Synchrosqueezing Wavelet Transform Research Articles

Dual-Core Denoised Synchrosqueezing Wavelet Transform for Gear Fault Detection

Due to the heavy background noise and strong interference, a blurry or even false time-frequency (TF) representation (TFR) by synchrosqueezing wavelet transform (SST) always results in inaccurate or meaningless gear fault extractions. To solve this problem, a novel TF analysis (TFA) method termed dual-core denoised SST is proposed in this article. The concepts critical to the proposed method are: 1) The dual-core denoising is proposed. First, the measured signal is transformed to the binary tree structure of the prewhitening and pseudo-characterizing signals by cepstrum editing. Second, two empirical mode decomposition (EMD)-based denoising techniques are, respectively, proposed for each binary-tree signal, focused on extracting different gear features such as the modulation and transients. Then, the purified feature signal is obtained by mixing the dual-core denoising results. 2) The multistep denoising strategy is studied for further improving the denoising accuracy. The steps are determined by the Rényi entropy. 3) By the multistep dual-core denoising, the denoised TFR with such meaningful TF signatures of gear faults as the accurate demodulation components and distinct transients could be obtained for gear fault detection. The repeatable simulations and engineering applications are used to verify the performance of denoising and TF resolution enhancement for gear fault detection.

An Improved Multi-Ridge Extraction Method Based on Differential Synchro-Squeezing Wavelet Transform

It is very important to accurately extract the instantaneous frequency (IF) of complex non-stationary signals, so the signal processing methods based on IF are widely used in engineering. However, in non-stationary complex vibration signals, it is difficult to extract the instantaneous frequency under strong noise because the frequency changes rapidly. This paper proposes an improved multi-ridge extraction method based on differential synchro-squeezing wavelet transform (DSWT). First, an improved method DSWT is proposed to reduce the computation time and image noise of synchro-squeezing wavelet transform (SWT). The running time of the algorithm can be further reduced by segmenting the signal and compressing the time-frequency matrix. The image noise can be significantly reduced by differentiating SWT time-frequency matrix. It lays a good foundation for the extraction of the time-frequency ridge line. Secondly, an improved multi-ridge extraction method is proposed. The ridge jump due to end effect can be eliminated adaptively in segmented extraction. It further improves the time-frequency aggregation and extraction effect of the wavelet ridgeline image. Finally, the improved multi-ridge extraction method based on DSWT (DSWT-IMRE) is verified by the simulation data and experimental data under different conditions. Compared with the method proposed in previous study, the results show that DSWT-IMRE has higher extraction accuracy.

Evaluation of wave-turbulence decomposition methods applied to experimental wave and grid-generated turbulence data

Tidal energy turbines are significantly impacted by surface gravity waves and high turbulence levels, which lead to increased blade loads and consequent device fatigue. Accurately describing turbulence quantities is a key factor to improve numerical models and ensure the minimum necessary device longevity. The application of an appropriate wave-turbulence decomposition technique substantially improves estimates and must be debated by the tidal energy community. This work analyses two wave-turbulence decomposition techniques: i) linear wave theory and ii) Synchrosqueezing Wavelet Transform (SWT) based on physical modelling. The experiments were conducted in a towing tank and the physical model used Froude scaling to simulate wave heights and frequencies based on field measurements from a tidal energy candidate site in Australia. Turbulence was generated using a grid with 47 mm openings replicating turbulence intensities of 17%, 23% and 25%. Both decomposition techniques present limitations in wave frequencies above 0.7 Hz. Our results suggest that the SWT technique is more versatile and more efficient under various conditions. Restrictions to the linear wave theory method are discussed with regards to ADCP geometry and possible non-linearity. The variability obtained from the wave-turbulence decomposition techniques emphasizes the importance of establishing guidelines for turbulence characterization in tidal energy sites.

Nonlinear Phase Estimation and Compensation for FMCW Ladar Based on Synchrosqueezing Wavelet Transform

Frequency modulation continuous wave (FMCW) laser radar (Ladar) is a new radar system suitable for long-range detection and high-resolution imaging. However, the transmitted signal inevitably suffers from nonlinear frequency modulation errors which reduce the quality of Ladar imaging. We propose a nonlinear phase estimation and compensation method based on synchrosqueezing wavelet transform (SST). We first use SST to synchrosqueeze the dechirp signal containing a reference range in time-frequency domain and obtain the time-frequency information of the reference dechirp signal. As SST could aggregate the time-frequency distribution of noise, the proposed method is effective even in a noisy environment. A nonlinearity model in time-frequency domain is then built to estimate the nonlinear phase of the transmitted signals by using the time-frequency information of the reference dechirp signal. For the case of long-range detection, we adopt a residual video phase filtering to convert the nonlinear phase of the dechirp signal to range-independent phase errors. Finally, the nonlinearity of the dechirp signal is compensated using the estimated nonlinear phase of the transmitted signals. The experimental and real data tests show that the proposed method effectively improves the resolution of long-range Ladar imaging by compensating for the nonlinearity of the dechirp signal. Its advantage is the effectiveness for noisy and multicomponent FMCW Ladar signals.

