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

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 kind of bearing failure diagnosis based on Johnson conversion and particle filter algorithm is with surplus Remaining life-span prediction method

Technical field

The invention belongs to bearing failure diagnosis and prediction field, particularly relate to a kind of conversion based on Johnson and particle filter The bearing failure diagnosis of ripple algorithm and method for predicting residual useful life.

Background technology

Bearing is indispensable parts in rotating machinery, electric power, petrochemical industry, metallurgy, machinery, Aero-Space and one It is widely used in a little war industry departments, is to ensure that the important equipment facility essences such as precision machine tool, high-speed railway, wind-driven generator Degree, performance, the kernel component of life and reliability, however it be also these equipments are easiest to the parts that break down it One.According to statistics, most of fault of rotating machinery causes due to bearing fault.Bearing breaks down, the most then reduce or lose Go some function of equipment, heavy then cause the most catastrophic serious consequence.Therefore the status monitoring of bearing, fault diagnosis With a prediction research emphasis the most in recent years.Occurring from initial failure in view of bearing, development is until losing efficacy is one Process non-linear, dynamic, hence with nonlinear filtering algorithm based on bayesian theory, such as EKF, nothing Mark Kalman filtering etc. has obtained quick development in terms of the failure predication of bearing.But axle of based on Kalman filtering framework Holding failure prediction method is that hypothesis based on sample Gaussian distributed grows up, and disobeys Gauss distribution when sample and assumes When, bearing fault Forecasting Methodology based on Kalman filtering framework is the most inapplicable.

Summary of the invention

In order to overcome existing Nonlinear Bayesian filtering algorithm predicting residual useful life essence when solving bearing fault prediction Spending failure prediction method relatively low, based on Kalman filtering framework, not to be suitable for that non-gaussian distribution sample is carried out residual life pre- The deficiencies such as survey, the invention provides a kind of precision of prediction higher, the shortest, and be applicable to non-gaussian distribution sample based on Johnson converts the bearing failure diagnosis with particle filter algorithm and method for predicting residual useful life.

The technical scheme provided to solve above-mentioned technical problem is:

A kind of based on Johnson conversion and the bearing failure diagnosis of particle filter algorithm and method for predicting residual useful life, institute The method of stating comprises the following steps:

S1. the life cycle management vibration signal of bearing is gathered；

S2. utilize vibration signal to calculate K-S distance, construct the index of reflection bearing health status based on K-S distance；

S3. constructed health index, on the whole bearing life cycle, is rendered as two head heights, and middle low curve is right The health index of non-gaussian distribution during bearing health, uses Johnson conversion, is converted into the data of Gauss distribution, utilizes Gauss The character of distribution, determines the threshold value of health index when bearing occurs abnormal；

S4. the health index data of Fitting Analysis bearing consume phase, build degradation model and set up state-space model, profit The health index data arrived with Current observation and particle filter algorithm update model parameter, and predict residual life, and process is as follows:

Health index data to the consume phase, the degradation model that Fitting Analysis structure is following:

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

In above formula, HI (k) is the bearing health index in the k moment, and k is time parameter, and a, b, c, d are model parameter, base In this degradation model structure state equation:

$a_k=a_{k-1}+w_{k-1}^a---\left(2\right)$

$b_k=b_{k-1}+w_{k-1}^b---\left(3\right)$

$c_k=c_{k-1}+w_{k-1}^c---\left(4\right)$

$d_k=d_{k-1}+w_{k-1}^d---\left(5\right)$

In above formula, a_k,b_k,c_k,d_kAnd a_k-1,b_k-1,c_k-1,d_k-1For respectively in k moment and state variable a in k-1 moment, The value of b, c, d,For in the k-1 moment, independent and corresponding states variable a respectively, b, c, d make an uproar Sound；

Build simultaneously and measure equation:

HI_k=a_k·exp(b_k·k)+c_k·exp(d_k·k)+v_k (6)

In above formula, HI_kFor the measured value at k moment health index, v_kFor the measurement noise in the k moment；

Utilize particle filter algorithm to update state equation and measure equation parameter to the k moment, when calculating k+l by formula (1) The health index HI (k+l) carved:

HI (k+l)=a_k·exp(b_k·(k+l))+c_k·exp(d_k·(k+l)) (7)

In above formula, l=1,2 ..., ∞；Calculating makes the value of the l that inequality (8) sets up, and records the minima of l at k The bearing residual life of moment prediction；

HI (k+l) ＞ fault threshold (8).

