CN106092575A

CN106092575A - A kind of based on Johnson conversion and the bearing failure diagnosis of particle filter algorithm and method for predicting residual useful life

Info

Publication number: CN106092575A
Application number: CN201610379897.2A
Authority: CN
Inventors: 金晓航; 阙子俊; 孙毅
Original assignee: Zhejiang University of Technology ZJUT
Current assignee: Zhejiang University of Technology ZJUT
Priority date: 2016-06-01
Filing date: 2016-06-01
Publication date: 2016-11-09

Abstract

A kind of based on Johnson conversion and the bearing failure diagnosis of particle filter algorithm and method for predicting residual useful life, comprise the following steps: 1) gather bearing life cycle management vibration signal；2) utilize vibration signal to calculate K S distance, construct the index of reflection bearing health status based on K S distance；3) based on constructed health index, to the health index data of non-gaussian distribution during working healthily, use Johnson conversion, be converted into the data of Gauss distribution, utilize the character of Gauss distribution, determine relevant abnormalities threshold range；4) the health index data Fitting Analysis to the consume phase, builds and characterizes bearing degradation status of processes spatial model, utilizes health index data that Current observation obtains and particle filter algorithm update model parameter and predict the residual life of bearing.Efficient diagnosis of the present invention goes out bearing fault in early days and occurs, thus intercepts out the Performance Degradation Data of bearing consume phase exactly, and the method calculates speed and predicting residual useful life precision is higher.

Description

A Bearing Fault Diagnosis and Residual Analysis Based on Johnson Transform and Particle Filter Algorithm remaining life prediction method

技术领域technical field

本发明属于轴承故障诊断与预测领域，尤其涉及一种基于Johnson变换和粒子滤波算法的轴承故障诊断与剩余寿命预测方法。The invention belongs to the field of bearing fault diagnosis and prediction, in particular to a method for bearing fault diagnosis and remaining life prediction based on Johnson transformation and particle filter algorithm.

背景技术Background technique

轴承是旋转机械中不可缺少的零部件，在电力、石化、冶金、机械、航空航天以及一些军事工业部门中广泛使用，是保证精密机床、高速铁路、风力发电机等重要装备设施精度、性能、寿命和可靠性的核心零部件，然而它也是这些装备中最容易发生故障的部件之一。据统计，旋转机械的大部分故障是由于轴承故障引起的。轴承发生故障，轻则降低或失去装备的某些功能，重则造成严重的甚至是灾难性的后果。因此轴承的状态监测、故障诊断与预测一直是近年来的一个研究重点。考虑到轴承从早期故障发生，发展直至失效是一个非线性、动态的过程，因此利用基于贝叶斯理论的非线性滤波算法，如扩展卡尔曼滤波、无迹卡尔曼滤波等在轴承的故障预测方面得到了快速的发展。然而基于卡尔曼滤波框架的轴承故障预测方法是基于样本服从高斯分布的假设发展起来的，当样本不服从高斯分布假设的时候，基于卡尔曼滤波框架的轴承故障预测方法并不适用。Bearings are an indispensable part of rotating machinery. They are widely used in electric power, petrochemical, metallurgy, machinery, aerospace, and some military industrial sectors. They are used to ensure the accuracy, performance, and A key component for longevity and reliability, yet it is also one of the most failure-prone parts of these pieces of equipment. According to statistics, most of the failures of rotating machinery are caused by bearing failures. If the bearing fails, it will reduce or lose some functions of the equipment, and it will cause serious or even catastrophic consequences. Therefore, condition monitoring, fault diagnosis and prediction of bearings have been a research focus in recent years. Considering that it is a nonlinear and dynamic process from the occurrence of early faults to the failure of bearings, nonlinear filtering algorithms based on Bayesian theory, such as extended Kalman filtering and unscented Kalman filtering, are used in bearing fault prediction. has developed rapidly. However, the bearing fault prediction method based on the Kalman filter framework is developed based on the assumption that the samples obey the Gaussian distribution. When the samples do not obey the Gaussian distribution assumption, the bearing fault prediction method based on the Kalman filter framework is not applicable.

发明内容Contents of the invention

为了克服现有的非线性贝叶斯滤波算法在解决轴承故障预测时剩余寿命预测精度较低、基于卡尔曼滤波框架的故障预测方法不适用于对非高斯分布样本进行剩余寿命预测等不足，本发明提供了一种预测精度较高、耗时较短，且适用于非高斯分布样本的基于Johnson变换和粒子滤波算法的轴承故障诊断与剩余寿命预测方法。In order to overcome the shortcomings of the existing nonlinear Bayesian filter algorithm in solving bearing fault prediction, the remaining life prediction accuracy is low, and the fault prediction method based on the Kalman filter framework is not suitable for the remaining life prediction of non-Gaussian distribution samples. The invention provides a bearing fault diagnosis and remaining life prediction method based on Johnson transformation and particle filter algorithm, which has high prediction accuracy, short time consumption, and is suitable for non-Gaussian distribution samples.

