CN103679280B - A kind of equipment optimum maintaining method of the gradual degeneration of performance - Google Patents

Abstract

The invention belongs to reliability engineering technique field, the method relating to the high reliability equipment with the slow degradation characteristics of performance carries out optimum maintenance.According to the ruuning situation of equipment, rationally select performance degradation Monitoring Data, set up the Performance Degradation Data storehouse of equipment, specifically include: build dynamic property degraded data storehouse；The foundation of equipment performance degradation model；Predicting residual useful life；The determination on optimum maintenance opportunity.The invention provides the complex device optimum maintaining method under the conditions of product occurs gradual performance degradation, it is possible not only to be predicted the characteristic quantity degenerate case of equipment analyzing, it is also used as a kind of effective tool of pre-measurement equipment individual life span, maintenance support for equipment provides strong theoretical foundation and technical support, thus reduction of expenditure spending, avoid unnecessary economic loss, there is good engineer applied and be worth.

Description

A kind of equipment optimum maintaining method of the gradual degeneration of performance

Technical field

The invention belongs to reliability engineering technique field, relate to the high reliability equipment with the slow degradation characteristics of performance The method carrying out optimum maintenance；

Background technology

About existing optimum maintenance based on predicting residual useful life, what Christer and Wang et al. was correlated with grinds Study carefully；These research work are all based on statistical method, and its basic thought is: by testing historical data, choose just When statistical distribution pattern the residual life change procedure of equipment is modeled, then according to status monitoring information with residue the longevity Relation between life, model parameter is updated by the information acquired in utilization, thus pre-measurement equipment is in the residue of current time In the life-span, on this basis according to the result of predicting residual useful life, build with maintenance cost as decision objective, with the opportunity of safeguarding and dimension Protect the strategy maintenance model for decision variable；By making maintenance cost reach minimum, and most preferably safeguarded opportunity or optimum Maintenance strategy；But, in engineering practice, the fail data of equipment is the most fewer so that selected statistical distribution is difficult to The residual life change procedure of accurate description equipment, causes the optimal maintenance opportunity solved or optimum maintenance strategy to exist relatively Big error；

Summary of the invention

For above-mentioned prior art situation, it is an object of the invention to: provide one to make full use of equipment and slowly become in performance The Performance Degradation Data recorded during change, scientific forecasting high reliability equipment individual life span characteristic quantity numerical value, and basis at this On determine the method for optimum maintenance time, with solve traditional determine optimum maintenance opportunity based on fail data time the nothing that run into The problem of fail data；

Now present inventive concept 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 at dynamic loading, burn into mill Under the long term of damage, fatigue load etc., some device will occur aging, defect occurs；It addition, at prolonged storage In, owing to being affected by temperature, humidity and power on/off circulation etc., generation is drifted about by some performance state of equipment；When equipment When performance degradation amount at a time exceedes threshold value, equipment can not complete assigned tasks well, thus the generation of causing trouble； Therefore, it should according to the ruuning situation of equipment, performance degradation Monitoring Data is rationally selected, such as oil analysis data, temperature, pressure And sound Monitoring Data etc., set up the Performance Degradation Data storehouse of equipment, and by effective maintaining method, send out reducing equipment The probability of raw fault；

The equipment optimum maintaining method 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 include testing time and test data；When new test data After arrival, data are directly stored in test database, mainly include two row, wherein first be classified as testing time, secondary series For test data；Thus data base is dynamic；When degradation model is modeled, the data of a length of N can be chosen, right Model parameter is updated；

Step 2: the foundation of equipment performance degradation model

Owing to the factors such as inherent strain, running environment and random shock are random to the effect of equipment so that equipment There is the strongest non-linear and randomness in the degenerative process of energy；Performance degradation process is intended by the Wiener model using band drift Close:

$y\left(t\right)=a_0+a_1{t}_i+{\mathrm{\σ}}_{W}W\left(t_i\right)---\left(1\right)$

