Non-stationary Signal Processing Research Articles

The Method for Determining Optimal Analysis Length of Vibration Data Based on Improved Multiscale Permutation Entropy

Research on damage diagnosis or safety monitoring based on structural vibration response is one of the hot issues in the engineering field. The characteristic information of the structure is obtained by analyzing the structure response data. In the process of data analysis, the choice of data length is very important, which is related to the validity of the structure monitoring results. At present, the selection of data length is usually subjective, which reduces the rigor of the structure monitoring process. Therefore, a method based on improved multiscale permutation entropy (IMPE) is proposed to determine the optimal data analytical length (ODAL) of vibration data. This method creatively applies multiscale permutation entropy (MPE) to the field of data length analysis when processing nonlinear and nonstationary signals and optimizes MPE with the help of the improved coarse-grained method to obtain IMPE. IMPE is sensitive to different data lengths, and the entropy changes with the increase of the data length and tends to be stable. Here, the stable value is defined as a standard entropy. The entropy satisfying 97% of the standard entropy is used as the effective entropy, and the corresponding data length value of the effective entropy is selected as the ODAL of the vibration data. This method is suitable for many fields, provides a reliable data analytical length for data analysis, and has good engineering practicability.

Block-wise recursive APES aided with frequency-squeezing postprocessing and the application in online analysis of vibration monitoring signals

The amplitude and phase estimation of a sinusoid (APES) method, receiving superior results to conventional Fourier transform (FT) featured as narrower spectral peaks and lower side-lobe levels, has been widely applied in the fields of medical imaging, remote sensing, synthetic aperture radar, etc. Both FT and APES suppose the signal collected is stationary. When handing with non-stationary signals, we have to resort to the adaptive extension of FT, i.e., the short time Fourier transform (STFT). Likewise, we also need to extend APES to adapt to changing signal spectrum while maintaining the advantage of high-resolution. To this end, this paper proposes a block-wise recursive APES (BRAPES) method for online spectral estimation of time-varying signals, in which the size of the updating block is adjustable to accommodate the real-time requirement of online computing. Additionally, inspired by recent developments in reassignment method (RM) and synchrosqueezing transform (SST) against the Heisenberg uncertainty principle, we construct a frequency-squeezing postprocessing (FSP) technique aiming at improving the concentration of time–frequency (TF) representation by BRAPES, which essence is to move the spectral lines towards the nearest natural frequency rather than changing the amplitude. The numerical examples demonstrate that the proposed approach, BRAPES aided with FSP (BRAPES-FSP), not only has high accuracy in processing nonstationary signals, but also can adopt a much shorter data sequence for analysis than Fourier class methods, which greatly guarantee the real-time performance of computation in online environment. Furthermore, we employ BRAPES-FSP to process the acceleration responses of cables of a real cable-stayed bridge and a experimental cable in workshop, proving its capability and potential of dealing with vibration monitoring signals in such fields as structural health monitoring.

GPR noise reduction by TVD and TVD-EMD

The existence of coherent and incoherent (random) noises in the ground penetration radar (GPR) signals using high-frequency electromagnetic waves is inevitable; therefore, the elimination of noise from GPR data before performing any additional analysis is of great importance to increase the efficiency of the interpretations. We apply the Total Variation De-noising (TVD) and Savitzky-Golay (SG) filter, on the synthetic and real GPR data. For a better perception, we compare the same trace of the data before and after the experiences. The results indicate that the TVD method is more effective than common adaptive filtering in the time domain for reducing noise such as the SG filter which acts as a low-pass filter for smoothing data based on a polynomial least-squares approximation; however, due to the visibility of staircase artifacts using the TVD method, GPR data is first transferred to the empirical mode decomposition (EMD) frame which is useful for non-linear and non-stationary signal processing, then the TVD method is applied on it; ultimately, noise reduction using TVD is compared in the time and EMD domains. The comparison of the outputs shows that the TVD algorithm in the EMD domain, based on the sequential extraction of the energy belonging to the different intrinsic time scales of the signal, provides better noise attenuation than the other algorithms. In addition, TVD-EMD preserves the event forms, signal forms and improves the continuity in sections.

