CN103679280A - Optimal maintaining method for equipment with performance slow degradation - Google Patents

Abstract

The invention belongs to the technical field of reliability engineering and relates to a method for carrying out optimal maintaining on high reliability equipment with a performance slow degradation characteristic. According to the operation of the equipment, performance degradation monitoring data is reasonably selected, and the performance degradation database of the equipment is established. The method concretely comprises the steps of constructing a dynamic performance degradation database, establishing an equipment performance degradation model, predicating the remaining life, and determining the optimal maintenance time. The invention provides a complex equipment optimal maintenance method in the condition that a product has slow performance degradation, the characteristic amount degradation of the equipment can be predicated and analyzed, the method can be used as an effective tool for predicating equipment individual life, a powerful theoretical basis and technical support are provided for the repair and maintenance of the equipment, thus the spending is saved, the unnecessary economic loss is avoided, and the method has a good engineering application value.

Description

The optimum maintaining method of equipment of the gradual degeneration of a kind of performance

Technical field

The invention belongs to reliability engineering technical field, relate to and carry out the optimum method of safeguarding to thering is the high reliability equipment of the slow degradation characteristics of performance;

Background technology

About the existing optimum based on predicting residual useful life, safeguard, the people such as Christer and Wang have carried out relevant research; These research work are all based on statistical method, its basic thought is: by historical data is tested, choose appropriate statistical distribution pattern the residual life change procedure of equipment is carried out to modeling, then according to the relation between status monitoring information and residual life, utilize the information of obtaining to upgrade model parameter, thereby predict device is at the residual life of current time, on this basis according to the result of predicting residual useful life, structure be take maintenance cost as decision objective, take the Maintenance Model that maintenance opportunity and maintenance strategy be decision variable; By making maintenance cost reach minimum, and obtain best maintenance opportunity or optimum maintenance strategy; Yet in engineering practice, the fail data of equipment is often fewer, make selected statistical distribution be difficult to the residual life change procedure of accurate description equipment, cause the best solving to safeguard that opportunity or optimum maintenance strategy exist larger error;

Summary of the invention

For above-mentioned prior art situation, the object of the invention is: a kind of Performance Degradation Data that equipment records in the slow change procedure of performance that makes full use of is provided, scientific forecasting high reliability equipment individual life span characteristic quantity numerical value, and determine on this basis the method for optimum maintenance time, to solve traditional problem of determining the no-failure data that optimum maintenance was run into during opportunity based on fail data;

Now design of the present invention and technical solution are described below:

In equipment During Process of Long-term Operation, due to the release of components and parts inherent strain own, and under the long term of dynamic loading, burn into wearing and tearing, fatigue load etc., it is aging that some device will occur, and occurs defect; In addition, in standing storage process, owing to being subject to the impacts such as temperature, humidity and power on/off circulation, some performance state of equipment will produce drift; When the performance degradation amount of equipment at a time surpasses threshold value, equipment can not complete set task well, thereby causes the generation of fault; Therefore, should be according to the ruuning situation of equipment, choose reasonable performance degradation Monitoring Data, as oil analysis data, temperature, pressure and sound Monitoring Data etc., the Performance Degradation Data storehouse of apparatus for establishing, and by effective maintaining method, to reduce the probability of device fails;

The optimum maintaining method of equipment of the gradual degeneration of a kind of performance of the present invention, comprises the following steps:

Step 1: the structure in dynamic property degraded data storehouse

In constructed Performance Degradation Data storehouse, mainly comprise test duration and test data; After new test data arrives, data are directly deposited in test database, mainly comprise two row, wherein first classify the test duration as, second classifies test data as; Thereby database is dynamic; When degradation model is carried out to modeling, can choose the data that length is N, model parameter is upgraded;

Step 2: the foundation of equipment performance degradation model

Because the factors such as inherent strain, running environment and random shock are random to the effect of equipment, make the degenerative process of equipment performance have very strong non-linear and randomness; Adopt the Wiener model of band drift to carry out matching to performance degradation process:

y(t)＝a ₀+a ₁t _i+σ _WW(t _i) (1)

