Adaptive Time-frequency Analysis Research Articles

An ultrasonic signal processing method to improve defect depth estimation in composites based on empirical mode decomposition

In this paper, an ultrasonic signal processing method is proposed to improve depth evaluation of phased array ultrasonic non-destructive testing in composite structures. The proposed algorithm is based on an improved adaptive time–frequency analysis algorithm, and is a combination of empirical mode decomposition, correlation coefficient analysis, a fuzzy entropy algorithm and Hilbert transform. The ultrasonic signal is decomposed into intrinsic mode functions (IMFs) using an improved complete ensemble empirical mode decomposition with adaptive noises. Subsequently, the correlation coefficient and fuzzy entropy are used to select the optimal IMFs to reconstruct the signal. Then, Hilbert transform is executed to obtain the envelope of the reconstructed signal. Finally, the arrival time of the ultrasonic echo is estimated through the signal envelope, and then used to calculate the defect depth. The simulation and experimental results demonstrated that the proposed method has high evaluation accuracy in processing intense noisy signals or overlapped echoes. For simulated signals with different signal-to-noise ratios, the maximum estimation error of arrival time is 0.06 µs. Compared with the traditional gating method, the defect depth evaluation result is significantly improved. In particular, for near-surface defects, the maximum depth detection error is reduced from 0.13 mm to 0.06 mm.

A Weld Quality Classification Approach Based on Local Mean Decomposition and Deep Belief Network

Weld quality directly affects the performance and reliability of structural parts and can be critically ensured by online monitoring. In this study, local mean decomposition (LMD), an adaptive time-frequency analysis is used to analyze the current signals of welding, and then combined with deep belief network (DBN) to classify the weld quality. Firstly, the current signals are decomposed by LMD into a series of product functions. Each product function is a complex signal, and its complexity is calculated by multi-scale entropy to select the most relevant product function with weld quality. Finally, DBN is applied to classify weld quality into four types. This method has a higher classification and recognition rate compared with principal component analysis and extreme learning machine classification. Thus, LMD is a potentially effective method to diagnose weld quality.

A robust condition monitoring methodology for grinding wheel wear identification using Hilbert Huang transform

Grinding is a finishing operation performed to obtain the desired finish on the component. Wheel wear is one of the primary constraints in achieving the desired productivity in grinding. A new methodology is proposed for accurate and timely identification of wheel wear in cylindrical grinding using Hilbert Huang transform and support vector machine. During the grinding of EN31 carbon steel, the condition of the wheel and its wear was monitored with an accelerometer and power cell. Both vibration and power signals captured were used to identify the condition of the wheel and its wear. An exhaustive feature set is generated in the frequency and the time-frequency domain. Hilbert Huang transform, an adaptive time-frequency analysis technique, was used to extract the features of tool wear in the time-frequency domain. The first three IMF constituents were further chosen for feature extraction of statistical parameters based on their mean energy. Random forests algorithm was used to identify the relevant features. The methodology was validated with several grinding experiments and, is found to give an accuracy of 100% with both low and high cutting depths. The results indicated the robust and reliable wheel wear detection in cylindrical grinding with the use of relatively cheap sensors like accelerometers. The proposed method can be widely used in many applications in the industry where grinding is predominantly used as the finishing operation.

Method of Gravitational Wave Search Based on Adaptive Time-Frequency Analysis and Machine Learning

In simple terms, gravitational waves are ripples in space-time caused by energetic processes in the Universe, such as the movement of mass. One of the exciting things about them is that they can be used to observe systems that are basically impossible to detect using other means. These ripples were predicted by Albert Einstein almost a century ago, but it wasn't until 2016 that scientists announced, for the first time, the detection of gravitational waves. The Laser Interferometer Gravitational-Wave Observatory (LIGO) is the physics experiment responsible for this detection and it has since continued to make a significant impact in the field. LIGO collaborates closely with the Virgo interferometer; a large interferometer designed to detect gravitational waves, and the Japanese Gravitational Wave Detector in Kamioka Mine (KAGRA), the Large Scale Cryogenic Gravitational Wave Telescope; a project of the gravitational wave studies group led by the Institute for Cosmic Ray Research of The University of Tokyo. But there still remain many unknowns, such as challenges related to the data analysis of gravitational waves. Professor Hirotaka Takahashi is carrying out research on gravitational waves that is attempting to address these challenges by developing algorithms that can dramatically increase the speed and efficiency of gravitational wave searches, which he believes are currently insufficient. Takahashi is a member of the KAGRA collaboration, which, as of March 2020, consists of more than 390 researchers from 90 institutions in 14 countries and regions.

