Multicomponent Nonstationary Signals Research Articles

In-memory database load balancing optimization for massive information processing of the Internet of Things

In order to improve the operation effect of the in-memory database for massive information processing of the Internet of Things, this paper combines the load balancing signal processing algorithm to carry out the load balancing optimization analysis of the in-memory database. According to the local transformation characteristics of non-stationary multi-component signals, an adaptive FSST algorithm is proposed in this paper. According to the signal separability condition, this paper uses the local Rayleigh entropy to estimate the window function parameters of the adaptive FSST and the adaptive FSST2. In addition, this paper adopts an adaptive window function to automatically match the local changes of the signal, so that the signal has the optimal energy aggregation in any part. The results show that when the number of concurrent users is the same, the time consumption, throughput and bandwidth of the proposed method are always higher than the method proposed in reference [10]. When the number of concurrent books is 97, the time of the proposed method is 45000ms, the time of the proposed method is 40000ms, the highest throughput of the proposed method is 2.30 MB/s, the highest bandwidth is 11.9MB/s, the highest throughput of the method proposed in reference [10] is 2.2 MB/s, and the highest bandwidth is 11.8MB/s. The load balancing optimization algorithm of the memory database for massive information processing of the Internet of Things has good results.

Convolutional Neural Networks for Local Component Number Estimation from Time–Frequency Distributions of Multicomponent Nonstationary Signals

Frequency-modulated (FM) signals, prevalent across various applied disciplines, exhibit time-dependent frequencies and a multicomponent nature necessitating the utilization of time-frequency methods. Accurately determining the number of components in such signals is crucial for various applications reliant on this metric. However, this poses a challenge, particularly amidst interfering components of varying amplitudes in noisy environments. While the localized Rényi entropy (LRE) method is effective for component counting, its accuracy significantly diminishes when analyzing signals with intersecting components, components that deviate from the time axis, and components with different amplitudes. This paper addresses these limitations and proposes a convolutional neural network-based (CNN) approach for determining the local number of components using a time–frequency distribution of a signal as input. A comprehensive training set comprising single and multicomponent linear and quadratic FM components with diverse time and frequency supports has been constructed, emphasizing special cases of noisy signals with intersecting components and differing amplitudes. The results demonstrate that the estimated component numbers outperform those obtained using the LRE method for considered noisy multicomponent synthetic signals. Furthermore, we validate the efficacy of the proposed CNN approach on real-world gravitational and electroencephalogram signals, underscoring its robustness and applicability across different signal types and conditions.

Enhanced adaptive linear chirplet transform for crossing frequency trajectories

Time-frequency representation (TFR) is of great significance for capturing and analyzing nonlinear or nonstationary multi-component signals. The adaptive linear chirplet transform (ALCT) has proven effective for dealing with signals with frequencies that intersect, providing accurate estimations of instantaneous frequencies (IFs) for both intersecting and non-intersecting components. However, challenges still exist when handling signal components that have overlapping amplitudes, and when performing reconstruction, the components are mixed around the time of the intersection. To overcome these issues, we present the enhanced ALCT (EALCT) approach that synergistically combines several methods to overcome the previously described issues with the ALCT algorithm. The EALCT identifies the IFs by a modified ACLT as a set and separates them using the ridge path regrouping (RPRG) algorithm. Subsequently, the IFs and the corresponding chirp-rates of each component are employed to reconstruct the signal using an algorithm based on the chirplet transform. By implementing this approach, the EALCT accurately reconstructs the components with intersecting amplitudes at the time of intersection as well as the original signal. The EALCT also maintains the performance of the ALCT when applied to signals that do not have components with intersecting amplitudes, such that the proposed approach does not detract from existing success. The power of the EALCT is demonstrated using analytical and experimentally measured nonlinear and nonstationary signals and the results are compared with those produced by the ALCT.