Wherein, y (t) is performance degradation amount, t _itime span while being the i time measurement, a ₀for zero degree item, a ₁for once, be called coefficient of deviation, σ _wfor coefficient of diffusion, W (t _i) be the Wiener-Hopf equation of standard; Obtained data are sampled, with certain interval, in test data, get (n ₁for positive integer) individual point wherein

according to drift expression formula, can obtain:

Δy _i＝a ₁Δt _i+σ _WΔW(t _i) (2)

Wherein, a ₁Δ t _i=a ₁(t _i-t _i-1), σ _wΔ W (t _i)=σ _w[W (t _i)-W (t _i-1)], Δ y _i=y _i-y _i-1, i=1,2 ..., n ₁, by the known Δ W of the definition (t of Wiener-Hopf equation _i)～N (0, Δ t _i), thereby can obtain:

$\mathrm{\Δ}{y}_i~N(a_1{\mathrm{\Δt}}_i,{\mathrm{\σ}}_W^2{\mathrm{\Δt}}_i)---\left(3\right)$

Use Maximum Likelihood Estimation Method, the parameter in estimation model; By Wiener-Hopf equation stationary independent increment, can be obtained

joint probability density, i.e. sample likelihood function L (a ₁, σ _w) be:

$L(a_1,{\mathrm{\σ}}_W)=f({\mathrm{\Δy}}_1,{\mathrm{\Δy}}_2,\·\·\·,{\mathrm{\Δy}}_{n_1})=f\left({\mathrm{\Δy}}_1\right)f\left({\mathrm{\Δy}}_2\right)\·\·\·f\left({\mathrm{\Δy}}_{n_1}\right)---\left(4\right)$

Above likelihood function is taken the logarithm, and respectively to a ₁, σ _wask partial differential to obtain:

$\frac{\∂L}{\∂a_1}=\underset{i=1}{\overset{n_1}{\mathrm{\Σ}}}\frac{\mathrm{\Δ}{y}_i-a_1\mathrm{\Δ}{t}_i}{{\mathrm{\σ}}_W^2{\mathrm{\Δt}}_i}=0---\left(5\right)$

$\frac{\∂L}{\∂{\mathrm{\σ}}_W}=\underset{i=1}{\overset{n_1}{\mathrm{\Σ}}}-\frac{1}{{\mathrm{\σ}}_W}+\frac{(\mathrm{\Δ}{y}_i-a_1\mathrm{\Δ}{t}_i{)}^2}{{\mathrm{\σ}}_W^2{\mathrm{\Δt}}_i}=0---\left(6\right)$

Solve above system of equations and can obtain following estimated result:

${\hat{a}}_1=\frac{1}{n_1}\underset{i=1}{\overset{n_1}{\mathrm{\Σ}}}\frac{{\mathrm{\Δy}}_i}{{\mathrm{\Δt}}_i}---\left(7\right)$ ${\widehat{\mathrm{\σ}}}_W=\sqrt{\frac{1}{n_1}\underset{i=1}{\overset{n_1}{\mathrm{\Σ}}}{\frac{({\mathrm{\Δy}}_i-{\hat{a}}_1{\mathrm{\Δt}}_i)}{{\mathrm{\Δt}}_i}}^2}---\left(8\right)$

According to above estimated result, will

with

bring y (t)=a into ₀+ a ₁t _i+ σ _ww(t _i) can obtain a ₀estimated value

Step 3: predicting residual useful life

In the life-span of equipment, be often referred to serviceable life of equipment, and according to the definition of national military standard GJB451A-2005, be " equipment uses technically or considers economically and all should not re-use, and must overhaul or the life unit number while scrapping " serviceable life; More specifically, equipment (can) refer to the life unit number when being accomplished to appearance and can not repairing the fault of (or be unworthy repair) or unacceptable failure rate from device fabrication serviceable life; Residual life (remaining life:RL), be often referred to remaining useful life (remaining useful life:RUL), also referred to as residue service life (remaining servicelife:RSL) or residual life (residual life); Predicting residual useful life, refers in actual applications under current device state and the known condition of historical state data, goes prediction to lose efficacy one (or a plurality of) also how long remaining before occurring; Be defined as condition random variable:

P{T-t|T＞t，Z(t)} (9)

Here T represents the stochastic variable of out-of-service time, and t is the current life-span, and Z (t) is the historical state data to current time; Because RUL is stochastic variable, effecting surplus time prediction typically refers to: ask the distribution of RUL, i.e. and formula (9), or ask the expectation of RUL, that is:

E[T-t|T＞t，Z(t)] (10)

The main thought that carries out life prediction is: the first step: the head that solves degenerative process reaches time distribution; Second step: utilize the first residual life that reaches time forecast of distribution equipment, the residual life that obtains equipment distributes;

According to the definition of above parameter estimation result and residual life, the time that can obtain hitting first failure threshold is contrary Gaussian distribution, and its mathematical description is:

$g\left(t\right|{\hat{a}}_0,{\hat{a}}_1,{\widehat{\mathrm{\σ}}}_w,\mathrm{\ξ})=\frac{\mathrm{\ξ}}{\sqrt{2\mathrm{\π}{\widehat{\mathrm{\σ}}}_W^2{t}^3}}{e}^{-{(\mathrm{\ξ}-{\hat{a}}_0{-\hat{a}}_{1}t)}^2/2{\widehat{\mathrm{\σ}}}_W^{2}t}---\left(11\right)$

Wherein,

for estimated value;

Step 4: the determining of optimum maintenance opportunity

Equipment is carried out to the expense that necessary maintenance, maintenance, inspection and repairing need to pay great number, and if smeltery's upkeep cost of a year is all several ten million, the maintenance cost of great number directly hampers the raising of Business Economic Benefit; Meanwhile, a lot of main equipments are because the failure costs that shutdown maintenance causes also improves constantly; Therefore, select optimum maintenance opportunity, to reducing maintenance cost, extension device serviceable life, significant; By solving the minimum value of the objective function of maintenance cost, can obtain optimum maintenance time;

Suppose that current time is t, remaining useful life is Δ t, the normal probability of etching system while making R (t+ Δ t|t) be illustrated in (t+ Δ t|t), and the expense of preventive maintenance is c _p, the expense of replacing after losing efficacy is c _f, c wherein _f> c _p, in residue, the scale of charges in effective time is so:

C _R(Δt)＝c _PR(t+Δt|t)+c _F(1-R(t+Δt|t)) (12)

Wherein,

$R(t+\mathrm{\Δt}|t)=P\{T>t+\mathrm{\Δt}|T>t\}={\∫}_{+\mathrm{\Δt}}^{+\∞}g\left(s\right|a_0,a_1,{\mathrm{\σ}}_W,\mathrm{\ξ})\mathrm{ds}---\left(13\right)$

In above expression formula, need to provide and solve integration

In unit interval, expectation maintenance cost is:

$C\left(\mathrm{\Δt}\right)=\frac{C_R\left(\mathrm{\Δt}\right)}{T_R\left(\mathrm{\Δt}\right)}=\frac{c_{P}R(t+\mathrm{\Δt}|t)+c_F(1-R(t+\mathrm{\Δt}|t))}{{\∫}_0^{\mathrm{\Δt}}R\left(s\right)\mathrm{ds}}---\left(14\right)$

The optimum time point of safeguarding should be chosen at and make following objective function reach minimum:

Δt _R＝min{Δt：C(Δt)} (15)

In above expression formula, because t is all chosen at discrete time point, therefore, the solution procedure of above optimization problem is to find the minimal value of one group of discrete value in essence, therefore than being easier to, solves; Through above solving, can obtain the optimum time of safeguarding is t _r=t+ Δ t _r.