Synchro spline-kernelled chirplet extracting transform: A useful tool for characterizing time-varying features under noisy environments and applications to bearing fault diagnosis

Profiting from the good ability in time–frequency (TF) representation (TFR), synchroextracting transform (SET) has been extensively used for non-stationary signal processing. Vibration signals of bearing often contain strong noise, whose time-varying features are easily contaminated by noise information, affecting the TF readability of SET. Effectively identifying the time-varying features from noise are important for fault diagnosis. For this purpose, by introducing the frequency-rotating operator and frequency-shifting operator of spline-kernelled chirplet transform (SCT), this paper studies a new time–frequency analysis (TFA) method called synchro spline-kernelled chirplet extracting transform (SSCET). It is shown that the proposed method can effectively reveal the variations of time-varying features while retaining the energy concentration in noisy cases. Besides, the proposed method uses the studied binary TF image separation strategy to extract the time-varying features of multi-component signals. The comparative analysis results in simulations verified its effectiveness in energy concentration and anti-noise. The proposed method is finally successfully applied to the analysis of a bat echo signal as well as the fault diagnosis of a rolling bearing.

Signal Nonstationary Degree Evaluation Method Based on Moving Statistics Theory

Nonstationary signal refers to the signal whose statistics change with time, and its nonstationary degree evaluation can provide effective support for the evaluation of the operating state of the signal source. This paper introduced a variety of typical signal global and local nonstationary degree evaluation methods and compared the applicable scope of different evaluation methods. In view of the limitations of the existing evaluation methods in the scope of application, considering the influence of adjacent signal points, this paper proposed the concepts and calculation methods of the moving mean, moving standard deviation, moving variation coefficient, and moving Hurst exponent based on the theory of moving statistics. According to different nonstationary degree evaluation methods, three different fields of signals (sinusoidal signal, mechanical fault signal, and ECG signal) are analyzed. The results show that, compared with the existing nonstationary degree evaluation methods, the signal nonstationary degree evaluation method proposed in this paper can reveal the time-varying details of the nonstationary signals, with high precision and strong stability, and has unique advantages in nonstationary signal processing.

Time–frequency analysis via complementary ensemble adaptive local iterative filtering and enhanced maximum correlation kurtosis deconvolution for wind turbine fault diagnosis

A complementary ensemble adaptive local iterative filtering (CEALIF) and enhanced maximum correlation kurtosis deconvolution (EMCKD) approach is proposed for weak fault signals in wind turbine bearings, which are easily concealed by strong background noise and susceptible to intermittent interference. The adaptive local iterative filtering (ALIF), as a novel nonstationary signal processing technique, can perform adaptive filtering based on the signal itself characteristics. However, its mode mixing is an annoying problem. To relieve this problem, the noise-assisted CEALIF-based filtering is proposed. Nonetheless, the ambient noise present in the original signal is retained in the component of interest. Maximum correlation kurtosis deconvolution (MCKD) is an effective tool for enhancing periodic pulses. However, its deconvolution parameters need to be set manually, and are more demanding when the bearing failure is weak. To address this circumstance, this paper introduces the particle swarm algorithm (PSO) to solve the optimal deconvolution parameters and proposes EMCKD. Firstly, by employing CEALIF, the original signal is adaptively filtered into a sequence of IMFs. Then, the IMF that best characterizes the fault information is selected based on the weighted kurtosis index (WKI). Finally, the shock components of the selected IMF are enhanced to extract the periodic shock based on EMCKD. The proposed approach can accurately extract fault characteristics by analyzing the whole life cycle signals of bearings and fault signals of a 1.5 MW direct-drive wind turbine within strong background noise. Further, the proposed approach is implemented for the compound fault extraction of bearings, and the compound fault information of the inner race as well as the outer race of the bearings is successfully extracted.

An Improved Empirical Mode Decomposition Method for Vibration Signal

With the development of electronic measurement and signal processing technology, nonstationary and nonlinear signal characteristics are widely used in the fields of error diagnosis, system recognition, and biomedical instruments. Whether these features can be extracted effectively usually affects the performance of the entire system. Based on the above background, the research purpose of this paper is an improved vibration empirical mode decomposition method. This article introduces a method of blasting vibration signal processing—Differential Empirical Mode Decomposition (DEMD), combined with phosphate rock engineering blasting vibration monitoring test, and Empirical Mode Decomposition (EMD) to compare and analyze the frequency screening of blasting vibration signals, the aliasing distortion, and the power spectrum characteristics of the decomposed signal. The results show that compared with EMD, DEMD effectively suppresses signal aliasing and distortion, and from the characteristics of signal power spectrum changes, DEMD extracts different dominant frequency components, and the frequency screening effect of blasting vibration signals is superior to EMD. It can bring about an obvious improvement in accuracy, and the calculation time is about 4 times that of the EMD method. Based on the ground analysis of ground motion signals, this paper uses the EMD algorithm to analyze measured ground blast motion signals and study its velocity characteristics and differential time, which provides a new way of studying motion signals.