Further, in described S2, the bearing life cycle management vibration signal to S1 gained, build health index, process is such as Under；

If kth moment health index X_k, wherein comprising N number of sampled point, then sample data set is combined into X_k=(X₁,X₂,…, X_N), by the observation of sample according to arranging X from small to large₍₁₎≤X₍₂₎…≤X_(N), then the cumulative distribution function of sample is:

$F_X\left(x\right)=\left\{\begin{array}{cc}0& x<X_{\left(1\right)}\\ \frac{j}{N}& X_{\left(j\right)}\&le;x<X_{(j+1)}\\ 1& x\&GreaterEqual;X_{\left(N\right)}\end{array}\right.---\left(9\right)$

In above formula, j=1,2 ..., N-1；

Take any one moment point when bearing normally works as a reference point, if the cumulative distribution function of this reference point is R_X X (), the cumulative distribution function of kth moment vibration signal is F_X(x), then K-S distance definition is as follows:

$D\left(k\right)=\underset{-\mathrm{\&infin;}<x<\mathrm{\&infin;}}{sup}|F_X\left(x\right)-R_X\left(x\right)|---\left(10\right)$

Health index HI comprises the information of horizontal and vertical directions, and it is calculated by following formula:

$HI\left(k\right)=\sqrt{(D_x{\left(k\right)}^2+D_y{\left(k\right)}^2)}---\left(11\right)$

In above formula, D_x(k) and D_y(k) be respectively on horizontal vibration signal and vertical vibration signal calculated K-S away from From.

Further, in described S3, the health index to S2 gained, intercept the health index data of bearing consume phase；

The index representing bearing health, being good for non-gaussian distribution during bearing health is constructed based on K-S distance Health index, uses Johnson conversion, is converted into the data of Gauss distribution, and utilize the character of Gauss distribution, determine that bearing occurs The threshold value of health index time abnormal；

If corresponding to the variable λ=[λ of health index during bearing working healthily₁,λ₂,…,λ_M], M is health index sample Number, selects a suitable z, by searching standard normal distribution table, finds out corresponding to { the distribution probability of-3z ,-z, z, 3z} P_-3z、P_-z、P_z、P_3z, λ finds out corresponding quantile λ_-3z, λ_-z, λ_z, λ_3z, and define m=λ_3z-λ_z, n=λ_-z-λ_-3z, p =λ_z-λ_-z, thus shown in definition quantile ratio QR such as formula (12)；

$QR=\frac{mn}{p^2}---\left(12\right)$

When QR < when 1, selects the S in Johnson conversion_BTranslation type, its conversion formula is:

$y_i=\mathrm{\&gamma;}+\mathrm{\&eta;}ln\left(\frac{{\mathrm{\&lambda;}}_i-\mathrm{\&epsiv;}}{\mathrm{\&mu;}+\mathrm{\&epsiv;}-{\mathrm{\&lambda;}}_i}\right)---\left(13\right)$

In above formula, y_iCorresponding to λ_iValue after Johnson converts, 1≤i≤M, the parameter in formula (13) is defined as follows:

$\mathrm{\&eta;}=z{\{{\cosh }^{-1}\&lsqb;\frac{1}{2}{\&lsqb;(1+\frac{p}{m})(1+\frac{p}{n})\&rsqb;}^{\frac{1}{2}}\&rsqb;\}}^{-1}---\left(14\right)$

$\mathrm{\&gamma;}={\mathrm{\&eta;sinh}}^{-1}\left\{(\frac{p}{n}-\frac{p}{m}){\&lsqb;(1+\frac{p}{m})(1+\frac{p}{n})-4\&rsqb;}^{\frac{1}{2}}{\&lsqb;2(\frac{p^2}{mn}-1)\&rsqb;}^{-1}\right\}---\left(15\right)$

$\mathrm{\&mu;}=p{\{{\&lsqb;(1+\frac{p}{n})(1+\frac{p}{m})-2\&rsqb;}^2-4\}}^{\frac{1}{2}}{(\frac{p^2}{mn}-1)}^{-1}---\left(16\right)$

$\mathrm{\&epsiv;}=\frac{{\mathrm{\&lambda;}}_z+{\mathrm{\&lambda;}}_{-z}}{2}-\frac{\mathrm{\&mu;}}{2}+p(\frac{p}{n}-\frac{p}{m}){\&lsqb;2(\frac{p^2}{mn}-1)\&rsqb;}^{-1}---\left(17\right)$

