Accurate Frequency Estimation Research Articles

Second-order Synchrosqueezing Modified S Transform for wind turbine fault diagnosis

Under the working condition of variable speed, vibration signals of wind turbine gearboxes are characterized by instability coupled with noise interference, which has made it difficult to identify early fault characteristics through common Time-Frequency (TF) Analysis (TFA) methods. Stockwell Transform (ST) has such advantages as undergoing inverse transformation without loss and being free from cross-term interference when processing signals. Therefore, this paper has put forward Modified Stockwell Transform (MST), which enables the window width to change proportionally with the varying frequency. Moreover, the change caused by parameter adjustment is much more purposeful. It ensures that TF analysis windows are more flexible and changeable at different positions in the TF plane. Furthermore, to obtain much more accurate Instantaneous Frequency (IF) estimation of multi-component vibration signals, this paper uses the second-order partial derivative of phase function to modify it. Eventually, in order to achieve a concentrated Time-Frequency Representations (TFR) of wind turbines vibration signals, this paper proposes Second-order Synchrosqueezing Modified S Transform, namely SSMST2, through making use of the theoretical framework of Synchrosqueezing Transform (SST) and second-order IF estimations to extend MST. By reassigning the TF transform coefficients of MST, the proposed SSMST2 can better show the time-varying features. To verify this method is feasible, this paper will apply it to fault diagnosis of bearing test rig and to vibration signal processing of rolling bearing in 2 MW wind turbine. The result demonstrates that SSMST2 has yielded great outcome in TFR performance of variable speed vibration signals.

Recursive DFT-Based Method for Fast and Accurate Estimation of Three-Phase Grid Frequency

This letter proposes a method for fast and accurate estimation of three-phase grid frequency under unbalanced and distorted conditions. It includes a recursive discrete Fourier transform-based frequency adaptive bandpass filter for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</i> – <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">β</i> signals generated by the Clarke transform and a two-point-based algorithm for frequency estimation. The proposed method is relatively simple to implement and can eliminate adverse influences created by the imbalances, dc offset and both odd and even harmonics. It can also provide fast estimation with a response time of almost one fundamental cycle under grid disturbances. Moreover, it can present improved performance when compared to several methods reported in the technical literature. The advantages of the proposed method are confirmed by both simulated and real-time experimental results.

Parameter Estimation and Grid Synchronization Using a First-Order Frequency-Locked Loop

Fast and accurate estimation of frequency, phase angle, and amplitude are necessary for seamless synchronization of grid-connected converters. Therefore, this article proposes a first-order frequency-locked loop (FLL) structure for single-phase grid applications. The proposed FLL relies on signals generated from a first-order integrator orthogonal signal generator (OSG). With this approach, the generated signals exhibit a semi-quadrature phase angle offset with respect to the single-phase input voltage. Thus, unlike in existing FLLs where a 90° phase delay is introduced in the input signal, delay introduced using the proposed approach is halved. More so, the other orthogonal signal in the proposed approach exhibits a leading phase angle with respect to the single-phase input voltage. These distinctions assist the proposed FLL in achieving improved transient performance. A linearized model of the FLL is obtained where it is shown that the proposed FLL realizes a type-1 control system, giving it the ability to track step changes in the input voltage’s frequency with zero steady-state phase angle error. Extension of the proposed FLL for applications involving disturbances such as harmonics, dc-offset, and noise is also presented. Experimental results are provided to evaluate the performance of the proposed FLL in comparison with other FLL-based schemes where it is shown that the proposed FLL offers advantages such as simplicity, fast response, and minimum deviation in its frequency, phase angle, and amplitude estimations.

