing different extreme value modeling techniques and evaluating their performance in estimating crash frequencies. Within a non-stationary Bayesian hierarchical modeling framework, the analyzed models include the block maxima model, the r largest order statistic model, and the peak-over-threshold model with the fixed and dynamic threshold, across univariate and bivariate traffic conflict cases. The analysis utilizes modified time-to-collision and post-encroachment time conflict indicator data collected from four signalized intersections in the City of Surrey, British Columbia, Canada. The results show that incorporating additional order statistics in the r largest order statistic model improves predictive performance, particularly with limited extreme conflict samples. Moreover, employing the dynamic threshold within the peak-over-threshold model enhances model goodness-of-fit and yields more accurate crash frequency estimates compared to using the fixed threshold. While the performance of the block maxima and peak-over-threshold models varies with the selected conflict indicator in the univariate case, the bivariate peak-over-threshold model with the dynamic threshold exhibits superior overall prediction accuracy over the corresponding block maxima model. This is likely due to the effectiveness of the dynamic threshold in precisely identifying truly critical extreme conflicts.

Frequency Recognition of a Free Damped Vibration Signal Based on Improved Elias Aboutanios Interpolation Method

The free damped vibration signal of engineering structures is an energy-limited signal, and the effective signal length is limited by the damped factor. The classical periodic graph method is affected by signal damped coefficient and noise, and it is difficult to obtain satisfactory recognition accuracy. This article proposes the IEAI method for frequency estimation of freely damped vibration signal, considering the influence of initial phase. By combining discrete Fourier transform with complex operations, the signal is iteratively interpolated to improve the accuracy of frequency estimation .The simulation results show that the mean error of the IEAI method is 1.3%~26.5% of the traditional Periodogram method, A&M method and Welch method, and the Root-mean-square deviation is 7.4%~40.3% of the latter three methods under the condition of high signal-to-noise ratio; In the case of low signal-to-noise ratio, the mean error of the IEAI method is 16.2%~43.0% of the latter three, and the Root-mean-square deviation is 20.8%~81.8% of the latter three. The experimental results of cantilever beam damage identification show that the IEAI method is more sensitive to small structural damages and can be used for the identification and diagnosis of small structural damages.

An Efficient Algorithm to Retrieve Multiple Fundamental Frequencies of Harmonic Interference in Surface-NMR Measurements

Summary The successful recovery of hydrogeophysical parameters through surface-NMR measurements depends on the quality of the signal, which can be significantly degraded by harmonics from multiple noise sources with different fundamental frequencies in urban areas. Accurate estimation of the fundamental frequencies of harmonics is the main step in harmonic noise cancellation-based methods. The existing 1D and 2D model-based approaches involve a computationally expensive process that sets limits for processing of large surface-NMR data sets. In addition, the classical Nyman, Gaiser, and Saucier estimation (NGSE) algorithm, despite its fast implementation, may not accurately recover harmonic components when there is no prior knowledge of the expected value of the frequency offset between the true fundamental frequencies and their nominal values. This lack of knowledge can make it difficult to accurately estimate the maximum number of harmonics and, consequently, result in an incorrect recovery of the fundamental frequency. To surmount these limitations, we propose an enhanced version of the NGSE approach based on an efficient maximum number of harmonics search approach to process surface-NMR signals corrupted by powerline harmonics with both single and multiple frequency content. We verify the efficiency of our algorithm on a synthetic dataset embedded in simulated powerline harmonic signals, and real electromagnetic noise recordings, as well as a real surface-NMR data set. Our numerical experiments confirm that the proposed algorithm can retrieve the multiple fundamental frequencies simultaneously with a significant speedup ranging from 4 to 87 times, depending on whether the signal has single, dual, or triple frequency content, in the overall computation time compared to the model-based methods.