为了解决上述技术问题提供的技术方案为：The technical scheme that provides in order to solve the above-mentioned technical problem is:

一种基于Johnson变换和粒子滤波算法的轴承故障诊断与剩余寿命预测方法，所述方法包括以下步骤：A kind of bearing fault diagnosis and residual life prediction method based on Johnson transformation and particle filter algorithm, described method comprises the following steps:

S1.采集轴承的全寿命周期振动信号；S1. Collect the vibration signal of the whole life cycle of the bearing;

S2.利用振动信号计算K-S距离，基于K-S距离构建出反映轴承健康状态的指数；S2. Use the vibration signal to calculate the K-S distance, and construct an index reflecting the health status of the bearing based on the K-S distance;

S3.所构建的健康指数在整个轴承寿命周期上，呈现为两头高，中间低的曲线，对轴承健康时非高斯分布的健康指数，运用Johnson变换，转换成高斯分布的数据，利用高斯分布的性质，确定轴承发生异常时的健康指数的阈值；S3. The constructed health index presents a curve with two high ends and a low middle in the entire bearing life cycle. For the non-Gaussian distribution health index when the bearing is healthy, use Johnson transformation to convert it into Gaussian distribution data, and use Gaussian distribution. Nature, to determine the threshold of the health index when the bearing is abnormal;

S4.拟合分析轴承耗损期的健康指数数据，构建退化模型并建立状态空间模型，利用当前观测到的健康指数数据和粒子滤波算法更新模型参数，并预测剩余寿命，过程如下：S4. Fit and analyze the health index data of the bearing wear-out period, build a degradation model and establish a state space model, use the currently observed health index data and particle filter algorithm to update model parameters, and predict the remaining life. The process is as follows:

对耗损期的健康指数数据，拟合分析构建如下的退化模型：For the health index data in the depletion period, the fitting analysis constructs the following degradation model:

HI(k)＝a·exp(b·k)+c·exp(d·k) (1)HI(k)=a·exp(b·k)+c·exp(d·k) (1)

上式中，HI(k)为轴承在k时刻的健康指数，k为时间参数，a,b,c,d为模型参数，基于该退化模型构建状态方程：In the above formula, HI(k) is the health index of the bearing at time k, k is the time parameter, a, b, c, d are the model parameters, and the state equation is constructed based on the degradation model:

${a a}_{k k} = = {a a}_{k k - - 11} + + {w w}_{k k - - 11}^{a a} - - - - - - ((22))$

${b b}_{k k} = = {b b}_{k k - - 11} + + {w w}_{k k - - 11}^{b b} - - - - - - ((33))$

${c c}_{k k} = = {c c}_{k k - - 11} + + {w w}_{k k - - 11}^{c c} - - - - - - ((44))$

${d d}_{k k} = = {d d}_{k k - - 11} + + {w w}_{k k - - 11}^{d d} - - - - - - ((55))$

上式中，a_k,b_k,c_k,d_k和a_k-1,b_k-1,c_k-1,d_k-1为分别在k时刻和k-1时刻的状态变量a,b,c,d的值，为在k-1时刻，独立的且分别对应状态变量a,b,c,d的噪声；In the above formula, a _k , b _k , c _k , d _k and a _k-1 , b _k-1 , c _k-1 , d _k-1 are the state variables a at time k and k-1 respectively, the value of b,c,d, is the independent noise corresponding to the state variables a, b, c, and d at time k-1;

同时构建测量方程：Simultaneously construct the measurement equation:

HI_k＝a_k·exp(b_k·k)+c_k·exp(d_k·k)+v_k (6)HI _k ＝a _k exp(b _k k)+c _k exp(d _k k)+v _k (6)

上式中，HI_k为在k时刻健康指数的测量值，v_k为在k时刻的测量噪声；In the above formula, HI _k is the measured value of the health index at time k, and v _k is the measurement noise at time k;

利用粒子滤波算法更新状态方程和测量方程参数至k时刻，按公式(1)计算k+l时刻的健康指数HI(k+l)：Use the particle filter algorithm to update the state equation and measurement equation parameters to k time, and calculate the health index HI(k+l) at k+l time according to the formula (1):

HI(k+l)＝a_k·exp(b_k·(k+l))+c_k·exp(d_k·(k+l)) (7)HI(k+l)＝a _k ·exp(b _k ·(k+l))+c _k ·exp(d _k ·(k+l)) (7)

上式中，l＝1,2,…,∞；计算使得不等式(8)成立的l的值，并记录l的最小值为在k时刻预测的轴承剩余寿命；In the above formula, l=1,2,...,∞; calculate the value of l that makes the inequality (8) true, and record the minimum value of l as the predicted remaining life of the bearing at time k;

HI(k+l)＞故障阀值 (8)。HI(k+l)>fault threshold (8).

