CN111476339A - Rolling bearing fault feature extraction method, intelligent diagnosis method and system - Google Patents
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Abstract
本发明提供了滚动轴承故障特征提取方法、智能诊断方法及系统,包括:采集电动驱动端的轴承信号数据,对信号数据进行预处理,将信号数据分为测试集和训练集;采用小波频带能量法提取信号数据的特征,分别得到训练集和测试集的第一特征矩阵;采用小波包—AR谱估计法提取信号数据的特征,分别得到训练集和测试集的第二特征矩阵;采用EMD‑SVD法提取信号数据的特征,分别得到训练集和测试集的第三特征矩阵;将第一、第二和第三特征矩阵拼接处理,并通过PCA进行数据压缩得到降维后的训练集和测试集,并输入到分类器进行数据分析,对故障进行诊断,能够有效保证信号特征的完备性和稀疏性,提高特征提取的泛化准确率,提高分类器的泛化能力。
The invention provides a rolling bearing fault feature extraction method, an intelligent diagnosis method and a system, including: collecting bearing signal data of an electric drive end, preprocessing the signal data, dividing the signal data into a test set and a training set; According to the characteristics of the signal data, the first characteristic matrix of the training set and the test set are obtained respectively; the wavelet packet-AR spectrum estimation method is used to extract the characteristics of the signal data, and the second characteristic matrix of the training set and the test set are obtained respectively; the EMD-SVD method is used Extract the features of the signal data to obtain the third feature matrix of the training set and the test set respectively; splicing the first, second and third feature matrices, and compressing the data through PCA to obtain the training set and test set after dimension reduction, And input it to the classifier for data analysis and fault diagnosis, which can effectively ensure the completeness and sparsity of signal features, improve the generalization accuracy of feature extraction, and improve the generalization ability of the classifier.
Description
技术领域technical field
本发明专利属于机械故障诊断领域,尤其是融合了多种特征处理方法和故障识别手段的滚动轴承故障特征提取方法、智能诊断方法及系统。The patent of the present invention belongs to the field of mechanical fault diagnosis, in particular to a rolling bearing fault feature extraction method, an intelligent diagnosis method and a system integrating various feature processing methods and fault identification methods.
背景技术Background technique
机械故障诊断是在故障发生预期最短的周期内,基于可测量的信号特征,自动的对设备进行监督维护的一种方法。而滚动轴承作为旋转机械中最重要,也是最容易受损的部件一直深受工业界的关注。Mechanical fault diagnosis is a method to automatically supervise and maintain equipment based on measurable signal characteristics within the shortest expected period of failure. Rolling bearings, as the most important and most easily damaged components in rotating machinery, have always attracted the attention of the industry.
现有的轴承故障诊断技术通常包括三个步骤:采集数字信号,处理数字信号,分类器分类。其中采集数字信号主要通过加速传感器获取,而分类器通常采用机器监督学习算法来进行故障识别,虽然此类算法在当今已经相当完善,但是采用监督学习算法进行故障识别在很大程度上依赖于所提取的信号特征。所提取的特征越完整,越具有代表性,其故障识别能力越强,而传统的使用单一特征提取方法,往往不能得到全面有效的特征,因此分类器分类很难表现好的泛化能力。The existing bearing fault diagnosis technology usually includes three steps: collecting digital signal, processing digital signal, and classifying by classifier. Among them, the digital signal is mainly acquired by the acceleration sensor, and the classifier usually uses the machine supervised learning algorithm for fault identification. Although such algorithms are quite perfect today, the use of the supervised learning algorithm for fault identification largely depends on the Extracted signal features. The more complete and representative the extracted features are, the stronger the fault identification ability is. However, the traditional single feature extraction method often cannot obtain comprehensive and effective features, so it is difficult for the classifier to perform good generalization ability.
发明内容SUMMARY OF THE INVENTION
针对现有技术存在的上述不足,本发明采用多种方法从不同角度进行特征提取,并通过一定手段进行降维处理,这保证了所提取特征的完备性和稀疏性,而在分类器分类识别阶段,针对SVM(支持向量机)的参数优化问题,提出采用PSO(粒子群算法)加快参数寻优速度。In view of the above deficiencies in the prior art, the present invention adopts a variety of methods to extract features from different angles, and performs dimensionality reduction processing through certain means, which ensures the completeness and sparseness of the extracted features. In the first stage, for the parameter optimization problem of SVM (Support Vector Machine), it is proposed to use PSO (Particle Swarm Optimization) to speed up the parameter optimization.
第一方面,本发明提供了滚动轴承故障特征提取方法,步骤包括:采集电动驱动端的轴承信号数据,对信号数据进行预处理,将信号数据分为测试集和训练集;In a first aspect, the present invention provides a method for extracting fault features of a rolling bearing. The steps include: collecting bearing signal data at an electric drive end, preprocessing the signal data, and dividing the signal data into a test set and a training set;
采用小波频带能量法提取信号数据的特征,分别得到训练集和测试集的第一特征矩阵;The features of the signal data are extracted by the wavelet frequency band energy method, and the first feature matrices of the training set and the test set are obtained respectively;
采用小波包—AR谱估计法提取信号数据的特征,分别得到训练集和测试集的第二特征矩阵;The wavelet packet-AR spectral estimation method is used to extract the features of the signal data, and the second feature matrices of the training set and the test set are obtained respectively;
采用EMD-SVD法提取信号数据的特征,分别得到训练集和测试集的第三特征矩阵;The EMD-SVD method is used to extract the features of the signal data, and the third feature matrices of the training set and the test set are obtained respectively;
将第一、第二和第三特征矩阵拼接处理,并通过PCA进行数据压缩得到降维后的训练集和测试集,即,为轴承故障特征。The first, second and third feature matrices are spliced and processed, and data compression is performed by PCA to obtain the training set and test set after dimensionality reduction, that is, bearing fault features.
