The empirical optimal envelope and its application to local mean decomposition

Envelopes, which represent the overall information of the signal amplitude variation, are the necessary mediums in many signal decomposition methods. The phenomena of undershoot and overshoot result in the error of envelope estimation and unexpected signal decomposition components. In this paper, an accurate envelope estimation method, called the empirical optimal envelope (EOE), is proposed and applied to the local mean decomposition (LMD). First, an indicator of envelope distance is defined to describe the features of the ideal envelope. Utilizing the indicator, an iterative algorithm for the approximation of tangency points is designed. The tangency points, instead of the extreme points, are interpolated to realize the EOE. Then, the EOE is integrated with the LMD, and two interpolation functions, the cubic spline and the piecewise cubic Hermite interpolating polynomial, are combined to improve the efficiency and convergence of signal decomposition. Finally, the proposed method is verified by simulated signals and actual signals.     

A rotating machinery fault diagnosis method based on local mean decomposition

Local mean decomposition (LMD) is a novel self-adaptive time–frequency analysis method, which is particularly suitable for the processing of multi-component amplitude-modulated and frequency-modulated (AM–FM) signals. By using LMD, any complicated signal can be decomposed into a number of product functions (PFs), each of which is the product of an envelope signal and a purely frequency modulated signal from which physically meaningful instantaneous frequencies can be obtained. In fact, each PF is just a mono-component AM–FM signal. Therefore, the procedure of LMD may be regarded as the process of demodulation. While fault occurs in gear or roller bearing, the vibration signals picked up would exactly display AM–FM characteristics. So it is possible to diagnose gear and roller bearing fault by LMD. Targeting the modulation features of the gear or roller bearing fault vibration signal, a rotating machinery fault diagnosis method based on LMD is proposed. In this paper, firstly the LMD method is introduced; secondly, the LMD method is compared with another competing time–frequency analysis approach, namely, empirical mode decomposition (EMD) method and the results show the superiority of the LMD method; finally, the LMD method is applied to the gear and roller bearing fault diagnosis. The analysis results from the practical gearbox vibration signal demonstrate that the diagnosis approach based on LMD could identify gear and roller bearing work condition accurately and effectively.     

基于条件局部均值分解与变量预测模型的轴承故障诊断方法

针对局部均值分解(LMD)方法在分解非线性、非平稳振动信号过程中存在的模态混淆现象,从而影响故障识别准确性的问题,提出了基于条件局部均值分解方法(CLMD)与模式识别变量预测模型(VPMCD)的故障诊断方法。该方法将数字图像处理的频率分辨率方法与LMD相结合,首先确定振动信号中所有局部极值点的频率分辨率,将振动信号分为低频率分辨率区域和高频率分辨率区域;然后对高频率分辨率区域进行LMD分解,可得若干乘积函数(PF)分量;最后用折线将所有PF分量连接起来,经滑动平均处理可得PF分量,提取PF分量的偏度系数和能量系数构成故障特征向量,用于VPMCD故障识别。将该方法应用于轴承故障诊断,实验结果表明,与LMD方法相比,识别效率提高了8.33%,表明了该方法的有效性和可行性。     

基于改进LMD方法的风电机组齿轮箱故障诊断研究

局部均值函数的求取是局部均值分解(LMD)的关键环节.针对局部均值函数求取存在偏差进而造成模态混叠的问题,提出了一种基于局部积分均值的LMD风电机组齿轮箱故障诊断方法.该方法改变了对相邻两极值点求平均值的思路,采用求取相邻两极值点的局部积分均值,再通过滑动平均法进行平滑处理,最终得到局部均值函数.为实现风电机组齿轮箱故...     

