Decomposition Of Multicomponent Signals Research Articles

Radar Detection-Inspired Signal Retrieval from the Short-Time Fourier Transform.

This paper presents a novel adaptive algorithm for multicomponent signal decomposition from the time–frequency (TF) plane using the short-time Fourier transform (STFT). The approach is inspired by a common technique used within radar detection called constant false alarm rate (CFAR). The areas with the strongest magnitude are detected and clustered, allowing for TF mask creation and filtering only those signal modes that contribute the most. As a result, one can extract a particular component void of noise and interference regardless of the signal character. The superiority understood as an improved reconstructed waveform quality of the proposed method is shown using both simulated and real-life radar signals.

Seismic Denoising Based on Time-Varying Filtering and Empirical Mode Decomposition in the fx Domain

Ground roll is a type of coherent noise with low velocity, low frequency and high energy, which negatively affects the quality of the seismic data. The contamination of the ground roll is a persistent problem in the seismic processing field. For this reason, we considered the predictability of useful signals in the fx domain, introduced the time-varying filtering based on the empirical mode decomposition (TVFEMD) into the fx domain, and therefore proposed a novel algorithm (Ada-fx-TVFEMD). Similar to the Variational Mode Decomposition (VMD), the TVFEMD algorithm consists in adaptive decomposition of multi-component signals. The TVFEMD algorithm is more suitable for nonstationary signals because of its time-varying characteristic. The proposed Ada-fx-TVFEMD algorithm performs decomposition of each frequency slice and reconstruction of partial Intrinsic Mode Functions (IMFs). Moreover, it allows to accurately select the IMFs that contain ground roll based on automatic ground roll identification. A presented synthetic example illustrates the superiority of the Ada-fx-TVFEMD algorithm in ground roll attenuation. Applying the proposed method on field data further demonstrates its potential in industrial applications, compared with frequency-wavenumber (FK) filtering and fx-VMD.

A Multi-component Signal Decomposition Application Research on Improved Algorithm Based on Improved Wavelet Ridge

Multi-component signal decomposition method with noise has become a research hotspot of equipment condition monitoring. Aiming at the iterative divergence problem of traditional wavelet ridge extraction algorithm for multi-component harmonic signals widely existing in mechanical and electrical systems, in order to achieve the goal of high decomposition accuracy and anti-noise performance of multi-component signals, the relationship between the initial scale and the extracted components is analyzed. Compared with the time domain of noisy harmonic signals, an improved wavelet ridge extraction algorithm is proposed （WRSD） After the instantaneous frequency of a component is obtained by this extraction algorithm, the component can be separated from the original signal and its instantaneous amplitude can be obtained by using the synchronous demodulation method. This method has high accuracy and certain anti-noise performance for instantaneous frequency estimation. Through simulation analysis and engineering application, the key zero point in intelligent manufacturing equipment of high-performance composite parts can be realized Fault detection of components.

Multicomponent decomposition by wavelet modulus maxima and synchronous detection

There are various signal decomposition methods, but none of them is satisfactory and all have their own drawbacks. It is worth exploring a new signal decomposition approach with better performance for processing the complex vibration signals. By employing the wavelet modulus maxima and synchronous detection, a novel multicomponent signal decomposition method is proposed in this paper. Firstly, the wavelet modulus maxima of a multicomponent signal are calculated by optimized complex wavelet transform, then the highest instantaneous frequency (IF) is extracted by searching the wavelet modulus maxima with the smallest scales at all the time instants. With the obtained IF, the synchronous detection method is used to calculate the phase offset and the instantaneous amplitude. It follows that the corresponding component with highest IF can be reconstructed. Then the used wavelet modulus maxima in this iteration are removed from the wavelet scalogram and the next IF is sequentially computed. By repeating this process, all components are successively separated from high frequency to low frequency. Compared with ensemble empirical mode decomposition and Hilbert vibration decomposition, it has been proved by three typical multicomponent signals with different noise intensity that the proposed signal decomposition method has higher accuracy, frequency resolution and is more robust to noises. Moreover, the application results further show that the proposed method can be more effectively applied to fault diagnosis of gearboxes, especially when the operating condition is varying or the fault feature is weak.

Superiorities of variational mode decomposition over empirical mode decomposition particularly in time–frequency feature extraction and wind turbine condition monitoring

Due to constantly varying wind speed, wind turbine (WT) components often operate at variable speeds in order to capture more energy from wind. As a consequence, WT condition monitoring (CM) signals always contain intra-wave features, which are difficult to extract through performing conventional time–frequency analysis (TFA) because none of which is locally adaptive. So far, only empirical mode decomposition (EMD) and its extension forms can extract intra-wave features. However, the EMD and those EMD-based techniques also suffer a number of defects in TFA (e.g. weak robustness of against noise, unidentified ripples, inefficiency in detecting side-band frequencies etc.). The existence of these issues has significantly limited the extensive application of the EMD family techniques to WT CM. Recently, an alternative TFA method, namely variational mode decomposition (VMD), was proposed to overcome all these issues. The purpose of this study is to verify the superiorities of the VMD over the EMD and investigate its potential application to the future WT CM. Experiment has shown that the VMD outperforms the EMD not only in noise robustness but also in multi-component signal decomposition, side-band detection, and intra-wave feature extraction. Thus, it has potential as a promising technique for WT CM.

