Synchrosqueezed Wavelet Transform Research Articles

Noise-robust self-adaptive support vector machine for residual oxygen concentration measurement

In this article, a noise-robust self-adaptive support vector machine (namely, NSSVM) is developed for the multiclass classification problem in the residual oxygen concentration measurement of pharmaceutical vials. Two key elements are emphasized by the NSSVM framework: First, targeting the fast time-varying noises, two mutually compensated signal enhancement measures of synchrosqueezed wavelet transform (SWT)-based filtering and adaptive iterative reweighted penalty least squares (AIRPLS)-based baseline corrector are contributed to obtain stable features being fed to classifier. Second, most typical slow time-varying interferences are dynamically avoided by the self-adaptive thresholding scheme learned from the intrinsic priori of production line. The experimental results indicate that our NSSVM-based measurement method achieves a considerable performance, with an average accuracy of 97.24% when applied on an automated visual inspection (AVI) machine of Truking Tech., which indicates that the proposed method is promising to the in situ instrumentation for the residual oxygen concentration measurement of pharmaceutical glass vials.

Application of Synchrosqueezed Wavelet Transform in Microseismic Monitoring of Mines

Microseismic monitoring technique is an important means of ground pressure monitoring to ensure safe, high-efficient and sustainable development of mines. Microseismic data obtained by sensors in mines are easily influenced by non-stationary noises with a wide frequency band, resulting in the lack of available high-quality data for microseismic monitoring. Instead of traditional analysis in frequency domain, this paper introduces a new method, synchrosqueezed wavelet transform (SSWT), which provides a way to decompose data into time domain and frequency domain simultaneously. With higher time-frequency resolution of SSWT spectrum, purer microseismic signals can be extracted from raw data. Besides, two wavelet bases, Morlet wavelet and bump wavelet, are compared to match the microseismic signal in this paper. Two field data with different signal-noise rate (SNR) are used to show the application of the algorithm in the mine industry. The results of data graphical filtering method show that the SSWT has great practical value to extract the microseismic signal from raw data and improves SNR of signals effectively than traditional methods.

Automatic mode extraction of ultrasonic guided waves using synchrosqueezed wavelet transform

Multimodal and dispersive characteristics of ultrasonic guided waves (GWs) cause the wave-packet overlapping in time domain and frequency domain, which challenges the signal interpretation. In this study, we propose an automatic method for individual mode extraction. The inversible synchrosqueezed wavelet transform (SWT) is employed to obtain the high-resolution time-frequency representation (TFR) of the GW signal. Then, two image processing steps, i.e., watershed transform and region growing, are used to process the TFR distributions and extract the TFR trajectory of each individual component. After the TFR segmentation, the individual modes are reconstructed by using the inverse SWT. The algorithm performance is investigated by synthesized multimodal signals. The results show that the reconstructed individual modes are consistent with the original ones. The experimental results measured in a bovine tibia plate and a steel plate are further employed to testify the proposed algorithm. Results suggest that the presented study provides a robust tool for processing multimodal ultrasonic GW signals.

Characteristic Analysis of Welding Crack Acoustic Emission Signals Using Synchrosqueezed Wavelet Transform

Abstract The synchrosqueezed wavelet transform (SST) is introduced to conduct analysis and processing of the acoustic emission (AE) signal in the welding process. The energy distribution of the signal in the time-scale plane is compressed and reorganized by SST, which obtains the time-frequency diagram of the AE signal. Meanwhile, the correlation coefficient is introduced as the criterion for removing the undesirable frequency components, which can effectively eliminate the noise and retain the characteristics of the welding crack AE signal. The test experiment of the AE signals in the welding process is designed. The time-frequency distribution characteristics of the AE signals in the welding process are described and extracted by SST, which is characterized by high aggregation and prominent instantaneous frequency information. Experimental results are provided to confirm the effectiveness of this approach to extract the AE signal physical information related to the welding crack.