Wherein, y (t) is performance degradation amount, t_iTime span when measuring for i & lt, a₀For zero degree item, a₁For first order, claim For coefficient of deviation, σ_WFor diffusion coefficient, W (t_i) it is the Wiener-Hopf equation of standard；Acquired data are sampled, between certain It is interposed between in test data and takes (n₁+1)(n₁For positive integer) individual pointWherein Can obtain according to drift expression formula:

$\mathrm{\Δ}{y}_i=a_1\mathrm{\Δ}{t}_i+{\mathrm{\σ}}_W\mathrm{\ΔW}\left(t_i\right)---\left(2\right)$

Wherein, $a_1\mathrm{\Δ}{t}_i=a_1(t_i-t_{i-1}),{\mathrm{\σ}}_W\mathrm{\ΔW}\left(t_i\right)={\mathrm{\σ}}_W[W\left(t_i\right)-W\left(t_{i-1}\right)],\mathrm{\Δ}{y}_i=y_i-y_{i-1},i=\mathrm{1,2},...,n_1,$ Δ W (t is understood by the definition of Wiener-Hopf equation_i)～N (0, Δ t_i), thus can obtain:

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

Use Maximum Likelihood Estimation Method, estimate the parameter in model；Can be obtained by Wiener-Hopf equation stationary independent incrementJoint probability density, i.e. sample likelihood function L (a₁, σ_W) it is:

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

Above likelihood function is taken the logarithm, and respectively to a₁, σ_WPartial differential is asked to obtain:

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

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

Solve above equation group and i.e. can get following estimated result:

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

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

According to above estimated result, willWithBring y (t)=a into₀+a₁t_i+σ_WW(t_i) i.e. can get a₀Estimated value

Step 3: predicting residual useful life

In the life-span of equipment, it is often referred to the service life of equipment, according to the definition of national military standard GJB451A-2005, service life It is that " equipment uses technically or economically considers all should not re-use, and must overhaul or life-span when scrapping Units "；More specifically, equipment (can) refer to that being accomplished to appearance from device fabrication can not repair and (or do not worth service life Must repair) fault or life unit number during unacceptable fault rate；Residual life (remaining life:RL) is logical Often refer to remaining useful life (remaining useful life:RUL), also referred to as remain service life (remaining Service life:RSL) or residual life (residual life)；Predicting residual useful life, refers to working as in actual applications Under the conditions of known to front equipment state and historical state data, prediction is gone to there remains before one (or multiple) lost efficacy generation many Few time；It is defined as conditional random variable:

$P\{T-t|T>t,Z\left(t\right)\}---\left(9\right)$

Here T represents the stochastic variable of out-of-service time, and t is current age, and Z (t) is the historic state to current time Data；Owing to RUL is stochastic variable, effecting surplus time prediction typically refers to: asks the distribution of RUL, i.e. formula (9), or seeks RUL Expectation, it may be assumed that

$E[T-t|T>t,Z\left(t\right)]---\left(10\right)$

The main thought carrying out biometry is: the first step: solve the first-hitting time distribution of degenerative process；Second step: profit With the residual life of first-hitting time forecast of distribution equipment, obtain the residual life distribution of equipment；

According to above parameter estimation result and the definition of residual life, the time of failure threshold can be hit first For dead wind area, 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 determination on optimum maintenance opportunity

Equipment is carried out the maintenance of necessity, maintains, check and repair the expense needing to pay great number, such as smeltery 1 year Maintenance cost is all several ten million, and the maintenance cost of great number directly hampers the raising of Business Economic Benefit；Meanwhile, the most large-scale set Also improve constantly for the failure costs caused due to shutdown maintenance；Therefore, select optimum maintenance opportunity, to reducing maintenance expense With, extension device service life, significant；By solving the minima of the object function of maintenance cost, can obtain Optimum maintenance time；

Assuming that current time is t, remaining useful life is Δ t, makes R (t+ Δ t | t) represent the etching system when (t+ Δ t | t) Normal probability, the expense of preventive maintenance is c_P, the expense replaced after inefficacy is then c_F, wherein c_F＞ c_P, then have in residue Scale of charges in the effect time is:

$C_R\left(\mathrm{\Δt}\right)=c_{P}R(t+\mathrm{\Δt}|t)+c_F(1-R(t+\mathrm{\Δt}|t))---\left(12\right)$

