Analysis Of Non-stationary Signals Research Articles

Harmonic analysis of nonstationary signals with application to LHC beam measurements

Harmonic analysis has provided powerful tools to accurately determine the tune from turn-by-turn data originating from numerical simulations or beam measurements in circular accelerators and storage rings. Methods that have been developed since the 1990s are suitable for stationary signals, i.e., time series whose properties do not vary with time and are represented by stationary signals. However, it is common experience that accelerator physics is a rich source of time series in which the signal amplitude varies over time. Furthermore, the properties of the amplitude variation of the signal often contain essential information about the phenomena under consideration. In this paper, a novel approach is presented, suitable for determining the tune of a nonstationary signal, which is based on the use of the Hilbert transform. The accuracy of the proposed methods is assessed in detail, and an application to the analysis of beam data collected at the CERN Large Hadron Collider is presented and discussed in detail. Published by the American Physical Society 2024

The linear canonical W-transform

The time-frequency spectrum of seismic data is commonly used as an attribute in the analysis and interpretation of nonstationary seismic signals. To improve the capability of the W-transform to analyze nonstationary data, we introduce the linear canonical W-transform (LCWT) by implementing an affine matrix along with scaling parameters to generate high resolution and energy-concentrated time-frequency spectra. More features of nonstationary signals can be explored in the time-linear canonical frequency domain by transforming the time-frequency plane, which makes the algorithm more applicable to seismic signals. For the completeness of the LCWT, we also develop the inverse LCWT to extend its applications. Examples of synthetic and field seismic data show that a highly resolved and energy-concentrated time-frequency spectrum can be estimated with the LCWT with negligible additional computational burden. In addition, our algorithm is promising for several seismic data processing and interpretation techniques, such as reservoir characterization and thin layer identification.

Refined linear chirplet transform for time–frequency analysis of non-stationary signals

Time-Frequency Analysis (TFA) stands as a pivotal technique for unraveling the inherent properties of signals, which are omnipresent across natural phenomena. Current methodologies encounter significant challenges in the analysis of non-stationary signals, especially those characterized by closely-spaced or intersecting instantaneous frequencies. In this study, we present the refined linear chirplet transform (RLCT), inspired by the concept of the generalized linear chirplet transform (GLCT), to derive the time–frequency representation of non-stationary signals. By increasing the number of chirp rate searches in GLCT, one can derive higher time–frequency concentration, however, this costs much higher computational resources. In the proposed RLCT, the capacity in searching the optimal chirp rates, or equivalently the rotation angles on the time–frequency plane, is dramatically improved by adopting a local search strategy for mono-component signals. As a sequence, the resolution for the multi-component signals, even with overlapping instantaneous frequency, is greatly enhanced by adopting the idea of the adaptive linear chirplet transform (ALCT), where the components with high energy concentration are consecutively detected and subtracted from consideration. Two critical metrics are employed to assess the performance (accuracy and resolution) of the TFA methods: total energy and energy ratio. The latter is defined as the proportion of energy within a narrowly defined frequency band centered around the actual instantaneous frequency, relative to the total energy. The validation examples demonstrate that the LCT-based methods dramatically enhance the accuracy compared to short-time Fourier transform, in terms of total energy. Furthermore, among the LCT family investigated, the proposed method offers marked improvements in resolution, in terms of energy ratio, while maintaining algorithmic simplicity. The seismic responses of a lighthouse during a severe earthquake are investigated by the RLCT to reveal its frequency drop and recovery due to the opening and closing of the existing cracks.

Context-aware voltage sag waveform decomposition method using hybrid models for complex power quality detection

To analyze the voltage sag characteristics of distribution networks, automotive companies need an accurate and efficient non-stationary signal analysis tool to extract voltage sag feature information from power quality monitors and fault recorders, which is crucial for automotive companies to analyze grid characteristics and improve localized charging strategies. We innovatively propose a hybrid decomposition method to decompose voltage sag waveforms from composite disturbance data. Subsequently, we design a context-aware mechanism to adapt the proposed decomposition method to the complex power quality data in different regions. In addition, tests were conducted on an integrated power quality simulation system to verify that this method can accurately decompose the voltage sag waveform from the composite disturbance signals. Finally, the experimental simulation results also show the better performance of the method in decomposing voltage sag waveforms with different causes in different composite disturbance signals compared with other mainstream methods.

