Optimized Variational Mode Decomposition and Permutation Entropy with Their Application in Feature Extraction of Ship-Radiated Noise

The complex and changeable marine environment surrounded by a variety of noise, including sounds of marine animals, industrial noise, traffic noise and the noise formed by molecular movement, not only interferes with the normal life of residents near the port, but also exerts a significant influence on feature extraction of ship-radiated noise (S-RN). In this paper, a novel feature extraction technique for S-RN signals based on optimized variational mode decomposition (OVMD), permutation entropy (PE), and normalized Spearman correlation coefficient (NSCC) is proposed. Firstly, with the mode number determined by reverse weighted permutation entropy (RWPE), OVMD decomposes the target signal into a set of intrinsic mode functions (IMFs). The PE of all the IMFs and SCC between each IMF with the raw signal are then calculated, respectively. Subsequently, feature parameters are extracted through the sum of PE weighted by NSCC for the IMFs. Lastly, the obtained feature vectors are input into the support vector machine multi-class classifier (SVM) to discriminate various types of ships. Experimental results indicate that five kinds of S-RN samples can be accurately identified with a recognition rate of 94% by the proposed scheme, which is higher than other previously published methods. Hence, the proposed method is more advantageous in practical applications.     

Double Feature Extraction Method of Ship-Radiated Noise Signal Based on Slope Entropy and Permutation Entropy

In order to accurately identify various types of ships and develop coastal defenses, a single feature extraction method based on slope entropy (SlEn) and a double feature extraction method based on SlEn combined with permutation entropy (SlEn&PE) are proposed. Firstly, SlEn is used for the feature extraction of ship-radiated noise signal (SNS) compared with permutation entropy (PE), dispersion entropy (DE), fluctuation dispersion entropy (FDE), and reverse dispersion entropy (RDE), so that the effectiveness of SlEn is verified, and SlEn has the highest recognition rate calculated by the k-Nearest Neighbor (KNN) algorithm. Secondly, SlEn is combined with PE, DE, FDE, and RDE, respectively, to extract the feature of SNS for a higher recognition rate, and SlEn&PE has the highest recognition rate after the calculation of the KNN algorithm. Lastly, the recognition rates of SlEn and SlEn&PE are compared, and the recognition rates of SlEn&PE are higher than SlEn by 4.22%. Therefore, the double feature extraction method proposed in this paper is more effective in the application of ship type recognition.     

Composite Multivariate Multi-Scale Permutation Entropy and Laplacian Score Based Fault Diagnosis of Rolling Bearing

As a powerful tool for measuring complexity and randomness, multivariate multi-scale permutation entropy (MMPE) has been widely applied to the feature representation and extraction of multi-channel signals. However, MMPE still has some intrinsic shortcomings that exist in the coarse-grained procedure, and it lacks the precise estimation of entropy value. To address these issues, in this paper a novel non-linear dynamic method named composite multivariate multi-scale permutation entropy (CMMPE) is proposed, for optimizing insufficient coarse-grained process in MMPE, and thus to avoid the loss of information. The simulated signals are used to verify the validity of CMMPE by comparing it with the often-used MMPE method. An intelligent fault diagnosis method is then put forward on the basis of CMMPE, Laplacian score (LS), and bat optimization algorithm-based support vector machine (BA-SVM). Finally, the proposed fault diagnosis method is utilized to analyze the test data of rolling bearings and is then compared with the MMPE, multivariate multi-scale multiscale entropy (MMFE), and multi-scale permutation entropy (MPE) based fault diagnosis methods. The results indicate that the proposed fault diagnosis method of rolling bearing can achieve effective identification of fault categories and is superior to comparative methods.     

A Rolling Bearing Fault Classification Scheme Based on k-Optimized Adaptive Local Iterative Filtering and Improved Multiscale Permutation Entropy

The health condition of the rolling bearing seriously affects the operation of the whole mechanical system. When the rolling bearing parts fail, the time series collected in the field generally shows strong nonlinearity and non-stationarity. To obtain the faulty characteristics of mechanical equipment accurately, a rolling bearing fault detection technique based on k-optimized adaptive local iterative filtering (ALIF), improved multiscale permutation entropy (improved MPE), and BP neural network was proposed. In the ALIF algorithm, a k-optimized ALIF method based on permutation entropy (PE) is presented to select the number of ALIF decomposition layers adaptively. The completely average coarse-graining method was proposed to excavate more hidden information. The performance analysis of the simulation signal shows that the improved MPE can more accurately dig out the depth information of the time series, and the entropy value obtained is more consistent and stable. In the research application, rolling bearing time series are decomposed by k-optimized ALIF to obtain a certain number of intrinsic mode functions (IMFs). Then the improved MPE value of effective IMF is calculated and input into backpropagation (BP) neural network as the feature vector for automatic fault identification. The comparative analysis of simulation signals shows that this method can extract fault information effectively. At the same time, the experimental part shows that this scheme not only effectively extracts the fault features, but also realizes the classification and identification of different fault modes and faults of different degrees, which has a certain application prospect in the research and application direction of rolling bearing fault identification.     