进一步，所述S2中，对S1所得的轴承全寿命周期振动信号，构建健康指数，过程如下；Further, in S2, the health index is constructed for the vibration signal of the bearing life cycle obtained in S1, and the process is as follows;

设第k时刻健康指数X_k，其中包含N个采样点，则样本数据集合为X_k＝(X₁,X₂,…,X_N)，将样本的观测值按照从小到大排列X₍₁₎≤X₍₂₎…≤X_(N)，则样本的累积分布函数为：Assuming that the health index X _k at the kth moment contains N sampling points, the sample data set is X _k = (X ₁ ,X ₂ ,…,X _N ), and the observed values of the samples are arranged in ascending order of X _{(1 )} ≤X ₍₂₎ …≤X _(N) , then the cumulative distribution function of the sample is:

${F f}_{X x} ((x x)) = = \{\begin{matrix} 00 & x x < < {X x}_{((11))} \\ \frac{j j}{N N} & {X x}_{((j j))} \leq \leq x x < < {X x}_{((j j + + 11))} \\ 11 & x x &GreaterEqual; &Greater Equal; {X x}_{((N N))} \end{matrix} - - - - - - ((99))$

上式中，j＝1,2,…,N-1；In the above formula, j=1,2,...,N-1;

取轴承正常工作时的任意一时刻点作为参考点，设该参考点的累积分布函数为R_X(x)，第k时刻振动信号的累积分布函数为F_X(x)，则K-S距离定义如下：Take any moment when the bearing is working normally as a reference point, set the cumulative distribution function of the reference point as R _X (x), and the cumulative distribution function of the vibration signal at the kth moment is F _X (x), then the KS distance is defined as follows :

$D D. ((k k)) = = \underset{- - ∞ ∞ < < x x < < ∞ ∞}{s the s u u p p} | | {F f}_{X x} ((x x)) - - {R R}_{X x} ((x x)) | | - - - - - - ((1010))$

健康指数HI包含水平和垂直两个方向的信息，其由下式计算得到：The health index HI contains information in both horizontal and vertical directions, which is calculated by the following formula:

$H h I I ((k k)) = = \sqrt{(({D D.}_{x x} {((k k))}^{22} + + {D D.}_{y the y} {((k k))}^{22}))} - - - - - - ((1111))$

上式中，D_x(k)和D_y(k)分别为在水平振动信号和垂直振动信号上计算得到的K-S距离。In the above formula, D _x (k) and D _y (k) are the KS distances calculated on the horizontal vibration signal and the vertical vibration signal, respectively.

再进一步，所述S3中，对S2所得的健康指数，截取轴承耗损期的健康指数数据；Still further, in said S3, for the health index obtained in S2, the health index data of the bearing wear-out period is intercepted;

基于K-S距离构建出表示轴承健康状况的指数，对轴承健康时的非高斯分布的健康指数，运用Johnson变换，转换成高斯分布的数据，并利用高斯分布的性质，确定轴承发生异常时健康指数的阈值；Based on the K-S distance, an index representing the health status of the bearing is constructed. For the health index of the non-Gaussian distribution when the bearing is healthy, the Johnson transformation is used to convert the data into Gaussian distribution, and the nature of the Gaussian distribution is used to determine the health index when the bearing is abnormal. threshold;

设对应于轴承健康工作时健康指数的变量λ＝[λ₁,λ₂,…,λ_M]，M为健康指数样本的个数，选择一个合适的z，通过查找标准正态分布表，找出对应于{-3z,-z,z,3z}的分布概率P_-3z、P_-z、P_z、P_3z，在λ中找出相对应的分位数λ_-3z，λ_-z，λ_z，λ_3z，并定义m＝λ_3z-λ_z，n＝λ_-z-λ_-3z，p＝λ_z-λ_-z，由此定义分位数比率QR如式(12)所示；Let the variable λ=[λ ₁ ,λ ₂ ,…,λ _M ] corresponding to the health index corresponding to the healthy work of the bearing, M be the number of health index samples, choose a suitable z, and find out by looking up the standard normal distribution table Find the distribution probability P _-3z , P _-z , P _z , P _3z corresponding to {-3z, -z, z, 3z}, and find the corresponding quantile λ _-3z , λ _-z in λ, λ _z , λ _3z , and define m=λ _3z -λ _z , n=λ _-z -λ _-3z , p=λ _z -λ _-z , thus defining the quantile ratio QR as shown in formula (12) ;

$Q Q R R = = \frac{m m n no}{{p p}^{22}} - - - - - - ((1212))$

当QR<1时，选择Johnson变换中的S_B转换类型，其转换公式为：When QR<1, select the S _B transformation type in Johnson transformation, and its transformation formula is:

${y the y}_{i i} = = γ γ + + η η l l n no ((\frac{{λ λ}_{i i} - - ϵ ϵ}{μ μ + + ϵ ϵ - - {λ λ}_{i i}})) - - - - - - ((1313))$

上式中，y_i对应于λ_i经Johnson变换后的值，1≤i≤M，式(13)中的参数定义如下：In the above formula, y _i corresponds to the value of λ _i after Johnson transformation, 1≤i≤M, and the parameters in formula (13) are defined as follows:

$η η = = z z {{{cosh cosh}^{- - 11} [[\frac{11}{22} {[[((11 + + \frac{p p}{m m})) ((11 + + \frac{p p}{n no}))]]}^{\frac{11}{22}}]]}}^{- - 11} - - - - - - ((1414))$

$γ γ = = {ηsinh ηsinh}^{- - 11} {{((\frac{p p}{n no} - - \frac{p p}{m m})) {[[((11 + + \frac{p p}{m m})) ((11 + + \frac{p p}{n no})) - - 44]]}^{\frac{11}{22}} {[[22 ((\frac{{p p}^{22}}{m m n no} - - 11))]]}^{- - 11}}} - - - - - - ((1515))$