Time-Frequency Analysis Based on Improved Variational Mode Decomposition and Teager Energy Operator for Rotor System Fault Diagnosis

A time-frequency analysis method based on improved variational mode decomposition and Teager energy operator (IVMD-TEO) is proposed for fault diagnosis of turbine rotor. Variational mode decomposition (VMD) can decompose a multicomponent signal into a number of band-limited monocomponent signals and can effectively avoid model mixing. To determine the number of monocomponents adaptively, VMD is improved using the correlation coefficient criterion. Firstly, IVMD algorithm is used to decompose a multicomponent signal into a number of monocompositions adaptively. Second, all the monocomponent signals’ instantaneous amplitude and instantaneous frequency are demodulated via TEO, respectively, because TEO has fast and high precision demodulation advantages to monocomponent signal. Finally, the time-frequency representation of original signal is exhibited by superposing the time-frequency representations of all the monocomponents. The analysis results of simulation signal and experimental turbine rotor in rising speed condition demonstrate that the proposed method has perfect multicomponent signal decomposition capacity and good time-frequency expression. It is a promising time-frequency analysis method for rotor fault diagnosis.

Adaptive signal decomposition based on wavelet ridge and its application

Signal decomposition is a widely-used approach for multicomponent signal processing. To improve the accuracy and anti-noise performance of multicomponent decomposition, this paper proposes a novel multicomponent signal decomposition method based on wavelet ridge extraction, called the Wavelet ridge signal decomposition (WRSD). A wavelet ridge extraction algorithm is introduced. We find that this algorithm can obtain the wavelet ridge of one component in a multicomponent signal and the initial scale will determine the wavelet ridge of which component is extracted. Since the instantaneous frequency obtained by wavelet ridge has small frequency fluctuation, low-pass filtering is used to increase the accuracy of instantaneous frequency estimation. With the improved instantaneous frequency, the synchronous demodulation method is used to separate the corresponding component from the signal composition. By repeating this process, all components can be adaptively and automatically obtained. This method is employed to analyze three typical simulated vibration signals and compared with Hilbet vibration decomposition and empirical mode decomposition. The comparison results demonstrate its superiority in decomposition accuracy and noise insensitivity. Finally, the proposed WRSD method is successfully applied to the diagnosis of a shaft misalignment fault and a gearbox wear fault.

An iterative approach for decomposition of multi-component non-stationary signals based on eigenvalue decomposition of the Hankel matrix

The decomposition of multi-component signals finds use in signal analysis. A new iterative approach to decompose a multi-component non-stationary signal into amplitude–frequency modulated (AM–FM) mono-component signals is presented in this paper. The proposed iterative approach is based on repeatedly performing eigenvalue decomposition (EVD) of the Hankel matrix, initially constructed from the samples of the multi-component signal. The components corresponding to significant eigenvalue pairs of the Hankel matrix are extracted. The process of constructing the Hankel matrix, performing EVD of the Hankel matrix and extraction of components corresponding to significant eigenvalue pairs, which we refer to as ‘Iteration’ is repeated till all the extracted components satisfy the defined mono-component signal criteria (MSC). The proposed decomposition approach being adaptive is suitable for analysis of non-stationary signals. The experimental results obtained by decomposing different kinds of synthetic and natural multi-component signals using the proposed iterative approach are presented and compared with the results obtained by empirical mode decomposition (EMD) and singular spectrum analysis (SSA). It is shown that unlike EMD, the ability of the proposed iterative approach to separate constituent mono-component signals is neither affected by the ratio of their mean frequencies nor by their relative amplitudes.

Multi component signal decomposition based on chirplet pursuit and genetic algorithms

In this paper, we will propose a method based on genetic algorithms, chirplet atoms and the matching pursuit algorithm that by using prior knowledge about the chirplet parameters can do higher quality decomposition of multi component signals. The Matching pursuit is an iterative greedy algorithm that can be used for decomposing of the biological signals into basis functions in time and frequency domain. Decomposition of a non-stationary multi component biological signal by using chirplet basis functions in the matching pursuit algorithm is an optimization problem. We will use a genetic algorithm for solving this optimization problem. We will compare the mean and variance of estimated parameters of chirplets with Cramér–Rao Lower Bounds (CRLB) and the actual values. As we will see, the algorithm is robust against noise, and can do efficient decompositions. In addition, the results show that the algorithm can improve the SNR of the multi component signals. The traditional Adaptive Chirplet Decomposition (ACD) method is commonly used to decompose the multi-component signals to the chirplets. The ACD method uses the Quasi–Newton optimization method and expectation maximization refinement. The comparison between the results of the proposed method with the ACD method for real experimental data shows the improvement in “Signal to Reconstructed Error Ratio (SRER)” using the proposed method.