Second-order synchroextracting wavelet transform for nonstationary signal analysis of rotating machinery

Characterizing nonstationary signals with widely changing instantaneous frequency features is a challenging issue for time-frequency analysis (TFA) method. A novel TFA method termed second-order synchroextracting wavelet transform (SSEWT) is proposed for this purpose. The method extends the existing synchroextracting transform to the context of wavelet transform, and introduces the second-order instantaneous frequency estimate to improve its capability of processing nonstationary signals. The proposed method provides concentrated time-frequency representation with multiple resolutions, and retains good invertibility. The theories concerned and discrete implementation of the SSEWT are presented. Numerical simulations and experimental data collected from rotating machinery are employed to verify the competitive advantages of the SSEWT in revealing the local time-frequency features of nonstationary signals.

An extended bi-dimensional empirical wavelet transform based filtering approach for engineering surface separation using high definition metrology

Surface topography is an important index to evaluate product quality, and filtering is a key step to realize the extraction of embedded surface components. Based the reported achievements, bi-dimensional empirical wavelet transform (BEWT) outperforms the traditional filtering approaches in nonlinear and non-stationary signal processing. High definition metrology (HDM) is used to measure the engineering surface, which provides a 3D inspection of the entire surface. This paper proposes a novel extended bi-dimensional empirical wavelet transform (EBEWT) based filtering approach for engineering surface separation. The proposed approach consists of HDM data preprocessing, adaptive spectrum segmentation, EBEWT and areal surface evaluation. To verify the performance, the proposed approach is compared with areal Gaussian filter and the original BEWT by numerical simulations and four real-world cases. The results demonstrate that the EBEWT based filtering approach can separate the engineering surface properly, thereby indicating the irregularities of manufacturing process and function behaviors of the part.

An automated classification of EEG signals based on spectrogram and CNN for epilepsy diagnosis

Epilepsy disease is one of the most prevalent neurological disorders caused by malfunction of large symptoms number of neurons. That’s lead us to propose an automated approach to classify Electroencephalography (EEG) signals of the aforementioned pathology. To realize an efficient seizures detection the output of our classification is divided into three classes; normal, pre-ictal and ictal class. In fact, we propose to use the Short-Time Fourier Transform (STFT) as a non-stationary signal processing technique to extract useful information from the EEG signals. After that, we transform the STFT into a spectrogram image which will be used as an input in the classification process. In this context, we developed a deep convolutional neural network (CNN) model capable to efficiently detect and classify epilepsy seizures based on the EEG spectrogram images. It should be noted that the database used in this work is the publicly available EEG data set of Bonn University. In order to evaluate the performance of the proposed classification method several metrics are calculated, such as; sensitivity, specificity, accuracy and precision. The experimental results prove that the proposed method is a powerful tool in classifying EEG signals with a high average accuracy rate of 98.22%.

A Spectrum Adaptive Segmentation Empirical Wavelet Transform for Noisy and Nonstationary Signal Processing

Compared with thresholding methods based on the traditional wavelet transform (WT), empirical wavelet transform (EWT) has been demonstrated to outperform in terms of noise elimination by constructing an adaptive filter bank. However, as the state-of-the-art version of EWT, enhanced EWT (EEWT) requires that the number of components in the superposed signal as prior knowledge is known, which is impractical in reality and limits the application of this method. In this paper, a novel EWT that can adaptively estimate the number of components in the signal and achieve spectrum segmentation is proposed and is referred to as the spectrum adaptive segmentation empirical wavelet transform (SAS-EWT). Furthermore, a customized SAS-EWT for speech enhancement is proposed. According to the experimental results, our proposed SAS-EWT provides more accurate boundary detection and better denoising performance. The proposed method improves the performance by up to 5% in terms of PESQ, STOI, and SNR in comparison to EEWT.

Cyclostationary Signals Analysis Methods Based on High-Dimensional Space Transformation Under Impulsive Noise

Cyclostationary signals analysis is a highly widespread tool for non-stationary signals processing. In practical transmission, signals may be contaminated by non-stationary non-Gaussian impulse noises. However, cyclostationary is weak in dealing with such non-Gaussian distributions. In this paper, a cyclic mean kernel function is proposed for cyclostationary signal analysis under impulse noise, based on a high-dimensional space transformation. Then, the generalized cyclic mean kernel function is proposed based on the constructed generalized Hankel matrix. The simulation results show that the cyclostationary signal frequency estimation methods based on these two functions have advantages in performance and robustness over the existing methods under impulsive noise.