$μ μ = = p p {{{[[((11 + + \frac{p p}{n no})) ((11 + + \frac{p p}{m m})) - - 22]]}^{22} - - 44}}^{\frac{11}{22}} {((\frac{{p p}^{22}}{m m n no} - - 11))}^{- - 11} - - - - - - ((1616))$

$ϵ ϵ = = \frac{{λ λ}_{z z} + + {λ λ}_{- - z z}}{22} - - \frac{μ μ}{22} + + p p ((\frac{p p}{n no} - - \frac{p p}{m m})) {[[22 ((\frac{{p p}^{22}}{m m n no} - - 11))]]}^{- - 11} - - - - - - ((1717))$

当QR＝1时，选取Johnson变换中的S_L转换类型，其转换公式为：When QR=1, select the S _L conversion type in the Johnson transformation, and its conversion formula is:

y_i＝γ+ηln(λ_i-ε) (18)y _i =γ+ηln(λ _i -ε) (18)

上式中，y_i对应于λ_i经Johnson变换后的值，1≤i≤M，式(18)中的参数定义如下：In the above formula, y _i corresponds to the value of λ _i after Johnson transformation, 1≤i≤M, and the parameters in formula (18) are defined as follows:

$η η = = \frac{22 z z}{l l n no ((m m / / p p))} - - - - - - ((1919))$

$γ γ = = η η l l n no [[\frac{m m / / p p - - 11}{p p {((m m / / p p))}^{11 / / 22}}]] - - - - - - ((2020))$

$ϵ ϵ = = \frac{{λ λ}_{z z} + + {λ λ}_{- - z z}}{22} - - \frac{p p}{22} [[\frac{m m / / p p + + 11}{m m / / p p - - 11}]] - - - - - - ((21 twenty one))$

当QR>1时，选取Johnson变换中的S_U转换类型，其转换公式为：When QR>1, select the S _U transformation type in Johnson transformation, and its transformation formula is:

${y the y}_{i i} = = γ γ + + {ηsinh ηsinh}^{- - 11} ((\frac{{λ λ}_{i i} - - ϵ ϵ}{μ μ})) - - - - - - ((22 twenty two))$

上式中，y_i对应于λ_i经Johnson变换后的值，1≤i≤M，式(22)中的参数定义如下：In the above formula, y _i corresponds to the value of λ _i after Johnson transformation, 1≤i≤M, and the parameters in formula (22) are defined as follows:

$η η = = 22 z z {{{cosh cosh}^{- - 11} [[\frac{11}{22} ((\frac{m m}{p p} + + \frac{n no}{p p}))]]}}^{- - 11} - - - - - - ((23 twenty three))$

$γ γ = = {ηsinh ηsinh}^{- - 11} {{((\frac{n no}{p p} - - \frac{m m}{p p})) {[[22 {((\frac{m m n no}{{p p}^{22}} - - 11))}^{\frac{11}{22}}]]}^{- - 11}}} - - - - - - ((24 twenty four))$

$μ μ = = 22 p p {((\frac{m m n no}{{p p}^{22}} - - 11))}^{\frac{11}{22}} {[[((\frac{m m}{p p} + + \frac{n no}{p p} - - 22)) ((\frac{m m}{p p} + + \frac{n no}{p p} + + 22))]]}^{- - \frac{11}{22}} - - - - - - ((2525))$

$ϵ ϵ = = \frac{{λ λ}_{z z} + + {λ λ}_{- - z z}}{22} + + p p ((\frac{n no}{p p} - - \frac{m m}{p p})) {[[22 ((\frac{n no}{p p} + + \frac{m m}{p p} - - 22))]]}^{- - 11} - - - - - - ((2626))$

通过Johnson变换，将非高斯分布的健康指数转换成符合高斯分布的数据，并利用高斯分布的性质，确定轴承发生异常时健康指数的阈值。Through Johnson transformation, the health index of non-Gaussian distribution is converted into data conforming to Gaussian distribution, and the property of Gaussian distribution is used to determine the threshold of the health index when the bearing is abnormal.

本发明的技术构思为：通过采集轴承振动信号，基于对振动信号K-S距离的计算构建健康指数，利用Johnson变换确定轴承发生异常时的健康指数的阈值，利用该阀值把轴承整个寿命周期区分为如下三个阶段：磨合期，有效寿命期和耗损期。通过拟合分析轴承耗损期的健康指数数据，构建用于描述轴承退化过程的状态空间模型，利用当前观测到的健康指数数据和粒子滤波算法更新模型参数，并预测剩余寿命。The technical concept of the present invention is: by collecting the vibration signal of the bearing, constructing the health index based on the calculation of the K-S distance of the vibration signal, using Johnson transformation to determine the threshold of the health index when the bearing is abnormal, and using the threshold to distinguish the entire life cycle of the bearing into The following three stages: break-in period, effective life period and wear-out period. By fitting and analyzing the health index data of the bearing wear-out period, a state space model for describing the bearing degradation process is constructed, and the model parameters are updated by using the currently observed health index data and particle filter algorithm, and the remaining life is predicted.