Application Research of a New Adaptive Noise Reduction Method in Fault Diagnosis

The feature extraction of composite fault of gearbox in mining machinery has always been a difficulty in the field of fault diagnosis. Especially in strong background noise, the frequency of each fault feature is different, so an adaptive time-frequency analysis method is urgently needed to extract different types of faults. Considering that the signal after complementary ensemble empirical mode decomposition (CEEMD) contains a lot of pseudo components, which further leads to misdiagnosis. The article proposes a new method for actively removing noise components. Firstly, the best scale factor of multi-scale sample entropy (MSE) is determined by signals with different signal to noise ratios (SNRs); secondly, the minimum value of a large number of random noise MSE is extracted and used as the threshold of CEEMD; then, the effective Intrinsic mode functions(IMFs) component is reconstructed, and the reconstructed signal is CEEMD decomposed again; finally, after multiple iterations, the MSE values of the component signal that are less than the threshold are obtained, and the iteration is terminated. The proposed method is applied to the composite fault simulation signal and mining machinery vibration signal, and the composite fault feature is accurately extracted.

Spike Detection Based on the Adaptive Time–Frequency Analysis

This paper presents a novel spike detection algorithm in nonstationary signals using a time–frequency (t–f) approach. The proposed algorithm exploits the direction of signal energy in the t–f domain to detect spikes in the presence of high-frequency nonstationary signals even at low signal-to-noise ratio. The performance of the proposed approach is evaluated using synthetic nonstationary signals, synthesized signals mimicking electroencephalogram (EEG) signals, manually selected segments of speech signals, and manually selected segments of real EEG signals. The statistical measures, such as hit rate and precision, are used to demonstrate that the proposed algorithm performs better than other widely used algorithms, such as the smoothed nonlinear energy detector.

Research on Adaptive Reclosing Discriminant Method Based on LMD Sample Entropy

Based on the adaptive time-frequency analysis characteristics of local mean decomposition and the nonlinear quantization ability of sample entropy, an adaptive reclosing discriminant method based on LMD sample entropy is proposed. Firstly, the local mean decomposition method is applied to decompose the original signal of the transmission line fault into several product function components (PF component). Then calculate the sample entropy of the first three PF components to achieve feature quantization of the PF component. Finally, the sum of the sample entropy of first three PF components is used as the eigenvalue to distinguish the fault type of the transmission line. Obtained from the simulation results, the method can identify the type of fault.

A spike denoising method combined principal component analysis with wavelet and ensemble empirical mode decomposition

Spike recorded by multi-channel microelectrode array is very weak and susceptible to interference, whose noisy characteristic affects the accuracy of spike detection. Aiming at the independent white noise, correlation noise and colored noise in the process of spike detection, combining principal component analysis (PCA), wavelet analysis and adaptive time-frequency analysis, a new denoising method (PCWE) that combines PCA-wavelet (PCAW) and ensemble empirical mode decomposition is proposed. Firstly, the principal component was extracted and removed as correlation noise using PCA. Then the wavelet-threshold method was used to remove the independent white noise. Finally, EEMD was used to decompose the noise into the intrinsic modal function of each layer and remove the colored noise. The simulation results showed that PCWE can increase the signal-to-noise ratio by about 2.67 dB and decrease the standard deviation by about 0.4 μV, which apparently improved the accuracy of spike detection. The results of measured data showed that PCWE can increase the signal-to-noise ratio by about 1.33 dB and reduce the standard deviation by about 18.33 μV, which showed its good denoising performance. The results of this study suggests that PCWE can improve the reliability of spike signal and provide an accurate and effective spike denoising new method for the encoding and decoding of neural signal.

Real-time damage detection of bridges using adaptive time-frequency analysis and ANN

Real-time damage detection of bridges using adaptive time-frequency analysis and ANN

A new method of harmonic time-frequency decomposition: The K-S decomposition

S transform and its improved algorithms are limited by the Gaussian window, which cannot realize high time-frequency energy concentration and exact identification of harmonic time-frequency parameters. A significant improvement has done in this paper: K-S decomposition is built based on the idea of FFT + Kaiser window + IFFT. The Each column vector of the two-dimensional time-frequency complex matrix obtained by K-S decomposition represents the frequency of the signal and each row is instantaneous magnitude in each selected frequency in time domain. Thus the parameter of amplitude, spectrum, time and phase can be achieved and adaptive time-frequency analysis is realized. The simulation experiments of the complex power system harmonic verify the feasibility and adaptive ability of K-S decomposition.