第二方面,本发明还提供了一种滚动轴承故障的智能诊断方法,包括采用如第一方面所述的滚动轴承故障特征提取方法获取降维后的训练集和测试集,将降维后的训练集和测试集输入分类器进行训练,对轴承故障进行诊断;In a second aspect, the present invention also provides an intelligent diagnosis method for rolling bearing faults, including using the rolling bearing fault feature extraction method described in the first aspect to obtain a training set and a test set after dimensionality reduction, and the training set after dimensionality reduction is obtained and the test set input classifier for training to diagnose bearing faults;
所述将降维后的训练集和测试集输入分类器进行训练的具体步骤包括:初始化粒子群,对粒子速度和位置初始化;The specific steps of inputting the dimensionality-reduced training set and test set into the classifier for training include: initializing the particle swarm, and initializing the particle velocity and position;
计算粒子的适应度,在当前惩罚项系数和核函数宽度下,计算SVM识别准确率;Calculate the fitness of the particle, and calculate the SVM recognition accuracy under the current penalty term coefficient and kernel function width;
寻找极值;更新粒子速度和位置;判断SVM分类误差是否满足终止条件;若满足终止条件,则将测试集放入分类器进行分类,对训练集和测试集的分类结果进行分析;若不满足,则返回寻找极值处继续处理。Find the extreme value; update the particle velocity and position; judge whether the SVM classification error meets the termination condition; if the termination condition is met, put the test set into the classifier for classification, and analyze the classification results of the training set and test set; , then return to find the extreme value to continue processing.
第三方面,本发明还提供了一种滚动轴承故障特征提取系统,包括:In a third aspect, the present invention also provides a rolling bearing fault feature extraction system, including:
采集模块:被配置为,采集电动驱动端的轴承信号数据;Acquisition module: configured to collect the bearing signal data of the electric drive end;
预处理模块:被配置为,对信号数据进行预处理,将信号数据分为测试集和训练集;Preprocessing module: configured to preprocess the signal data, and divide the signal data into a test set and a training set;
特征提取模块:被配置为,采用小波频带能量法提取信号数据的特征,分别得到训练集和测试集的第一特征矩阵;采用小波包—AR谱估计法提取信号数据的特征,分别得到训练集和测试集的第二特征矩阵;采用EMD-SVD法提取信号数据的特征,分别得到训练集和测试集的第三特征矩阵;将第一、第二和第三特征矩阵拼接处理,并通过PCA进行数据压缩得到降维后的训练集和测试集。Feature extraction module: configured to extract the features of the signal data by using the wavelet frequency band energy method to obtain the first feature matrix of the training set and the test set respectively; use the wavelet packet-AR spectrum estimation method to extract the features of the signal data to obtain the training set respectively and the second feature matrix of the test set; use the EMD-SVD method to extract the features of the signal data, and obtain the third feature matrix of the training set and the test set respectively; splicing the first, second and third feature matrices, and pass PCA Perform data compression to obtain the dimensionality-reduced training set and test set.
第四方面,本发明还提供了一种计算机可读存储介质,用于存储计算机指令,所述计算机指令被处理器执行时,完成如第一方面所述的滚动轴承故障特征提取方法。In a fourth aspect, the present invention further provides a computer-readable storage medium for storing computer instructions, when the computer instructions are executed by a processor, the method for extracting fault features of a rolling bearing according to the first aspect is completed.
第五方面,本发明还提供了一种滚动轴承故障的智能诊断系统,包括分类器和如第三方面所述的采集模块、预处理模块、特征提取模块;所述分类器,被配置为:输入特征提取模块降维后的训练集和测试集;初始化粒子群,对粒子的惩罚项系数和核函数宽度的速度、位置初始化;在当前惩罚项系数和核函数宽度下,计算SVM识别准确率;寻找极值;更新粒子速度和位置;判断SVM分类误差是否满足终止条件;若满足终止条件,则将测试集放入分类器进行分类,对训练集和测试集的分类结果进行分析;若不满足,则返回寻找极值处继续处理。In a fifth aspect, the present invention also provides an intelligent diagnosis system for rolling bearing faults, including a classifier and the acquisition module, preprocessing module, and feature extraction module as described in the third aspect; the classifier is configured to: input The training set and test set after dimensionality reduction of the feature extraction module; initialize the particle swarm, initialize the speed and position of the particle's penalty term coefficient and kernel function width; calculate the SVM recognition accuracy under the current penalty term coefficient and kernel function width; Find the extreme value; update the particle velocity and position; judge whether the SVM classification error meets the termination condition; if the termination condition is met, put the test set into the classifier for classification, and analyze the classification results of the training set and test set; , then return to find the extreme value to continue processing.
与现有技术对比,本发明具备以下有益效果:Compared with the prior art, the present invention has the following beneficial effects:
1、本发明采用多种方法对信号进行特征提取,并采用PCA(奇异值分解)进行降维处理,与单一的方法进行特征提取相比,能够有效保证信号特征的完备性和稀疏性,提高特征提取的泛化准确率。1. The present invention uses a variety of methods to perform feature extraction on the signal, and uses PCA (singular value decomposition) for dimensionality reduction processing. Compared with a single method for feature extraction, it can effectively ensure the completeness and sparsity of signal features, and improve the performance of signal features. Generalization accuracy of feature extraction.
2、本发明针对SVM的参数优化问题,利用PSO算法实现对SVM的两个重要参数C和g的优化速度,与常规的SVM分类器相比,能有效避免过拟合和欠拟合问题,提高分类器的泛化能力。2. Aiming at the parameter optimization problem of SVM, the present invention utilizes the PSO algorithm to realize the optimization speed of two important parameters C and g of SVM. Compared with the conventional SVM classifier, the problem of overfitting and underfitting can be effectively avoided, Improve the generalization ability of the classifier.
3、本发明通过预处理能够在大量的数据中,提取出精确,且具有代表性的特征,采用多种方法从不同角度进行特征提取,并通过一定手段进行降维处理,这保证了所提取特征的完备性和稀疏性,而在分类器分类识别阶段,针对SVM(支持向量机)的参数优化问题,提出采用PSO(粒子群算法)加快参数寻优速度。3. The present invention can extract accurate and representative features from a large amount of data through preprocessing, use a variety of methods to extract features from different angles, and perform dimensionality reduction processing through certain means, which ensures that the extracted features are extracted. The completeness and sparseness of features, and in the classification and identification stage of the classifier, for the parameter optimization problem of SVM (Support Vector Machine), it is proposed to use PSO (Particle Swarm Optimization) to speed up the parameter optimization.