Smart Sensor-Based Monitoring Technology for Machinery Fault Detection.

Rotary machines commonly use rolling element bearings to support rotation of the shafts. Most machine performance imperfections are related to bearing defects. Thus, reliable bearing condition monitoring systems are critically needed in industries to provide early warning of bearing fault so as to prevent machine performance degradation and reduce maintenance costs. The objective of this paper is to develop a smart monitoring system for real-time bearing fault detection and diagnostics. Firstly, a smart sensor-based data acquisition (DAQ) system is developed for wireless vibration signal collection. Secondly, a modified variational mode decomposition (MVMD) technique is proposed for nonstationary signal analysis and bearing fault detection. The proposed MVMD technique has several processing steps: (1) the signal is decomposed into a series of intrinsic mode functions (IMFs); (2) a correlation kurtosis method is suggested to choose the most representative IMFs and construct the analytical signal; (3) envelope spectrum analysis is performed to identify the representative features and to predict bearing fault. The effectiveness of the developed smart sensor DAQ system and the proposed MVMD technique is examined by systematic experimental tests.

Non-stationary signal analysis utilizing VMD and EMD algorithm for multiple fault classification for industrial applications

The Hilbert spectrum images of intrinsic mode functions (IMF) of empirical mode decomposition (EMD) analysis and variational mode decomposition (VMD) analysis of faulty machine vibration signals are used in deep convolutional neural network (DCNN) for machine fault classification in which the DCNN automatically learns the features from spectral images using convolution layer. Though both EMD and VMD analysis suit well for non-stationary signal analysis, VMD has the merit of aliasing free IMFs. In this paper, the performance improvement of DCNN classification for a non-stationary vibration signal dataset using VMD is brought out. The numerical experiment uses the Hilbert spectrum images of 4 EMD-IMFs and 4 VMD-IMFs in DCNN to classify 10 different faults of the Case Western Reserve University (CWRU) bearing dataset. The confusion matrices are obtained and the plot of model accuracies in terms of epochs for the DCNN is analysed. It is shown that the spectrum images of one of the four EMD-IMFs, IMF0, give a validation accuracy of 100% and in the case of VMD the spectrum images of two of the four VMD-IMFs, IMF0, and IMF1 give a validation accuracy of 100%. This reveals that non-aliasing IMFs of VMD are better at classifying bearing faults. Further to bring out the merits of VMD analysis for non-stationary signals the numerical experiment is conducted using VMD analysis for binary fault classification of the milling dataset which is more non-stationary than the bearing dataset which is proved by plotting the statistical parameters of both datasets against time. It is found that the DCNN classification is 100% accurate for IMF3 of VMD analysis which is much better than the 81% accuracy provided by EMD analysis as per existing literature. The performance comparison highlights the merits of VMD analysis over EMD analysis and other state-of-the-art methods and ensemble learning methods.

Risk and impact-centered non-stationary signal analysis based on fault signatures for Djibouti power system

Risk and impact-centered non-stationary signal analysis based on fault signatures for Djibouti power system

Improving time–frequency resolution in non-stationary signal analysis using a convolutional recurrent neural network

Improving time–frequency resolution in non-stationary signal analysis using a convolutional recurrent neural network

Generalized singular spectrum analysis for the decomposition and analysis of non-stationary signals