Simultaneous Frequency and Amplitude Estimation for Grid Quality Monitoring: New Partitioning with Memory Based Newton-Schulz Corrections

High penetration level of renewable energy sources and introduction of controllable loads will result in significant harmonic emissions and sag and swell events in the future electricity networks. Development of the methods for high performance simultaneous estimation of the frequency and amplitude events is required for stable operation of the future electricity networks since zero crossing frequency detection method (which is widely used nowadays in industry) is not accurate enough and does not allow estimation of the amplitude events. The multiple model method which is suitable for simultaneous estimation of the frequency and amplitude is extended in this paper with introduction of a new decomposition technique based on stepwise partitioning, which allows simultaneous construction and accurate and computationally efficient inversion of the information matrix. Recursive calculations of the inverse introduce error accumulation and a new general high order memory based Newton-Schulz iteration is proposed in this paper for correction and reduction of the accumulated error. Moreover, parallel Richardson iterations which are based on partitioning method are proposed in this paper for reduction of the computational complexity. The methods are especially efficient for approximation of the signals with large number of harmonics. The approaches were tested for simultaneous estimation of the frequency and sag and swell signatures in the one-phase synchronized voltage waveform measured at the wall outlet. Simulation results show that the multiple model method provides more accurate frequency estimation in comparison to zero crossing method.In addition, the cascade multiple model method which is based on the multi-windowing technique (where the components of the signals are separated via a proper choice of the window sizes) is introduced in this paper for estimation of the significantly separated frequencies of the electrical signals. The approach was tested in the problem of frequency estimation using the measurement record from the electric vehicle with on-board charger connected to the supply voltage in the laboratory.

Fundamental investigation of dynamic response data processing method to improve the estimation accuracy of natural frequency using stochastic subsplace identification method

Fundamental investigation of dynamic response data processing method to improve the estimation accuracy of natural frequency using stochastic subsplace identification method

Noisy Speech Based Temporal Decomposition to Improve Fundamental Frequency Estimation

This paper introduces a novel method to separate voiced frames of noisy speech signals into low-frequency or high-frequency. This separation improves the accuracy of fundamental frequency (F0) estimators. In this proposal, the target signal is analyzed by means of the ensemble empirical mode decomposition. Next, the pitch information is extracted from the first decomposition modes. This feature indicates the frequency region where the speech F0 should be located, thus separating the frames into low-frequency or high-frequency. The frames separation is then applied to correct pitch candidates extracted from a F0 detection method, improving the estimation accuracy. The proposed method and a baseline separation approach are evaluated considering four different F0 estimation algorithms. Experiments are conducted with the CSTR and TIMIT databases, and six noises with various signal-to-noise ratios. The Gross Error (GE) and Mean Absolute Error (MAE) metrics are adopted to evaluate the solutions in terms of F0 estimation errors. Results show that the proposed method outperforms the baseline, in terms of low/high frequency separation accuracy. Moreover, the novel solution is able to better improve F0 detection accuracy under different noisy conditions.

Smoothed Lv Distribution Based Three-Dimensional Imaging for Spinning Space Debris

Three-dimensional (3-D) imaging plays a vital role in the recognition of spinning space debris. However, the image may be blurred due to the range migration caused by fast rotation of space debris. Moreover, the image quality, which depends on the estimation accuracy of Doppler frequency and chirp rate of scattering centers, is influenced by cross-terms and sidelobes. In this paper, we propose a novel 3-D imaging method based on smoothed Lv distribution (SLVD). Firstly, the selection criterion for best imaging time based on the time-frequency moment is proposed to guarantee that the echo is approximated as a linear frequency modulation signal. Then, we operate the Khatri-Rao product on the centroid frequency and chirp rate (CFCR) representation and the range-Doppler (RD) image to obtain the 3-D image. To decrease the influence of range migration, we process a short time window during the RD imaging procedure. For cross-term and sidelobe suppression, the SLVD is proposed to obtain the CFCR representation by expressing the Lv distribution (LVD) in a convolution form and introducing a centroid frequency window. Experimental results verify the effectiveness of the proposed imaging method and the good performance of the proposed SLVD for cross-term and sidelobe suppression.