Wave-Turbulence Decomposition Methods Applied to Tidal Energy Site Assessment

High levels of turbulence have been proven to substantially increase the blade loadings on tidal turbines, outlining the need of properly characterizing turbulence parameters in tidal energy sites. The presence of long surface gravity waves may cause a significant bias on the estimation of these parameters, which requires wave-turbulence decomposition methods that are currently missing from guidelines. Here, three techniques of decomposing wave and turbulence are tested: the stopband filter (SB), moving average filter (MA), and synchrosqueezing wavelet transform (SWT). The study site, Banks Strait, Tasmania, is a 16 km wide channel that presents high potential for tidal energy generation. Wave peak periods at the study site were found to vary mostly between 7 and 12 s, with maximum exceeding 15 s. Turbulence intensities (TI), turbulent kinetic energy (TKE), and integral scales are quantified. Our results indicate differences between the estimates obtained from each method. The MA highly underestimates turbulence, resulting in TI values which were nearly 50% lower than those obtained from other decomposition methods. While TI and TKE estimated from the SB and the SWT techniques are quite similar, integral length scales are considerably underestimated by the SB. These findings reveal that the SWT is a more reliable method because of the more accurate estimates of turbulence parameters and indicate the need of establishing guidelines which address wave-turbulence decomposition in tidal stream energy site assessments. Despite having shown to be quite a versatile technique, further investigation of its applicability in data from other prospective tidal energy sites is necessary to fully assess the generality of the SWT technique.

Research on a Signal Separation Method Based on Vold-Kalman Filter of Improved Adaptive Instantaneous Frequency Estimation

The fault vibration signal of rotating machinery system under strong background noise has the characteristics of non-stationary, non-Gaussian and complex components. In view of these characteristics, an improved method of signal separation based on Vold-Kalman filter (VKF) of adaptive instantaneous frequency estimation is proposed. First, a method for adaptive multiridge extraction of peaks detection based on synchro-squeezing wavelet transform (SWT) is proposed as the high-precision adaptive instantaneous frequency (IF) estimation method. The high precision IF estimation is used as the instantaneous frequency parameter of VKF, so that the complex multi-component non-stationary signal can be separated directly in the time domain and transformed into a signal combination composed of multiple stationary single-component signals and signal residues. Secondly, an improved method is proposed combining the adaptive IF estimation method with order tracking analysis and diagonal slice of bispectrum. In the improved method, the corresponding IF estimation of each component signal is taken as the reference frequency of its order tracking and the order spectrum analysis of each component signal is carried out respectively. Meanwhile, the signal residual is analyzed by diagonal slice of bispectrum, so as to suppress Gaussian noise and effectively separate and extract fault features in the vibration signal. Finally, the method is verified on simulation data and experimental data under different conditions. The results show that the improved method has higher extraction accuracy than other traditional methods. It has the superiority and the great potential for practical applications.

A novel non-unit transient based boundary protection for HVDC transmission lines using synchrosqueezing wavelet transform

Since high voltage direct current (HVDC) transmission system takes on significant tasks in coordinating the power grids asynchronous interconnection and the comprehensive utilization of energy resources, the reliable and fast faults clearance to guarantee the safety and stability of the power system should be attached great attention. This paper, based on the analysis of the HVDC boundary characteristics, proposes a novel non-unit transient based boundary protection as the main protection for HVDC transmission lines, and uses the novel synchrosqueezing wavelet transform (SWT) for time-frequency (T-F) representation. By synchrosqueezing and reassigning the T-F spectrum of the continuous wavelet transform (CWT), SWT can obtain a high resolution T-F spectrum, which brings higher reliability to protection. Based on the transmission differences between tuning voltage and low-frequency voltage by the boundary, this paper proposes the SWT-based non-unit transient boundary protection algorithm, and the ratio of the positive and negative voltage micro-increment is used to select the faulty line. Extensive PSCAD simulations of ±800 kV HVDC project and some field data are used to test the proposed protection scheme. Compared with the CWT-based boundary protection, experimental results verified the proposed method could perform rapidly and reliably in various types of fault, especially can be immune to commutation failure and shows good performance for switching operation as well as fault closer to the very begging of the line, and with high selectivity and sensitivity.