Structural instantaneous frequency identification based on synchrosqueezing fractional Fourier transform

The fractional Fourier transform can transform the signal or function into any intermediate domain between time and frequency domains called fractional Fourier domain, in which the non-stationary signals can be processed. To be a time-frequency analysis tool, the fractional Fourier transform may face the same ridge line blurred problem for noisy signals as other time-frequency analysis methods. To improve the instantaneous frequency identification accuracy of fractional Fourier transform, this paper proposes the synchrosqueezing fractional Fourier transform by using the mechanism that can rearrange the energy in the time-frequency plane and make the frequencies more concentrated on the real frequency of the signal. The synchrosqueezing fractional Fourier transform and its corresponding inverse transformation are theoretically derived. Then the corresponding instantaneous frequency identification based on synchrosqueezing fractional Fourier transform is formulated. The accuracy and effectiveness of proposed instantaneous frequency method is verified by a numerical example of three-degree-of-freedom damped time-varying structural system and experiments of moving vehicle-beam system with simply supported and continuously supported beam tested in the laboratory. Compared with the fractional Fourier transform without synchrosqueezing transform, synchrosqueezing wavelet transform and Fourier synchrosqueezing transform, it is demonstrated that the synchrosqueezing fractional Fourier transform can effectively improve the time-frequency distribution divergence and enhance the accuracy of the instantaneous frequency identification. The method has a certain anti-noise performance. Due to quick calculation by means of traditional fast Fourier transform and superior orthogonal transform feature, the proposed synchrosqueezing fractional Fourier transform can be used as an effective time-frequency signal processing tool for multi-component non-stationary signals.

A statistical frequency-chirprate extractor for mode retrieval with crossover instantaneous frequencies

It is challenging to analyze oscillatory signals whose instantaneous frequencies (IFs) are crossover in the time-frequency (TF) domain. Driven by this need, we propose a statistical frequency-chirprate extractor (SFCE) to analyze multi-component non-stationary signals whose IF lines intersect each other at the TF plane. In this paper, an effective sliding real-valued frequency filter is designed to realize the local representation of the instantaneous attribute value in the linear chirplet transform (LCT) inner product space. On this basis, we obtain SFCE by extracting the fixed-point condition of the statistical frequency-chirprate estimator from the time-frequency-chirprate (TFC) domain. Finally, the TFC information is extracted to the estimated IF and chirprate (CR) trajectories by SFCE, thus providing a novel three-dimension synchroextracting chirplet transform (TDSECT), which obtains high precision model retrieval for crossover signals. In addition, we provide a relatively rigorous theoretical analysis of SFCE for multi-component non-stationary signals. Simultaneously error analysis is given. Numerical experiments on two synthetic signals are employed to verify the successfulness of the proposed method.

Bearing failure diagnosis at time-varying speed based on adaptive clustered fractional Gabor transform

For bearing fault diagnosis at time-varying speed with tachometer-free and non-resampling, the crucial process is to obtain a high-resolution time-frequency representation and extract fault features. However, current multi-component non-stationary signal feature extraction methods based on time-frequency transform suffer from fixed parameter settings and insufficient resolution for low signal-to-noise ratio signals. To address these issues, a novel adaptive clustered fractional Gabor transform is proposed and applied to extract bearing fault features at time-varying speed. Firstly, the grey wolf optimization is utilized to adaptively search for the optimal fractional order and Gauss window length based on the maximum spectral kurtosis and the generalized time-bandwidth product to achieve the most adequate fractional Gabor spectrum (FrGS). Then, the Clustering by Fast Search and Find of Density Peaks algorithm reconstructs the sparse representation of the FrGS, remapping multi-component signals into single-component clusters. Bearing fault diagnosis is achieved by matching the relative order of each cluster with the bearing fault characteristic coefficients. Simulation signals validate the superiority of the feature extraction method, and experimental signals validate the feasibility of the bearing fault diagnosis method.

IF Estimation of Multicomponent Nonstationary Signals Based on AFSST

IF Estimation of Multicomponent Nonstationary Signals Based on AFSST

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.

Electromechanical Modes Identification Based on an Iterative Eigenvalue Decomposition of the Hankel Matrix

This paper proposes a novel strategy to precisely extract modal patterns from non-stationary multi-component signals associated with electromechanical oscillations in large-scale power systems. The strategy is composed of two stages: ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</i> ) a time-frequency representation (TFR) method; and ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ii</i> ) an energy-based operator. The former is equipped with a multivariate and iterative eigenvalue decomposition of the Hankel matrix (IEVDHM) that captures the swing dynamics as a mono-component signal criterion is fulfilled, meanwhile the latter instantaneously estimates the modal information (damping and frequency) through the discrete energy separation algorithm (DESA) that implements the discrete-time energy operators derived from the Teager-Kaiser energy operators (TKEO). The attained results and their comparisons with state-of-the-art techniques confirm the effectiveness and performance of the proposed strategy to demodulate synthetic, simulated and real oscillating signals, even under high noisy conditions, and to be a useful tool for off-line contingency analysis thanks to the capability of differentiating concurrent modes with close frequencies.