Refined Multifrequency Interferometric SAR Phase Unwrapping for Extremely Steep Terrain

Multifrequency (MF) interferometric synthetic aperture radar (InSAR) phase unwrapping (PU) technology is proposed for PU in steep terrains where the phase changes of adjacent pixels exceed the commonly required threshold of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pi $ </tex-math></inline-formula> . Traditional MF PU methods will fail in the case of extremely steep terrain such as artificial buildings due to insufficient quality of phase noise suppression (PNS). In this article, we propose a refined MF-InSAR PU method that can be robustly applied for extremely steep terrain PU via two main contributions. First, an additional steep edge extraction step is introduced for geological local PU window generation to prevent inaccurate PNS across the extracted steep edges. Second, the traditional linear phase model is extended to a nonlinear one for more accurate MF local fringe frequency estimation in PNS. The computer simulations and the real dual-frequency airborne experiment validate the presented approach.

Accurate Damping Factor and Frequency Estimation for Damped Real-Valued Sinusoidal Signals

The interpolated discrete Fourier transform (IpDFT) is one of the most popular techniques to estimate the parameters of a damped real-valued sinusoidal signal (DRSS). However, its accuracy is affected by strong noise presence and short observation windows. To this end, this letter proposes a novel two-point IpDFT method, called I2pZDFT, for the parameter estimation of a DRSS. The proposed I2pZDFT uses the zero-padding technique to increase the sampling rate in the frequency domain. The conjugate symmetry and the parity of the zero-padded signal are utilized to eliminate the influence of the spectral leakage. Simulation results highlight that the proposed I2pZDFT outperforms the existing IpDFT-based methods in terms of noise immunity, especially in the case of observation windows as short as 0.5 ~ 1 cycles.

DFT-Based Frequency Estimation of Multiple Sinusoids

An accurate frequency estimation method of multi-component sinusoidal signal in additive white Gaussian noise (AWGN) is proposed. The algorithm is implemented in the frequency domain and based on discrete Fourier transform (DFT). The maximum DFT spectral line and two Discrete-Time Fourier Transform (DTFT) samples located on the same side of the maximum DFT spectral line are used to estimate the frequency of a sinusoidal component. And this algorithm is utilized in both the coarse estimation and the fine estimation. Simulation results show that compared with the competing estimators, the presented method is closer to the Cramer-Rao lower bound (CRLB). And it is almost independent of the frequency displacement. The numerical complexity of the presented method is similar with the competing DFT-based algorithms.

Accurate Frequency Estimation of Signals with Symbol Transition by Using Interpolated Dft

Accurate Frequency Estimation of Signals with Symbol Transition by Using Interpolated Dft

Sub-Nyquist Sampling of Multiple Exponentially Damped Sinusoids With Feedback Structure

Multiple exponentially damped sinusoids (MEDS) signals have been widely applied to the fields of speech analysis and nuclear magnetic resonance imaging systems. Although sub-Nyquist sampling schemes were proposed in previous works, either the image frequency aliasing was not resolved, or the parameters measuring process required a large number of samples. In this paper, a feedback based sub-Nyquist sampling and parameters measurement scheme for MEDS signals is proposed to address these problems. Since sub-Nyquist sampling would lead to frequencies ambiguity, an additional sampling is designed to determine the true frequencies. Moreover, image frequency aliasing would occur when the difference between two true frequencies is an integer multiple the sampling rate. To prevent image frequency aliasing, a feedback sampling strategy and a dealiasing algorithm are proposed. The proposed scheme enables sub-Nyquist sampling and parameters measurement of MEDS signals with K frequency components, by using only 4K samples. We also propose a hardware prototype to implement the proposed system. Simulation and hardware experiment results have shown that the frequency estimation accuracy of the proposed method has been improved on average by about 11.65 dB than previous works under noise environment, and the statistical variance experiments have shown that it has better stability.

An Improved Radar Echo Signal Processing Algorithm for Industrial Liquid Level Measurement

In this paper, based on the study of Linear Frequency Modulated Continuous Wave (LFMCW) radar, a ranging algorithm for the high-precision liquid level measurement in industry is proposed. A new algorithm is developed based on the MacLeod algorithm. The frequency offset δ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> is estimated, and then (δ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> -q, δ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> +q) is used as the iterative estimation initial iteration interval to determine the frequency offset δ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> more precisely. The improved algorithm is the Golden-MacLeod algorithm, referred to as the GM algorithm. Simulation results show that the GM can effectively reduce the estimation error and maintain the high frequency estimation accuracy at signal-to-noise ratio (SNR) up to -10 dB, which is better than the MacLeod algorithm. In addition, the estimation accuracy, stability and noise immunity are better than other algorithms in the variation interval of SNR greater than -5 dB. Liquid level measurement experiment is tested by TI’s IWR 6843ISK and DCA1000EVM. The measurement results also show that the measurement accuracy of the GM can meet the requirements of industrial applications. This also proves the reliability of the GM in practical applications.