基于深度学习的船舶辐射噪声识别研究

为了改善船舶辐射噪声识别系统的性能,进一步提高船舶辐射噪声识别的正确率,该文提出采用一种基于深度学习的船舶辐射噪声识别方法。该方法首先提取了船舶辐射噪声的频谱、梅尔倒谱系数等特征,将提取特征后的图像样本分别用于训练卷积神经网络和深度置信网络,再对船舶辐射噪声进行识别。通过文中所给实例,将深度学习和支持向量机两种识别方法的性能进行比较,得出深度学习方法可以有效地提高船舶辐射噪声识别正确率的初步结论。     

Identification of vehicle suspension shock absorber squeak and rattle noise based on wavelet packet transforms and a genetic algorithm-support vector machine

The squeak and rattle (S&R) noise of a vehicle’s suspension shock absorber substantially influences the psychological and physiological perception of passengers. In this paper, a state-of-the-art method, specifically, a genetic algorithm-optimized support vector machine (GA-SVM), which can select the most effective feature subsets and optimize the model’s free parameters, is proposed to identify this specific noise. A vehicular road test and a shock absorber rig test are conducted to investigate the relationship between these features, and then an approach for quantifying the shock absorber S&R noise is given. Pre-processed signals are decomposed through a wavelet packet transform (WPT), and two criteria, namely, the wavelet packet energy (WPE) and wavelet packet sample entropy (WPSE), are introduced as the feature extraction methods. Then, the two extracted feature sets are compared based on this genetic algorithm. Another advanced method, known as the genetic algorithm-optimized back propagation neural network (GA-BPNN), is introduced for comparison to illustrate the superiority of the newly developed GA-SVM model. The result shows that the WPSE can extract more useful features than the WPE and that the GA-SVM is more effective and efficient than the GA-BPNN. The proposed approach could be retrained and extended to address other fault identification problems.     

基于变分模态分解与多尺度排列熵的生物组织变性识别

根据高强度聚焦超声(HIFU)治疗中超声散射回波信号的特点,本文利用变分模态分解(VMD)与多尺度排列熵(MPE)对生物组织变性识别进行了研究.首先对生物组织中的超声散射回波信号进行变分模态分解,根据各阶模态的功率谱信息熵值分离出噪声分量和有用分量;对分离出的有用信号进行重构并提取其多尺度排列熵;然后通过Gustafson-Kessel (GK)模糊聚类确定聚类中心,采用欧氏贴近度与择近原则对生物组织进行变性识别.将所提方法应用于HIFU治疗中超声散射回波信号实验数据,用遗传算法对多尺度排列熵的参数优化后,对293例未变性组织和变性组织的超声散射回波信号数据进行了多尺度排列熵分析,发现变性组织的超声散射回波信号的多尺度排列熵值要高于未变性组织;多尺度排列熵可以较好地识别生物组织是否变性.相对于EMD-MPE-GK模糊聚类以及VMD-小波熵(WE)-GK模糊聚类变性识别方法,本文所提方法中变性与未变性组织特征交叠区域数据点更少,聚类效果和分类性能更好;本实验环境下生物组织变性识别结果表明,该方法的识别率更高,高达93.81%.     

Entropy-based link prediction in weighted networks

Information entropy has been proved to be an effective tool to quantify the structural importance of complex networks.In a previous work [Xu et al. Physica A, 456 294(2016)], we measure the contribution of a path in link prediction with information entropy. In this paper, we further quantify the contribution of a path with both path entropy and path weight,and propose a weighted prediction index based on the contributions of paths, namely weighted path entropy(WPE), to improve the prediction accuracy in weighted networks. Empirical experiments on six weighted real-world networks show that WPE achieves higher prediction accuracy than three other typical weighted indices.     