As QR=1, choose the S in Johnson conversion_LTranslation type, its conversion formula is:

y_i=γ+η ln (λ_i-ε) (18)

In above formula, y_iCorresponding to λ_iValue after Johnson converts, 1≤i≤M, the parameter in formula (18) is defined as follows:

$\mathrm{\&eta;}=\frac{2z}{ln(m/p)}---\left(19\right)$

$\mathrm{\&gamma;}=\mathrm{\&eta;}ln\&lsqb;\frac{m/p-1}{p{(m/p)}^{1/2}}\&rsqb;---\left(20\right)$

$\mathrm{\&epsiv;}=\frac{{\mathrm{\&lambda;}}_z+{\mathrm{\&lambda;}}_{-z}}{2}-\frac{p}{2}\&lsqb;\frac{m/p+1}{m/p-1}\&rsqb;---\left(21\right)$

As QR > 1 time, choose Johnson conversion in S_UTranslation type, its conversion formula is:

$y_i=\mathrm{\&gamma;}+{\mathrm{\&eta;sinh}}^{-1}\left(\frac{{\mathrm{\&lambda;}}_i-\mathrm{\&epsiv;}}{\mathrm{\&mu;}}\right)---\left(22\right)$

In above formula, y_iCorresponding to λ_iValue after Johnson converts, 1≤i≤M, the parameter in formula (22) is defined as follows:

$\mathrm{\&eta;}=2z{\{{\cosh }^{-1}\&lsqb;\frac{1}{2}(\frac{m}{p}+\frac{n}{p})\&rsqb;\}}^{-1}---\left(23\right)$

$\mathrm{\&gamma;}={\mathrm{\&eta;sinh}}^{-1}\left\{(\frac{n}{p}-\frac{m}{p}){\&lsqb;2{(\frac{mn}{p^2}-1)}^{\frac{1}{2}}\&rsqb;}^{-1}\right\}---\left(24\right)$

$\mathrm{\&mu;}=2p{(\frac{mn}{p^2}-1)}^{\frac{1}{2}}{\&lsqb;(\frac{m}{p}+\frac{n}{p}-2)(\frac{m}{p}+\frac{n}{p}+2)\&rsqb;}^{-\frac{1}{2}}---\left(25\right)$

$\mathrm{\&epsiv;}=\frac{{\mathrm{\&lambda;}}_z+{\mathrm{\&lambda;}}_{-z}}{2}+p(\frac{n}{p}-\frac{m}{p}){\&lsqb;2(\frac{n}{p}+\frac{m}{p}-2)\&rsqb;}^{-1}---\left(26\right)$

Converted by Johnson, the health index of non-gaussian distribution is converted into the data meeting Gauss distribution, and utilizes The character of Gauss distribution, determines the threshold value of health index when bearing occurs abnormal.

The technology of the present invention is contemplated that: by gathering bearing vibration signal, based on the calculating structure to vibration signal K-S distance Build health index, utilize Johnson conversion to determine the threshold value of health index when bearing occurs abnormal, utilize this threshold values bearing Whole life cycle divides into the following three stage: running-in period, useful life phase and consume phase.Consumed by Fitting Analysis bearing The health index data of phase, build and are used for describing bearing degradation status of processes spatial model, utilize the health that Current observation arrives Exponent data and particle filter algorithm update model parameter, and predict residual life.

The invention have the benefit that the generation being effectively diagnosed to be bearing fault in early days, thus intercept shaft exactly Holding the Performance Degradation Data of consume phase, the method calculates speed and predicting residual useful life precision is higher.

Accompanying drawing explanation

Fig. 1 is to convert the bearing failure diagnosis with particle filter algorithm and method for predicting residual useful life stream based on Johnson Cheng Tu；

Fig. 2 is bearing whole life cycle health index schematic diagram；

The normal probability plot of health index data when Fig. 3 is bearing working healthily；

Health index data normal probability plot after Johnson converts when Fig. 4 is bearing working healthily；

Fig. 5 is the bearing health index data in the consume phase；

Fig. 6 is bearing predicting residual useful life within the consume phase.

Detailed description of the invention

The invention will be further described below in conjunction with the accompanying drawings.