An adaptive synchroextracting transform for the analysis of noise contaminated multi-component nonstationary signals

The Synchro-Extracting Transform technique (SET) can capture the changing dynamic in a non-stationary signal which can be applied for fault diagnosis of rotating machinery operating under varying speed or/and load conditions. However, the time frequency representation (TFR) of a signal produced by SET can be affected by noise contained in the signal, which can largely reduce the accuracy of fault diagnosis. This paper addresses this drawback and presents a new extraction operator to improve the energy concentration of the TFR of a noise contaminated multi-component signal by using an adaptive ridge curve identification process together with SET. The adaptive ridge curve extraction is deployed to extract the signal components of a multi-component signal via an iterative approach. The effectiveness of the algorithm is verified using one set of simulated noise-added signals and two sets of experimental bearing and gearbox defect signals. The result shows that the proposed technique can accurately identify the fault components from noise contaminated multi-component non-stationary machine defect signals.

A statistical instantaneous frequency estimator for high-concentration time-frequency representation

The instantaneous frequency (IF)-based post-processing methods, synchrosqueezing and synchroextracting, can accurately characterize the time-varying frequency and amplitude of multi-component nonstationary signals. However, the window's length needs to be a tradeoff between time-frequency (TF) localization and mode separation. To broaden the limitation of window's length on TF localization, this study theoretically proposes a statistical IF estimator (SIFE) to extract the IFs and concentrate the short-time Fourier transform (STFT) spectrum. First, we introduce a frequency filter associated with the window function and convolve it with STFTs to define an inner product space, in which the IF trajectories of multi-component signals can be better highlighted with low dependence on the window function. Then, the SIFE is derived from a macroscopic perspective in the inner product space rather than in the STFT space as the previous post-processing method does. Finally, the STFT energies are significantly concentrated by extracting only the TF coefficients at all IFs or reassigning the TF coefficients to the respective IFs. Numerical examples demonstrate that the SIFE is superior to previous methods in extracting IFs and concentrating TF energies.

Tunable hyperbolic Cohen-class kernel for cross-term diminishing in time–frequency distributions

Nonstationary signals are found in many engineering applications. The analysis of nonstationary signals trough bi-dimensional functions allows tracing their time and frequency evolution. In this regard, energy-distribution representations allocate the analyzed-signal power over two description variables, time and frequency, and offer a large number of mathematical properties, such as an ideal infinite resolution in both domains. Unfortunately, energy-distribution representations generate cross terms for multi-component nonstationary signals, which might mislead the analysis interpretation. Cross-term effects can be lessened by applying an appropriate smoothing kernel; they distort the shape of auto terms at the same time. In this work, a novel tunable signal-independent hyperbolic kernel function is introduced for reducing cross-term effects, preserving valuable properties, during the analysis of multi-component nonstationary signals. Obtained results from computer-model and real-life cases of study validate and demonstrate the performance superiority of the proposed kernel function, in terms of cross-term suppression and time–frequency resolution, against the well-known and widely used the Choi-Williams distribution and the cone-shape distribution.

Synchrosqueezing transform meets [formula omitted]-stable distribution: An adaptive fractional lower-order SST for instantaneous frequency estimation and non-stationary signal recovery

Most of the noises in practice are non-Gaussian and presented as impulsive phenomena. Impulsive noise brings enormous difficulties for signal processing, especially for multicomponent non-stationary signal representation and separation. The synchrosqueezing transform (SST) is a time-frequency (TF) analysis method with high energy concentration and inverse transform. Although SST and its variants have been used for instantaneous frequency estimation and modes recovery in many applications, they are unable to represent the signals clearly under impulsive noise. In this paper, we model the impulsive noise with the α-stable distribution, which satisfies the generalized central limit theorem. Based on the short-time Fourier transform (STFT), we proposed the fractional lower-order SST with adaptive order and adaptive window for multicomponent signal separation with single-channel observation, called the adaptive window and fractional lower-order SST (AWO-SST). Moreover, we consider the 2nd-order phase transformation for AWO-SST and provide a component recovery method under adaptive parameters. The proposed method can be easily extended to the cases of the continuous wavelet transform, the S-transform, and other linear TF analysis methods. The experimental results demonstrate that the proposed methods have the ability to suppress the α-stable distribution noise effectively, and are capable of recovering the component signal accurately.