Radial vibration measurement of rotating shaft using constant density fringe pattern and line scan camera

The radial vibration signals of the rotor can provide abundant information about the health condition of the machine. In this paper, a simple vision-based measurement system is proposed to simultaneously measure two-dimensional displacements in radial directions for the rotating shaft, where the system consists of a constant density fringe pattern (CDFP), a line scan camera (LSC), and a lens. The CDFP should be installed around the surface of the rotating shaft to make the density of the fringe constant along the shaft axis, while the shaft axis is vertical to the optical axis of the LSC but not parallel to the line-array sensor of the LSC. Therefore, the density of the fringe imaged on the LSC is not constant because of the modulation of the circular surface of the shaft, and the distribution of the fringe density on the LSC is a U-shaped curve. Thus, the shaft centreline orbit can be tracked by the lowest point of the density distribution curve (DDC) of the fringe. Then, an efficient and accurate parameterized instantaneous frequency estimation method is employed to estimate the DDC of the fringe, because the variable density fringe can be regarded as an amplitude-modulated and frequency-modulated nonstationary signal whose instantaneous frequency function is equivalent to the DDC. Experimental results verify the feasibility and effectiveness of the proposed method by comparing it to the eddy current sensors.

Assisting the analysis of insertions and deletions using regional allele frequencies.

Accurate estimation of population allele frequency (AF) is crucial for gene discovery and genetic diagnostics. However, determining AF for frameshift-inducing small insertions and deletions (indels) faces challenges due to discrepancies in mapping and variant calling methods. Here, we propose an innovative approach to assess indel AF. We developed CRAFTS-indels (Calculating Regional Allele Frequency Targeting Small indels), an algorithm that combines AF of distinct indels within a given region and provides "regional AF" (rAF). We tested and validated CRAFTS-indels using three independent datasets: gnomAD v2 (n=125,748 samples), an internal dataset (IGM; n=39,367), and the UK BioBank (UKBB; n=469,835). By comparing rAF against standard AF, we identified rare indels with rAF exceeding standard AF (sAF≤10-4 and rAF>10-4) as "rAF-hi" indels. Notably, a high percentage of rare indels were "rAF-hi", with a higher proportion in gnomAD v2 (11-20%) and IGM (11-22%) compared to the UKBB (5-9% depending on the CRAFTS-indels' parameters). Analysis of the overlap of regions based on their rAF with low complexity regions and with ClinVar classification supported the pertinence of rAF. Using the internal dataset, we illustrated the utility of CRAFTS-indel in the analysis of de novo variants and the potential negative impact of rAF-hi indels in gene discovery. In summary, annotation of indels with cohort specific rAF can be used to handle some of the limitations of current annotation pipelines and facilitate detection of novel gene disease associations. CRAFTS-indels offers a user-friendly approach to providing rAF annotation. It can be integrated into public databases such as gnomAD, UKBB and used by ClinVar to revise indel classifications.

HeavySeparation: A Generic framework for stream processing faster and more accurate

Sketch as a probability data structure has been widely used in high volume, fast data streams. At the cost of a tiny accuracy in frequency estimation, it achieves a high speed with small memory usage. However, skewed data streams pose a significant challenge for existing sketches in terms of accuracy and speed using limited memory. To address this issue, we proposed a framework, called HeavySeparation, to enhance existing sketches by filtering elephant flow efficiently and accurately. We adopt a power-weakening increment strategy to allow sufficient competition in the early stages of identifying elephant flows and amplifying relative advantage when the frequency of candidate flow is large. To verify the effectiveness and efficiency of our framework, we apply the framework to two typical sketches and two common stream processing tasks. Results show that HeavySeparation framework reduces the error by around 1–2 orders of magnitude on average compared to the state-of-the-art in frequency estimation.

Optimizing Bangkaew dog breed identification using DNA technology.