With reference to Fig. 1～Fig. 6, a kind of bearing failure diagnosis based on Johnson conversion and particle filter algorithm and residue longevity Life Forecasting Methodology, said method comprising the steps of:

S1. the life cycle management vibration signal of bearing is gathered；

S2. utilize vibration signal to calculate K-S distance, construct the index of reflection bearing health status, side based on K-S distance Just subsequent step utilizes this index to carry out the judgement of bearing health status and the prediction of residual life；

S3. constructed health index, on the whole bearing life cycle, is rendered as two head heights, and middle low curve is right The health index of non-gaussian distribution during bearing working healthily, uses Johnson conversion, is converted into the data of Gauss distribution, utilize The character of Gauss distribution, determines the threshold value of health index when bearing occurs abnormal；

S4. the health index data of Fitting Analysis bearing consume phase, build degradation model and set up state-space model, profit The health index data arrived with Current observation and particle filter algorithm update model parameter, and predict residual life.

In described S1, as shown in Figure 2, the life cycle management of bearing can be divided into three phases: running-in period, effectively works Phase and consume phase.

In described S2, the bearing life cycle management vibration signal to S1 gained, build health index, process is as follows；

If kth moment vibration signal X_k, wherein comprising N number of sampled point, then sample data set is combined into X_k=(X₁,X₂,…, X_N), by the observation of sample according to arranging X from small to large₍₁₎≤X₍₂₎…≤X_(N), then the cumulative distribution function of sample is:

$F_X\left(x\right)=\left\{\begin{array}{cc}0& x<X_{\left(1\right)}\\ \frac{j}{N}& X_{\left(j\right)}\&le;x<X_{(j+1)}\\ 1& x\&GreaterEqual;X_{\left(N\right)}\end{array}\right.---\left(9\right)$

In above formula, j=1,2 ..., N-1；

Take any one moment point when bearing normally works as a reference point, if the cumulative distribution function of this reference point is R_X X (), the cumulative distribution function of kth moment vibration signal is F_X(x), then K-S distance definition is as follows:

$D\left(k\right)=\underset{-\mathrm{\&infin;}<x<\mathrm{\&infin;}}{sup}|F_X\left(x\right)-R_X\left(x\right)|---\left(10\right)$

Health index HI comprises the information of horizontal and vertical directions, and it is calculated by following formula:

$HI\left(k\right)=\sqrt{(D_x{\left(k\right)}^2+D_y{\left(k\right)}^2)}---\left(11\right)$

In above formula, D_x(k) and D_y(k) be respectively on horizontal vibration signal and vertical vibration signal calculated K-S away from From.

3, in described S3, to the health index of gained in S2, the health index data of bearing consume phase are intercepted；

The index representing bearing health, being good for non-gaussian distribution during bearing health is constructed based on K-S distance Health index, uses Johnson conversion, is converted into the data of Gauss distribution, and utilize the character of Gauss distribution, determine that bearing occurs The threshold value of health index time abnormal；

If corresponding to the variable λ=[λ of health index during bearing working healthily₁,λ₂,…,λ_M], M is health index sample Number, selects a suitable z, by searching standard normal distribution table, finds out corresponding to { the distribution probability of-3z ,-z, z, 3z} P_-3z、P_-z、P_z、P_3z, λ finds out corresponding quantile λ_-3z, λ_-z, λ_z, λ_3z, and define m=λ_3z-λ_z, n=λ_-z-λ_-3z, p =λ_z-λ_-z, thus shown in definition quantile ratio QR such as formula (12)；

$QR=\frac{mn}{p^2}---\left(12\right)$

When QR < when 1, selects the S in Johnson conversion_BTranslation type, its conversion formula is:

$y_i=\mathrm{\&gamma;}+\mathrm{\&eta;}ln\left(\frac{{\mathrm{\&lambda;}}_i-\mathrm{\&epsiv;}}{\mathrm{\&mu;}+\mathrm{\&epsiv;}-{\mathrm{\&lambda;}}_i}\right)---\left(13\right)$

In above formula, y_iCorresponding to λ_iValue after Johnson converts, 1≤i≤M, the parameter in formula (13) is defined as follows:

$\mathrm{\&eta;}=z{\{{\cosh }^{-1}\&lsqb;\frac{1}{2}{\&lsqb;(1+\frac{p}{m})(1+\frac{p}{n})\&rsqb;}^{\frac{1}{2}}\&rsqb;\}}^{-1}---\left(14\right)$

$\mathrm{\&gamma;}={\mathrm{\&eta;sinh}}^{-1}\left\{(\frac{p}{n}-\frac{p}{m}){\&lsqb;(1+\frac{p}{m})(1+\frac{p}{n})-4\&rsqb;}^{\frac{1}{2}}{\&lsqb;2(\frac{p^2}{mn}-1)\&rsqb;}^{-1}\right\}---\left(15\right)$