Time-Varying Linear and Nonlinear Structural Identification with Analytical Mode Decomposition and Hilbert Transform

AbstractAnalytical mode decomposition (AMD) of a time series concerning any preselected bisecting frequency with Hilbert transform has been developed for closely spaced multicomponent signal decomposition. For this class of structures, it is often challenging, if not impossible, to apply empirical mode decomposition. In this study, the instantaneous structural frequencies are directly derived from the decomposed modal responses for systems with single and multiple degrees of freedom with both free and force vibrations, based on AMD combined with Hilbert transform analysis. The results show that the slow varying component of the instantaneous frequency of the signal is approximately equal to the instantaneous frequency of the systems for slowly time varying linear or weakly nonlinear structures. Both numerical simulations and experimental tests show that the proposed method is capable of tracking the frequency variations with high accuracy for time varying linear structures or weakly nonlinear structures.

The Application of Dual Tree Complex Wavelet Transform in Mechanical Multi-component Signal Decomposition and Feature Extraction

The Application of Dual Tree Complex Wavelet Transform in Mechanical Multi-component Signal Decomposition and Feature Extraction

A new method for multicomponent signal decomposition based on self-adaptive filtering

Since the empirical mode decomposition (EMD) lacks strict orthogonality, a new method for multicomponent signal decomposition, orthogonal empirical mode decomposition (OEMD), is proposed by this paper. The essential principle of this method is to obtain the intrinsic mode functions (IMFs) and the residue by self-adaptive band-pass filtering. Firstly, the feasibility of OEMD is theoretically analyzed, then its strict orthogonality and completeness is proved, and the orthogonal basis used in OEMD is generated. Secondly, the method of analytical band-pass filtering which preserves perfect band-pass feature in the frequency domain is presented, then two fast algorithms to implement OEMD are proposed, i.e. IMF sequential searching (ISS) algorithm and IMF binary searching (IBS) algorithm. The speed of IBS is faster than that of ISS, whereas IBS algorithm may obtain much more false IMFs than ISS when signals are of complex spectral constitutions. Finally, OEMD is applied to both synthetic signals and mechanical vibration signals, the results show that compared with EMD, OEMD better solves mode aliasing, avoids the occurrence of false mode, is free of end extension, and can be effectively applied to mechanical fault diagnosis.

Convex Variational Formulation with Smooth Coupling for Multicomponent Signal Decomposition and Recovery

A convex variational formulation is proposed to solve multicomponent signal processing problems in Hilbert spaces. The cost function consists of a separable term, in which each component is modeled through its own potential, and of a coupling term, in which constraints on linear transformations of the components are penalized with smooth functionals. An algorithm with guaranteed weak convergence to a solution to the problem is provided. Various multicomponent signal decomposition and recovery applications are discussed. AMS subject classifications: 94A12, 90C25

Application of the improved generalized demodulation time–frequency analysis method to multi-component signal decomposition

The generalized demodulation time–frequency analysis approach is a novel signal processing method, which is suitable for processing non-stationary signals, especially for processing amplitude-modulated and frequency-modulated (AM–FM) signals. The novelty of this method is that the signal whose time–frequency distributions are curved paths can be transformed into that whose time–frequency distributions are linear paths paralleling time axis by using generalized demodulation. Furthermore, the generalized demodulated signal can be decomposed into a number of mono-component signals whose instantaneous frequencies have physical meaning through the use of the maximal overlap discrete wavelet packet transform (MODWPT). Therefore, the complete time–frequency distributions of the original signal can be obtained. However, the generalized demodulation time–frequency analysis method fails to provide the time domain waveform of each mono-component signal. In this paper, aiming at the multi-component AM–FM signal, each mono-component signal of which only has single-sided spectra, the improvement to the generalized demodulation time–frequency analysis approach has been made and the improved method is introduced into certain multi-component AM–FM signal decomposition. The analysis results demonstrate that the validity of the proposed approach. In addition, the estimation of the phase function that is key step in the generalized demodulation time–frequency analysis approach is also discussed.

MONITORING OF SIGNALS FROM MANUFACTURING PROCESSES USING THE KARHUNEN–LOÈVE TRANSFORM

Monitoring the condition of signals during manufacturing can provide valuable information about the status of the parts being produced, as well as that of the components of the manufacturing machine. To this end, we introduce a monitoring technique based on the Karhunen–Loève transform, which decomposes measured manufacturing signals into decorrelated components in the form of fundamental eigenfunctions. The isolated eigenfunctions are monitored by means of the corresponding coefficient vectors, which indicate stationary and non-stationary changes in the deterministic and stochastic fundamental patterns. In this paper, the mathematical foundations of the technique are explored to form a good understanding of the mechanics of the transformation. This understanding is achieved with simple illustrative examples in the discrete and continuous domains, followed by an example of multicomponent signal decomposition by means of numerical simulations. The monitoring potential of the technique is illustrated with an example from a milling process, where the main modes are extracted by means of the eigenvectors and coefficient vectors.