本发明的有益效果为：有效地诊断出早期轴承故障的发生，从而准确地截取出轴承耗损期的性能退化数据，该方法计算速度较快且剩余寿命预测精度较高。The beneficial effect of the present invention is: effectively diagnosing the occurrence of early bearing faults, thereby accurately intercepting performance degradation data during the wear-out period of the bearing, and the method has fast calculation speed and high prediction accuracy of remaining life.

附图说明Description of drawings

图1为基于Johnson变换和粒子滤波算法的轴承故障诊断与剩余寿命预测方法流程图；Figure 1 is a flowchart of bearing fault diagnosis and remaining life prediction method based on Johnson transform and particle filter algorithm;

图2为轴承整个寿命周期健康指数示意图；Figure 2 is a schematic diagram of the health index of the entire life cycle of the bearing;

图3为轴承健康工作时健康指数数据的正态概率图；Fig. 3 is the normal probability diagram of the health index data when the bearing is in healthy operation;

图4为轴承健康工作时健康指数数据经过Johnson变换后的正态概率图；Figure 4 is the normal probability map of the health index data after Johnson transformation when the bearing is in healthy work;

图5为轴承在耗损期的健康指数数据；Figure 5 shows the health index data of the bearing during the wear and tear period;

图6为轴承在耗损期内的剩余寿命预测。Figure 6 shows the prediction of the remaining life of the bearing during the wear period.

具体实施方式detailed description

下面结合附图对本发明作进一步描述。The present invention will be further described below in conjunction with the accompanying drawings.

参照图1～图6，一种基于Johnson变换和粒子滤波算法的轴承故障诊断与剩余寿命预测方法，所述方法包括以下步骤：Referring to Figures 1 to 6, a bearing fault diagnosis and remaining life prediction method based on Johnson transform and particle filter algorithm, the method includes the following steps:

S2.利用振动信号计算K-S距离，基于K-S距离构建出反映轴承健康状态的指数，方便后续步骤利用该指数进行轴承健康状态的判断和剩余寿命的预测；S2. Use the vibration signal to calculate the K-S distance, and construct an index reflecting the bearing health status based on the K-S distance, which is convenient for subsequent steps to use the index to judge the bearing health status and predict the remaining life;

S3.所构建的健康指数在整个轴承寿命周期上，呈现为两头高，中间低的曲线，对轴承健康工作时非高斯分布的健康指数，运用Johnson变换，转换成高斯分布的数据，利用高斯分布的性质，确定轴承发生异常时的健康指数的阈值；S3. The constructed health index presents a curve with two high ends and a low middle in the entire bearing life cycle. For the health index of non-Gaussian distribution when the bearing is in healthy operation, use Johnson transformation to convert the data into Gaussian distribution, and use Gaussian distribution. The nature of the bearing to determine the threshold of the health index when the bearing is abnormal;

S4.拟合分析轴承耗损期的健康指数数据，构建退化模型并建立状态空间模型，利用当前观测到的健康指数数据和粒子滤波算法更新模型参数，并预测剩余寿命。S4. Fitting and analyzing the health index data of the bearing wear-out period, constructing a degradation model and a state space model, using the currently observed health index data and particle filter algorithm to update the model parameters, and predicting the remaining life.

所述S1中，如附图2所示，轴承的全寿命周期可以分为三个阶段：磨合期，有效工作期和耗损期。In the above S1, as shown in Fig. 2, the whole life cycle of the bearing can be divided into three stages: running-in period, effective working period and wear-out period.

所述S2中，对S1所得的轴承全寿命周期振动信号，构建健康指数，过程如下；In said S2, the health index is constructed for the vibration signal of the bearing life cycle obtained in S1, and the process is as follows;

设第k时刻振动信号X_k，其中包含N个采样点，则样本数据集合为X_k＝(X₁,X₂,…,X_N)，将样本的观测值按照从小到大排列X₍₁₎≤X₍₂₎…≤X_(N)，则样本的累积分布函数为：Assuming that the vibration signal X _k at the kth moment contains N sampling points, the sample data set is X _k = (X ₁ ,X ₂ ,…,X _N ), and the observed values of the samples are arranged in ascending order of X _{(1 )} ≤X ₍₂₎ …≤X _(N) , then the cumulative distribution function of the sample is:

上式中，j＝1,2,…,N-1；In the above formula, j=1,2,...,N-1;

3、所述S3中，对S2中所得的健康指数，截取轴承耗损期的健康指数数据；3. In S3, the health index data obtained in S2 is intercepted for the health index data in the wear-out period of the bearing;

基于K-S距离构建出表示轴承健康状况的指数，对轴承健康时的非高斯分布的健康指数，运用Johnson变换，转换成高斯分布的数据，并利用高斯分布的性质，确定轴承发生异常时健康指数的阈值；Based on the K-S distance, an index representing the health status of the bearing is constructed. For the health index of the non-Gaussian distribution when the bearing is healthy, the Johnson transformation is used to convert it into Gaussian distribution data, and the nature of the Gaussian distribution is used to determine the health index when the bearing is abnormal. threshold;

$Q Q R R = = \frac{m m n no}{{p p}^{22}} - - - - - - ((1212))$

当QR＝1时，选择Johnson变换中的S_L转换类型，其转换公式为：When QR=1, select the S _L transformation type in Johnson transformation, and its transformation formula is:

y_i＝γ+ηln(λ_i-ε) (18)y _i =γ+ηln(λ _i -ε) (18)

$η η = = \frac{22 z z}{l l n no ((m m / / p p))} - - - - - - ((1919))$

当QR>1时，选择Johnson变换中的S_U转换类型，其转换公式为：When QR>1, select the S _U transformation type in Johnson transformation, and its transformation formula is:

通过Johnson变换，将非高斯分布的健康指数转换成符合高斯分布的数据，并利用高斯分布的性质，确定轴承发生异常时健康指数的阈值。Through Johnson transformation, the health index of non-Gaussian distribution is converted into data conforming to Gaussian distribution, and the property of Gaussian distribution is used to determine the threshold of health index when the bearing is abnormal.