Nonstationary harmonic signal extraction from strong chaotic interference based on synchrosqueezed wavelet transform

To overcome the shortcomings of the synchrosqueezed wavelet transform (SWT) in extracting nonstationary harmonic signals from chaotic backgrounds, an improved nonstationary extraction method with SWT is proposed based on an adaptive optimal accumulation frequency range. First, according to the relationship between the wavelet coefficients of the nonstationary harmonic signals and the support interval of the mother wavelet function, an adaptive accumulation frequency range formula is derived for extracting the nonstationary harmonic signal. Then, the optimal value of the parameter of the adaptive accumulation frequency range formula is determined using the minimum energy error criterion to realize the adaptive SWT extraction of nonstationary harmonic signals. In experiments, various types of nonstationary harmonic signals are extracted from the Lorenz background and Duffing background using both a classic SWT method and the proposed method. The experimental results show that the proposed method can effectively extract nonstationary harmonic signals from noisy backgrounds. Compared with the classical SWT method, the mean square error of the extracted harmonic signal by the proposed method is lower, and the correlation coefficient is higher.

A novel method of realizing stochastic chaotic secure communication by synchrosqueezed wavelet transform

Based on synchrosqueezed wavelet transform (SWT) algorithm, a new stochastic chaotic secure communication scheme is proposed in this paper. Information signals are modulated by additive chaos masking in the sending terminal. In order to improve the anti-jamming ability of chaotic systems, the proper controllers are designed to realize mean square asymptotic synchronization for a class of chaotic systems with random perturbation. In the receiving terminal, unlike the traditional extraction methods, a novel SWT algorithm is introduced to recover information signals correctly. Simulation results verify that both the synchronization approach and the security communication scheme are effective. For multi-component sinusoidal signal with adjacent frequency, the accuracy of signals recovered by SWT is higher than that recovered by empirical mode decomposition (EMD) method, even at the high noise level. Finally, the simulation experiment of the orthogonal frequency division multiplexing (OFDM) signal has been carried out, which proves that the proposed scheme based on SWT can reduce the Bit-Error-Rate than other algorithms even under high noise level.

Autodetection of J Wave Based on Random Forest with Synchrosqueezed Wavelet Transform.

J wave is the bulge generated in the descending slope of the terminal portion of the QRS complex in the electrocardiogram. The presence of J wave may lead to sudden death. However, the diagnosis of J wave variation only depends on doctor's clinical experiences at present and missed diagnosis is easy to occur. In this paper, a new method is proposed to realize the automatic detection of J wave. First, the synchrosqueezed wavelet transform is used to obtain the precise time-frequency information of the ECG. Then, the inverse transformation of SST is computed to get the intrinsic mode function of the ECG. At last, the time-frequency features and SST-based and the entropy features based on modes are fed to Random forest to realize the automatic detection of J wave. As the experimental results shown, the proposed method has achieved the highest accuracy, sensitivity, and specificity compared with existing techniques.

On Estimating Turbulent Reynolds Stress in Wavy Aquatic Environment

AbstractSeveral methods have been developed for the estimation of the turbulent Reynolds stress in wavy aquatic environment. They are based on different physical assumptions and often give discrepant results. It is practically difficult to quantify the uncertainties in these estimations. Using high‐resolution velocity measurements of acoustic Doppler velocimeter (ADV) from a coastal benthic layer subject to moderate wave influence (the ratio of rms wave orbital velocity to current magnitude was 0.23–0.92), this study tests a Synchrosqueezed Wavelet Transform (SWT)‐based method and three existing methods (i.e., the Coherence, Cospectra, and Ensemble Empirical Mode Decomposition [EEMD] methods) for wave‐turbulence decomposition. In particular, we evaluate the performance of different methods for objective estimation of the turbulent Reynolds stress. Power spectra and cospectra analysis is conducted to quantify the uncertainties in the estimations. The results suggest that the Coherence method tends to overestimate the Reynolds stress due to incomplete removal of wave motions from the observed velocity records; the Cospectra method performs poorly because the empirical model does not fit the observed cospectra well; both the EEMD and SWT methods underestimate the Reynolds stress, as they tend to attribute turbulent fluctuations at frequencies in the vicinity of the wave frequencies to wave motions. In general, the SWT method performs best inducing lowest uncertainty in the Reynolds stress estimation. For the data set analyzed in this study, the estimations with the Coherence, Cospectra, EEMD, and SWT methods account for 70%, 50%, 51%, and 60% of the total covariance of horizontal and vertical velocities, respectively.