The Bangkaew dog is an indigenous dog breed in the Phitsanulok province of Thailand. This breed is recognized by the Fédération Cynologique Internationale (FCI), a global canine organization. The unique traits of the Bangkaew breed lead to purebred selection for breeding, while only their traits and pedigree from parental history are recorded. Determination of the risk of inbreeding depression and the origin of unknown DNA profiles is essential due to the challenges in predicting puppy characteristics, which are crucial for breed management and conservation. This study aimed to emphasize that current allelic frequency data for the Bangkaew dog breed must be considered for precise individual identification. Approximately 82 Bangkaew dogs from various Thai localities were studied using 15 microsatellite markers for genotypic monitoring and individual identification. Maternal genetic inheritance was assessed via mtDNA D-loop analysis. The results revealed high genetic diversity in the Bangkaew breed, indicating low potential for inbreeding. We also found that using a 15 loci microsatellite panel was effective for the identification of Bangkaew dogs. The optimized 10 loci microsatellite genotyping panel developed in this study presents improved identification testing efficiency, promoting both time- and cost-effectiveness. Analysis of microsatellite DNA markers in Bangkaew dogs using an optimized panel of 10 loci selected from 15 loci effectively facilitated individual identification. This approach not only enhances time and cost efficiency, but also provides accurate allelic frequency estimates, which are crucial for the realistic evaluation of DNA evidence.

A novel design method for a family of single-phase frequency estimators based on discrete oscillator for micro-grid application

The family of frequency estimators based on discrete oscillator is believed to be the simplest one for single-phase grid voltage. In order to make this family of frequency estimators more feasible in micro-grid, a novel design is proposed in this paper. The novelty includes a clear input–output relationship for the family of frequency estimators based on the discrete oscillator, an optimized design of the discrete oscillator model (DOM), and an enhanced pre-filter. Firstly, the input–output relationship is established by the time-domain feedback analysis, and it reveals that the frequency estimators inherently possess complex-coefficient comb filtering ability. Then, an optimized DOM design is presented to enhance the frequency estimators' filtering ability near the nominal frequency. Lastly, an enhanced pre-filter is proposed to match this optimized DOM for high filtering ability in a wide frequency range. The proposed design method has no stability issues and a very low computational burden. Compared with previous methods, the proposed method demonstrates higher accuracy in frequency estimation and similar response speed in micro-grid with significant frequency fluctuation and harmonic pollution, verified by experimental results.

Improved windowed phase difference method for frequency estimation of distorted power signals

Frequency is one of the most significant indicators of power system, which needs accurate estimation to provide a reliable basis for monitoring, control, and protection. Owning to the efficiency, DFT is widely used in the frequency measurement of power systems. However, the inherent defects, that is, the spectral leakage and picket fence effect, decrease the accuracy of DFT. One of the variants, named the windowed phase difference method (WPD), addresses the problem using the phase variation of two windowed sequences in the frequency domain and achieves accurate frequency estimation. Suffering from the ignored negative component and contamination of noise, there are still undesired errors in WPD-based frequency estimation. To reduce the influence of the undesired errors, this paper first analyzes the systematic error of WPD introduced by spectrum leakage and proposes an improved WPD (IWPD) through systematic error compensation to achieve more accurate frequency estimations. Then, the windowing effect on IWPD-based frequency estimation of a noisy signal is studied by deducing the theoretical expression of frequency estimation variance. Finally, the proposed IWPD is validated by extensive computer simulations and practical experiments.

Delay-Tracking Loop for Frequency Estimation of Grid-Interfaced Inverter Under Distorted Conditions

Fast and accurate frequency estimation is difficult for grid-interfaced inverter under distorted grid conditions with off-nominal frequency. A popular solution considers the multiple second-order generalized integrator-based frequency-locked loop yet can hardly achieve a fast dynamic response under significant phase jump and voltage sag. Another solution uses an adaptive sliding window filter with an additional frequency estimator. However, it is challenging to handle numerical instability due to the adjusting marginally-stable resonator and the accumulation error. This letter proposes a delay-tracking loop to overcome these problems. This loop allows the delay length to track the frequency with an inherent harmonics rejection at off-nominal frequency. At the same time, the fast response speed is maintained, and the marginally stable resonator is avoided. Comparative experimental results validate the above claims.