基于改进LMD与GRU网络的短期燃气负荷预测

针对燃气负荷数据非线性、非平稳性的特点,本文提出一种基于改进的LMD算法与GRU神经网络的组合预测模型.模型首先利用改进后的LMD算法对燃气负荷数据进行序列分解,改进的LMD方法采用分段牛顿插值法代替传统的滑动平均值法来获得局部均值函数和包络估计函数,改善了传统LMD方法存在的过平滑问题.之后,再将得到的若干PF分量进行小波阈值去噪处理,获得有效的分量数据.最后,利用GRU神经网络分别预测各分量值,将它们相加得到最终的负荷预测值.仿真实验表明,提出的方法与单个GRU神经网络以及结合传统LMD算法的GRU网络相比,预测精度更高.     

基于LMD和GNN-Adaboost的滚动轴承故障严重程度识别

提出一种基于局部均值分解（Local Mean Decomposition,LMD）和遗传神经网络自适应增强（Genetic Neural Network Adaptive Boosting,GNN-Adaboost）的滚动轴承损伤程度识别方法。通过LMD方法将轴承振动信号分解为若干个瞬时频率有物理意义的乘积函数（Production Function,PF）,对能反映信号主要特征的PF提取能量矩,结合原始振动信号的时域特征参数（方差、偏度、峭度）,组成故障严重程度识别特征参数矩阵。将基于LMD方法的特征参数矩阵作为GNN-Adaboost方法的输入向量,对不同载荷与转速工况下的轴承进行故障严重程度识别。结果表明,基于LMD和GNN-Adaboost的方法能够有效提高轴承故障严重程度识别准确率,对滚动轴承等关键旋转部件的故障识别与定位具有重要意义。     

The complex local mean decomposition

The local mean decomposition (LMD) has been recently developed for the analysis of time series which have nonlinearity and nonstationarity. The smoothed local mean of the LMD surpasses the cubic spline method used by the empirical mode decomposition (EMD) to extract amplitude and frequency modulated components. To process complex-valued data, we propose complex LMD, a natural and generic extension to the complex domain of the original LMD algorithm. It is shown that complex LMD extracts the frequency modulated rotation and envelope components. Simulations on both artificial and real-world complex-valued signals support the analysis.     

A quantitative estimation technique for welding quality using local mean decomposition and support vector machine

The experimental nonlinear time series of welding current contain the arc feature information related to welding quality. The local mean decomposition (LMD) combining with the support vector machine (SVM) is put forward to quantitatively estimate the rationality of welding parameters and welding formation quality. The LMD is used to investigate the time–frequency distribution of arc energy, and the energy entropy is employed to quantitatively judge the welding arc characteristics related to welding quality. The collected current signal is decomposed into a number of product functions (PFs) by LMD. The energy entropy of each PF is calculated to establish the welding arc energy feature vectors, which are inputted into support vector machine classifier. The LMD combining with SVM can quantitatively estimate the time–frequency energy distribution characteristics of the arc current signal at different welding parameters and welding formation quality. Experimental results are provided to confirm the effectiveness of this approach to estimate the rationality of welding parameters and welding formation quality.     

LMD特征融合与SVM的供水管道堵塞识别

针对城市供水管道早期堵塞难以检测的问题,提出了一种基于局部均值分解(LMD)的分量信号特征提取,结合支持向量机(SVM)的堵塞故障识别方法.先对声响应信号进行LMD,得到若干乘积函数(PF)分量,进而采用相关分析法选取有效PF分量,对有效PF分量分别提取能量熵、近似熵和平均声压三个指标的特征,构建分类特征集.最后利用交叉验证(CV)方法优化参数的SVM分类器识别堵塞故障信号.实验结果表明:采取基于LMD特征融合和通过CV优化的SVM相结合的方法可以有效识别供水管道的初期堵塞.与基于LMD特征融合和BP神经网络的方法进行了对比,结果表明:本文方法具有更好的堵塞故障识别效果.     

Data discovering of inverse Robin boundary conditions problem in arbitrary connected domain through meshless radial point Hermite interpolation

In this paper, a suitable method is presented to treat the partial derivative equations, especially the Laplace equation having the Robin boundary conditions. These equations come from classical physics, especially the branch of thermodynamics, and have an efficient role in the field of heat and temperature. Our motivation is to reset a harmonic data obtained from Robin’s conditions in the arbitrary plane domain particularly on its boundaries. The applied method is a nodal Hermite meshless collocation technique at which it is formed of radial basis functions to get out the shape functions which is the key to construct the local bases in the neighborhoods of the nodal points. Moreover, by taking into consideration the Hermite interpolation technique, we can impose the boundary conditions directly, the named technique is called “MRPHI,” meshless radial point Hermite interpolation, and it is done on some examples so that trustworthy results are obtained.