所述S4中，拟合分析轴承耗损期的健康指数数据，构建退化模型并建立状态空间模型，利用当前观测到的健康指数数据和粒子滤波算法更新模型参数，并预测剩余寿命，过程如下：In said S4, fit and analyze the health index data of the bearing wear-out period, build a degradation model and establish a state space model, use the currently observed health index data and the particle filter algorithm to update the model parameters, and predict the remaining life, the process is as follows:

HI(k)＝a·exp(b·k)+c·exp(d·k) (1)HI(k)=a·exp(b·k)+c·exp(d·k) (1)

同时构建测量方程：Simultaneously construct the measurement equation:

HI(k+l)＞故障阀值 (8)HI(k+l)＞Fault Threshold (8)

本实施例利用PRONOSTIA平台轴承全周期寿命数据对基于Johnson变换和粒子滤波算法的轴承故障诊断与剩余寿命预测方法进行验证。具体过程如下：In this embodiment, the bearing fault diagnosis and remaining life prediction method based on Johnson transform and particle filter algorithm are verified by using the full-cycle life data of bearings on the PRONOSTIA platform. The specific process is as follows:

(1)采集轴承的振动信号。通过加速度传感器采集水平方向和垂直方向的振动信号，信号每10s采集一次，每一次采集时长为0.1s。数据采样频率为25.6kHz；(1) Collect the vibration signal of the bearing. Vibration signals in the horizontal and vertical directions are collected by the acceleration sensor, and the signal is collected every 10s, and the duration of each collection is 0.1s. The data sampling frequency is 25.6kHz;

(2)利用振动信号计算K-S距离，基于K-S距离构建出反映轴承健康状态的指数，方便后续步骤利用该指数进行剩余寿命预测，构建出轴承健康指数反应其健康状态如附图2所示；(2) Use the vibration signal to calculate the K-S distance, and build an index reflecting the bearing health status based on the K-S distance, which is convenient for subsequent steps to use the index to predict the remaining life, and construct the bearing health index to reflect its health status, as shown in Figure 2;

(3)所构建的健康指数在整个轴承寿命周期上，呈现为两头高，中间低的曲线，对轴承健康时非高斯分布的健康指数，运用Johnson变换，转换成高斯分布的数据，利用高斯分布的性质，确定轴承发生异常时的健康指数的阈值。由附图3可以得知轴承在健康工作时的健康指数数据没有服从高斯分布，因此利用Johnson变换。如附图4所示，Johnson变换后的数据服从平均值为-0.0087，标准差为0.9938的高斯分布，由此得到轴承发生异常时所对应的健康指数阈值为0.1589；(3) The constructed health index presents a curve with high ends and low middle in the whole bearing life cycle. For the health index with non-Gaussian distribution when the bearing is healthy, Johnson transform is used to convert the data into Gaussian distribution, and the Gaussian distribution is used. The nature of the bearing determines the threshold of the health index when the bearing is abnormal. It can be known from Figure 3 that the health index data of the bearing in healthy operation does not obey the Gaussian distribution, so the Johnson transformation is used. As shown in Figure 4, the Johnson-transformed data obey the Gaussian distribution with an average value of -0.0087 and a standard deviation of 0.9938, and thus the health index threshold corresponding to bearing abnormalities is 0.1589;

(4)轴承耗损期的数据如附图5所示，拟合耗损期内的轴承数据，构建轴承性能退化状态空间模型，利用当前观测到的健康指数数据和粒子滤波算法更新模型参数，并预测剩余寿命。利用粒子滤波算法更新模型参数和预测剩余寿命，建立剩余寿命预测模型为：(4) The data of the bearing wear-out period is shown in Figure 5. Fit the bearing data during the wear-out period to build a state-space model of bearing performance degradation. Use the currently observed health index data and the particle filter algorithm to update the model parameters and predict remaining life. Using the particle filter algorithm to update the model parameters and predict the remaining life, the remaining life prediction model is established as follows:

HI(k+l)＞故障阀值 (8)HI(k+l)＞Fault Threshold (8)

附图6表示轴承数据的预测曲线，从曲线中可以看出，一开始由于数据不足，预测值与实际剩余寿命值的偏差较大，随着观测数据的不断增多，最终的预测值与实际剩余寿命值相吻合。有效的验证了粒子滤波算法在轴承剩余寿命预测中的可行性。Attached Figure 6 shows the prediction curve of bearing data. It can be seen from the curve that at the beginning, due to insufficient data, the deviation between the predicted value and the actual remaining life value is large. With the continuous increase of observation data, the final predicted value and the actual remaining life Lifetime values match. Effectively verified the feasibility of the particle filter algorithm in the prediction of bearing remaining life.