A Novel Noise Reduction Method of UAV Magnetic Survey Data Based on CEEMDAN,Permutation Entropy,Correlation Coefficient and Wavelet Threshold Denoising

Despite the increased attention that has been given to the unmanned aerial vehicle (UAV)-based magnetic survey systems in the past decade, the processing of UAV magnetic data is still a tough task. In this paper, we propose a novel noise reduction method of UAV magnetic data based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), permutation entropy (PE), correlation coefficient and wavelet threshold denoising. The original signal is first decomposed into several intrinsic mode functions (IMFs) by CEEMDAN, and the PE of each IMF is calculated. Second, IMFs are divided into four categories according to the quartiles of PE, namely, noise IMFs, noise-dominant IMFs, signal-dominant IMFs, and signal IMFs. Then the noise IMFs are removed, and correlation coefficients are used to identify the real signal-dominant IMFs. Finally, the wavelet threshold denoising is applied to the real signal-dominant IMFs, the denoised signal can be obtained by combining the signal IMFs and the denoised IMFs. Both synthetic and field experiments are conducted to verify the effectiveness of the proposed method. The results show that the proposed method can eliminate the interference to a great extent, which lays a foundation for the further interpretation of UAV magnetic data.     

Fault Diagnosis of a Wind Turbine Gearbox Based on Improved Variational Mode Algorithm and Information Entropy

The working environment of wind turbine gearboxes is complex, complicating the effective monitoring of their running state. In this paper, a new gearbox fault diagnosis method based on improved variational mode decomposition (IVMD), combined with time-shift multi-scale sample entropy (TSMSE) and a sparrow search algorithm-based support vector machine (SSA-SVM), is proposed. Firstly, a novel algorithm, IVMD, is presented for solving the problem where VMD parameters (K and α) need to be selected in advance, which mainly contains two steps: the maximum kurtosis index is employed to preliminarily determine a series of local optimal decomposition parameters (K and α), then from the local parameters, the global optimum parameters are selected based on the minimum energy loss coefficient (ELC). After decomposition by IVMD, the raw signal is divided into K intrinsic mode functions (IMFs), the optimal IMF(s) with abundant fault information is (are) chosen based on the minimum envelopment entropy criterion. Secondly, the time-shift technique is introduced to information entropy, the time-shift multi-scale sample entropy algorithm is applied for the analysis of the complexity of the chosen optimal IMF and extract fault feature vectors. Finally, the sparrow search algorithm, which takes the classification error rate of SVM as the fitness function, is used to adaptively optimize the SVM parameters. Next, the extracted TSMSEs are input into the SSA-SVM model as the feature vector to identify the gear signal types under different conditions. The simulation and experimental results confirm that the proposed method is feasible and superior in gearbox fault diagnosis when compared with other methods.     

多类运动想象脑电信号特征提取与分类

针对多类运动想象情况下存在的脑电信号识别正确率比较低的问题,提出了一种将小波包方差,小波包熵和共同空间模式相结合的脑电信号特征提取,输入到支持向量机达到分类目的。首先选择小波包去噪后重要导联的脑电信号,进行小波包分解;然后对通道优化选取的重要导联的每个通道信号计算方差和熵值,对重要导联的每个通道信号的子带系数进行重构后,进行共同空间模式特征提取;最后结合2种不同导联方式所获取的特征向量进行分类。采用BCI2005desc_IIIa中l1b数据,该算法的分类正确率最高达到88.75%,相对2种单一的提取方法分别提高28.27%和6.55%。结果表明该算法能够有效提取特征向量,进而改善多类识别正确率较低的问题。     

The Systematic Bias of Entropy Calculation in the Multi-Scale Entropy Algorithm

Entropy indicates irregularity or randomness of a dynamic system. Over the decades, entropy calculated at different scales of the system through subsampling or coarse graining has been used as a surrogate measure of system complexity. One popular multi-scale entropy analysis is the multi-scale sample entropy (MSE), which calculates entropy through the sample entropy (SampEn) formula at each time scale. SampEn is defined by the “logarithmic likelihood” that a small section (within a window of a length m) of the data “matches” with other sections will still “match” the others if the section window length increases by one. “Match” is defined by a threshold of r times standard deviation of the entire time series. A problem of current MSE algorithm is that SampEn calculations at different scales are based on the same matching threshold defined by the original time series but data standard deviation actually changes with the subsampling scales. Using a fixed threshold will automatically introduce systematic bias to the calculation results. The purpose of this paper is to mathematically present this systematic bias and to provide methods for correcting it. Our work will help the large MSE user community avoiding introducing the bias to their multi-scale SampEn calculation results.     