New shift-invariant spaces for the linear canonical transform and their applications

The shift-invariant spaces act as a crucial roll in signal processing and multiresolution analysis. With the linear canonical transform (LCT) has attracted much attention in signal processing, the researches of the shift-invariant spaces for the LCT have been studied in some literature. However, these results are still related to the traditional Fourier transform (FT), which leads to the limitations for processing non-stationary signals. To overcome these shortcomings, in this paper, the new definition of shift-invariant spaces associated with the LCT and their applications have been presented. First, by applying the classical LCT convolution theorem, the new shift-invariant spaces for the LCT have been developed. Subsequently, by utilizing the new definition, the typical uniform sampling, the sampling using arbitrary basis functions, and the non-ideal sampling for the LCT have been presented. In addition, as another important application, the fractional delay filters for the LCT have also been studied. Finally, the simulations have been presented to show the effectiveness and correctness of the developed theorems.

Synchrosqueezing extracting transform and its application in bearing fault diagnosis under non-stationary conditions

The measured vibration signals of mechanical equipment with defects are generally non-stationary. Time–frequency analysis is an effective tool in processing non-stationary signals. However, the concentration of time–frequency representation will greatly affect the performance of feature extraction. Thus, a more concentrated time–frequency analysis method plays an important role in mechanical signal processing and fault diagnosis. A novel time–frequency analysis method, called synchrosqueezing extracting transform has been proposed in this study. The proposed method can not only well extract the time-varying information of the nonstationary signal then achieve a better-concentrated time–frequency representation, but also have better noise robustness and lower time-consuming than the traditional time–frequency analysis methods. The analysis of numerical signals verified the great performance of this method. Finally, synchrosqueezing extracting transform is used to process the bearing vibration signals under variable speed conditions. It has been demonstrated that the proposed method achieves better results than other state-of-art time–frequency analysis methods.

An Improved BEMD Method for Denoising the Phase-OTDR Signal

Empirical mode decomposition (EMD) is often used for the processing of non-linear and non-stationary signals, but it needs further improvement in some specific application scenarios. According to the characteristics of Phase-OTDR signal, this paper improves the two-dimensional empirical mode (BEMD) and uses it to denoise the Phase-OTDR signal. The improved method takes into account the inconsistency of the correlation between the time axis and the space axis, and uses the spatial resolution of the Phase-OTDR signal as the minimum interval to enter the envelope surface structure. At the same time, the boundary is smoothed during the reconstruction of the sub-envelope surface. Experiments on the noisy Phase-OTDR signal verified the effectiveness of the improved method in this paper.

Degradation Status Recognition of Axial Piston Pumps under Variable Conditions Based on Improved Information Entropy and Gaussian Mixture Models

Axial piston pumps are crucial for the safe operation of hydraulic systems and usually work under variable operating conditions. However, deterioration status recognition for such pumps under variable conditions has rarely been reported until now. Therefore, it is valuable to develop effective methods suitable for processing variable conditions. Firstly, considering that information entropy has strong robustness to variable conditions and empirical mode decomposition (EMD) has the advantages of processing nonlinear and nonstationary signals, a new degradation feature parameter, named local instantaneous energy moment entropy, which combines information entropy theory and EMD, is proposed in this paper. To obtain more accurate degradation feature, a waveform matching extrema mirror extension EMD, which is used to suppress the end effects of EMD decomposition, was employed to decompose the original pump’s outlet pressure signals, taking the quasi-periodic characteristics of the signals into consideration. Subsequently, given that different failure modes of pumps have different degradation rates in practice, which makes it difficult to effectively recognize degradation status when using the modeling methods that need the normal and failure data, a Gaussian mixture model (GMM), which has no need for failure data when building a degradation identification model, was introduced to capture the new degradation status index (DSI) to quantitatively assess the degradation state of the pumps. Finally, the effectiveness of the proposed approach was validated using both simulations and experiments. It was demonstrated that the defined local instantaneous energy moment entropy is able to effectively characterize the degree of degradation of the pumps under variable operating conditions, and the DSI derived from the GMM is able to accurately identify different degradation states when compared with the previously published methods.