Claims

1. A bearing fault diagnosis and remaining life prediction method based on Johnson transform and particle filter algorithm, is characterized in that: described method comprises the following steps:

S1. Collect the vibration signal of the whole life cycle of the bearing;

S2. Use the vibration signal to calculate the K-S distance, and construct an index reflecting the health status of the bearing based on the K-S distance;

S3. The constructed health index presents a curve with two high ends and a low middle in the entire bearing life cycle. For the non-Gaussian distribution health index when the bearing is healthy, use Johnson transformation to convert it into Gaussian distribution data, and use Gaussian distribution. Nature, to determine the threshold of the health index when the bearing is abnormal;

S4. Fit and analyze the health index data of the bearing wear-out period, build a degradation model and establish a state space model, use the currently observed health index data and particle filter algorithm to update model parameters, and predict the remaining life. The process is as follows:

For the health index data in the depletion period, the fitting analysis constructs the following degradation model:

HI(k)=a·exp(b·k)+c·exp(d·k) (1)

In the above formula, HI(k) is the health index of the bearing at time k, k is the time parameter, a, b, c, d are the model parameters, and the state equation is constructed based on the degradation model:

{a a}_{k k} = = {a a}_{k k - - 11} + + {w w}_{k k - - 11}^{a a} - - - - - - ((22))

{b b}_{k k} = = {b b}_{k k - - 11} + + {w w}_{k k - - 11}^{b b} - - - - - - ((33))

{c c}_{k k} = = {c c}_{k k - - 11} + + {w w}_{k k - - 11}^{c c} - - - - - - ((44))

{d d}_{k k} = = {d d}_{k k - - 11} + + {w w}_{k k - - 11}^{d d} - - - - - - ((55))

In the above formula, a _k , b _k , c _k , d _k and a _k-1 , b _k-1 , c _k-1 , d _k-1 are the state variables a at time k and k-1 respectively, the value of b,c,d, is the independent noise corresponding to the state variables a, b, c, and d at time k-1;

Simultaneously construct the measurement equation:

HI _k ＝a _k exp(b _k k)+c _k exp(d _k k)+v _k (6)

In the above formula, HI _k is the measured value of the health index at time k, and v _k is the measurement noise at time k;

Use the particle filter algorithm to update the state equation and measurement equation parameters to k time, and calculate the health index HI(k+l) at k+l time according to the formula (1):

HI(k+l)＝a _k ·exp(b _k ·(k+l))+c _k ·exp(d _k ·(k+l)) (7)

In the above formula, l=1,2,...,∞; calculate the value of l that makes the inequality (8) true, and record the minimum value of l as the predicted remaining life of the bearing at time k;

HI(k+l)>fault threshold (8).

2. A kind of bearing fault diagnosis and residual life prediction method based on Johnson transformation and particle filter algorithm as claimed in claim 1, it is characterized in that: in said S2, construct health Index, the process is as follows;

Assuming that the vibration signal X _k at the kth moment contains N sampling points, the sample data set is X _k = (X ₁ ,X ₂ ,…,X _N ), and the observed values of the samples are arranged in ascending order of X _{(1 )} ≤X ₍₂₎ …≤X _(N) , then the cumulative distribution function of the sample is:

{F f}_{X x} ((x x)) = = \{\begin{matrix} 00 & x x < < {X x}_{((11))} \\ \frac{j j}{N N} & {X x}_{((j j))} \leq \leq x x < < {X x}_{((j j + + 11))} \\ 11 & x x &GreaterEqual; &Greater Equal; {X x}_{((N N))} \end{matrix} - - - - - - ((99))

In the above formula, j=1,2,...,N-1;

Take any moment when the bearing is healthy and working as a reference point, set the cumulative distribution function of the reference point as R _X (x), and the cumulative distribution function of the vibration signal at the kth moment is F _X (x), then the KS distance is defined as follows :

D D. ((k k)) = = \underset{- - ∞ ∞ < < x x < < ∞ ∞}{s the s u u p p} | | {F f}_{X x} ((x x)) - - {R R}_{X x} ((x x)) | | - - - - - - ((1010))

The health index HI contains information in both horizontal and vertical directions, which is calculated by the following formula:

H h I I ((k k)) = = \sqrt{(({D D.}_{x x} {((k k))}^{22} + + {D D.}_{y the y} {((k k))}^{22}))} - - - - - - ((1111))

In the above formula, D _x (k) and D _y (k) are the KS distances calculated on the horizontal vibration signal and the vertical vibration signal, respectively.