附图说明Description of drawings
构成本申请的一部分的说明书附图用来提供对本申请的进一步理解,本申请的示意性实施例及其说明用于解释本申请,并不构成对本申请的不当限定。The accompanying drawings that form a part of the present application are used to provide further understanding of the present application, and the schematic embodiments and descriptions of the present application are used to explain the present application and do not constitute improper limitations on the present application.
图1为本发明的轴承振动信号处理的流程示意图;1 is a schematic flowchart of bearing vibration signal processing according to the present invention;
图2为本发明的小波分解树;Fig. 2 is the wavelet decomposition tree of the present invention;
图3为本发明的小波包分解树;Fig. 3 is the wavelet packet decomposition tree of the present invention;
图4为本发明的SVM-PSO算法流程图。FIG. 4 is a flowchart of the SVM-PSO algorithm of the present invention.
具体实施方式:Detailed ways:
下面结合附图与实施例对本发明作进一步说明。The present invention will be further described below with reference to the accompanying drawings and embodiments.
应该指出,以下详细说明都是示例性的,旨在对本申请提供进一步的说明。除非另有指明,本文使用的所有技术和科学术语具有与本申请所属技术领域的普通技术人员通常理解的相同含义。It should be noted that the following detailed description is exemplary and intended to provide further explanation of the application. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs.
需要注意的是,这里所使用的术语仅是为了描述具体实施方式,而非意图限制根据本申请的示例性实施方式。如在这里所使用的,除非上下文另外明确指出,否则单数形式也意图包括复数形式,此外,还应当理解的是,当在本说明书中使用术语“包含”和/或“包括”时,其指明存在特征、步骤、操作、器件、组件和/或它们的组合。It should be noted that the terminology used herein is for the purpose of describing specific embodiments only, and is not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly dictates otherwise, the singular is intended to include the plural as well, furthermore, it is to be understood that when the terms "comprising" and/or "including" are used in this specification, it indicates that There are features, steps, operations, devices, components and/or combinations thereof.
在本发明中,术语如“上”、“下”、“左”、“右”、“前”、“后”、“竖直”、“水平”、“侧”、“底”等指示的方位或位置关系为基于附图所示的方位或位置关系,只是为了便于叙述本发明各部件或元件结构关系而确定的关系词,并非特指本发明中任一部件或元件,不能理解为对本发明的限制。In the present invention, terms such as "upper", "lower", "left", "right", "front", "rear", "vertical", "horizontal", "side", "bottom", etc. The orientation or positional relationship is based on the orientation or positional relationship shown in the accompanying drawings, and is only a relational word determined for the convenience of describing the structural relationship of each component or element of the present invention, and does not specifically refer to any component or element in the present invention, and should not be construed as a reference to the present invention. Invention limitations.
本发明中,术语如“固接”、“相连”、“连接”等应做广义理解,表示可以是固定连接,也可以是一体的连接或可拆卸连接;可以是直接相连,也可以通过中间媒介间接相连。对于本领域的相关科研或技术人员,可以根据具体情况确定上述术语在本发明中的具体含义,不能理解为对本发明的限制。In the present invention, terms such as "fixed connection", "connected", "connected", etc. should be understood in a broad sense, indicating that it can be a fixed connection, an integral connection or a detachable connection; it can be directly connected, or it can be connected through the middle media are indirectly connected. For the relevant scientific research or technical personnel in the field, the specific meanings of the above terms in the present invention can be determined according to the specific situation, and should not be construed as a limitation of the present invention.
实施例1Example 1
为了在大量的数据中,提取出精确,且具有代表性的特征,本发明采用多种方法从不同角度进行特征提取,并通过一定手段进行降维处理,这保证了所提取特征的完备性和稀疏性,而在分类器分类识别阶段,针对SVM(支持向量机)的参数优化问题,提出采用PSO(粒子群算法)加快参数寻优速度。In order to extract accurate and representative features from a large amount of data, the present invention adopts various methods to extract features from different angles, and performs dimensionality reduction processing by certain means, which ensures the completeness and integrity of the extracted features. Sparsity, and in the classification and identification stage of the classifier, for the parameter optimization problem of SVM (support vector machine), it is proposed to use PSO (particle swarm algorithm) to speed up the parameter optimization speed.
为了实现以上的目的,本发明解决方案如下:In order to achieve the above purpose, the solution of the present invention is as follows:
滚动轴承故障特征提取方法,步骤包括:采集电动驱动端的轴承信号数据,对信号数据进行预处理,将信号数据分为测试集和训练集;The method for extracting fault features of a rolling bearing includes the following steps: collecting bearing signal data of an electric drive end, preprocessing the signal data, and dividing the signal data into a test set and a training set;
采用小波频带能量法提取信号数据的特征,分别得到训练集和测试集的第一特征矩阵;The features of the signal data are extracted by the wavelet frequency band energy method, and the first feature matrices of the training set and the test set are obtained respectively;
采用小波包—AR谱估计法提取信号数据的特征,分别得到训练集和测试集的第二特征矩阵;The wavelet packet-AR spectral estimation method is used to extract the features of the signal data, and the second feature matrices of the training set and the test set are obtained respectively;
采用EMD-SVD法提取信号数据的特征,分别得到训练集和测试集的第三特征矩阵;The EMD-SVD method is used to extract the features of the signal data, and the third feature matrices of the training set and the test set are obtained respectively;
将第一、第二和第三特征矩阵拼接处理,并通过PCA进行数据压缩得到降维后的训练集和测试集,即,为轴承故障特征。The first, second and third feature matrices are spliced and processed, and data compression is performed by PCA to obtain the training set and test set after dimensionality reduction, that is, bearing fault features.