Chaotic Signal Denoising Based on Hierarchical Threshold Synchrosqueezed Wavelet Transform

In order to overcoming the shortcoming of single threshold synchrosqueezed wavelet transform(SWT) denoising method, an adaptive hierarchical threshold SWT chaotic signal denoising method is proposed. Firstly, a new SWT threshold function is constructed based on Stein unbiased risk estimation, which is two order continuous derivable. Then, by using of the new threshold function, a threshold process based on the minimum mean square error was implemented, and the optimal estimation value of each layer threshold in SWT chaotic denoising is obtained. The experimental results of the simulating chaotic signal and measured sunspot signals show that, the proposed method can filter the noise of chaotic signal well, and the intrinsic chaotic characteristic of the original signal can be recovered very well. Compared with the EEMD denoising method and the single threshold SWT denoising method, the proposed method can obtain better denoising result for the chaotic signal.

QRS Complex Detection in ECG Signals Using the Synchrosqueezed Wavelet Transform

ABSTRACTThe QRS complex is the most distinctive feature in an electrocardiogram (ECG) signal. Therefore, its detection serves as the starting point for various applications, such as detection of other waves and segments, heart-rate calculation, derivation of respiration, etc. In this paper, a novel technique for QRS detection is proposed. The technique is based on the recently proposed synchrosqueezed wavelet transform (SSWT), which is obtained by application of a post-processing technique known as synchrosqueezing to the continuous wavelet transform. Following SSWT, various other processing steps are applied, including a nonlinear mapping technique, which is novel in the context of QRS detection, to finally detect the R-peaks. The proposed algorithm is evaluated on the MIT-BIH arrhythmia database and overall sensitivity, positive predictivity and error rate obtained are 99.92%, 99.93%, and 0.15%, respectively.

Synchrosqueezed wavelet transform for damping identification

Synchrosqueezing is a procedure for improving the frequency localization of a continuous wavelet transform. This research focuses on using a synchrosqueezed wavelet transform (SWT) to determine the damping ratios of a vibrating system using a free-response signal. While synchrosqueezing is advantageous due to its localisation in the frequency, damping identification with the original SWT is not sufficiently accurate. Here, the synchrosqueezing was researched in detail, and it was found that an error in the frequency occurs as a result of the numerical calculation of the preliminary frequencies. If this error were to be compensated, a better damping identification would be expected. To minimize the frequency-shift error, three different strategies are investigated: the scale-dependent coefficient method, the shifted-coefficient method and the autocorrelated-frequency method. Furthermore, to improve the SWT, two synchrosqueezing criteria are introduced: the average SWT and the proportional SWT. Finally, the proposed modifications are tested against close modes and the noise in the signals. It was numerically and experimentally confirmed that the SWT with the proportional criterion offers better frequency localization and performs better than the continuous wavelet transform when tested against noisy signals.

Extractraction of non-stationary harmonic from chaotic background based on synchrosqueezed wavelet transform