$\mathrm{\&mu;}=p{\{{\&lsqb;(1+\frac{p}{n})(1+\frac{p}{m})-2\&rsqb;}^2-4\}}^{\frac{1}{2}}{(\frac{p^2}{mn}-1)}^{-1}---\left(16\right)$

$\mathrm{\&epsiv;}=\frac{{\mathrm{\&lambda;}}_z+{\mathrm{\&lambda;}}_{-z}}{2}-\frac{\mathrm{\&mu;}}{2}+p(\frac{p}{n}-\frac{p}{m}){\&lsqb;2(\frac{p^2}{mn}-1)\&rsqb;}^{-1}---\left(17\right)$

As QR=1, select the S in Johnson conversion_LTranslation type, its conversion formula is:

y_i=γ+η ln (λ_i-ε) (18)

In above formula, y_iCorresponding to λ_iValue after Johnson converts, 1≤i≤M, the parameter in formula (18) is defined as follows:

$\mathrm{\&eta;}=\frac{2z}{ln(m/p)}---\left(19\right)$

$\mathrm{\&gamma;}=\mathrm{\&eta;}ln\&lsqb;\frac{m/p-1}{p{(m/p)}^{1/2}}\&rsqb;---\left(20\right)$

$\mathrm{\&epsiv;}=\frac{{\mathrm{\&lambda;}}_z+{\mathrm{\&lambda;}}_{-z}}{2}-\frac{p}{2}\&lsqb;\frac{m/p+1}{m/p-1}\&rsqb;---\left(21\right)$

As QR > 1 time, select Johnson conversion in S_UTranslation type, its conversion formula is:

$y_i=\mathrm{\&gamma;}+{\mathrm{\&eta;sinh}}^{-1}\left(\frac{{\mathrm{\&lambda;}}_i-\mathrm{\&epsiv;}}{\mathrm{\&mu;}}\right)---\left(22\right)$

In above formula, y_iCorresponding to λ_iValue after Johnson converts, 1≤i≤M, the parameter in formula (22) is defined as follows:

$\mathrm{\&eta;}=2z{\{{\cosh }^{-1}\&lsqb;\frac{1}{2}(\frac{m}{p}+\frac{n}{p})\&rsqb;\}}^{-1}---\left(23\right)$

$\mathrm{\&gamma;}={\mathrm{\&eta;sinh}}^{-1}\left\{(\frac{n}{p}-\frac{m}{p}){\&lsqb;2{(\frac{mn}{p^2}-1)}^{\frac{1}{2}}\&rsqb;}^{-1}\right\}---\left(24\right)$

$\mathrm{\&mu;}=2p{(\frac{mn}{p^2}-1)}^{\frac{1}{2}}{\&lsqb;(\frac{m}{p}+\frac{n}{p}-2)(\frac{m}{p}+\frac{n}{p}+2)\&rsqb;}^{-\frac{1}{2}}---\left(25\right)$

$\mathrm{\&epsiv;}=\frac{{\mathrm{\&lambda;}}_z+{\mathrm{\&lambda;}}_{-z}}{2}+p(\frac{n}{p}-\frac{m}{p}){\&lsqb;2(\frac{n}{p}+\frac{m}{p}-2)\&rsqb;}^{-1}---\left(26\right)$

Converted by Johnson, the health index of non-gaussian distribution is converted into the data meeting Gauss distribution, and utilizes The character of Gauss distribution, determines the threshold value of health index when bearing occurs abnormal.

In described S4, the health index data of Fitting Analysis bearing consume phase, build degradation model and set up state space Model, utilizes health index data that Current observation arrives and particle filter algorithm to update model parameter, and predicts residual life, mistake Journey is as follows:

Health index data to the consume phase, the degradation model that Fitting Analysis structure is following:

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

In above formula, HI (k) is the bearing health index in the k moment, and k is time parameter, and a, b, c, d are model parameter, base In this degradation model structure state equation:

$a_k=a_{k-1}+w_{k-1}^a---\left(2\right)$

$b_k=b_{k-1}+w_{k-1}^b---\left(3\right)$

$c_k=c_{k-1}+w_{k-1}^c---\left(4\right)$

$d_k=d_{k-1}+w_{k-1}^d---\left(5\right)$

In above formula, a_k,b_k,c_k,d_kAnd a_k-1,b_k-1,c_k-1,d_k-1For respectively in k moment and state variable a in k-1 moment, The value of b, c, d,For in the k-1 moment, independent and corresponding states variable a respectively, b, c, d make an uproar Sound；