主成分分析在舰船辐射噪声分类识别中的应用

主成分分析(PCA)是经典的多元统计分析方法,在处理多变量综合问题方面有比较突出的优势。本文主要探讨了主成分分析在舰船辐射噪声信号分类识别中的应用。在经典功率谱的基础上尝试将PCA技术运用在两种不同的方法中,对两种舰船辐射噪声进行了特征提取和分类识别,得到了较好的效果。     

A Fast Multi-Scale Generative Adversarial Network for Image Compressed Sensing

Recently, deep neural network-based image compressed sensing methods have achieved impressive success in reconstruction quality. However, these methods (1) have limitations in sampling pattern and (2) usually have the disadvantage of high computational complexity. To this end, a fast multi-scale generative adversarial network (FMSGAN) is implemented in this paper. Specifically, (1) an effective multi-scale sampling structure is proposed. It contains four different kernels with varying sizes so that decompose, and sample images effectively, which is capable of capturing different levels of spatial features at multiple scales. (2) An efficient lightweight multi-scale residual structure for deep image reconstruction is proposed to balance receptive field size and computational complexity. The key idea is to apply smaller convolution kernel sizes in the multi-scale residual structure to reduce the number of operations while maintaining the receptive field. Meanwhile, the channel attention structure is employed for enriching useful information. Moreover, perceptual loss is combined with MSE loss and adversarial loss as the optimization function to recover a finer image. Numerous experiments show that our FMSGAN achieves state-of-the-art image reconstruction quality with low computational complexity.     

多尺度条件卷积的OCT视网膜图像降噪研究

散斑噪声存在于光学相干层析成像(OCT)中,影响OCT图像质量.在使用OCT设备诊断各种常见眼科疾病时,高质量的OCT图像是极为重要的.利用深度神经网络对OCT图像进行降噪处理,使图像在保留空间结构细节的基础上能展示更多的信息.提出了一种基于残差学习网络的新型OCT图像降噪网络-CMCNN,其具有多尺度、多权重和多层次...     

一种多尺度边缘测度融合加权HD算法

一般的边缘加权Hausdorff算法,由于单尺度边缘检测算子本身对噪音敏感,会造成真实和虚假边缘显著性差异小,从而加权后对噪音鲁棒性改善有限.为此,提出了一种基于多尺度边缘测度融合加权的Hausdorff景象匹配算法.对图像提取多尺度边缘测度后,引入证据推理理论,提出一种双向指数基本置信指派构造方法,并构造出多尺度边缘...     

Analysis of complex time series using refined composite multiscale entropy

Multiscale entropy (MSE) is an effective algorithm for measuring the complexity of a time series that has been applied in many fields successfully. However, MSE may yield an inaccurate estimation of entropy or induce undefined entropy because the coarse-graining procedure reduces the length of a time series considerably at large scales. Composite multiscale entropy (CMSE) was recently proposed to improve the accuracy of MSE, but it does not resolve undefined entropy. Here we propose a refined composite multiscale entropy (RCMSE) to improve CMSE. For short time series analyses, we demonstrate that RCMSE increases the accuracy of entropy estimation and reduces the probability of inducing undefined entropy.     

一种多尺度边缘测度融合加权HD算法

一般的边缘加权Hausdorff算法,由于单尺度边缘检测算子本身对噪音敏感,会造成真实和虚假边缘显著性差异小,从而加权后对噪音鲁棒性改善有限.为此,提出了一种基于多尺度边缘测度融合加权的Hausdorff景象匹配算法.对图像提取多尺度边缘测度后,引入证据推理理论,提出一种双向指数基本置信指派构造方法,并构造出多尺度边缘测度的基本置信指派函数,然后采用冲突再分配DSmT组合规则进行融合.为了进一步区别真实边缘与高频噪音,对加权Hausdorff公式进行了一些改进,给出了更为有效利用融和后边缘测度的加权Hausdorff公式.对可见光和SAR景象的匹配实验证明:本文算法所提取边缘在抑制噪音的同时保留了大量景象细节信息,并通过横向对比验证本文算法提高了噪音鲁棒性.     

Fault Recognition of Rolling Bearings Based on Parameter Optimized Multi-Scale Permutation Entropy and Gath-Geva

To extract fault features of rolling bearing vibration signals precisely, a fault diagnosis method based on parameter optimized multi-scale permutation entropy (MPE) and Gath-Geva (GG) clustering is proposed. The method can select the important parameters of MPE method adaptively, overcome the disadvantages of fixed MPE parameters and greatly improve the accuracy of fault identification. Firstly, aiming at the problem of parameter determination and considering the interaction among parameters comprehensively of MPE, taking skewness of MPE as fitness function, the time series length and embedding dimension were optimized respectively by particle swarm optimization (PSO) algorithm. Then the fault features of rolling bearing were extracted by parameter optimized MPE and the standard clustering centers is obtained with GG clustering. Finally, the samples are clustered with the Euclid nearness degree to obtain recognition rate. The validity of the parameter optimization is proved by calculating the partition coefficient and average fuzzy entropy. Compared with unoptimized MPE, the propose method has a higher fault recognition rate.