The signal detection in chaotic background has gradually become one of the research focuses in recent years. Previous research showed that the measured signals were often unavoidable to be contaminated by the chaotic noise, such as the radar signal detection from sea clutter wave,signal source extraction from chaotic secure communication and ECG/EEG abnormal signal detection,etc.At present,there are two methods to detect the target signal from the chaotic background.One is to detect the target signals by using the difference in geometric structure between the chaotic signal and the target signal,and the other is to regard the chaotic signal as the noise,and the target signal is extracted from the chaotic background by the time frequency analysis method,such as wavelet transform and empirical mode decomposition. The first kind of method can detect the target signal well,but it needs to characterize the chaotic system and reconstruct the phase space,which is difficult in the practical applications.The second kind of method does not need to reconstruct the chaotic phase space and can effectively extract the target signal from the chaotic background.However,the wavelet transform lacks adaption and how to select the optimal wavelet basis and decomposition layers is a difficult problem.In the empirical mode decomposition there exists the mode mixing that is very sensitive to the noise.The synchrosqueezed wavelet transform (SST) effectively improves the mixing of mode by compressing the continuous wavelet coefficients in the frequency direction,but also it has good robustness to noise.Therefore,the SST can extract the harmonic signal well from the chaotic background.In the present algorithm of abstracting harmonic signal from chaotic background by SST,the harmonic signals are extracted by using single accumulation frequency range SST (SAFR-SST) based on wavelet ridge detection.If the target signal is stable harmonic signal,whose frequency does not change with time,the SAFR-SST method can have a high abstraction precision.But if the target signal is the non-stable harmonic signal whose frequency changes with time,the SAFR-SST method is not enough nor can obtain high abstraction precision.In order to overcome the shortcomings of the SST in extracting the non-stationary harmonic signal from the chaotic background, an improved SST extracting method is proposed which is based on the adaptive optimal cumulative frequency range. Firstly,the formulas of calculating the adaptive cumulative frequency range in SST extraction are deduced according to the relationship between the wavelet coefficient of non-stationary harmonic and the interval of supporting wavelet bases.Then,the optimal values of the parameters in the adaptive cumulative frequency range formula are calculated by the minimum energy error criterion according to the integrity and orthogonality of the intrinsic mode types function.Finally,the SST adaptive extraction of the non-stationary harmonic signal is realized according to the SST inverse transform.In experiment,the different types of non-stationary harmonics are extracted from the Lorenz and Duffing chaotic background.The experimental results show that the proposed method can effectively extract the non-stationary harmonic from the noisy chaotic background.Compared with the classical SST method with single cumulative frequency range,the proposed method has good performance in both mean square error and correlation coefficient.And when the chaotic background contains different-intenity Gauss white noises,the proposed method can also effectively abstract the non-stationary harmonic from the chaos and noise interference.So,the proposed method has a good practice value.

New methodology for modal parameters identification of smart civil structures using ambient vibrations and synchrosqueezed wavelet transform

Many applications related to modeling, control and condition assessment of smart structures require an accurate identification of natural frequencies and damping ratios. This identification is generally carried out through artificial and natural vibration sources. The latter is often preferred in many situations; yet their analysis represents a challenge since the measured data are non-stationary with a high noise level. In this paper, a new methodology is proposed based on the synchrosqueezed wavelet transform (SWT). First, the random decrement technique (RDT) is applied to estimate the free vibration response from measured ambient vibration signals. Then, the SWT algorithm is used to decompose the vibration response into individual mode components. Finally, the Hilbert transform (HT) and the Kalman filter (KF) are used to estimate the natural frequencies and damping ratios of each mode and to filter and smoothen the results. The effectiveness of the proposed approach is first validated through numerical simulation of damped free vibration response of a 3-degree of freedom (DOF) system with two closely-spaced frequencies. Then, numerical and experimental data of a benchmark 4-story 2×2 bay 3D steel frame structure subjected to ambient vibrations is analyzed. Finally, the natural frequencies and damping ratios of a real-life bridge located in Queretaro, Mexico are obtained. For comparison purposes, two recent and advanced signal processing techniques, the complete ensemble empirical mode decomposition (CEEMD) technique and the short-time multiple signal classification (ST-MUSIC) are also tested. Numerical and experimental results show accurate identification of the natural frequencies and damping ratios even when the signal is embedded in high-level noise demonstrating that the proposed methodology provides a powerful approach to estimate the modal parameters of a civil structure using ambient vibration excitations.

Harmonic signal extraction from noisy chaotic interferencebased on synchrosqueezed wavelet transform**Project supported by the National Natural Science Foundation of China (Grant No. 61171075), the Natural Science Foundation of Hubei Province, China (Grant No. 2015CFB424), the State Key Laboratory Foundation of Satellite Ocean Environment Dynamics, China (Grant No. SOED1405), the Hubei Provincial Key Laboratory Foundation of Metallurgical Industry Process System Science,

For the harmonic signal extraction from chaotic interference, a harmonic signal extraction method is proposed based on synchrosqueezed wavelet transform (SWT). First, the mixed signal of chaotic signal, harmonic signal, and noise is decomposed into a series of intrinsic mode-type functions by synchrosqueezed wavelet transform (SWT) then the instantaneous frequency of intrinsic mode-type functions is analyzed by using of Hilbert transform, and the harmonic extraction is realized. In experiments of harmonic signal extraction, the Duffing and Lorenz chaotic signals are selected as interference signal, and the mixed signal of chaotic signal and harmonic signal is added by Gauss white noises of different intensities. The experimental results show that when the white noise intensity is in a certain range, the extracting harmonic signals measured by the proposed SWT method have higher precision, the harmonic signal extraction effect is obviously superior to the classical empirical mode decomposition method.