Video-based quantification of human movement frequency using pose estimation: A pilot study.

Assessment of repetitive movements (e.g., finger tapping) is a hallmark of motor examinations in several neurologic populations. These assessments are traditionally performed by a human rater via visual inspection; however, advances in computer vision offer potential for remote, quantitative assessment using simple video recordings. Here, we evaluated a pose estimation approach for measurement of human movement frequency from smartphone videos. Ten healthy young participants provided videos of themselves performing five repetitive movement tasks (finger tapping, hand open/close, hand pronation/supination, toe tapping, leg agility) at four target frequencies (1–4 Hz). We assessed the ability of a workflow that incorporated OpenPose (a freely available whole-body pose estimation algorithm) to estimate movement frequencies by comparing against manual frame-by-frame (i.e., ground-truth) measurements for all tasks and target frequencies using repeated measures ANOVA, Pearson’s correlations, and intraclass correlations. Our workflow produced largely accurate estimates of movement frequencies; only the hand open/close task showed a significant difference in the frequencies estimated by pose estimation and manual measurement (while statistically significant, these differences were small in magnitude). All other tasks and frequencies showed no significant differences between pose estimation and manual measurement. Pose estimation-based detections of individual events (e.g., finger taps, hand closures) showed strong correlations (all r>0.99) with manual detections for all tasks and frequencies. In summary, our pose estimation-based workflow accurately tracked repetitive movements in healthy adults across a range of tasks and movement frequencies. Future work will test this approach as a fast, quantitative, video-based approach to assessment of repetitive movements in clinical populations.

High-Order Synchroextracting Chirplet Transform for Accurate Instantaneous Frequency Estimation and Its Application in Fault Diagnosis of Rotary Machinery

Time-frequency analysis (TFA) technology is an effective tool for extracting time-varying characteristics of a signal, but for strong AM-FM signals, time-frequency representation (TFR) with high time-frequency (TF) resolution is often difficult to generate. The measured vibration signals of mechanical equipment often contain a large number of non-stationary features and are polluted by noise, which hinders the use of TFA technologies. In this paper, we propose a TFA method termed high-order synchroextracting chirplet transform (HSECT) to effectively process strong AM-FM signals. On the basis of Chirplet transform (CT), we first determine the best linear demodulation operator at each moment through the local maximum amplitude of the generated TFR. Subsequently, the amplitude and phase of the signal are subjected to high-order Taylor expansion, and a new frequency estimation operator termed high-order synchroextracting chirplet operator (HSECO) is obtained by the high-order approximation of the time-varying laws of the signal. HSECO can accurately extract the instantaneous frequency of strong AM-FM signal and the construction of HSECT is completed by Dirichlet function at last. HSECT can generate TFR with high energy concentration from which the time-varying law of strong AM-FM signal can be extracted accurately. Meanwhile, the signal reconstruction operation can be completed concisely. In addition, the proposed method is applied to the fault diagnosis of the rotor rub impact and variable speed equipment and compared with other TFA methods. Simulation and experiments can verify the effectiveness and competitiveness of the proposed method.

Reconstruction of gapped missing samples based on instantaneous frequency and instantaneous amplitude estimation

The recovery of missing samples in amplitude-modulation and frequency-modulation (AM-FM) signals is a challenging problem. This study proposes an effective approach to reconstruct missing samples from AM-FM signals through accurate estimation of instantaneous frequencies (IFs) and instantaneous amplitudes (IA) of signal components. Experimental results indicate that the proposed reconstruction method achieves better performance, in the terms of mean absolute error between the reconstructed signal and the original signal, as compared to the state of art methods including time-frequency filtering method and modified orthogonal matching pursuit algorithm.