进一步的,所述信号进行预处理的步骤包括:轴承数据信号中待使用的信号序列为F1~Fi,将Fi进行适当分割,形成l个信号序列,即Fi={fi1,fi2,fi3…fil},其中fi1为第i种故障序列分割而成的第一个子集序列;随机从Fi中选出一部分信号子序列作为原始训练集;另一部分作为原始测试集。Further, the step of preprocessing the signal includes: the signal sequences to be used in the bearing data signal are F 1 to F i , and F i is appropriately divided to form one signal sequence, that is, F i ={f i1 , f i2 , f i3 ...f il }, where f i1 is the first subset sequence divided by the i-th fault sequence; a part of the signal subsequence is randomly selected from F i as the original training set; the other part is used as the original test set.
进一步的,所述采用小波频带能量法提取信号数据的特征的具体步骤包括:Further, the specific steps of using the wavelet band energy method to extract the features of the signal data include:
对轴承信号数据进行小波分解;Perform wavelet decomposition on bearing signal data;
将轴承信号数据的不同分量分解到相应的频段内,计算出各个频段的能量特征;Decompose the different components of the bearing signal data into the corresponding frequency bands, and calculate the energy characteristics of each frequency band;
对能量特征向量归一化处理,分别获得训练集和测试集的第一特征矩阵。The energy eigenvectors are normalized to obtain the first eigenmatrix of the training set and the test set, respectively.
进一步的,所述采用小波包-AR谱估计法提取信号数据的特征的具体步骤包括:对轴承信号进行小波包分解;Further, the specific steps of using the wavelet packet-AR spectrum estimation method to extract the features of the signal data include: decomposing the bearing signal by wavelet packet;
将信号的不同分量分解到相应的频段内,并对每个分量进行小波包重构获得重构信号;Decompose different components of the signal into corresponding frequency bands, and perform wavelet packet reconstruction on each component to obtain a reconstructed signal;
对重构信号进行AR谱估计,计算出各个频段的AR功率谱密度;Perform AR spectrum estimation on the reconstructed signal, and calculate the AR power spectral density of each frequency band;
计算各频段AR谱能量特征,分别得到训练集和测试集的第二特征矩阵。Calculate the AR spectral energy features of each frequency band, and obtain the second feature matrix of the training set and the test set respectively.
进一步的,所述采用EMD-SVD法提取信号数据的特征的具体步骤包括:Further, the specific steps of using the EMD-SVD method to extract the features of the signal data include:
对信号进行EMD分解得到若干IMF分量;Decompose the signal by EMD to obtain several IMF components;
计算IMF分量的能量占比;Calculate the energy proportion of the IMF component;
设定阈值,提取能量占比超过阈值的若干IMF分量;Set a threshold to extract several IMF components whose energy ratio exceeds the threshold;
采用SVD对提取的IMF分量进行压缩处理,将压缩的IMF分量作为信号特征,分别得到训练集和测试集的第三特征矩阵。SVD is used to compress the extracted IMF components, and the compressed IMF components are used as signal features to obtain the third feature matrix of the training set and the test set respectively.
进一步的,所述将第一、第二和第三特征矩阵拼接处理的具体步骤包括:获得拼接处理后的训练集α和测试集β,其中α=[α1,α2,α3]A1×M,β=[β1,β2,β3]A2×M,A1,A2分别表示训练集和测试集的信号个数,M表示特征维数α1、α2和α3分别为训练集的第一、第二和第三特征矩阵,β1、β2和β3分别为测试集的第一、第二和第三特征矩阵。Further, the specific steps of splicing the first, second and third feature matrices include: obtaining training set α and test set β after splicing processing, where α=[α 1 , α 2 , α 3 ] A1 ×M , β=[β 1 , β 2 , β 3 ] A2×M , A1, A2 represent the number of signals in the training set and test set respectively, M represents the feature dimension α 1 , α 2 and α 3 are the training set and α 3 respectively The first, second and third feature matrices of the set, β 1 , β 2 and β 3 are the first, second and third feature matrices of the test set, respectively.
进一步的,所述通过PCA进行数据压缩的具体步骤包括:对于训练数据集α,计算其协方差矩阵;对协方差矩阵进行奇异值分解;输出降维后的训练集;同样的对测试集β进行相同处理得到降维后的测试集。Further, the specific steps of performing data compression by PCA include: for the training data set α, calculating its covariance matrix; performing singular value decomposition on the covariance matrix; outputting the training set after dimension reduction; similarly, for the test set β Perform the same processing to obtain the dimensionality-reduced test set.
实施例2Example 2
本发明以西储大学电机驱动端轴承信号数据集为基础,需要指出此类轴承故障数据信号分为内圈,外圈,滚动体三类,每类又包括直径分为0.1778,0.3556,0.5334mm的人为制造的电火花伤痕,再加上正常的轴承数据信号总共分为十种情况,因此确定待使用的信号序列为F1~Fi,其中i=1,2…10。The present invention is based on the bearing signal data set of the motor drive end of the Western Reserve University. It should be pointed out that such bearing fault data signals are divided into three categories: inner ring, outer ring, and rolling body, and each category includes diameters of 0.1778, 0.3556, and 0.5334mm. The artificial spark scars and the normal bearing data signals are divided into ten cases in total, so the signal sequence to be used is determined to be F 1 -Fi , where i =1, 2...10.
图1为本发明的轴承振动信号的特征提取与智能诊断流程图,如图1所示,本发明的轴承振动信号的特征提取与智能诊断方法,具体包含以下步骤:1 is a flowchart of feature extraction and intelligent diagnosis of bearing vibration signals of the present invention. As shown in FIG. 1 , the feature extraction and intelligent diagnosis method of bearing vibration signals of the present invention specifically includes the following steps:
(1)数据预处理(1) Data preprocessing
将Fi进行适当分割,形成1个信号序列,即Fi={fi1,fi2,fi3…fil},其中fi1为第i种故障序列分割而成的第一个子集序列。接下来随机从Fi中选出一部分信号子序列作为原始训练集;另一部分作为原始测试集。为表示方便设训练集为A1*B1的矩阵,测试集为A2*B2的矩阵,其中A1,A2为信号个数,B1,B2表示信号特征维数Divide F i appropriately to form a signal sequence, that is, F i ={f i1 , f i2 , f i3 ...f il }, where f i1 is the first subset sequence divided by the i-th fault sequence . Next, a part of signal subsequences are randomly selected from Fi as the original training set; the other part is used as the original test set. For convenience, the training set is a matrix of A1*B1, and the test set is a matrix of A2*B2, where A1 and A2 are the number of signals, and B1 and B2 are the signal feature dimensions.