Signal Reconstruction by Synchrosqueezed Wavelet Transform

Signal Reconstruction by Synchrosqueezed Wavelet Transform

Signal analysis via instantaneous frequency estimation of signal components

The empirical mode decomposition (EMD) algorithm, introduced by Huang et al. (Proc Roy Soc Lond Ser A Math Phys Eng Sci 454(1971):903–995, 1998), is arguably the most popular mathematical scheme for non-stationary signal decomposition and analysis. The objective of EMD is to separate a given signal into a number of components, called intrinsic mode functions (IMF’s) after which the instantaneous frequency (IF) and amplitude of each IMF are computed through Hilbert spectral analysis (HSA). On the other hand, the synchrosqueezed wavelet transform (SST), introduced by Daubechies and Maes (Wavelets in Medicine and Biology, pp. 527–546, 1996) and further developed by Daubechies et al. (Appl Comput Harmon Anal 30:243–261, 2011), is applied to estimate the IF’s of all signal components of the given signal, based on one single reference “IF function”, under the assumption that the signal components satisfy certain strict properties of a so-called adaptive harmonic model, before the signal components of the model are recovered. The objective of our paper is to develop a hybrid EMD-SST computational scheme by applying a “modified SST” to each IMF of the EMD, as an alternative approach to the original EMD-HSA method. While our modified SST assures non-negative instantaneous frequencies of the IMF’s, application of the EMD scheme eliminates the dependence on a single reference IF value as well as the guessing work of the number of signal components in the original SST approach. Our modification of the SST consists of applying vanishing moment wavelets (introduced in a recent paper by C.K. Chui, Y.-T. Lin and H.-T. Wu) with stacked knots to process signals on bounded or half-infinite time intervals, and spline curve fitting with optimal smoothing parameter selection through generalized cross-validation. In addition, we formulate a local cubic spline interpolation scheme for real-time realization of the EMD sifting process that improves over the standard global cubic spline interpolation, both in quality and computational cost, particularly when applied to bounded and half-infinite time intervals.

Harmonic signal extraction from chaotic interference based on synchrosqueezed wavelet transform

Extracting the harmonic signal from the chaotic interference background is very important for theory and practical application. The wavelet transform and empirical mode decomposition (EMD) have been widely applied to harmonic extraction from chaotic interference, but because the wavelet and EMD both present the mode mixing and are sensitive to noise, the harmonic signal often cannot be precisely separated out. The synchrosqueezing wavelet transform (SST) is based on the continuous wavelet transform, through compressing the time-frequency map of wavelet transform in the frequency domain, the highly accurate time-frequency curve is obtained. The time-frequency curve of SST which does not exist between cross terms, can better improve the mode mixing. The SST has also good robustness against noise. When the signal is a mixed strong noise, the SST can still obtain the clear time-frequency curve and approximate invariant decomposition results. In this paper, the SST is applied to the multiple harmonic signal extraction from chaotic interference background, and a new harmonic extracting method is proposed based on the SST. First, the signal obtained by mixing chaotic and harmonic signals is decomposed into intrinsic mode type function (IMTF) by the SST. Then using the Hilbert transform the frequency of each IMTF is analyzed, and the harmonic signals are separated from the mixed signal. Selecting the Duffing signal as the chaotic interference signal, the extracting ability of the proposed method for multiple harmonic signals is analyzed. The different harmonic extraction experiments are conducted by using the proposed SST method for different frequency intervals and different noise intensity multiple harmonic signals. And the experimental results are compared with those from the classical EMD method. When the chaotic interference signal is not contained by noise, the harmonic signal extraction effect is seriously affected by the frequency interval between harmonic signals. If the harmonic frequency interval between harmonic signals is relatively narrow, each harmonic signal cannot be accurately extracted by the EMD method. However, the harmonic extraction precision of SST method is not seriously influenced by the change of harmonic frequency interval, and when the frequency interval between harmonic signals is small the SST method can still accurately extract each harmonic signal from chaotic interference. When the noise contains a chaotic interference signal, the harmonic extraction effect of EMD method significantly decreases with noise intensity increasing. When the noise level reaches 80%, the extracted harmonic signal from the EMD method is seriously distorted, the correlation coefficient of the extracted harmonic signal with original harmonic signal is only about 0.6. With the increase of noise intensity, the harmonic extraction effect of SST method has also a declining trend. But as the noise intensity is within 120%, the harmonic extraction effect of SST method does not greatly change and the extracted harmonic signal precision is still higher, which shows that the harmonic extraction method based on the SST has good robustness against noise. The comprehensive experimental results show that the proposed SST method has high extracting precision for multiple harmonic signals of different frequency intervals, and the SST method has better robustness against Gauss white noise. The extracted results of harmonic signal are better than those from the classical empirical mode decomposition method.

