Denoising via truncated sparse decomposition

This paper proposes a denoising algorithm called truncated sparse decomposition （TSD） algorithm, which combines the advantage of the sparse decomposition with that of the minimum energy model truncation operation. Experimental results on two real chaotic signals show that the TSD algorithm outperforms the recently reported denoising algorithmsnon-negative sparse coding and singular value decomposition based method.

A bearing fault diagnosis method based on sparse decomposition theory

The bearing fault information is often interfered or lost in the background noise after the vibration signal being transferred complicatedly, which will make it very difficult to extract fault features from the vibration signals. To avoid the problem in choosing and extracting the fault features in bearing fault diagnosing, a novelty fault diagnosis method based on sparse decomposition theory is proposed. Certain over-complete dictionaries are obtained by training, on which the bearing vibration signals corresponded to different states can be decomposed sparsely. The fault detection and state identification can be achieved based on the fact that the sparse representation errors of the signal on different dictionaries are different. The effects of the representation error threshold and the number of dictionary atoms used in signal decomposition to the fault diagnosis are analyzed. The effectiveness of the proposed method is validated with experimental bearing vibration signals.

Chaotic signal denoising algorithm based on sparse decomposition

Denoising of chaotic signal is a challenge work due to its wide-band and noise-like characteristics.The algorithm should make the denoised signal have a high signal to noise ratio and retain the chaotic characteristics.We propose a denoising method of chaotic signals based on sparse decomposition and K-singular value decomposition(K-SVD)optimization.The observed signal is divided into segments and decomposed sparsely.The over-complete atomic library is constructed according to the differential equation of chaotic signals.The orthogonal matching pursuit algorithm is used to search the optimal matching atom.The atoms and coefficients are further processed to obtain the globally optimal atoms and coefficients by K-SVD.The simulation results show that the denoised signals have a higher signal to noise ratio and better preserve the chaotic characteristics.

Application of signal sparse decomposition in dynamic test

In dynamic test,sampling rate is high and noise is strong,so a signal sparse decomposition method based on Gabor dictionary is put forward.This method iteratively decomposes the signal with the matching pursuit(MP)algorithm and takes the coherence ratio of the threshold as a condition of iteration termination.Standard MP algorithm is time-consuming,thus an adaptive genetic algorithm is introduced to MP method,which makes computation speed accelerate effectively.Experimental results indicate that this method not only can effectively remove high-frequency noise but also can compress the signal greatly.

Application of sparse time-frequency decomposition to seismic data

The Gabor and S transforms are frequently used in time-frequency decomposition methods. Constrained by the uncertainty principle, both transforms produce low-resolution time-frequency decomposition results in the time and frequency domains. To improve the resolution of the time-frequency decomposition results, we use the instantaneous frequency distribution function（IFDF） to express the seismic signal. When the instantaneous frequencies of the nonstationary signal satisfy the requirements of the uncertainty principle, the support of IFDF is just the support of the amplitude ridges in the signal obtained using the short-time Fourier transform. Based on this feature, we propose a new iteration algorithm to achieve the sparse time-frequency decomposition of the signal. The iteration algorithm uses the support of the amplitude ridges of the residual signal obtained with the short-time Fourier transform to update the time-frequency components of the signal. The summation of the updated time-frequency components in each iteration is the result of the sparse timefrequency decomposition. Numerical examples show that the proposed method improves the resolution of the time-frequency decomposition results and the accuracy of the analysis of the nonstationary signal. We also use the proposed method to attenuate the ground roll of field seismic data with good results.

Compression algorithm for electrocardiograms based on sparse decomposition

Sparse decomposition is a new theory in signal processing,with the advantage in that the base(dictionary)used in this theory is over-complete,and can reflect the nature of a signal.Thus,the sparse decomposition of signal can obtain sparse representation,which is very important in data compression.The algorithm of compression based on sparse decomposition is investigated.By training on and learning electrocardiogram(ECG)data in the MIT-BIH Arrhythmia Database,we constructed an over-complete dictionary of ECGs.Since the atoms in this dictionary are in accord with the character of ECGs,it is possible that an extensive ECG datum is reconstructed by a few nonzero coefficients and atoms.The proposed compression algorithm can adjust compression ratio according to practical request,and the distortion is low(when the compression ratio is 20∶1,the standard error is 5.11%).The experiments prove the feasibility of the proposed compression algorithm.

A fast algorithm for image reconstruction based on sparse decomposition

It is very slow at present to reconstruct an image from its sparse decomposition results.To overcome this one of the main drawbacks in image sparse decomposition,the property of the energy distribution of atoms is studied in this paper.Based on the property that energy of most atoms is highly concentrated,an algorithm is proposed to fast reconstruct an image from atoms’parameters by limiting atom reconstruction calculating within the atom energy concentrating area.Moreover,methods for fast calculating atom energy and normalization are also put forward.The fast algorithm presented in this paper improves the speed of the image reconstructing by approximately 32 times without degrading the reconstructed image quality.