Adaptive multiple second-order synchrosqueezing wavelet transform and its application in wind turbine gearbox fault diagnosis

Wind turbines usually operate in harsh environments and in working conditions of variable speed, which easily causes their key components such as gearboxes to fail. The gearbox vibration signal of a wind turbine has nonstationary characteristics, and the existing time-frequency (TF) analysis (TFA) methods have some problems such as insufficient concentration of TF energy. In order to obtain a more apparent and more congregated time-frequency representation (TFR), this paper proposes a new TFA method, namely adaptive multiple second-order synchrosqueezing wavelet transform (AMWSST2). Firstly, a short-time window is innovatively introduced on the foundation of classical continuous wavelet transform, and the window width is adaptively optimized by using the center frequency and scale factor. After that, a smoothing process is carried out between different segments to eliminate the discontinuity and thus adaptive wavelet transform is generated. Then, on the basis of the theoretical framework of synchrosqueezing transform and accurate instantaneous frequency estimation by the utilization of second-order local demodulation operator, adaptive second-order synchrosqueezing wavelet transform (AWSST2) is formed. Considering that the quality of actual TFA is greatly disturbed by noise components, through performing multiple synchrosqueezing operations, the congregation of TFR energy is further improved, and finally, the AMWSST2 algorithm studied in this paper is proposed. Since synchrosqueezing operations are performed only in the frequency direction, this method AMWSST2 allows the signal to be perfectly reconstructed. For the verification of its effectiveness, this paper applies it to the processing of the vibration signal of the gearbox of a 750 kW wind turbine.

A Forward-Backward Iterative Procedure for Improving the Resolution of Resonant Microwave Sensors

This paper sets out a method for improving the resolution of resonant microwave sensors. Usually, the frequency response of these devices is associated with a low quality factor, and consequently with a low resolution in terms of tracking capacity of the resonance frequency shift. Furthermore, since only a finite number of samples can be acquired during the measurement process, the “true” resonance frequency may not be included in the set of acquired data. In order to have an accurate estimate of the resonance frequency, high performance systems with very fine frequency sampling are thus required. To limit these drawbacks, an iterative algorithm is presented which aims to refine the response of resonant microwave sensors by means of a suitable post-processing. The algorithm evaluation is first carried out on synthetic data, and then applied on experimental data referring to a practical scenario, which is inherent to return loss measurements performed by a microwave patch antenna immersed in a water-glucose solution with different concentrations.

Automatic modulation classification of noise‐like radar intrapulse signals using cascade classifier

Automatic modulation classification is essential in radar emitter identification. We propose a cascade classifier by combining a support vector machine (SVM) and convolutional neural network (CNN), considering that noise might be taken as radar signals. First, the SVM distinguishes noise signals by the main ridge slice feature of signals. Second, the complex envelope features of the predicted radar signals are extracted and placed into a designed CNN, where a modulation classification task is performed. Simulation results show that the SVM-CNN can effectively distinguish radar signals from noise. The overall probability of successful recognition (PSR) of modulation is 98.52% at 20 dB and 82.27% at −2 dB with low computation costs. Furthermore, we found that the accuracy of intermediate frequency estimation significantly affects the PSR. This study shows the possibility of training a classifier using complex envelope features. What the proposed CNN has learned can be interpreted as an equivalent matched filter consisting of a series of small filters that can provide different responses determined by envelope features.

A Robust Algorithm for Real-Time Phasor and Frequency Estimation under Diverse System Conditions

This paper presents a comprehensive approach for performing phasor and frequency estimation from voltage and/or current signals of the modern power system. Undesirable components, such as decaying DC, if present in the input signal, are first attenuated using a complex-gain filter. The initial estimates of phasor and frequency are obtained next using the discrete Fourier transform and an improved estimation of signal parameters via rotational invariance technique, respectively. Finally, the accuracy of phasor and frequency estimates are increased based on the identified system condition. Simulations performed to evaluate the proposed approach confirm that it can do fast and accurate estimation of phasor and frequency under diverse operating conditions, making it ideal for wide-area monitoring, protection, and control applications in power systems.