3. A bearing fault diagnosis and remaining life prediction method based on Johnson transform and particle filter algorithm as claimed in claim 1 or 2, characterized in that: in said S3, for the health index obtained in S2, the bearing wear period is intercepted health index data;

Based on the K-S distance, an index representing the health status of the bearing is constructed. For the health index of the non-Gaussian distribution when the bearing is healthy, use the Johnson transformation to convert it into Gaussian distribution data, and use the properties of the Gaussian distribution to determine the health index when the bearing is abnormal. the threshold;

Let the variable λ=[λ ₁ ,λ ₂ ,…,λ _M ] corresponding to the health index corresponding to the healthy work of the bearing, M be the number of health index samples, choose a suitable z, and find out by looking up the standard normal distribution table Find the distribution probability P _-3z , P _-z , P _z , P _3z corresponding to {-3z, -z, z, 3z}, and find the corresponding quantile λ _-3z , λ _-z in λ, λ _z , λ _3z , and define m=λ _3z -λ _z , n=λ _-z -λ _-3z , p=λ _z -λ _-z , thus defining the quantile ratio QR as shown in formula (12) ;

Q Q R R = = \frac{m m n no}{{p p}^{22}} - - - - - - ((1212))

When QR<1, select the S _B transformation type in Johnson transformation, and its transformation formula is:

{y the y}_{i i} = = γ γ + + η η l l n no ((\frac{{λ λ}_{i i} - - ϵ ϵ}{μ μ + + ϵ ϵ - - {λ λ}_{i i}})) - - - - - - ((1313))

In the above formula, y _i corresponds to the value of λ _i after Johnson transformation, 1≤i≤M, and the parameters in formula (13) are defined as follows:

η η = = z z {{{cosh cosh}^{- - 11} [[\frac{11}{22} {[[((11 + + \frac{p p}{m m})) ((11 + + \frac{p p}{n no}))]]}^{\frac{11}{22}}]]}}^{- - 11} - - - - - - ((1414))

γ γ = = {ηsinh ηsinh}^{- - 11} {{((\frac{p p}{n no} - - \frac{p p}{m m})) {[[((11 + + \frac{p p}{m m})) ((11 + + \frac{p p}{n no})) - - 44]]}^{\frac{11}{22}} {[[22 ((\frac{{p p}^{22}}{m m n no} - - 11))]]}^{- - 11}}} - - - - - - ((1515))

μ μ = = p p {{{[[((11 + + \frac{p p}{n no})) ((11 + + \frac{p p}{m m})) - - 22]]}^{22} - - 44}}^{\frac{11}{22}} {((\frac{{p p}^{22}}{m m n no} - - 11))}^{- - 11} - - - - - - ((1616))

ϵ ϵ = = \frac{{λ λ}_{z z} + + {λ λ}_{- - z z}}{22} - - \frac{μ μ}{22} + + p p ((\frac{p p}{n no} - - \frac{p p}{m m})) {[[22 ((\frac{{p p}^{22}}{m m n no} - - 11))]]}^{- - 11} - - - - - - ((1717))

When QR=1, select the S _L transformation type in Johnson transformation, and its transformation formula is:

y _i =γ+ηln(λ _i -ε) (18) In the above formula, y _i corresponds to the value of λ _i after Johnson transformation, 1≤i≤M, and the parameters in formula (18) are defined as follows:

η η = = \frac{22 z z}{ln ln ((m m / / p p))} - - - - - - ((1919))

γ γ = = η η l l n no [[\frac{m m / / p p - - 11}{p p {((m m / / p p))}^{11 / / 22}}]] - - - - - - ((2020))

ϵ ϵ = = \frac{{λ λ}_{z z} + + {λ λ}_{- - z z}}{22} - - \frac{p p}{22} [[\frac{m m / / p p + + 11}{m m / / p p - - 11}]] - - - - - - ((21 twenty one))

When QR>1, select the S _U transformation type in Johnson transformation, and its transformation formula is:

{y the y}_{i i} = = γ γ + + {ηsinh ηsinh}^{- - 11} ((\frac{{λ λ}_{i i} - - ϵ ϵ}{μ μ})) - - - - - - ((22 twenty two))

In the above formula, y _i corresponds to the value of λ _i after Johnson transformation, 1≤i≤M, and the parameters in formula (22) are defined as follows:

η η = = 22 z z {{{cosh cosh}^{- - 11} [[\frac{11}{22} ((\frac{m m}{p p} + + \frac{n no}{p p}))]]}}^{- - 11} - - - - - - ((23 twenty three))

γ γ = = {ηsinh ηsinh}^{- - 11} {{((\frac{n no}{p p} - - \frac{m m}{p p})) {[[22 {((\frac{m m n no}{{p p}^{22}} - - 11))}^{\frac{11}{22}}]]}^{- - 11}}} - - - - - - ((24 twenty four))

μ μ = = 22 p p {((\frac{m m n no}{{p p}^{22}} - - 11))}^{\frac{11}{22}} {[[((\frac{m m}{p p} + + \frac{n no}{p p} - - 22)) ((\frac{m m}{p p} + + \frac{n no}{p p} + + 22))]]}^{- - \frac{11}{22}} - - - - - - ((2525))

ϵ ϵ = = \frac{{λ λ}_{z z} + + {λ λ}_{- - z z}}{22} + + p p ((\frac{n no}{p p} - - \frac{m m}{p p})) {[[22 ((\frac{n no}{p p} + + \frac{m m}{p p} - - 22))]]}^{- - 11} - - - - - - ((2626))

Through Johnson transformation, the health index of non-Gaussian distribution is converted into data conforming to Gaussian distribution, and the property of Gaussian distribution is used to determine the threshold of the health index when the bearing is abnormal.