Fault diagnosis method of rolling bearing based on the multiple features of LMD and random forest

The occurrence of rolling bearing fault not only affects the operation efficiency of mechanical equipment, but also leads to the safety accidents. The research on fault diagnosis of rolling bearing is of great practical significance to improve the reliability of mechanical equipment, avoid unexpected faults and ensure safety in production. In this paper, a fault diagnosis method of rolling bearing based on the multiple features of local mean decomposition (LMD) and random forest is proposed. It is suitable for processing non-stationary vibration signals generated by rolling bearings and adaptively decomposing the characteristic information excited by faults into a series of product function (PF). Then, the mixed feature vectors of each PF are constructed from different angles to realize the extraction and quantification of the rolling bearing fault feature information. Finally, combined with the random forest algorithm, accurate identification of the type of rolling bearing failure is achieved. The overall recognition rate reached 94.4%. It proves that the method proposed in this paper is effective.

Mean-optimized mode decomposition: An improved EMD approach for non-stationary signal processing

As an effective signal separation method of non-stationary signal, empirical mode decomposition (EMD) has been widely used in the data or time series analysis of many engineering fields. However, the decomposing result of EMD often is affected by the fitting in mean curve construction and the sifting process. In this paper, the mean-optimized mode decomposition (MOMD) procedure is proposed to enhance the performance of the original EMD in mean curve construction. Also, the proposed MOMD algorithm is compared with original EMD through analyzing two artificial signals and the analysis results demonstrate that MOMD has much more significantly improvement in decomposition performance and precision than the original EMD. Last, MOMD is introduced to the signal processing stemming from the faulty rolling bearing and the rotor system with failure. Also, the comparison of the proposed MOMD method with EMD was made and the analysis results show that MOMD obtains much more accurate IMFs and fault diagnostic effect than the original EMD method.

Integration of Wavelet Denoising and HHT Applied to the Analysis of Bridge Dynamic Characteristics

When the dynamic characteristics of a bridge structure are analyzed though Hilbert–Huang transform (HHT), the noise contained in the bridge dynamic monitoring data may seriously affect the performance of the first natural frequency identification. A time-frequency analysis method that integrates wavelet threshold denoising and HHT is proposed to overcome this deficiency. The denoising effect of the experimental analysis on the simulated noisy signals proves the effectiveness of the proposed method. This method is used to perform denoising pre-processing on the dynamic monitoring data of Sutong Bridge, and the denoised results of different methods are compared and analyzed. Then, the best denoising data are selected as the input data of Hilbert spectrum analysis to identify the structural first natural frequency of the bridge. The results indicate that the wavelet-empirical mode decomposition (EMD) method effectively reduces the interference of random noise and eliminates useless intrinsic modal function (IMF) components, and the excellent properties of the signal evaluation index after denoising make the method suitable for processing non-stationary signals with noise. When Hilbert spectrum analysis is applied to the denoised data, the first natural frequency of the bridge structure can be identified clearly and is consistent with the theoretical calculation. The proposed method can effectively determine the natural vibration characteristics of the bridge structure.

Research on Rolling Bearing Fault Diagnosis Using Improved Majorization-Minimization-Based Total Variation and Empirical Wavelet Transform

Bearings are among the most widely used core components in mechanical equipment. Their failure creates the potential for serious accidents and economic losses. Vibration signature analyses are the most common approach to assess the viability of bearings due to its ease of measurement and high correlation with structural dynamics. However, the collected vibration signals of rolling bearings are usually nonstationary and are inevitably accompanied by noise interference. This makes it difficult to extract the feature frequency for the failed bearing and affects the diagnosis accuracy. The majorization-minimization-based total variation (TV-MM) denoising algorithm effectively removes the noise interference from the signal and highlights the related feature information. The value of its main parameter λ determines the quality of the denoising effect. However, manually selecting parameters requires professional experience in a process that it is time-consuming and laborious, while the use of genetic algorithms is cumbersome. Therefore, an improved particle swarm algorithm (IPSO) is used to find the optimal solution of λ. The IPSO utilises the mutation concept in genetic algorithms to reinitialise the particles with a certain probability after each update. In addition, the empirical wavelet transform (EWT) is an adaptive signal processing method suitable for processing nonlinear and nonstationary signals. Therefore, this paper presents an ensemble analysis method that combines the IPSO, TV-MM, and EWT. First, IPSO is used to optimise the denoising parameter λ. The TV-MM under this parameter effectively removes the background noise interference and improves the accuracy of the subsequent modal decomposition. Then, the EWT is used for the adaptive division to produce a set of sequences. Finally, Hilbert envelope demodulation is performed on each component to realise fault diagnosis. The results from simulations and signals received from defective bearings with outer race fault, inner race fault, and rolling element fault demonstrate the effectiveness of the proposed method for fault diagnosis of rolling bearings.