(2)利用小波变换进行多分辨率分析,提取信号在不同频段的能量特征(2) Multi-resolution analysis using wavelet transform to extract the energy characteristics of the signal in different frequency bands
对轴承信号进行小波分解,从而将信号的不同分量分解到相应的频段内,最后计算出各个频段的能量特征。具体如下:The bearing signal is decomposed by wavelet, so that the different components of the signal are decomposed into corresponding frequency bands, and finally the energy characteristics of each frequency band are calculated. details as follows:
(2-1)小波分解:选择离散小波函数j∈Z(1)为小波基函数,对信号进行分解,具体数学表达如下:(2-1) Wavelet decomposition: select discrete wavelet function j∈Z(1) is the wavelet basis function, which decomposes the signal. The specific mathematical expression is as follows:
式中j为分解尺度,x为分解的位置参数,W2jf(x)为信号f在分解尺度2j,位置为x的小波分解系数。where j is the decomposition scale, x is the position parameter of the decomposition, W 2j f(x) is the wavelet decomposition coefficient of the signal f at the decomposition scale 2j and the position is x.
以(2)式小波分解数学表达式为理论基础对信号进行M1层分解,提取各个叶子节点包含的信号特征。假设原始信号为f,用(m,n)表示小波分解树(如图2所示)的第m层第n个节点,其中m=0,1,2,3…M1,n=0,1;每个结点都代表一定的频段特征,(0,0)代表原始信号,(1,0)和(1,1)分别代表小波分解的低频系数S10和高频系数S11,依次类推(m,n)代表第m层第n个节点系数Smn。Based on the mathematical expression of formula (2) wavelet decomposition, the signal is decomposed at M1 level, and the signal features contained in each leaf node are extracted. Assuming the original signal is f, denote the nth node of the mth layer of the wavelet decomposition tree (as shown in Figure 2) by (m, n), where m=0, 1, 2, 3...M1, n=0, 1 ; Each node represents a certain frequency band feature, (0, 0) represents the original signal, (1, 0) and (1, 1) represent the low-frequency coefficient S 10 and high-frequency coefficient S 11 of the wavelet decomposition, respectively, and so on (m, n) represents the n-th node coefficient S mn of the m-th layer.
(2-2)计算频带能量:计算信号f各个叶子结点的能量Emn,计算公式如下:(2-2) Calculate the frequency band energy: Calculate the energy E mn of each leaf node of the signal f, and the calculation formula is as follows:
式中,n的取值受m约束且0<m≤M1;当m<M1时,n=1;当m=M1,n=0或n=1(实际意义为第M1层信号分解会得到一个低频叶子结点和一个高频叶子结点)。此时k代表Smn的特征维数In the formula, the value of n is constrained by m and 0<m≤M1; when m<M1, n=1; when m=M1, n=0 or n=1 (the actual meaning is that the M1 layer signal decomposition will get a low frequency leaf node and a high frequency leaf node). At this time k represents the feature dimension of S mn
(2-3)特征向量归一化:将特征向量归一化,各频带的能量比重作为的一个特征分量,如下所示:(2-3) Normalization of eigenvectors: the eigenvectors Normalized, the energy proportion of each frequency band is taken as a feature component of , As follows:
式中m,n的取值范围与(3)式相同。In the formula, the value range of m and n is the same as that of formula (3).
(2-4)获得特征矩阵:按上述步骤对于每个信号进行特征提取,最终得到第一个A1*M1的α1训练集和A2*M1的β1测试集。(2-4) Obtain feature matrix: perform feature extraction for each signal according to the above steps, and finally obtain the first A1*M1 α 1 training set and A2*M1 β 1 test set.
(3)利用小波包-AR谱估计方法提取信号在各频段AR谱能量特征(3) Using the wavelet packet-AR spectrum estimation method to extract the AR spectrum energy characteristics of the signal in each frequency band
对轴承信号进行小波包分解,从而将信号的不同分量分解到相应的频段内,并对每个分量进行重构,最后通过AR谱估计来计算出各个频段的AR谱能量特征。具体如下:The bearing signal is decomposed by wavelet packet, so that the different components of the signal are decomposed into corresponding frequency bands, and each component is reconstructed. Finally, the AR spectral energy characteristics of each frequency band are calculated by AR spectral estimation. details as follows:
(3-1)小波包分解:选取合适小波基函数,确定对信号的分解层数,具体数学表达如下:(3-1) Wavelet packet decomposition: Select the appropriate wavelet basis function to determine the number of decomposition layers for the signal. The specific mathematical expression is as follows:
式中k为平移时间因子;h代表低通滤波器系数;g代表高通滤波器系数;为信号f(x)经过j层小波包分解得到的第m个分解序列;为原数字信号f(x)。where k is the translation time factor; h is the low-pass filter coefficient; g is the high-pass filter coefficient; is the mth decomposition sequence obtained by decomposing the signal f(x) through the j-layer wavelet packet; is the original digital signal f(x).
以(5)式小波包分解数学表达式为理论基础对信号进行M2层分解,提取最后一层叶子节点包含的信号特征。假设原始信号为f,用(m,n)表示小波包分解树(如图3所示)的第m层第n个节点,其中m=0,1,2,3…M2,n=0,1,...2M2-1;每个结点都代表一定的频段特征,(0,0)代表原始信号,(1,0)和(1,1)分别代表小波分解的低频系数S10和高频系数S11,依次类推(m,n)表示代表第m层第n个节点系数Smn。Based on the mathematical expression of wavelet packet decomposition in formula (5), the signal is decomposed in M2 layer, and the signal features contained in the last layer of leaf nodes are extracted. Assuming the original signal is f, use (m, n) to represent the nth node of the mth layer of the wavelet packet decomposition tree (as shown in Figure 3), where m=0, 1, 2, 3...M2, n=0, 1,...2 M2 -1; each node represents a certain frequency band feature, (0, 0) represents the original signal, (1, 0) and (1, 1) represent the low-frequency coefficients S10 and The high-frequency coefficient S11, and so on (m, n) represents the coefficient S mn representing the n-th node of the m-th layer.