A New Fault Feature Extraction Method for Non-Stationary Signal Based on Advanced Synchrosqueezing Transform

The vibration signal of fault bearing is always non-stationary and multi-component. The strong background noise and low signal–noise-ratio make it more difficult to extract the fault features from the raw signal accurately. In this paper, based on the enhanced synchrosqueezing wavelet transform (SWT) which couples with the adaptive optimal cumulative frequency range, a new feature extracting method is proposed. The adaptive optimal cumulative frequency range is deduced according to the relationship between wavelet coefficient of vibration signal and the supporting interval of wavelet basis. The optimal parameters of wavelet and frequency range are calculated by the minimum-energy error criterion that is based on the integrity and orthogonality of the intrinsic mode types function. In the proposed method, first, the raw signal is denoised via a data-driven wavelet soft-threshold denoising method. Then, the preprocessed signal is decomposed into a series of intrinsic mode type (IMT) functions by the advanced SWT method, and the spectral kurtosis is used to select the sensitive IMT. Finally, the signal is reconstructed by the selected IMT and the ridge feature. The instantaneous frequency feature of sensitive IMT functions is analyzed by Hilbert transform. The proposed method is verified by two different experimental verifications, the results show that the proposed method could classify the fault type of bearing accurately.

Intelligent Bearing Fault Diagnosis Based on Tacholess Order Tracking for a Variable-Speed AC Electric Machine

Bearing fault diagnosis in an alternating-current (AC) electric machine (EM) under variable-speed conditions without a tachometer is a challenge. This issue is addressed through an intelligent method based on synchrosqueezing wavelet transform (SWT) and tacholess order tracking (TOT) techniques, which are used to analyze the synchronously sampled current and vibration signals, respectively. The current signal is typically an amplitude- and frequency-modulated (AM–FM) signal. SWT can not only extract the instantaneous frequencies of the AM–FM signal but also reconstruct the harmonic components accurately. Initially, the IF curve with the highest energy is extracted adaptively to reconstruct the rotation component. Subsequently, the mechanical rotation angle is calculated from the rotation component for TOT. The effectiveness of the proposed method is evaluated on a brushless direct-current motor and a permanent magnet synchronous generator with different fault bearings. The method’s superiority is verified through a comparative study. Given that the proposed method is intelligent and efficient, it can be used in the industry and extended to the fault diagnosis of other AC EMs.

Centrifugal pump fault detection based on SWT and SVM

Centrifugal pumps, like other rotating equipment, produce vibration signals during operation. Vibration signals often contain pump state information. Therefore, we can obtain pump state information by using appropriate signal processing methods. Synchrosqueezing wavelet transform (SWT) is a new time-frequency analysis technology. It is an algorithm for rebuilding time-frequency signals, which is similar to the empirical mode decomposition method. It can improve the time-frequency resolution of the signal compared with wavelet transform. In this paper, the SWT is used to analyze the vibration signal of centrifugal pump and extract characteristics. The data shows that the SWT can effectively extract the information of signal in time domain and frequency domain. Then we use the Support Vector Machine (SVM) to classify the features and realize the fault diagnosis of centrifugal pump. The result proves that the fault diagnosis method based on the SWT and SVM.

Seismic data analysis using synchrosqueezing short time Fourier transform

The synchrosqueezing wavelet transform (SWT) reallocates the wavelet transform values to different points, hence produces a sharp spectral decomposition for the input signal. The SWT method was widely used for de-noising, spectral decomposition, etc. In this paper, a new synchrosqueezing method was proposed based on short time Fourier transform. The proposed method reassigns the short time Fourier transform values to different points, thus produces a concentrated time–frequency map. Furthermore, the proposed method has an inverse formula, which allows the reconstruction of the input signal from its spectral decomposition. Examples showed that the proposed method is effective for revealing the time–frequency characterizations of non-stationary signals.