Enhanced seeded region growing algorithm and its application in signal decomposition

The components in an engineering signal may overlap in the frequency domain, which causes great inconvenience and even errors in traditional one-dimensional signal processing methods. To identify and extract components in the signal from the time-frequency domain, this paper proposes a time-frequency domain signal decomposition method based on enhanced seeded region growing (ESRG). This paper extends the seeded region growing method to adaptive recognition of target regions in the time-frequency representation and divides the time-frequency representation into several time-frequency components. ESRG can reduce the influence of noise, expand the self-adaptability of time-frequency decomposition and avoid errors caused by manually setting the growth point and threshold. The results of the numerical verification and decomposition of bat echo signals show that this method can accurately decompose multi-component non-stationary signals. The decomposition results of rotor fault and rolling bearing fault signals show that this method can be successfully applied to fault diagnosis.

Sparse spectrum based swarm decomposition for robust nonstationary signal analysis with application to sleep apnea detection from EEG

Background and motivationTime–frequency representation (TFR) of a signal finds its application in numerous fields for non-stationary multicomponent signal analysis. Due to underlying difficulties and improvement scope in the current methodology, developing a new time–frequency method can improve spectral analysis of real-life signals and further can be extended to practical applications. Materials and methodsThe proposed new method swarm-sparse decomposition method (SSDM) is an advanced version of swarm decomposition (SWD) for decomposing nonstationary multicomponent signals into a finite number of oscillatory components (OCs). Benefiting from sparse spectrum and SWD, the proposed SSDM method delivers optimal estimation of boundary frequencies in the sparse spectrum, resulting in improved filter banks. In addition to SSDM, we have also proposed the spectrum approximator function, i.e., fused least absolute shrinkage and selection operator to modify sparse spectrum and get significant OCs. The performance of the proposed SSDM has been evaluated by TFR analysis and compared to SWD and Hilbert-Huang transform methods. Also, it has been tested for automated sleep apnea classification using a convolutional neural network (CNN) and bidirectional long short-term memory (BiLSTM) on the publicly available EEG database. ResultsThe proposed SSDM-TFR-CNN and SSDM-feature-fusion-BiLSTM frameworks outperformed all the compared methods used for sleep apnea detection and achieved the highest classification accuracy of 96.24% and 95.86%, respectively, in the subject-independent cross-validation scheme. ConclusionSimulation result shows that the proposed SSDM method delivers substantial improvement in time–frequency analysis. Our developed sleep apnea detection model could be a vital aid in clinical solutions.

Fractional Fourier transform: Time-frequency representation and structural instantaneous frequency identification

The fractional Fourier transform involving a rotation angle as an additional variable is capable to transform a signal to any fractional Fourier domain in between time and frequency domain. With insight into the important role of rotation angle and time–frequency projection of fractional Fourier transform, the time–frequency representation of fractional Fourier transform is in this paper theoretically derived in terms of the window. It is demonstrated that the fractional Fourier transform in time–frequency domain is an algorithm of classical Fourier transform combined the chirp window that is adaptive dilation and translation. The window parameter properties are investigated in details and compared with those of wavelet window. To realize the structural instantaneous frequency identification, the analytical ridge point and corresponding ridge line based on the time–frequency representation of fractional Fourier transform is defined and presented. The fractional Fourier transform based instantaneous frequency identification algorithm is established accordingly by extracting ridge line. The effectiveness of proposed method is verified by a numerical multi-component non-stationary signal, a three-story frame on the shaking table excited by non-stationary inputs with different signal-to-noise ratios and a cable experiment with the time-varying tensioned forces. The identified instantaneous frequency results are compared with those obtained from short-time Fourier transform and wavelet transform. Both numerical and experimental verifications have demonstrated that the proposed fractional Fourier transform based method is capable of identification of instantaneous frequencies involving non-stationary signals with a sound robustness to noise. The fractional Fourier transform can be an alternative tool to process the non-stationary signals in time–frequency domain.