The present invention has provided at product the optimum maintaining method of complex apparatus under gradual performance degradation condition has occurred; Not only can carry out forecast analysis to the characteristic quantity degenerate case of equipment, can also be as a kind of effective tool of predict device individual life span, for the maintenance support of equipment provides strong theoretical foundation and technical support, thereby reduction of expenditure spending, avoid unnecessary economic loss, there is good engineering using value.

Accompanying drawing explanation

Fig. 1: step 2 drift measured curve y (t) of the present invention and prediction curve y (t) comparison diagram

Fig. 2: step 3 predicting residual useful life result figure of the present invention

Fig. 3: step 3 residual life probability density of the present invention is schemed over time

Fig. 4: step 4 maintenance cost of the present invention is than the curve map in the difference test moment

Embodiment

Embodiment

The present invention exists the optimum maintaining method of complex apparatus under the gradual degenerative conditions of performance to take the optimum maintaining method of certain model gyropanel as application example describes, and mainly comprises the following steps:

Step 1: the structure in dynamic property degraded data storehouse

The drift error of gyropanel is the key character parameter that characterizes gyropanel performance, and from drift test data, when gyropanel normally moves, data will fluctuate up and down around a certain fixed value; When platform breaks down, data are usually expressed as slow increase or sudden change; In constructed performance database, first classifies the test duration as, and second classifies test data as, i.e. the drift measured value of platform; After new drift measured value arrives, measured value is directly deposited in test database; As shown in table 1:

Table 1 test database example

Like this, database is exactly dynamic, when degradation model is carried out to modeling, chooses the data that length is N, and the parameter in the Performance Degradation Model of gyropanel is upgraded;

Step 2: the foundation of equipment performance degradation model

Choose formula (1) the drift measured value of gyropanel is carried out to modeling; Choose measurement length N=10, obtain 10 point (t ₀, y ₀), (t ₁, y ₁) ..., (t ₁₀, y ₁₀), t wherein ₀≤ t ₁≤ t ₂≤ t ₁₀, make Δ t _i=2.5; According to formula (2)-(8), can solve and obtain

by in estimates of parameters substitution fitting function, i.e. measurable next parameter degradation amount constantly; Fig. 1 is the comparison of drift measured curve and prediction curve; As can be seen from Figure 1, predict the outcome more accurate, degradation model matching degenerative process is preferably described;

Step 3: predicting residual useful life

According to the failure threshold of the model parameter value of trying to achieve in second step and gyropanel, solve the time that degenerative process is hit failure threshold first; As shown in Figure 2; As can be seen from Figure 2,, along with increasing of observation data, predicted value more and more approaches actual value; Recycling head reaches the residual life of time forecast of distribution equipment, can obtain the contrary Gaussian distribution of equipment residual life; Fig. 3 is residual life probability density figure; As can be seen from Figure 3, along with increasing of Monitoring Data, the prediction variance yields of residual life reduces gradually, and the precision of predicting residual useful life is more and more higher;

Step 4: the determining of optimum maintenance opportunity

Suppose that the current test of gyropanel is t constantly, residual life is Δ t, the probability of the normal operation of etching system while making R (t+ Δ t|t) be illustrated in (t+ Δ t|t), and the expense of preventive maintenance is c _p, the expense of replacing after losing efficacy is c _f, c wherein _f> c _p, in residue, the scale of charges in effective time is so:

C _R(Δt)＝c _PR(t+Δt|t)+c _F(1-R(t+Δt|t)) (16)

Wherein,

$R(t+\mathrm{\Δt}|t)=P\{T>t+\mathrm{\Δt}|T>t\}={\∫}_{+\mathrm{\Δt}}^{+\∞}g\left(s\right|a_0,a_1,{\mathrm{\σ}}_W,\mathrm{\ξ})\mathrm{ds}---\left(17\right)$

In above expression formula, need to provide and solve integration

this integration can pass through Numerical Methods Solve;

In unit interval, expectation maintenance cost is:

$C\left(\mathrm{\Δt}\right)=\frac{C_R\left(\mathrm{\Δt}\right)}{T_R\left(\mathrm{\Δt}\right)}=\frac{c_{P}R(t+\mathrm{\Δt}|t)+c_F(1-R(t+\mathrm{\Δt}|t))}{{\∫}_0^{\mathrm{\Δt}}R\left(s\right)\mathrm{ds}}---\left(18\right)$

The optimum time point of safeguarding should be chosen at and make following objective function reach minimum:

Δt _R＝min{Δt：C(Δt)} (19)

In above expression formula, because t is all chosen at discrete time point, therefore, the solution procedure of above optimization problem is to find the minimal value of one group of discrete value in essence; After obtaining minimum value, can calculate the optimum time of safeguarding is t _r=t+ Δ t _r; Fig. 4 is the associated maintenance expense in conjunction with this gyropanel, and the maintenance cost calculating is than the curve map in the difference test moment; As can be seen from Figure 4, the maintenance cost of gyropanel changes than the variation along with the test moment, after the 170th test, has a minimum expense ratio, and this point is predicted optimum maintenance time point.

Claims (1)

1. the optimum maintaining method of the equipment of the gradual degeneration of performance, is characterized in that: according to the ruuning situation of equipment, and choose reasonable performance degradation Monitoring Data, the Performance Degradation Data storehouse of apparatus for establishing, specifically comprises the following steps:

Step 1: build dynamic property degraded data storehouse

In constructed Performance Degradation Data storehouse, comprise test duration and test data; Database is dynamic; When degradation model is carried out to modeling, choose the data that length is N, model parameter is upgraded;

Step 2: the foundation of equipment performance degradation model

Adopt the Wiener model of band drift to carry out matching to performance degradation process:

y(t)＝a ₀+a ₁t _i+σ _WW(t _i) (1)

Wherein, y (t) is performance degradation amount, t _itime span while being the i time measurement, a ₀for zero degree item, a ₁for once, be called coefficient of deviation, σ _wfor coefficient of diffusion, W (t _i) be the Wiener-Hopf equation of standard; Obtained data are sampled, with certain interval, in test data, get (n ₁for positive integer) individual point

wherein

according to drift expression formula, can obtain:

Δy _i＝a ₁Δt _i+σ _WΔW(t _i) (2)

Wherein, a ₁Δ t _i=a ₁(t _i-t _i-1), σ _wΔ W (t _i)=σ _w[W (t _i)-W (t _i-1)], Δ y _i=y _i-y _i-1, i=1,2 ..., n ₁, by the known Δ W of the definition (t of Wiener-Hopf equation _i)～N (0, Δ t _i), thereby can obtain:

$\mathrm{\Δ}{y}_i~N(a_1{\mathrm{\Δt}}_i,{\mathrm{\σ}}_W^2{\mathrm{\Δt}}_i)---\left(3\right)$

Use Maximum Likelihood Estimation Method, the parameter in estimation model; By Wiener-Hopf equation stationary independent increment, can be obtained

joint probability density, i.e. sample likelihood function L (a ₁, σ _w) be:

$L(a_1,{\mathrm{\σ}}_W)=f({\mathrm{\Δy}}_1,{\mathrm{\Δy}}_2,\·\·\·,{\mathrm{\Δy}}_{n_1})=f\left({\mathrm{\Δy}}_1\right)f\left({\mathrm{\Δy}}_2\right)\·\·\·f\left({\mathrm{\Δy}}_{n_1}\right)---\left(4\right)$

Above likelihood function is taken the logarithm, and respectively to a ₁, σ _wask partial differential to obtain:

$\frac{\∂L}{\∂a_1}=\underset{i=1}{\overset{n_1}{\mathrm{\Σ}}}\frac{\mathrm{\Δ}{y}_i-a_1\mathrm{\Δ}{t}_i}{{\mathrm{\σ}}_W^2{\mathrm{\Δt}}_i}=0---\left(5\right)$