Multisensor signal denoising based on matching synchrosqueezing wavelet transform for mechanical fault condition assessment

Since it is difficult to obtain the accurate running status of mechanical equipment with only one sensor, multisensor measurement technology has attracted extensive attention. In the field of mechanical fault diagnosis and condition assessment based on vibration signal analysis, multisensor signal denoising has emerged as an important tool to improve the reliability of the measurement result. A reassignment technique termed the synchrosqueezing wavelet transform (SWT) has obvious superiority in slow time-varying signal representation and denoising for fault diagnosis applications. The SWT uses the time–frequency reassignment scheme, which can provide signal properties in 2D domains (time and frequency). However, when the measured signal contains strong noise components and fast varying instantaneous frequency, the performance of SWT-based analysis still depends on the accuracy of instantaneous frequency estimation. In this paper, a matching synchrosqueezing wavelet transform (MSWT) is investigated as a potential candidate to replace the conventional synchrosqueezing transform for the applications of denoising and fault feature extraction. The improved technology utilizes the comprehensive instantaneous frequency estimation by chirp rate estimation to achieve a highly concentrated time–frequency representation so that the signal resolution can be significantly improved. To exploit inter-channel dependencies, the multisensor denoising strategy is performed by using a modulated multivariate oscillation model to partition the time–frequency domain; then, the common characteristics of the multivariate data can be effectively identified. Furthermore, a modified universal threshold is utilized to remove noise components, while the signal components of interest can be retained. Thus, a novel MSWT-based multisensor signal denoising algorithm is proposed in this paper. The validity of this method is verified by numerical simulation, and experiments including a rolling bearing system and a gear system. The results show that the proposed multisensor matching synchronous squeezing wavelet transform (MMSWT) is superior to existing methods.

Blind separation of asymmetric signals based on Synchrosqueezing Wavelet Transform

A blind separation algorithm based on synchronous squeezing wavelet transform is proposed to solve the blind separation problem of single channel asymmetric signals in satellite communications. First, the algorithm is used to synchronize the strong signal. Then, the signal time-frequency curve is extracted by synchronous extrusion wavelet transform. Finally, the weak signal interference is filtered out from the mixed signal except the noise and the main frequency of the strong signal. Therefore, the ber of the strong signal demodulation is reduced. The algorithm has the characteristics of blind separation of single channel asymmetric signals without prior information sequence sent by cooperative communicators. The simulation results show that the performance of strong signal demodulation error is better than that of mixed signal direct hard decision.

Matching Synchrosqueezing Wavelet Transform and Application to Aeroengine Vibration Monitoring

This paper presents a new time–frequency (TF) analysis method called matching synchrosqueezing wavelet transform (MSWT) to signals with fast varying instantaneous frequency (IF). The original synchrosqueezing wavelet transform (SWT) can effectively improve the readability of TF representation (TFR) of signals with slowly varying IF. However, SWT still suffers from TF blurs for signals with fast varying IF. Moreover, the variable operating conditions of the aeroengine always make the vibration a signal with fast varying IF, especially when it comes to significant speed changes, which results in the obscure TFR for aeroengine vibration monitoring. In this paper, the MSWT introduces a chirp rate estimation into a comprehensive IF estimation to match the TF structure of the signals with fast varying IF and thus to achieve a highly concentrated TFR as the standard TF reassignment methods. Most importantly, the MSWT retains the reconstruction benefit like the SWT. The proposed MSWT is validated by both numerical simulation and applications in a bat echolocation signal analysis. Finally, a case study of a dual-rotor turbofan engine is given to illustrate the effectiveness of the proposed method for aeroengine vibration monitoring.

Zoom Synchrosqueezing Transform for Instantaneous Speed Estimation of High Speed Spindle

Instantaneous speed (IS) is of great significance of fault diagnosis and condition monitoring of the high speed spindle. In this paper, we propose a novel zoom synchrosqueezing transform (ZST) for IS estimation of the high speed spindle. Due to the limitation of the Heisenberg uncertainty principle, the conventional time-frequency analysis (TFA) methods cannot provide both good time and frequency resolution at the whole frequency region. Moreover, in most cases, the interested frequency component of a signal only locates in a narrow frequency region, so there is no need to analyze the signal in the whole frequency region. Different from conventional TFA methods, the proposed method arms to analyze the signal in a specific frequency region with both excellent time and frequency resolution so as to obtain accurate instantaneous frequency (IF) estimation results. The proposed ZST is an improvement of the synchrosqueezing wavelet transform (SWT) and consists of two steps, i.e., the frequency-shift operation and the partial zoom synchrosqueezing operation. The frequency-shift operation is to shift the interested frequency component from the lower frequency region to the higher frequency to obtain better time resolution. The partial zoom synchrosqueezing operation is conducted to analyze the shifted signal with excellent frequency resolution in a considered frequency region. Compared with SWT, the proposed method can provide satisfactory energy concentrated time-frequency representation (TFR) and accurate IF estimation results. Additionally, an application of the proposed ZST to the IS fluctuation estimation of a motorized spindle was conducted, and the result showed that the IS estimated by the proposed ZST can be used to detect the quality of the finished workpiece surface.

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.