Adaptive time-frequency analysis of signals in AFM

The probe-sample interactions during the AFM experiments represent a case of a multi-frequency behaviour, since they are characterized by the simultaneous excitation of cantilevers eigenmodes and/or their harmonics. Analysis of the data obtained as a result of the interaction between the probe and the sample is of a particular interest not only from a practical point of view, i.e. obtaining information about the surface of the sample, but also this is an interesting methodological task, since the instantaneous processes resulting from the interaction of the probe with the sample surface carry a huge amount of information. To obtain this information, it is necessary to provide an analysis method that is capable of characterizing all of the excited cantilevers frequencies simultaneously and without averaging. In other words, it is necessary to obtain the complete spectral response of the cantilever interacting with the sample surface, i.e. information about the dynamics of cantilever behaviour in time. The aim of the present work is to show the possibilities of time-frequency analysis techniques in analysing the signals of AFM experiments.

The Research of Machinery Fault Feature Extraction Methods Based On Vibration Signal

The vibration signal of machinery fault is complex, performing non-stationary characteristic. The classical filter can not extract low frequency impulse from the vibration signal. In this paper the machinery fault feature extraction methods will be discussed. These methods includes Fourier transform frequency spectrum feature extraction, envelopment analysis and local mean decomposition. Envelopment analysis can extract the low frequency envelopment from single amplitude modulated pure mode function. Local mean decomposition is an adaptive time-frequency analysis method, which can decompose a non-stationary and complex signal into a number of amplitude modulated pure mode functions and extract the low frequency envelopment from signal mixed with strong noise. The mathematical theory of every feature extraction method is elaborated. In each method the vibration signal of common machinery fault is designed. It extracts the signal feature with these methods and analyzes the simulation output. The simple vibration experiment is done with land leveler experiment system. It proves these feature extraction methods are correct.

The Application Research of the Natural Gas Pipeline Leakage Detection Based on Adaptive Time Frequency Analysis

The Application Research of the Natural Gas Pipeline Leakage Detection Based on Adaptive Time Frequency Analysis

Extracting a shape function for a signal with intra-wave frequency modulation.

In this paper, we develop an effective and robust adaptive time-frequency analysis method for signals with intra-wave frequency modulation. To handle this kind of signals effectively, we generalize our data-driven time-frequency analysis by using a shape function to describe the intra-wave frequency modulation. The idea of using a shape function in time-frequency analysis was first proposed by Wu (Wu 2013 Appl. Comput. Harmon. Anal. 35, 181-199. (doi:10.1016/j.acha.2012.08.008)). A shape function could be any smooth 2π-periodic function. Based on this model, we propose to solve an optimization problem to extract the shape function. By exploring the fact that the shape function is a periodic function with respect to its phase function, we can identify certain low-rank structure of the signal. This low-rank structure enables us to extract the shape function from the signal. Once the shape function is obtained, the instantaneous frequency with intra-wave modulation can be recovered from the shape function. We demonstrate the robustness and efficiency of our method by applying it to several synthetic and real signals. One important observation is that this approach is very stable to noise perturbation. By using the shape function approach, we can capture the intra-wave frequency modulation very well even for noise-polluted signals. In comparison, existing methods such as empirical mode decomposition/ensemble empirical mode decomposition seem to have difficulty in capturing the intra-wave modulation when the signal is polluted by noise.

Adaptive Time-Frequency Analysis for Noise Reduction in an Audio Filter Bank With Low Delay

In this paper, an adaptive time-frequency analysis scheme is proposed along with a synthesis scheme using an asymmetric window. The proposed scheme is suitable for audio noise reduction with a low delay in the range of 0 to 4 ms. The main novelty of the paper is the adaptive analysis scheme that can adapt to the incoming signal independently in both time and frequency by employing a complex filter on a DFT modulated filter bank. A number of adaptive time-frequency schemes are described that are suitable for low delay and low computational complexity. The adaptive time-frequency scheme is used for the computation of noise reduction gain factors, which are then adopted in a nonadaptive analysis/synthesis scheme. The synthesis scheme uses an asymmetric window to achieve a good tradeoff between low delay and a sharp frequency response. Examples are given of the adaptive analysis and measurements of the synthesis scheme are given to show that the filter bank has a gain dependent nonlinear phase response. Finally, a noise reduction task is performed that shows good performance compared to reference implementations in terms of segmental SNR and PESQ.

A new time-frequency method to reveal quantum dynamics of atomic hydrogen in intense laser pulses: Synchrosqueezing transform

This study introduces a new adaptive time-frequency (TF) analysis technique, the synchrosqueezing transform (SST), to explore the dynamics of a laser-driven hydrogen atom at an ab initio level, upon which we have demonstrated its versatility as a new viable venue for further exploring quantum dynamics. For a signal composed of oscillatory components which can be characterized by instantaneous frequency, the SST enables rendering the decomposed signal based on the phase information inherited in the linear TF representation with mathematical support. Compared with the classical type of TF methods, the SST clearly depicts several intrinsic quantum dynamical processes such as selection rules, AC Stark effects, and high harmonic generation.