$\frac{\∂L}{\∂{\mathrm{\σ}}_W}=\underset{i=1}{\overset{n_1}{\mathrm{\Σ}}}-\frac{1}{{\mathrm{\σ}}_W}+\frac{(\mathrm{\Δ}{y}_i-a_1\mathrm{\Δ}{t}_i{)}^2}{{\mathrm{\σ}}_W^2{\mathrm{\Δt}}_i}=0---\left(6\right)$

Solve above system of equations and can obtain following estimated result:

${\hat{a}}_1=\frac{1}{n_1}\underset{i=1}{\overset{n_1}{\mathrm{\Σ}}}\frac{{\mathrm{\Δy}}_i}{{\mathrm{\Δt}}_i}---\left(7\right)$

${\widehat{\mathrm{\σ}}}_W=\sqrt{\frac{1}{n_1}\underset{i=1}{\overset{n_1}{\mathrm{\Σ}}}{\frac{({\mathrm{\Δy}}_i-{\hat{a}}_1{\mathrm{\Δt}}_i)}{{\mathrm{\Δt}}_i}}^2}---\left(8\right)$

According to above estimated result, will

with

bring y (t)=a into ₀+ a ₁t _i+ σ _ww(t _i) can obtain a ₀estimated value

Step 3: predicting residual useful life

Be defined as condition random variable:

P{T-t|T＞t，Z(t)} (9)

T represents the stochastic variable of out-of-service time, and t is the current life-span, and Z (t) is the historical state data to current time; Because RUL is stochastic variable, effecting surplus time prediction typically refers to: ask the distribution of RUL, i.e. and formula (9), or ask the expectation of RUL, that is:

E[T-t|T＞t，Z(t)] (10)

The main thought that carries out life prediction is: the first step: the head that solves degenerative process reaches time distribution; Second step: utilize the first residual life that reaches time forecast of distribution equipment, the residual life that obtains equipment distributes;

According to the definition of above parameter estimation result and residual life, the time that can obtain hitting first failure threshold is contrary Gaussian distribution, and its mathematical description is:

$g\left(t\right|{\hat{a}}_0,{\hat{a}}_1,{\widehat{\mathrm{\σ}}}_W,\mathrm{\ξ})=\frac{\mathrm{\ξ}}{\sqrt{2\mathrm{\π}{\widehat{\mathrm{\σ}}}_W^2{t}^3}}{e}^{-{(\mathrm{\ξ}-{\hat{a}}_0{-\hat{a}}_{1}t)}^2/2{\widehat{\mathrm{\σ}}}_W^{2}t}---\left(11\right)$

Wherein,

for estimated value;

Step 4: the determining of optimum maintenance opportunity

Suppose that current time is t, remaining useful life is Δ t, the normal probability of etching system while making R (t+ Δ t|t) be illustrated in (t+ Δ t|t), and the expense of preventive maintenance is c _p, the expense of replacing after losing efficacy is c _f, c wherein _f> c _p, in residue, the scale of charges in effective time is so:

C _R(Δt)＝c _PR(t+Δt|t)+c _F(1-R(t+Δt|t)) (12)

Wherein,

$R(t+\mathrm{\Δt}|t)=P\{T>t+\mathrm{\Δt}|T>t\}={\∫}_{+\mathrm{\Δt}}^{+\∞}g\left(s\right|a_0,a_1,{\mathrm{\σ}}_W,\mathrm{\ξ})\mathrm{ds}---\left(13\right)$

In above expression formula, need to provide and solve integration

In unit interval, expectation maintenance cost is:

$C\left(\mathrm{\Δt}\right)=\frac{C_R\left(\mathrm{\Δt}\right)}{T_R\left(\mathrm{\Δt}\right)}=\frac{c_{P}R(t+\mathrm{\Δt}|t)+c_F(1-R(t+\mathrm{\Δt}|t))}{{\∫}_0^{\mathrm{\Δt}}R\left(s\right)\mathrm{ds}}---\left(14\right)$

The optimum time point of safeguarding should be chosen at and make following objective function reach minimum:

Δt _R＝min{Δt：C(Δt)} (15)

Through above solving, can obtain the optimum time of safeguarding is t _r=t+ Δ t _r.

Images