Gearbox Fault Diagnosis using Adaptive Zero Phase Time-varying Filter Based on Multi-scale Chirplet Sparse Signal Decomposition

When used for separating multi-component non-stationary signals, the adaptive time-varying filter(ATF) based on multi-scale chirplet sparse signal decomposition(MCSSD) generates phase shift and signal distortion. To overcome this drawback, the zero phase filter is introduced to the mentioned filter, and a fault diagnosis method for speed-changing gearbox is proposed. Firstly, the gear meshing frequency of each gearbox is estimated by chirplet path pursuit. Then, according to the estimated gear meshing frequencies, an adaptive zero phase time-varying filter(AZPTF) is designed to filter the original signal. Finally, the basis for fault diagnosis is acquired by the envelope order analysis to the filtered signal. The signal consisting of two time-varying amplitude modulation and frequency modulation(AM-FM) signals is respectively analyzed by ATF and AZPTF based on MCSSD. The simulation results show the variances between the original signals and the filtered signals yielded by AZPTF based on MCSSD are 13.67 and 41.14, which are far less than variances (323.45 and 482.86) between the original signals and the filtered signals obtained by ATF based on MCSSD. The experiment results on the vibration signals of gearboxes indicate that the vibration signals of the two speed-changing gearboxes installed on one foundation bed can be separated by AZPTF effectively. Based on the demodulation information of the vibration signal of each gearbox, the fault diagnosis can be implemented. Both simulation and experiment examples prove that the proposed filter can extract a mono-component time-varying AM-FM signal from the multi-component time-varying AM-FM signal without distortion.

OMP-BASED MULTI-BAND SIGNAL RECONSTRUCTION FOR ECOLOGICAL SOUNDS RECOGNITION

The paper proposes a new method of multi-band signal reconstruction based on Orthogonal Matching Pursuit(OMP),which aims to develop a robust Ecological Sounds Recognition(ESR)system.Firstly,the OMP is employed to sparsely decompose the original signal,thus the high correlation components are retained to reconstruct in the first stage.Then,according to the frequency distribution of both foreground sound and background noise,the signal can be compensated by the residual components in the second stage.Via the two-stage reconstruction,high non-stationary noises are effectively reduced,and the reconstruction precision of foreground sound is improved.At recognition stage,we employ deep belief networks to model the composite feature sets extracted from reconstructed signal.The experimental results show that the proposed approach achieved superior recognition performance on 60 classes of ecological sounds in different environments under different Signal-to-Noise Ratio(SNR),compared with the existing method.

Image smoothing based on global sparsity decomposition and a variable parameter

Smoothing images,especially with rich texture,is an important problem in computer vision.Obtaining an ideal result is difficult due to complexity,irregularity,and anisotropicity of the texture.Besides,some properties are shared by the texture and the structure in an image.It is a hard compromise to retain structure and simultaneously remove texture.To create an ideal algorithm for image smoothing,we face three problems.For images with rich textures,the smoothing effect should be enhanced.We should overcome inconsistency of smoothing results in different parts of the image.It is necessary to create a method to evaluate the smoothing effect.We apply texture pre-removal based on global sparse decomposition with a variable smoothing parameter to solve the first two problems.A parametric surface constructed by an improved Bessel method is used to determine the smoothing parameter.Three evaluation measures:edge integrity rate,texture removal rate,and gradient value distribution are proposed to cope with the third problem.We use the alternating direction method of multipliers to complete the whole algorithm and obtain the results.Experiments show that our algorithm is better than existing algorithms both visually and quantitatively.We also demonstrate our method’s ability in other applications such as clip-art compression artifact removal and content-aware image manipulation.

A Hybrid Compression Method for Compound Power Quality Disturbance Signals in Active Distribution Networks

In the compression of massive compound power quality disturbance(PQD) signals in active distribution networks, the compression ratio(CR) and reconstruction error(RE) act as a pair of contradictory indicators, and traditional compression algorithms have difficulties in simultaneously satisfying a high CR and low RE. To improve the CR and reduce the RE, a hybrid compression method that combines a strong tracking Kalman filter(STKF), sparse decomposition, Huffman coding, and run-length coding is proposed in this study. This study first uses a sparse decomposition algorithm based on a joint dictionary to separate the transient component(TC) and the steady-state component(SSC) in the PQD. The TC is then compressed by wavelet analysis and by Huffman and runlength coding algorithms. For the SSC, values that are greater than the threshold are reserved, and the compression is finally completed. In addition, the threshold of the wavelet depends on the fading factor of the STKF to obtain a high CR. Experimental results of real-life signals measured by fault recorders in a dynamic simulation laboratory show that the CR of the proposed method reaches as high as 50 and the RE is approximately 1.6%, which are better than those of competing methods. These results demonstrate the immunity of the proposed method to the interference of Gaussian noise and sampling frequency.

Multiple fault separation and detection by joint subspace learning for the health assessment of wind turbine gearboxes

The gearbox of a wind turbine （WT） has dominant failure rates and highest downtime loss among all WT subsystems. Thus, gearbox health assessment for maintenance cost reduction is of paramount importance. The concurrence of multiple faults in gearbox components is a common phenomenon due to fault induction mechanism. This problem should be considered before planning to replace the components of the WT gearbox. Therefore, the key fault patterns should be reliably identified from noisy observation data for the development of an effective maintenance strategy. However, most of the existing studies focusing on multiple fault diagnosis always suffer from inappropriate division of fault information in order to satisfy various rigorous decomposition principles or statistical assumptions, such as the smooth envelope principle of ensemble empirical mode decomposition and the mutual independence assumption of independent component analysis. Thus, this paper presents a joint subspace learning-based multiple fault detection （JSLMFD） technique to construct different subspaces adaptively for different fault pattems. Its main advantage is its capability to learn multiple fault subspaces directly from the observation signal itself. It can also sparsely concentrate the feature information into a few dominant subspace coefficients. Furthermore, it can eliminate noise by simply performing coefficient shrinkage operations. Consequently, multiple fault patterns are reliably identified by utilizing the maximum fault information criterion. The superiority of JSL-MFD in multiple fault separation and detection is comprehensively investigated and verified by the analysis of a data set of a 750 kW WT gearbox. Results show that JSL-MFD is superior to a state-of-the-art technique in detecting hidden fault patterns and enhancing detection accuracy.