(3-2)小波包重构:根据第M2层得到的系数序列进行信号重构。RSmn表示系数Smn的重构信号。小波重构数学表达如下:(3-2) Wavelet packet reconstruction: perform signal reconstruction according to the coefficient sequence obtained at the M2th layer. RS mn represents the reconstructed signal of coefficient S mn . The mathematical expression of wavelet reconstruction is as follows:
式中:和分别为h和g的对偶算子,为j-1层重构形成的第m个重构序列。where: and The dual operators of h and g, respectively, The mth reconstruction sequence formed for the j-1 layer reconstruction.
(3-3)AR谱分析:对RSmn重构信号进行AR谱估计,得到各个频段的AR谱功率密度Pmn,具体如下:(3-3) AR spectrum analysis: perform AR spectrum estimation on the RS mn reconstructed signal to obtain the AR spectrum power density P mn of each frequency band, as follows:
假设重构的信号序列为x(n),则该序列的自回归模型可表示为:Assuming that the reconstructed signal sequence is x(n), the autoregressive model of the sequence can be expressed as:
式中w(x)为具有零均值、方差为的正态分布白噪声;q为模型的阶次。通过相关的信号处理知识,求得AR模型参数aj(j=1,2…N)和然后由自传递函数,计算出信号x(n)的功率谱密度为:where w(x) has zero mean and variance is The normally distributed white noise; q is the order of the model. Through the relevant signal processing knowledge, the AR model parameters aj (j=1, 2...N) and Then from the self-transfer function, the power spectral density of the signal x(n) is calculated as:
(3-4)求解各个频段信号的AR谱能量:设Pmn对应的能量Epmn,则有:(3-4) Solving the AR spectral energy of each frequency band signal: Set the energy Ep mn corresponding to P mn , then:
式中k为特征维数;m=M2;n=0,1,2…2M2-1。In the formula, k is the characteristic dimension; m=M2; n=0, 1, 2...2 M2 -1.
(3-5)获得特征向量各频带的能量作为的一个特征分量,如下所示:(3-5) Obtain eigenvectors The energy of each frequency band is as a feature component of , As follows:
(3-6)获得特征矩阵:按上述步骤对于每个信号进行特征提取,最终得到大小为A1*(2M2-1)的α2训练集和A2*(2M2-1)的β2测试集。(3-6) Obtain feature matrix: perform feature extraction for each signal according to the above steps, and finally obtain α 2 training set of size A1*(2 M2 -1) and β 2 test of A2*(2 M2 -1) set.
(4)基于EMD-SVD的信号特征提取方法(4) Signal feature extraction method based on EMD-SVD
对信号进行EMD分解得到若干IMF分量;计算IMF分量的能量占比;提取能量比重较大的若干IMF分量;采用SVD对提取的IMF分量进行压缩处理,将压缩的IMF分量作为信号特征。The signal is decomposed by EMD to obtain several IMF components; the energy proportion of the IMF components is calculated; several IMF components with a large energy proportion are extracted; SVD is used to compress the extracted IMF components, and the compressed IMF components are used as signal features.
具体如下:details as follows:
(4-1)采用EMD分解提取排在前面且能量和超过98%的IMF分量,具体如下:(4-1) Use EMD decomposition to extract the IMF components that are ranked in the front and whose energy sum exceeds 98%, as follows:
找到原始信号f(t)的所有局部极值点Find all local extreme points of the original signal f(t)
利用插值算法,对找到的所有局部极值点进行拟合得出上包络线fmax(t)和下包络线fmin(t)Using the interpolation algorithm, fit all the local extreme points found to obtain the upper envelope f max (t) and the lower envelope f min (t)
由上下包络线得到均值a1 Obtain the mean value a 1 from the upper and lower envelopes
进一步的通过h1=f(t)-a1,判断h1是否满足IMF的两个条件,如果满足,则h1就是一阶IMF分量;如果不满足,以h1作为新的f(t),重复步骤a)~d),得到h11=h1-a11,其中a11为h1的上下包络线均值;若h11仍然不满足,则继续重复上述步骤直到h1k满足条件,记作C1=h1k为第一阶IMF分量Further through h 1 =f(t)-a 1 , it is judged whether h 1 satisfies the two conditions of IMF. If so, h 1 is the first-order IMF component; if not, h 1 is used as the new f(t ), repeat steps a) to d) to obtain h 11 =h 1 -a 11 , where a 11 is the mean value of the upper and lower envelopes of h1; if h 11 is still not satisfied, continue to repeat the above steps until h 1k satisfies the condition, Denoted as C 1 =h 1k is the first-order IMF component
分离出一阶IMF分量以后,得到r1=f(t)-C1,将r1作为新f(t),接着重复步骤a)~d),多次计算可得到n阶的IMF分量和残差rn,最终实现EMD分解,公式如下所示:After the first-order IMF component is separated, r 1 =f(t)-C 1 is obtained, and r 1 is taken as the new f(t), and then steps a) to d) are repeated, and the n-order IMF components and The residual r n , and finally realizes the EMD decomposition, the formula is as follows:
计算不同IMF分量Ci的能量Eci,其中i=1,2,3..n,接着找到所占能量比重较大且能量和占比超过98%以上的IMF分量Sm。Calculate the energy Eci of different IMF components Ci, where i=1, 2, 3..n, and then find the IMF component S m which accounts for a large proportion of energy and whose energy sum accounts for more than 98%.