Fast and Accurate Frequency Estimation for Renewable Energy Systems Using Maximum Decay Sidelobes Windows

Fast and accurate signal frequency estimation has great importance i.a. in renewable energy systems and power control systems. The energy produced by these systems shall fulfill quality requirements as defined in the respective directives and standards. More accurate and faster grid signal frequency estimation (which can be used to control the inverter) can improve the energy quality. This article presents an overview of methods for spectrum interpolation and signal frequency estimation and a generalized method for very accurate and fast frequency grid estimation by using the Fast Fourier Transform procedure and maximum decay sidelobes windows. An important feature of this algorithm is the elimination of the impact of the conjugate component on the estimation result. The article shows the statistical properties of the frequency estimator as well as the effect of noise for the estimation. The results of the simulation show that the algorithm can be successfully used for a fast and accurate estimation of the grid signal frequency i.a. in renewable energy systems and power control systems. The accuracy of the frequency estimation is in the order of 5·10-11 Hz for a 5 ms measurement window. Using different windows from the discussed family allows to adjust to the actual requirements of estimation.

The Accuracy of Frequency Estimation of Structure Vibration under Ambient Excitation: Problems, Causes, and Methods

Accurate identification of building structure frequencies forms the basis for damage detection. The structural dynamic response signal, under ambient excitation, can be transformed into a superposition of multiple single-frequency exponentially damped sinusoids combined with random white noise. However, the peak power spectrum of the response signal tends to exhibit line splitting, compromising the precision of frequency identification. This study examines the accuracy characteristics of the single-frequency free damping vibration signal (SFFDVS) and derives the Cramer–Rao lower bound for the frequency estimator. It thoroughly analyzes the factors influencing the accuracy of SFFDVS frequency identification. The study reveals that the primary cause of spectral line splitting is the random delay inherent in SFFDVS. Based on the maximum likelihood method (MLM), this research introduces the MLM algorithm for SFFDVS and provides a simulation analysis. The findings indicate that the MLM estimation algorithm for frequency parameters effectively addresses spectral line splitting and offers robust noise resistance and recognition accuracy.

Damage inference and residual capacity assessment for an E-Defense 2018 ten-story RC test structure

This paper presents an enhanced vision-based, post-earthquake performance assessment framework for RC building structures. This framework incorporates a damage inference method that can estimate the stiffness and strength reduction factors of components in stories without damage inspection based on the inter-story drift. The framework was validated by the application to the full-scale shaking table test of an E-Defense 2018 ten-story RC structure. The vision-based damage detection method effectively detected multicategory seismic damage on the component surfaces, and the damage states estimated by the vision-based method were consistent with the results estimated by the measured plastic hinge rotation. The proposed inter-story drift-based damage inference method reasonably estimated the reduction factors of components in the stories without damage photos. The numerical model updated by the reduction factors of damaged components provided accurate estimates of the fundamental vibrational frequencies after different levels of seismic shaking, and the drift-based inference method significantly improved the results compared with the trivial linear interpolation method. The residual capacity curves provided by pushover analysis of the updated model using the reduction factors as per FEMA 306 & Chiu et al. reasonably captured the hysteretic responses of the structure.

Carrier-frequency estimation for digital holograms of phase objects.

Accurate estimation of carrier fringe frequency is essential for the demodulation of off-axis digital holograms. The fringe frequency is often associated with the amplitude peak of the cross-term in the two-dimensional Fourier transform of a digital hologram. We point out that this definition of carrier frequency is not valid in general for holograms associated with phase objects. We examine the carrier-envelope representation for digital holograms from the viewpoint of Mandel's criterion [J. Opt. Soc. Am.57, 613 (1967)10.1364/JOSA.57.000613]. An appropriate definition of carrier frequency is observed to be the centroid of the power spectrum associated with the cross term. This definition is shown to apply uniformly to holograms associated with phase objects, is robust to noise, and leads to the smoothest (or least fluctuating) envelope representation for the demodulated object wave. The proposed definition is illustrated with simulated as well as experimentally recorded off-axis holograms.