Singular spectrum analysis (SSA) has been verified to be an effective method for decomposing non-stationary signals. The decomposition and reconstruction stages can be interpreted as a zero-phase filtering process where reconstructed components are obtained by inputting a signal through moving average filters. However, mathematical analysis indicates that the use of a default rectangular window in the embedding stage would corrupt the frequency characteristics of the trajectory matrix, resulting in spectral leakage. To attenuate the effect of spectral leakage and to obtain more concentrated SSA components, this study introduces a windowing technique in SSA, called generalized singular spectrum analysis (GSSA). In GSSA, the default rectangular window is replaced with adjustable taper windows, which are widely used for attenuating spectral leakage. Through windowing, GSSA can achieve less spectral leakage, and produce more energy-concentrated reconstructed components compared with conventional SSA. Grouped spectral entropy (GSE) is used as the metric for evaluating the performance of the proposed GSSA algorithm. Results from experiments, which were conducted on a synthetic signal and two real electroencephalogram signals, show that GSSA outperforms the conventional SSA and the baseline in the reduction of spectral leakage. Compared with the baseline, the proposed GSSA achieves a lower averaged GSE, resulting in reduction of 0.4 for eigenfilters and 0.11 for reconstructed components, respectively. Our results reveal the effectiveness of GSSA in the decomposition and analysis of non-stationary signals.

The short-time Wigner–Ville distribution

The Wigner–Ville distribution (WD) and ambiguity function (AF) are serviceable tools for the global analysis of non-stationary signals. However, when dealing with time-varying signals that exhibit changing characteristics and require real-time signal processing, they have high limitations due to the existence of cross-items. In this paper, we propose the short-time Wigner–Ville distribution (STWD) as a novel approach that effectively analyzes time-varying signals with changing characteristics. First, the definition of STWD and short-time ambiguity function (STAF) and their properties are advanced. Next, three uncertainty principles that define the lower bound for the product of signal spread and its bandwidth are derived. Then, the discrete STWD (DSTWD) and the process of computerization are also proposed which can be used more widely in practice. Finally, the optimization of window functions based on Rényi entropy is discussed. Simulation experiments show that the STWD can be effectively applied for the analysis of local change characteristics and real-time processing of signals with valid and accurate results.

Problems of analysis and modeling of non-stationary systems and signals with delay in a feedback loop

Problems of analysis and modeling of non-stationary systems and signals with delay in a feedback loop

An analytical link of disaggregated green energy sources in achieving carbon neutrality in China: A policy based novel wavelet local multiple correlation analysis

As China, the world's largest emerging economy, pursues its objective of achieving net-zero emissions by 2060, the role of reliable and green energy sources, such as biomass, geothermal, and hydro, in facilitating the country's decarbonization efforts assumes utmost significance. In this study, we employ the wavelet local multiple correlation (WLMC) methodology to explore the dynamic interactions between these variables in a multivariate setting, spanning the period of 1990Q1 to 2020Q4. The WLCM approach offers improved signal resolution in the time-frequency domain, allowing for more accurate analysis of non-stationary signals and provides enhanced capability to capture and represent localized features and patterns in data. This analysis uncovers long-run asymmetric dynamic inter-correlations, which describe the mechanisms underlying carbon emissions escalation. Our findings reveal that biomass and hydro energy consumption negatively impact the environment, leading to emissions mitigation, while geothermal energy contributes positively throughout the research period. Notably, we establish that hydro energy consumption is the primary driving factor of carbon neutrality, with a more significant impact than any other determinant, facilitating a substantial reduction in carbon emissions and enhancing environmental quality. Our study has critical policy implications for meeting the Sustainable Development Goals (SDGs) and provides valuable insights for environmentalists in China, emphasizing the need to prioritize hydro energy consumption to achieve carbon neutrality.

Bidirectional EMD-RLS: Performance analysis for denoising in speech signal

Empirical Mode Decomposition (EMD) is an alternative decomposition method that allows the analysis of non-stationary and non-linear signals, decomposing them into components called Intrinsic Mode Functions (IMFs). In this paper, we introduce the bidirectional combination between EMD and the Recursive Least Squares (RLS) adaptive filter and compare it to Least Mean Square (LMS), EMD-LMS and RLS methods. The hybrid algorithm relies on the determination of vertical (IMFs indexes) and horizontal (temporal indexes) weighting coefficients. We evaluated the effectiveness of the methods by filtering sets of speech signals artificially corrupted by white Gaussian noise. To find the method that provides the greatest noise reduction and the best speech quality, we took into account the Signal-to-Noise Ratio and the Perceptual Evaluation of Speech Quality (PESQ) score. The analyzed cases showed that EMD-RLS can provide results as good as the other methods, but with a shorter learning curve than LMS and EMD-LMS, despite the higher computational cost. For a single training iteration, the methods presented PESQ scores on average equivalent to each other. However, they showed a significant difference in performance regarding noise reduction, with the best result obtained by RLS, followed by EMD-RLS, EMD-LMS and LMS.