(4-2)获得IMF特征矩阵Um×τ:各IMF分量作为的Um×τ一个特征分量,Um×τ如下所示:(4-2) Obtain the IMF characteristic matrix U m×τ : each IMF component is a characteristic component of U m× τ , and U m×τ is as follows:
Um×τ矩阵中m代表向量个数,τ代表特征维数。In the U m×τ matrix, m represents the number of vectors, and τ represents the feature dimension.
(4-3)进一步的通过SVD进行特征值分解,实现对Um×τ矩阵的压缩,分解公式如下:(4-3) The eigenvalue decomposition is further carried out by SVD to realize the compression of the U m×τ matrix. The decomposition formula is as follows:
上式中Qm×m为左奇异矩阵,右奇异矩阵;Bm×τ为奇异值矩阵,且其为对角矩阵,具体如下所示:In the above formula, Q m×m is a left singular matrix, Right singular matrix; B m×τ is a singular value matrix, and it is a diagonal matrix, as follows:
在这里会根据情况取值比较大的前几个奇异值作为信号的特征,设提取的特征向量为且维数为M3,因此可得: Here, the first few singular values with relatively large values will be taken as the characteristics of the signal according to the situation. Let the extracted feature vector be And the dimension is M3, so we can get:
(4-4)获得特征矩阵:按上述步骤对于每个信号进行特征提取,最终得到大小为A1*M3的α3训练集和A2*M3的β3测试集。(4-4) Obtaining a feature matrix: perform feature extraction for each signal according to the above steps, and finally obtain an α 3 training set of A1*M3 and a β 3 test set of A2*M3.
(5)采用PCA对得到的数据集进行降维(5) Use PCA to reduce the dimensionality of the obtained data set
(5-1)获得训练集α和测试集β,其中α=[α1,α2,α3]A1×M,β=[β1,β2,β3]A2×M,A1,A2分别表示训练集和测试集的信号个数,M表示特征维数,且M=M1+2M2-1+M3进一步的对α和β进行展开表示具体如下:(5-1) Obtain training set α and test set β, where α=[α 1 , α 2 , α 3 ] A1×M , β=[β 1 , β 2 , β 3 ] A2×M , A1, A2 Respectively represent the number of signals in the training set and test set, M represents the feature dimension, and M=M1+2 M2 -1+M3 The further expansion of α and β is expressed as follows:
其中Tri和Tei分别代表A1*1和A2*1的向量。where Tri and Tei represent the vectors of A1*1 and A2*1, respectively.
(5-2)采用PCA将α和β进行压缩(5-2) Compress α and β using PCA
具体如下:details as follows:
对于训练数据集α,计算其协方差矩阵Q,公式如下:For the training data set α, calculate its covariance matrix Q, the formula is as follows:
对协方差矩阵进行奇异值分解:[U,S,V]=SVD(Q),其中U代表左奇异矩阵,V代表右奇异矩阵,S代表奇异值矩阵。Perform singular value decomposition on the covariance matrix: [U, S, V]=SVD(Q), where U represents the left singular matrix, V represents the right singular matrix, and S represents the singular value matrix.
寻找特征占比和满足阈值时所对应的k值,判断条件如下:其中evi代表Q的第i个奇异值。Find the feature ratio and the corresponding k value when the threshold is met. The judgment conditions are as follows: where ev i represents the ith singular value of Q.
选择U的前k列作为投影矩阵Ptr=[u1,u1,…uk],其中第k列为第k个奇异值对应的特征向量。Select the first k columns of U as the projection matrix Ptr=[u1, u1,...uk], where the kth column is the eigenvector corresponding to the kth singular value.
输出降维后的训练数据集TrianA1×k=Ptr×α,k<MOutput the training data set after dimensionality reduction Trian A1×k =Ptr×α, k<M
同样的对测试集β进行相同处理得到最终测试集TestA2×r=Pte×β,r<MThe same processing is performed on the test set β to obtain the final test set Test A2×r =Pte×β, r<M
(6)采用SVM方法对故障信号进行分类(6) Using the SVM method to classify the fault signal
(6-1)分类器训练(6-1) Classifier training
如图4SVM-PSO算法流程图所示,具体解释如下:As shown in the flowchart of SVM-PSO algorithm in Figure 4, the specific explanation is as follows:
(a)初始化粒子群,粒子群规模为N;迭代次数It;惩罚项系数ci的位置为Pci,速度为Vci;核函数宽度gi的位置为Pgi,速度为Vgi;定义SVM分类误差error(a) Initialize the particle swarm, the size of the particle swarm is N; the number of iterations It; the position of the penalty term coefficient ci is Pci, the velocity is Vci; the position of the kernel function width gi is Pgi, the velocity is Vgi; define the SVM classification error error
(b)计算粒子的适应度Fit[i],即在当前ci和gi下,计算SVM分类的准确度;(b) Calculate the fitness Fit[i] of the particle, that is, calculate the accuracy of the SVM classification under the current ci and gi;
(c)将Fit[i]与个体最优Pbest[i]进行比较,若Fit[i]>Pbest[i],则Pbest[i]=Fit[i];将Fit[i]与个体最优Gbest[i]进行比较,若Fit[i]>Gbest[i],则Gbest[i]=Fit[i](c) Compare Fit[i] with the individual optimal Pbest[i], if Fit[i]>Pbest[i], then Pbest[i]=Fit[i]; compare Fit[i] with the individual optimal Gbest[i] is compared, if Fit[i]>Gbest[i], then Gbest[i]=Fit[i]
(d)更新(Pci,Vci)和(Pgi,Vgi),即相当于更新了ci和gi;然后计算粒子的适应度Fit[i],更新公式如(13)(14)所示:(d) Update (Pci, Vci) and (Pgi, Vgi), which is equivalent to updating ci and gi; then calculate the fitness Fit[i] of the particle, and the update formula is shown in (13) (14):
vim=w·vim(k)+c1r1·(Pim(k)-xid(k))+c2r2·(Pgm(k)-xim(k)) (13)v im =w· vim (k)+c 1 r 1 ·(P im (k)-x id (k))+c 2 r 2 ·(P gm (k)-x im (k)) (13 )
xim(k+1)=xim(k)+vim(k+1) (14)x im (k+1)=x im (k)+v im (k+1) (14)
上式中w叫做惯性权重,c1和c2代表加速度常数,r1和r2均为(0,1)之间的随机数,k为迭代次数。In the above formula, w is called inertia weight, c1 and c2 represent acceleration constants, r1 and r2 are random numbers between (0, 1), and k is the number of iterations.