The optimal fractional Gabor transform based on the adaptive window function and its application

We designed the window function of the optimal Gabor transform based on the time-frequency rotation property of the fractional Fourier transform. Thus, we obtained the adaptive optimal Gabor transform in the fractional domain and improved the time-frequency concentration of the Gabor transform. The algorithm first searches for the optimal rotation factor, then performs the p-th FrFT of the signal and, finally, performs time and frequency analysis of the FrFT result. Finally, the algorithm rotates the plane in the fractional domain back to the normal time-frequency plane. This promotes the application of FrFT in the field of high-resolution reservoir prediction. Additionally, we proposed an adaptive search method for the optimal rotation factor using the Parseval principle in the fractional domain, which simplifies the algorithm. We carried out spectrum decomposition of the seismic signal, which showed that the instantaneous frequency slices obtained by the proposed algorithm are superior to the ones obtained by the traditional Gabor transform. The adaptive time frequency analysis is of great significance to seismic signal processing.

Time–frequency analysis for parametric and non-parametric identification of nonlinear dynamical systems

This paper points out the differences between linear and nonlinear system identification tasks, shows that time–frequency analysis is most appropriate for nonlinearity identification, and presents advanced signal processing techniques that combine time–frequency decomposition and perturbation methods for parametric and non-parametric identification of nonlinear dynamical systems. Hilbert–Huang transform (HHT) is a recent data-driven adaptive time–frequency analysis technique that combines the use of empirical mode decomposition (EMD) and Hilbert transform (HT). Because EMD does not use predetermined basis functions and function orthogonality for component extraction, HHT provides more concise component decomposition and more accurate time–frequency analysis than the short-time Fourier transform and wavelet transform for extraction of system characteristics and nonlinearities. However, HHT's accuracy seriously suffers from the end effect caused by the discontinuity-induced Gibbs' phenomenon. Moreover, because HHT requires a long set of data obtained by high-frequency sampling, it is not appropriate for online frequency tracking. This paper presents a conjugate-pair decomposition (CPD) method that requires only a few recent data points sampled at a low-frequency for sliding-window point-by-point adaptive time–frequency analysis and can be used for online frequency tracking. To improve adaptive time–frequency analysis, a methodology is developed by combining EMD and CPD for noise filtering in the time domain, reducing the end effect, and dissolving other mathematical and numerical problems in time–frequency analysis. For parametric identification of a nonlinear system, the methodology processes one steady-state response and/or one free damped transient response and uses amplitude-dependent dynamic characteristics derived from perturbation analysis to determine the type and order of nonlinearity and system parameters. For non-parametric identification, the methodology uses the maximum displacement states to determine the displacement–stiffness curve and the maximum velocity states to determine the velocity–damping curve. Numerical simulations and experimental verifications of several nonlinear discrete and continuous systems show that the proposed methodology can provide accurate parametric and non-parametric identifications of different nonlinear dynamical systems.

EIT Image Processing Based on 2-D Empirical Mode Decomposition

Electrical impedance tomography (EIT) imaging is a new kind of imaging technology that has developed in recent years. This technology has many advantages such as noninvasive, small volume and so on, but there are also many shortcomings such as imaging quality is not high, in order to improve the image quality, image processing methods is used in this paper. Significant different with the traditional method, empirical mode decomposition method does not require any prior basis function. It is an adaptive time-frequency analysis method. The two-dimensional empirical mode decomposition algorithm is adopted to process EIT images in this paper, and the compactly supported radial basis function interpolation algorithm is used for the post-processing of three organic glass rod EIT imaging. The image is decomposed into six IMFs in the experiment, some IMFs contain useful information, and the rest of them contains a lot of noise. The experimental results show that this method can significantly improve the EIT image quality.

Sparse Contour Representations of Sound

Many signals are naturally described by continuous contours in the time-frequency plane, but standard time-frequency methods disassociate continuous structures into isolated “atoms” of energy. Here we propose a method that represents any discrete time-series as a set of time-frequency contours. The edges of the contours are defined by fixed points of a generalized reassignment algorithm. These edges are linked together by continuity such that each contour represents a single phase-coherent region of the time-frequency plane. By analyzing the signal across many time-scales, an over-complete set of contours is generated, and from this redundant set of shapes the simplest, most parsimonious forms may be selected. The result is an adaptive time-frequency analysis that can emphasize the continuity of long-range structure. The proposed method is demonstrated with a few examples.