Asthma incidence can be influenced by climate change in Italy: findings from the GEIRD study—a climatological and epidemiological assessment

An association between climatic conditions and asthma incidence has been widely assumed. However, it is unclear whether climatic variations have a fingerprint on asthma dynamics over long time intervals. The aim of this study is to detect a possible correlation of the Summer North Atlantic Oscillation (S-NAO) index and the self-calibrated palmer drought severity index (scPDSI) with asthma incidence over the period from 1957 to 2006 in Italy. To this aim, an analysis of non-stationary and non-linear signals was performed on the time series of the Italian databases on respiratory health (ISAYA and GEIRD) including 36,255 individuals overall, S-NAO, and scPDSI indices to search for characteristic periodicities. The ISAYA (Italian Study on Asthma in Young Adults) and GEIRD (Gene Environment Interactions in Respiratory Diseases) studies collected information on respiratory health in general population samples, born between 1925 and 1989 and aged 20–84 years at the time of the interview, from 13 Italian centres. We found that annual asthma total incidence shared the same periodicity throughout the 1957–2006 time interval. Asthma incidence turned out to be correlated with the dynamics of the scPDSI, modulated by the S-NAO, sharing the same averaged 6 year-periodicity. Since climate patterns appear to influence asthma incidence, future studies aimed at elucidating the complex relationships between climate and asthma incidence are warranted.

Empirical mixed Ramanujan Fourier decomposition and its application to early fault diagnosis of planetary gears

The noise robustness of adaptive empirical Fourier decomposition (AEFD) is not ideal, and Ramanujan Fourier mode decomposition (RFMD) often occurs over decomposition, causing the fault information to be dispersed. Based on this, an original method called empirical mixed Ramanujan Fourier decomposition (EMRFD) is proposed for nonlinear and non-stationary signal analysis. Firstly, EMRFD obtains the coefficients of mixed Ramanujan Fourier transform (MRFT) through the new mixed transform matrix. Then, EMRFD obtains the partition boundary through adaptive frequency band division. Finally, the mode components named mixed Ramanujan Fourier intrinsic band functions (MRFIBFs) of frequency bands are obtained by inverse MRFT. The simulation and experimental signal analysis results show that EMRFD not only has excellent signal decomposition accuracy, but also has effective ability of extracting periodic components, which is a valid method for early fault diagnosis of planetary gears.

An Improved Second-Order Multi-Synchrosqueezing Transform for the Analysis of Non-Stationary Signals

Second-order multi-synchrosqueezing transform (SMSST), an effective tool for the analysis of non-stationary signals, can significantly improve the time-frequency resolution of a non-stationary signal. Though, the noise energy in the signal can also be enhanced in the transform which can largely affect the characteristic frequency component identification for an accurate fault diagnostic. An improved algorithm termed as an improved second-order multi-synchrosqueezing transform (ISMSST) is then proposed in this study to alleviate the problem of noise interference in the analysis of non-stationary signals. In the study, the time-frequency (TF) distribution of a non-stationary signal is calculated first using SMSST, and then a δ function is constructed based on a newly proposed time-frequency operator (TFO) which is then substituted back into SMSST to produce a noise-free time frequency result. The effectiveness of the technique is validated by comparing the TF results obtained using the proposed algorithm and those using other TFA techniques in the analysis of a simulated signal and an experimental data. The result shows that the current technique can render the most accurate TFA result within the TFA techniques employed in this study.