(e)判断当前error足够小或当前迭代iter大于It,则退出,输出c和g参数,以及目标函数(15)中w和b的目标参数值;否则返回第二步。(e) Judging that the current error is small enough or the current iteration iter is greater than It, then exit, output the c and g parameters, and the target parameter values of w and b in the objective function (15); otherwise, return to the second step.
Subject to:yi(WTxi+b)≥1-ξi,ξi≥0Subject to: y i (W T x i +b)≥1-ξ i , ξ i ≥0
(6-2)将测试集放入分类器进行分类(6-2) Put the test set into the classifier for classification
(6-3)对训练集Train和测试集Test的分类结果进行分析(6-3) Analyze the classification results of the training set Train and the test set Test
以上就是本发明的具体流程。The above is the specific flow of the present invention.
在其他具体实施例还提供了:Other specific embodiments also provide:
一种滚动轴承故障的智能诊断方法,包括采用如实施例1所述的滚动轴承故障特征提取方法获取降维后的训练集和测试集,将降维后的训练集和测试集输入分类器进行训练,对轴承故障进行诊断。An intelligent diagnosis method for rolling bearing faults, comprising using the rolling bearing fault feature extraction method as described in
进一步的,所述将降维后的训练集和测试集输入分类器进行训练的具体步骤包括:初始化粒子群,对粒子的惩罚项系数ci和核函数宽度gi的速度、位置初始化;在当前惩罚项系数ci和核函数宽度gi下,计算粒子适应度(SVM识别准确率);寻找极值;更新粒子速度和位置;判断SVM分类误差是否满足终止条件;若满足终止条件,则将测试集放入分类器进行分类,对训练集和测试集的分类结果进行分析;若不满足,则返回寻找极值处继续处理。Further, the specific steps of inputting the dimensionality-reduced training set and test set into the classifier for training include: initializing the particle swarm, initializing the speed and position of the particle's penalty term coefficient ci and the kernel function width gi; Under the term coefficient ci and the kernel function width gi, calculate the particle fitness (SVM recognition accuracy); find the extreme value; update the particle speed and position; judge whether the SVM classification error meets the termination condition; if the termination condition is met, put the test set into Enter the classifier for classification, and analyze the classification results of the training set and the test set; if not satisfied, return to finding the extreme value to continue processing.
一种滚动轴承故障特征提取系统,包括:A rolling bearing fault feature extraction system, comprising:
采集模块:被配置为,采集电动驱动端的轴承信号数据;Acquisition module: configured to collect the bearing signal data of the electric drive end;
预处理模块:被配置为,对信号数据进行预处理,将信号数据分为测试集和训练集;Preprocessing module: configured to preprocess the signal data, and divide the signal data into a test set and a training set;
特征提取模块:被配置为,采用小波频带能量法提取信号数据的特征,分别得到训练集和测试集的第一特征矩阵;采用小波包-AR谱估计法提取信号数据的特征,分别得到训练集和测试集的第二特征矩阵;采用EMD-SVD法提取信号数据的特征,分别得到训练集和测试集的第三特征矩阵;将第一、第二和第三特征矩阵拼接处理,并通过PCA进行数据压缩得到降维后的训练集和测试集。Feature extraction module: configured to extract the features of the signal data by using the wavelet frequency band energy method to obtain the first feature matrix of the training set and the test set respectively; use the wavelet packet-AR spectrum estimation method to extract the features of the signal data and obtain the training set respectively and the second feature matrix of the test set; use the EMD-SVD method to extract the features of the signal data, and obtain the third feature matrix of the training set and the test set respectively; splicing the first, second and third feature matrices, and pass PCA Perform data compression to obtain the dimensionality-reduced training set and test set.
一种计算机可读存储介质,用于存储计算机指令,所述计算机指令被处理器执行时,完成如实施例1所述的滚动轴承故障特征提取方法。A computer-readable storage medium for storing computer instructions, when the computer instructions are executed by a processor, the method for extracting fault features of a rolling bearing as described in
一种滚动轴承故障的智能诊断系统,包括分类器和上述实施例中所述的采集模块、预处理模块、特征提取模块;所述分类器,被配置为:输入特征提取模块降维后的训练集和测试集;初始化粒子群,对粒子c和g的速度和位置初始化;在当前惩罚项系数c和核函数宽度g下,计算粒子适应度(SVM识别准确率);寻找极值;更新粒子速度和位置;判断SVM分类误差是否满足终止条件;若满足终止条件,则将测试集放入分类器进行分类,对训练集和测试集的分类结果进行分析;若不满足,则返回寻找极值处继续处理。An intelligent diagnosis system for rolling bearing faults, comprising a classifier and the acquisition module, preprocessing module, and feature extraction module described in the above embodiments; the classifier is configured to: input a training set after dimension reduction by the feature extraction module and test set; initialize the particle swarm, initialize the speed and position of particles c and g; under the current penalty term coefficient c and kernel function width g, calculate particle fitness (SVM recognition accuracy); find extreme values; update particle speed and position; judge whether the SVM classification error satisfies the termination condition; if it satisfies the termination condition, put the test set into the classifier for classification, and analyze the classification results of the training set and test set; if not, return to find the extreme value Continue processing.
上述虽然结合附图对本发明的具体实施方式进行了描述,但并非对本发明保护范围的限制,所属领域技术人员应该明白,在本发明的技术方案的基础上,本领域技术人员不需要付出创造性劳动即可做出的各种修改或变形仍在本发明的保护范围以内。Although the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, they do not limit the scope of protection of the present invention. Those skilled in the art should understand that on the basis of the technical solutions of the present invention, those skilled in the art do not need to pay creative efforts. Various modifications or deformations that can be made are still within the protection scope of the present invention.
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