     

Extensions and generalisations of rational and high order transformation methods

A review of previously published work extending the rational basis to include Hermite interpolation is given. New high order transformation methods are described for Hermite interpolation. The intimate connection between the two basic methods both in the construction of transformations and the construction of basis functions is highlighted and the basic high order transformation method is generalised to handle elements with an arbitrary number of sides.     

基于MED和边际谱的自动倾斜器轴承故障诊断

针对直升机自动倾斜器轴承早期微弱故障特征易被强烈背景噪声淹没的问题，提出了一种基于最小熵反褶积（Minimum Entropy Deconvolution，MED）和边际谱的自动倾斜器轴承故障诊断方法。采用MED对采集的振动信号进行滤波降噪，提高了信号的信噪比，突出了轴承早期微弱故障特征；通过Hilbert变换和经验模态分解（Empirical Mode Decomposition，EMD）获取去噪包络信号的本征模态函数（Intrinsic Mode Functions，IMF）集，并引入峭度筛选准则选取合理IMF集计算局部Hilbert边际谱，有效地提取了故障特征频率，能够通过故障特征频率进行故障类型判别。通过某型直升机自动倾斜器故障诊断试验系统验证了该诊断方法的合理性和可行性。     

三次Hermite参数曲线与曲面的扩展

在给定插值条件时,标准三次Hermite参数曲线与曲面的形状无法调整。为克服标准三次Hermite参数曲线与曲面的不足,首先通过提高基函数次数的方法给出了一种带形状参数的四次Hermite基函数,然后生成了相应的带形状参数的四次Hermite参数曲线与曲面。所生成的曲线与曲面是标准三次Hermite参数曲线与曲面的扩展,不仅与标准三次Hermite曲线与曲面具有完全相同的性质,而且当插值条件给定时,其形状可通过修改形状参数的取值进行局部或整体调节,为插值曲线与曲面的构造提供了一种新方法。     

Generalized rational Bézier curves for the rigid body motion design

In this paper, we present a new method for the smooth interpolation of the orientations of a rigid body motion. The method is based on the geometrical Hermite interpolation in a hypersphere. However, the non-Euclidean structure of a sphere brings a great challenge to the interpolation problem. For this consideration and the requirements for practical application, we construct the spherical analogue of classical rational Bézier curves, called generalized rational Bézier curves. The new spherical curves are obtained using the generalized rational de Casteljau algorithm, which is a generalization of the classical rational de Casteljau algorithm to a hypersphere. Then, \(G^2\) Hermite interpolation problem in hypersphere is solved analytically using the generalized rational Bézier curve of degree 5. The new method offers residual free parameters including shape parameters and weights, which guarantee the existence of the interpolant to arbitrary motion data and offer great flexibility for the shape design of the motion. Numerical examples show that our method is far better behaved according to the energy functional which is regarded as a measure of the motion shape.     

基于参数联合优化VMD-SVM的工业机器人旋转部件故障诊断方法

针对因工业机器人旋转部件故障诊断模型最优参数难以自适应确定导致故障识别率低的问题,提出了一种参数联合优化的VMD-SVM的工业机器人旋转部件故障诊断方法;提出了一种基于遗传变异的改进灰狼算法,该算法采用Logistic混沌映射进行种群初始化,将非线性因子引入位置更新公式,并利用遗传变异策略解决算法陷入局部最优时的停滞现象;基于该算法对VMD和SVM进行参数联合优化;利用参数优化的VMD对故障信号进行分解,对所得的本征模态函数计算改进样本熵以构成特征向量,再输入至参数优化的SVM完成工业机器人旋转部件的故障诊断;仿真和实验结果表明,本文方法能够准确地进行故障诊断,在信号无噪和含噪的条件下准确率最高均达100%,较EMD、LMD、DTCWT、VMD等四种方法具有更优的指标。     