An enhanced K-SVD denoising algorithm based on adaptive soft-threshold shrinkage for fault detection of wind turbine rolling bearing

Due to nonstationary operating conditions of wind turbines and surrounding harsh working environments, the impulse features induced by bearing faults are always overwhelmed by heavy noise, which brings challenges to accurately detect rolling bearing faults. Sparse representation exhibits excellent performance in nonstationary signal analysis, but it is closely bound up with the degree of similarity between the atoms in a dictionary and signals. Therefore, this paper investigates an enhanced K-SVD denoising method based on adaptive soft-threshold shrinkage to achieve high-precision extraction of impulse signals, and applies it to fault detection of generator bearing of wind turbines. An adaptive sparse coding shrinkage soft-threshold denoising is first proposed to remove noise and harmonic interference in the residual term of dictionary updating, so that the updated atoms show obvious impact characteristics. Furthermore, a soft-threshold shrinkage function with adaptive threshold is designed to further suppress clutter in atoms of the learned dictionary, so as to obtain an optimized dictionary for recovering impulse signals. Two actual engineering cases are selected for analysis, and the envelope spectrum correlation kurtosis corresponding to the results obtained by the proposed method is significantly higher than that of other comparison methods, thus verifying its superiority in detecting rolling bearing faults.

Fault Diagnosis for Rolling Bearing of Combine Harvester Based on Composite-Scale-Variable Dispersion Entropy and Self-Optimization Variational Mode Decomposition Algorithm.

Because of the influence of harsh and variable working environments, the vibration signals of rolling bearings for combine harvesters usually show obvious characteristics of strong non-stationarity and nonlinearity. Accomplishing accurate fault diagnosis using these signals for rolling bearings is a challenging subject. In this paper, a novel fault diagnosis method based on composite-scale-variable dispersion entropy (CSvDE) and self-optimization variational mode decomposition (SoVMD) is proposed, systematically combining the nonstationary signal analysis approach and machine learning technology. Firstly, an improved SoVMD algorithm is developed to realize adaptive parameter optimization and to further extract multiscale frequency components from original signals. Subsequently, a CSvDE-based feature learning model is established to generate the multiscale fault feature space (MsFFS) of frequency components for the improvement of fault feature learning ability. Finally, the generated MsFFS can serve as the inputs of the Softmax classifier for fault category identification. Extensive experiments on the vibration datasets collected from rolling bearings of combine harvesters are conducted, and the experimental results demonstrate the more superior and robust fault diagnosis performance of the proposed method compared to other existing approaches.

A parameterized iterative synchrosqueezing transform for the analysis of noise contaminated non-stationary signals

Synchrosqueezing transform (SST) is a powerful post-processing tool in the analysis of non-stationary signals, though it has limited capacity in the handling of strong time-varying signals or signals with low signal-to-noise ratio (SNR). In this study, a parameterized iterative SST is proposed for an accurate machine fault diagnosis. Firstly, a parameterized chirplet transform is used to capture the fast-varying instantaneous frequencies (IF) of a strong time varying signal. Secondly, the TF coefficients are reassigned to the IF trajectory by an iterative SST technique. Finally, the blurry transition between two neighboring TF points is eliminated by the construction of a local maxima operator. The effectiveness of the current technique is examined using two simulated non-stationary signals and two sets of machine defect data acquired under varying speed condition. The results show that the current technique can produce a highly energy concentrated time frequency result for an accurate mechanical fault diagnosis under either strong speed variation or/and noise contamination conditions. The effectiveness of the technique is also validated by comparing the result with those obtained via other TFA techniques. The result showed that the current technique can render the most accurate result within the TFA techniques used in this study.

Proportion-Extracting Chirplet Transform for Nonstationary Signal Analysis of Rotating Machinery

Multicomponent nonstationary signals with close instantaneous frequencies (IFs) are commonly encountered in rotating machinery condition monitoring and fault diagnosis. It is very challenging to accurately reveal the physical natures of such signals. To address the issue, this article presents the proportion-extracting chirplet transform (PECT). In the PECT, the proportional kernel functions can match with the time-varying patterns of all constituent components. This enables the PECT to eliminate the artifacts caused by spectral overlaps in short-time windows and to achieve fine frequency resolution. Meanwhile, the corresponding proportional frequency shifting operators ensure satisfactory time resolution. Therefore, the PECT provides high time-frequency resolution and suffices to characterize the time–frequency structures of nonstationary signals with close IFs. The experimental and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">in situ</i> measured data analysis results of typical rotating machinery validate the effectiveness of the PECT.