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 be given to 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 safeguarded should be chosen at and make following object function reach minimum:

$\mathrm{\Δ}{t}_R=\min \{\mathrm{\Δt}:C\left(\mathrm{\Δt}\right)\}---\left(15\right)$

In above expression formula, all it is chosen at discrete time point, therefore, the solution procedure of above optimization problem due to t It is substantially the minimum finding one group of centrifugal pump, is therefore easier to solve；Solve through above, i.e. available optimum dimension The time protected is t_R=t+ Δ t_R。

The present invention gives the complex device optimum maintaining method under the conditions of product occurs gradual performance degradation；Not only may be used It is predicted analyzing with the characteristic quantity degenerate case to equipment, it is also possible to as a kind of effectively work of pre-measurement equipment individual life span Tool, the maintenance support for equipment provides strong theoretical foundation and technical support, thus reduction of expenditure is paid wages, it is to avoid unnecessary Economic loss, has good engineer applied and is worth.

Accompanying drawing explanation

Fig. 1: step 2 of the present invention is drifted about measured curve y (t) 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 chart in the difference test moment

Detailed description of the invention

Embodiment

There is the complex device optimum maintaining method under the gradual degenerative conditions of performance with certain model gyropanel in the present invention Optimum maintaining method is that application example illustrates, and mainly comprises the steps that

Step 1: the structure in dynamic property degraded data storehouse

The drift error of gyropanel is the key character parameter characterizing gyropanel performance, in terms of drift test data, When gyropanel is properly functioning, data will be around a certain fixed value and fluctuate up and down；When platform breaks down, the usual table of data It is now slowly to increase or sudden change；In constructed performance database, first is classified as the testing time, and second is classified as test data, The i.e. drift measured value of platform；After new drift measured value arrives, measured value is directly stored in test database；Such as table Shown in 1:

Table 1 test database example

So, data base is exactly dynamic, when being modeled degradation model, chooses the data of a length of N, to gyro Parameter in the Performance Degradation Model of platform is updated；

Step 2: the foundation of equipment performance degradation model

Choose formula (1) the drift measured value of gyropanel is modeled；Choose measurement length N=11, obtain 11 points (t₀, y₀), (t₁, y₁) ..., (t₁₀, y₁₀), wherein t₀≤t₁≤t₂…≤t₁₀, make Δ t_i=2.5；According to formula (2)-(8), permissible Solve and obtain Estimates of parameters is substituted in fitting function, the parameter degradation amount of the most measurable subsequent time；Fig. 1 is drift Move measured curve and the comparison of prediction curve；More accurate from figure 1 it appears that predict the outcome, illustrate that degradation model can Preferably matching degenerative process；

Step 3: predicting residual useful life

According to the model parameter value tried to achieve in second step and the failure threshold of gyropanel, solve degenerative process and hit first The time of middle failure threshold；As shown in Figure 2；From figure 2 it can be seen that increasing along with observation data, it was predicted that value increasingly connects Nearly actual value；The residual life of recycling first-hitting time forecast of distribution equipment, the inverse Gauss that can obtain equipment residual life divides Cloth；Fig. 3 is residual life probability density figure；From figure 3, it can be seen that increasing along with Monitoring Data, the prediction of residual life Variance yields is gradually reduced, i.e. the precision of predicting residual useful life is more and more higher；

Step 4: the determination on optimum maintenance opportunity

Assuming that gyropanel current test moment is t, residual life is Δ t, make R (t+ Δ t | t) represent (t+ Δ t | T) probability that time, etching system is properly functioning, the expense of preventive maintenance is c_P, the expense replaced after inefficacy is then c_F, wherein c_F＞ c_P, then the scale of charges in residue effective time is:

$C_R\left(\mathrm{\Δt}\right)=c_{P}R(t+\mathrm{\Δt}|t)+c_F(1-R(t+\mathrm{\Δt}|t))---\left(16\right)$

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 be given to solve integrationThis integration can pass through numerical value Method solves；