Weak fault feature extraction using adaptive chirp mode decomposition with sparsity index regrouping scheme and time-delayed feedback stochastic resonance

The failure features of rolling bearings are often weak due to the influence of strong background noise. In addition, the vibration signals of faulty rolling bearing often show nonlinear and non-stationary characteristics, and the conventional time-frequency method is no longer suitable for extracting effective fault features. In order to extract the early weak fault characteristics of rolling bearing accurately, a weak fault feature extraction method for rolling bearing by combining adaptive chirp mode decomposition (ACMD) based on sparsity index regrouping scheme with time-delayed feedback stochastic resonance (TDSR) is proposed in the paper. The proposed method comprehensively utilizes the adaptive decomposition characteristics of ACMD for multi-component non-stationary signals and the enhancement effect of TDFSR on low-frequency signals in the fast Fourier transform (FFT) result. Firstly, ACMD is used to decompose the early weak fault signal of rolling bearing into a series of mode signals, then the proposed signal regrouping scheme based on sparsity index is utilized to regroup the obtained series of modes. Secondly, the optimal reconstructed component containing the main fault information is input into the calculation model of TDSR. Finally, FFT is performed on the output signal of TDSR to extract the fault characteristics effectively.

Instantaneous Frequency-Embedded Synchrosqueezing Transform for Signal Separation

The synchrosqueezing transform (SST) and its variants have been developed recently as an alternative to the empirical mode decomposition scheme to model a non-stationary signal as a superposition of amplitude- and frequency-modulated Fourier-like oscillatory modes. In particular, SST performs very well in estimating instantaneous frequencies (IFs) and separating the components of non-stationary multicomponent signals with slowly changing frequencies. However its performance is not desirable for signals having fast-changing frequencies. Two approaches have been proposed for this issue. One is to use the 2nd-order or high-order SST, and the other is to apply the instantaneous frequency-embedded SST (IFE-SST). For the SST or high order SST approach, one single phase transformation is applied to estimate the IFs of all components of a signal, which may yield not very accurate results in IF estimation and component recovery. IFE-SST uses an estimation of the IF of a targeted component to produce accurate IF estimation. The phase transformation of IFE-SST is associated with the targeted component. Hence the IFE-SST has certain advantages over SST in IF estimation and signal separation. In this article, we provide theoretical study on the instantaneous frequency-embedded short-time Fourier transform (IFE-STFT) and the associated SST, called IFE-FSST. We establish reconstructing properties of IFE-STFT with integrals involving the frequency variable only and provide reconstruction formula for individual components. We also consider the 2nd-order IFE-FSST.

Self-paced learning for instantaneous frequencies estimation in heavy noise environments

Estimating instantaneous frequencies (IFs) overlap in both time and frequency domains is desired in time-frequency (TF) analysis. In this paper, a simple method, called IFs estimation based on self-paced learning (IFsESPL) algorithm, is proposed to separate overlapped components of multi-component (MC) non-stationary signals in TF plane, and simultaneously estimate IFs. The proposed IFsESPL algorithm first detects TF ridge points from a TF representation, and then the TF ridge points are used to construct training dataset of self-paced learning (SPL). In the following, minimization of particular objective function of SPL yields iteratively selecting and classifying the samples in training dataset into clusters. Each cluster is corresponding to one component of a MC signal and hence component separation is achieved. In addition, together with the partitioning of the training dataset, the IF of each component is estimated by a predefined parameterized model. IFsESPL incorporates SPL regime into TF ridge points regrouping to sequentially include ridge points into IFs estimation from easy to hard, which not only can separate crossed components in TF plane, but also can prevent interference of noise and outliers. The effectiveness of the proposed method is verified through analytical results and numerical examples.

Parameterized Resampling Time-Frequency Transform

Many signals contain multiple components with time-varying instantaneous frequencies (IFs) which share a common trajectory trend, such as machinery vibration signals, speech signals, and biomedical signals. To analyze this kind of signals and achieve high time-frequency resolution, we propose a method called parameterized resampling time-frequency transform (PRTF transform) in this paper. Adapting the idea of the general parameterized time-frequency transform (GPTF transform), we use a parameterized kernel to represent a resampling function and further construct time-varying and time-invariant resampling operators to eliminate IF variations and relocate IF positions. These operators can improve the energy concentration of multiple components simultaneously in the time-frequency representation (TFR). Typical kernel functions containing the polynomial function and Fourier series are provided for different kinds of signals. A corresponding kernel estimation method is proposed to detect the shared trend of IFs by utilizing multiple components and to recursively approximate kernel parameters. Both numerical simulations and practical experiments show the effectiveness of the proposed method in improving the time-frequency resolution of TFRs for non-stationary multi-component signals.