The monogenic synchrosqueezed wavelet transform: a tool for the decomposition/demodulation of AM–FM images

The synchrosqueezing method aims at decomposing 1D functions into superpositions of a small number of “Intrinsic Modes”, supposed to be well separated both in time and frequency. Based on the unidimensional wavelet transform and its reconstruction properties, the synchrosqueezing transform provides a powerful representation of multicomponent signals in the time–frequency plane, together with a reconstruction of each mode.In this paper, a bidimensional version of the synchrosqueezing transform is defined, by considering a well-adapted extension of the concept of analytic signal to images: the monogenic signal. We introduce the concept of “Intrinsic Monogenic Mode”, that is the bidimensional counterpart of the notion of Intrinsic Mode. We also investigate the properties of its associated Monogenic Wavelet Decomposition. This leads to a natural bivariate extension of the Synchrosqueezed Wavelet Transform, for decomposing and processing multicomponent images. Numerical tests validate the effectiveness of the method on synthetic and real images.

Synchrosqueezed wavelet transform for frequency and damping identification from noisy signals

Identification of vibration parameters from the analysis of the dynamic response of a structure plays a key role in current health monitoring systems. This study evaluates the capabilities of the recently developed Synchrosqueezed Wavelet Transform (SWT) to extract instant frequencies and damping values from the simulated noise-contaminated response of a structure. Two approaches to estimate the modal damping ratio from the results of the SWT are presented. The results obtained are compared to other signal processing methods based on Continuous Wavelet (CWT) and Hilbert-Huang (HHT) transforms. It was found that the time-frequency representation obtained via SWT is sharped than the obtained using just the CWT and it allows a more robust extraction of the individual modal responses than using the HHT. However, the identification of damping ratios is more stable when the CWT coefficients are employed.

Ultrasonic thickness gauge measures moving sheets: Harris, R.V.Automation, 10, No. 8, p. 71 (1963)

Many applications related to modeling, control and condition assessment of smart structures require an accurate identification of natural frequencies and damping ratios. This identification is generally carried out through artificial and natural vibration sources. The latter is often preferred in many situations; yet their analysis represents a challenge since the measured data are non-stationary with a high noise level. In this paper, a new methodology is proposed based on the synchrosqueezed wavelet transform (SWT). First, the random decrement technique (RDT) is applied to estimate the free vibration response from measured ambient vibration signals. Then, the SWT algorithm is used to decompose the vibration response into individual mode components. Finally, the Hilbert transform (HT) and the Kalman filter (KF) are used to estimate the natural frequencies and damping ratios of each mode and to filter and smoothen the results. The effectiveness of the proposed approach is first validated through numerical simulation of damped free vibration response of a 3-degree of freedom (DOF) system with two closely-spaced frequencies. Then, numerical and experimental data of a benchmark 4-story 2×2 bay 3D steel frame structure subjected to ambient vibrations is analyzed. Finally, the natural frequencies and damping ratios of a real-life bridge located in Queretaro, Mexico are obtained. For comparison purposes, two recent and advanced signal processing techniques, the complete ensemble empirical mode decomposition (CEEMD) technique and the short-time multiple signal classification (ST-MUSIC) are also tested. Numerical and experimental results show accurate identification of the natural frequencies and damping ratios even when the signal is embedded in high-level noise demonstrating that the proposed methodology provides a powerful approach to estimate the modal parameters of a civil structure using ambient vibration excitations.