Build simultaneously and measure equation:

HI_k=a_k·exp(b_k·k)+c_k·exp(d_k·k)+v_k (6)

In above formula, HI_kFor the measured value at k moment health index, v_kFor the measurement noise in the k moment；

Utilize particle filter algorithm to update state equation and measure equation parameter to the k moment, when calculating k+l by formula (1) The health index HI (k+l) carved:

HI (k+l)=a_k·exp(b_k·(k+l))+c_k·exp(d_k·(k+l)) (7)

In above formula, l=1,2 ..., ∞；Calculating makes the value of the l that inequality (8) sets up, and records the minima of l at k The bearing residual life of moment prediction；

HI (k+l) ＞ fault threshold (8)

The present embodiment utilizes PRONOSTIA platform bearing complete period lifetime data to based on Johnson conversion and particle filter The bearing failure diagnosis of ripple algorithm is verified with method for predicting residual useful life.Detailed process is as follows:

(1) vibration signal of bearing is gathered.Gather vibration horizontally and vertically by acceleration transducer to believe Number, the every 10s of signal gathers once, a length of 0.1s when gathering each time.Data sampling frequency is 25.6kHz；

(2) utilize vibration signal to calculate K-S distance, construct the index of reflection bearing health status, side based on K-S distance Just subsequent step utilizes this index to carry out predicting residual useful life, constructs bearing health index and reacts its health status such as accompanying drawing 2 Shown in；

(3) health index constructed by, on the whole bearing life cycle, is rendered as two head heights, middle low curve, right The health index of non-gaussian distribution during bearing health, uses Johnson conversion, is converted into the data of Gauss distribution, utilizes Gauss The character of distribution, determines the threshold value of health index when bearing occurs abnormal.It is appreciated that bearing is when working healthily by accompanying drawing 3 Health index data there is no Gaussian distributed, hence with Johnson convert.As shown in Figure 4, after Johnson conversion Data to obey meansigma methods be-0.0087, standard deviation is the Gauss distribution of 0.9938, thus obtain when bearing occurs abnormal right The health index threshold value answered is 0.1589；

(4) data of bearing consume phase are as shown in Figure 5, and the bearing data in the matching consume phase build bearing performance and move back Change state-space model, utilize health index data that Current observation arrives and particle filter algorithm to update model parameter, and predict Residual life.Utilizing particle filter algorithm to update model parameter and prediction residual life, setting up predicting residual useful life model is:

HI (k+l)=a_k·exp(b_k·(k+l))+c_k·exp(d_k·(k+l)) (7)

In above formula, l=1,2 ..., ∞；Calculating makes the value of the l that inequality (8) sets up, and records the minima of l at k The bearing residual life of moment prediction；

HI (k+l) ＞ fault threshold (8)

Accompanying drawing 6 represents the prediction curve of bearing data, it can be seen that at the beginning due to data deficiencies from curve, it was predicted that Value is relatively big with the deviation of real surplus life value, along with being on the increase of observation data, final predictive value and real surplus longevity Life value matches.Effectively demonstrate particle filter algorithm feasibility in bearing predicting residual useful life.

Claims (3)

1. converting the bearing failure diagnosis with particle filter algorithm and a method for predicting residual useful life based on Johnson, it is special Levy and be: said method comprising the steps of:

S1. the life cycle management vibration signal of bearing is gathered；

S2. utilize vibration signal to calculate K-S distance, construct the index of reflection bearing health status based on K-S distance；

S3. constructed health index, on the whole bearing life cycle, is rendered as two head heights, and middle low curve, to bearing The health index of non-gaussian distribution time healthy, uses Johnson conversion, is converted into the data of Gauss distribution, utilizes Gauss distribution Character, determine the threshold value of health index when bearing occurs abnormal；

S4. the health index data of Fitting Analysis bearing consume phase, build degradation model and set up state-space model, utilize and work as Before the health index data that observe and particle filter algorithm update model parameter, and predict residual life, process is as follows:

Health index data to the consume phase, the degradation model that Fitting Analysis structure is following:

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

In above formula, HI (k) is the bearing health index in the k moment, and k is time parameter, and a, b, c, d are model parameter, based on this Degradation model structure state equation:

$a_k=a_{k-1}+w_{k-1}^a---\left(2\right)$

$b_k=b_{k-1}+w_{k-1}^b---\left(3\right)$

$c_k=c_{k-1}+w_{k-1}^c---\left(4\right)$

$d_k=d_{k-1}+w_{k-1}^d---\left(5\right)$

In above formula, a_k,b_k,c_k,d_kAnd a_k-1,b_k-1,c_k-1,d_k-1For respectively at k moment and state variable a in k-1 moment, b, c, d Value,For in the k-1 moment, independent and corresponding states variable a, the noise of b, c, d respectively；

Build simultaneously and measure equation:

HI_k=a_k·exp(b_k·k)+c_k·exp(d_k·k)+v_k (6)

In above formula, HI_kFor the measured value at k moment health index, v_kFor the measurement noise in the k moment；

Utilize particle filter algorithm to update state equation and measure equation parameter to the k moment, calculating the k+l moment by formula (1) Health index HI (k+l):

HI (k+l)=a_k·exp(b_k·(k+l))+c_k·exp(d_k·(k+l)) (7)

In above formula, l=1,2 ..., ∞；Calculating makes the value of the l that inequality (8) sets up, and records the minima of l in the k moment The bearing residual life of prediction；

HI (k+l) ＞ fault threshold (8).

A kind of based on Johnson conversion and the bearing failure diagnosis of particle filter algorithm and residue Life-span prediction method, it is characterised in that: in described S2, the bearing life cycle management vibration signal to S1 gained, build health and refer to Number, process is as follows；

If kth moment vibration signal X_k, wherein comprising N number of sampled point, then sample data set is combined into X_k=(X₁,X₂,…,X_N), will The observation of sample is according to arranging X from small to large₍₁₎≤X₍₂₎…≤X_(N), then the cumulative distribution function of sample is:

$F_X\left(x\right)=\left\{\begin{array}{cc}0& x<X_{\left(1\right)}\\ \frac{j}{N}& X_{\left(j\right)}\&le;x<X_{(j+1)}\\ 1& x\&GreaterEqual;X_{\left(N\right)}\end{array}\right.---\left(9\right)$

In above formula, j=1,2 ..., N-1；

Any one moment point when taking bearing working healthily is as a reference point, if the cumulative distribution function of this reference point is R_X(x), The cumulative distribution function of kth moment vibration signal is F_X(x), then K-S distance definition is as follows:

$D\left(k\right)=\underset{-\mathrm{\&infin;}<x<\mathrm{\&infin;}}{sup}|F_X\left(x\right)-R_X\left(x\right)|---\left(10\right)$

Health index HI comprises the information of horizontal and vertical directions, and it is calculated by following formula:

$HI\left(k\right)=\sqrt{(D_x{\left(k\right)}^2+D_y{\left(k\right)}^2)}---\left(11\right)$

In above formula, D_x(k) and D_yK () is respectively calculated K-S distance on horizontal vibration signal and vertical vibration signal.

A kind of bearing failure diagnosis based on Johnson conversion and particle filter algorithm is with surplus Remaining life-span prediction method, it is characterised in that: in described S3, the health index to S2 gained, intercept the health of bearing consume phase and refer to Number data；

The index representing bearing health, being good for non-gaussian distribution during bearing working healthily is constructed based on K-S distance Health index, uses Johnson conversion, is converted into the data of Gauss distribution, and utilize the character of Gauss distribution, determine that bearing occurs The threshold value of health index time abnormal；

If corresponding to the variable λ=[λ of health index during bearing working healthily₁,λ₂,…,λ_M], M is the individual of health index sample Number, selects a suitable z, by searching standard normal distribution table, finds out corresponding to { the distribution probability of-3z ,-z, z, 3z} P_-3z、P_-z、P_z、P_3z, λ finds out corresponding quantile λ_-3z, λ_-z, λ_z, λ_3z, and define m=λ_3z-λ_z, n=λ_-z-λ_-3z, p =λ_z-λ_-z, thus shown in definition quantile ratio QR such as formula (12)；

$QR=\frac{mn}{p^2}---\left(12\right)$

When QR < when 1, selects the S in Johnson conversion_BTranslation type, its conversion formula is:

$y_i=\mathrm{\&gamma;}+\mathrm{\&eta;}ln\left(\frac{{\mathrm{\&lambda;}}_i-\mathrm{\&epsiv;}}{\mathrm{\&mu;}+\mathrm{\&epsiv;}-{\mathrm{\&lambda;}}_i}\right)---\left(13\right)$