有理[2m+1,2m]型分段插值样条

常见的较低次有理带单形状因子分段有理插值样条通过代数运算,可用Bernstein基函数等价表示,这类分段插值样条利用Hermite插值的方法推广到高次有理[2m+1,2m]型,样条的生成曲线满足Cm-连续,并给出了具体的Bern-stein基函数表示方法的表达式,其形式较为简单,最后分别讨论了这类有理插值的逼近阶与约束域及保单调等方面的形状因子的选取情况,并给出了例子分析。     

局部形状可调插值曲线曲面及其参数选取方案

以形状可调插值曲线曲面为研究主题的文献多数侧重于分析曲线曲面性质,少有文献介绍可调插值曲线曲面的构造方法,以及调节参数的选取方案。这里以3次Hermite插值曲线为基础,通过在导矢中引入参数来构造形状可调插值曲线,将曲线按照插值数据进行整理,即可得到含参数的插值基函数,进而由之构造张量积插值曲面。为了帮助设计者寻找合适的参数,提供了4种用于确定曲线中形状参数的准则,其中的3种还推广应用于曲面,每种准则都提供了可以直接使用的公式。所给可调插值曲线曲面的构造方法以及参数选取方案具有一般性,数值实例验证了方案的有效性。     

LMD方法在脑电信号处理中的应用研究

局部均值分解(LMD)是一种新的非线性非平稳信号处理方法,该方法具有较强的自适应性,能将复杂信号分解为一系列具有物理意义的PF(production function)分量。但在信号分解过程中会产生端点效应,这将影响LMD分解精度,严重时会导致信号失真。在详细分析了LMD产生端点效应的原因之后,提出了一种基于相似波形加权匹配的端点延拓算法。通过对视觉诱发脑电信号进行仿真,并且和不做延拓的LMD分解结果做对比,说明该方法能够有效抑制LMD的端点效应,取得较好的分解效果。     

A novel integral extension LMD method based on integral local waveform matching

This paper proposed a novel integral extension local mean decomposition (IELMD) method, which can be widely applied in wind turbine fault diagnosis. Firstly, the characteristic waveform and its corresponding integral values are calculated. Then, the similar waveform is established according to signal extreme points and their integral values. The similar waveform and characteristic waveform are compared in order to obtain an optimal waveform, which can match the characteristic waveform in the best way. Finally, the optimal waveform is used to extend the left side and right side of the original signal. According to the simulation experimental analysis, the novel IELMD method is reasonable and effective in suppressing LMD end effect, and this method can be applied in wind turbine fault diagnosis.     

A spiking neural network-based approach to bearing fault diagnosis

Fault diagnosis, with the aim of accurately identifying the presence of various faults as early as possible so at to provide effective information for maintenance planning, has been extensively concerned in advanced manufacturing systems. With the increase of the amount of condition monitoring data, fault diagnosis methods have gradually shifted from the model-based paradigm to data-driven paradigm. Intelligent fault diagnosis approaches which can automatically mine useful information from a huge amount of raw data are becoming promising ways to identify faults of manufacturing systems in the context of massive data. In this paper, the Spiking Neural Network (SNN), as the third generation neural network, is tailored as an intelligent fault diagnosis tool for bearings in rotating machinery. Compared to the perceptron and the back propagation neural network (BPNN) which are respectively the first and second generations of neural networks. SNN, which introduces the concept of time into its operating model can more closely mimic natural neural networks and possesses high bionic characteristics. In the proposed SNN-based approach to bearing fault diagnosis, features extracted from raw vibration signals through the local mean decomposition (LMD) are encoded into spikes to train an SNN with the improved tempotron learning rule. The performance of the proposed method is examined by the CWRU and MFPT datasets, and the experimental results show that the method can achieve a promising accuracy in bearing fault diagnosis.