In above formula, y_iCorresponding to λ_iValue after Johnson converts, 1≤i≤M, the parameter in formula (13) is defined as follows:

$\mathrm{\&eta;}=z{\{{\cosh }^{-1}\&lsqb;\frac{1}{2}{\&lsqb;(1+\frac{p}{m})(1+\frac{p}{n})\&rsqb;}^{\frac{1}{2}}\&rsqb;\}}^{-1}---\left(14\right)$

$\mathrm{\&gamma;}={\mathrm{\&eta;sinh}}^{-1}\left\{(\frac{p}{n}-\frac{p}{m}){\&lsqb;(1+\frac{p}{m})(1+\frac{p}{n})-4\&rsqb;}^{\frac{1}{2}}{\&lsqb;2(\frac{p^2}{mn}-1)\&rsqb;}^{-1}\right\}---\left(15\right)$

$\mathrm{\&mu;}=p{\{{\&lsqb;(1+\frac{p}{n})(1+\frac{p}{m})-2\&rsqb;}^2-4\}}^{\frac{1}{2}}{(\frac{p^2}{mn}-1)}^{-1}---\left(16\right)$

$\mathrm{\&epsiv;}=\frac{{\mathrm{\&lambda;}}_z+{\mathrm{\&lambda;}}_{-z}}{2}-\frac{\mathrm{\&mu;}}{2}+p(\frac{p}{n}-\frac{p}{m}){\&lsqb;2(\frac{p^2}{mn}-1)\&rsqb;}^{-1}---\left(17\right)$

As QR=1, select the S in Johnson conversion_LTranslation type, its conversion formula is:

y_i=γ+η ln (λ_i-ε) in (18) above formula, y_iCorresponding to λ_iAfter Johnson converts Value, 1≤i≤M, the parameter in formula (18) is defined as follows:

$\mathrm{\&eta;}=\frac{2z}{\ln (m/p)}---\left(19\right)$

$\mathrm{\&gamma;}=\mathrm{\&eta;}ln\&lsqb;\frac{m/p-1}{p{(m/p)}^{1/2}}\&rsqb;---\left(20\right)$

$\mathrm{\&epsiv;}=\frac{{\mathrm{\&lambda;}}_z+{\mathrm{\&lambda;}}_{-z}}{2}-\frac{p}{2}\&lsqb;\frac{m/p+1}{m/p-1}\&rsqb;---\left(21\right)$

As QR > 1 time, select Johnson conversion in S_UTranslation type, its conversion formula is:

$y_i=\mathrm{\&gamma;}+{\mathrm{\&eta;sinh}}^{-1}\left(\frac{{\mathrm{\&lambda;}}_i-\mathrm{\&epsiv;}}{\mathrm{\&mu;}}\right)---\left(22\right)$

In above formula, y_iCorresponding to λ_iValue after Johnson converts, 1≤i≤M, the parameter in formula (22) is defined as follows:

$\mathrm{\&eta;}=2z{\{{\cosh }^{-1}\&lsqb;\frac{1}{2}(\frac{m}{p}+\frac{n}{p})\&rsqb;\}}^{-1}---\left(23\right)$

$\mathrm{\&gamma;}={\mathrm{\&eta;sinh}}^{-1}\left\{(\frac{n}{p}-\frac{m}{p}){\&lsqb;2{(\frac{mn}{p^2}-1)}^{\frac{1}{2}}\&rsqb;}^{-1}\right\}---\left(24\right)$

$\mathrm{\&mu;}=2p{(\frac{mn}{p^2}-1)}^{\frac{1}{2}}{\&lsqb;(\frac{m}{p}+\frac{n}{p}-2)(\frac{m}{p}+\frac{n}{p}+2)\&rsqb;}^{-\frac{1}{2}}---\left(25\right)$

$\mathrm{\&epsiv;}=\frac{{\mathrm{\&lambda;}}_z+{\mathrm{\&lambda;}}_{-z}}{2}+p(\frac{n}{p}-\frac{m}{p}){\&lsqb;2(\frac{n}{p}+\frac{m}{p}-2)\&rsqb;}^{-1}---\left(26\right)$

Converted by Johnson, the health index of non-gaussian distribution is converted into the data meeting Gauss distribution, and utilizes Gauss The character of distribution, determines the threshold value of health index when bearing occurs abnormal.