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 safeguarded should be chosen at and make following object function reach minimum:

$\mathrm{\Δ}{t}_R=\min \{\mathrm{\Δt}:C\left(\mathrm{\Δt}\right)\}---\left(19\right)$

In above expression formula, all it is chosen at discrete time point, therefore, the solution procedure of above optimization problem due to t It it is substantially the minimum finding one group of centrifugal pump；After obtaining minima, the time that can calculate optimum maintenance is t_R=t +Δt_R；Fig. 4 is the associated maintenance expense combining this gyropanel, and calculated maintenance cost ratio is in the difference test moment Curve chart；Figure 4, it is seen that the maintenance cost of gyropanel changes, at the 170th time than the change along with the test moment A minimum expense ratio, i.e. this point is had by the optimum maintenance time point predicted after test.

Claims (1)

1. the equipment optimum maintaining method of the gradual degeneration of performance, it is characterised in that: according to the ruuning situation of equipment, rationally select Select performance degradation Monitoring Data, set up the Performance Degradation Data storehouse of equipment, specifically include following steps:

Step 1: build dynamic property degraded data storehouse

In constructed Performance Degradation Data storehouse, including testing time and test data；Data base is dynamic；When to degeneration When model is modeled, chooses the data of a length of N, model parameter is updated；

Step 2: the foundation of equipment performance degradation model

Performance degradation process is fitted by the Wiener model using band drift:

Y (t)=a₀+a₁t_i+σ_WW(t_i) (1)

Wherein, y (t) is performance degradation amount, t_iTime span when measuring for i & lt, a₀For zero degree item, a₁For first order, it is referred to as Coefficient of deviation, σ_WFor diffusion coefficient, W (t_i) it is the Wiener-Hopf equation of standard；Acquired data are sampled, at certain intervals (n is being taken in test data₁+1)(n₁For positive integer) individual pointWherein Can obtain according to formula (1):

Δy_i=a₁Δt_i+σ_WΔW(t_i) (2)

Wherein, a₁Δt_i=a₁(t_i-t_i-1), σ_WΔW(t_i)=σ_W[W(t_i)-W(t_i-1)], Δ y_i=y_i-y_i-1, i=1,2 ..., n₁, the definition of Wiener-Hopf equation understand Δ W (t_i)～N (0, Δ t_i), thus can obtain:

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

Use Maximum Likelihood Estimation Method, estimate the parameter in model；Can be obtained by Wiener-Hopf equation stationary independent increment Joint probability density, i.e. sample likelihood function L (a₁,σ_W) it is:

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

Above likelihood function is taken the logarithm, and respectively to a₁,σ_WPartial differential is asked to obtain:

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

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

Solve above equation group and i.e. can get following estimated result:

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

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

According to above estimated result, willWithBring y (t)=a into₀+a₁t_i+σ_WW(t_i) i.e. can get a₀Estimated valueStep 3: predicting residual useful life

It is defined as conditional random variable:

P{T-t | T ＞ t, Z (t) } (9)

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

E [T-t | T ＞ t, Z (t)] (10)

The main thought carrying out biometry is: the first step: solve the first-hitting time distribution of degenerative process；Second step: utilize head Reach the residual life of the pre-measurement equipment of Annual distribution, obtain the residual life distribution of equipment；

According to above parameter estimation result and the definition of residual life, the time that can be hit failure threshold first is inverse Gauss distribution, 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 determination on optimum maintenance opportunity

Assuming that current time is t, remaining useful life is Δ t, and etching system is normal when (t+ Δ t | t) to make R (t+ Δ t | t) represent Probability, the expense of preventive maintenance is c_P, the expense replaced after inefficacy is then c_F, wherein c_F＞ c_P, then when remaining effective Interior scale of charges is:

C_R(Δ t)=c_PR(t+Δt|t)+c_F(1-R(t+Δt|t)) (12)

Wherein,

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

In above expression formula, need to be given to solve integration

In unit interval, expectation maintenance cost is:

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

The optimum time point safeguarded should be chosen at and make following object function reach minimum:

Δt_R=min{ Δ t:C (Δ t) } (15)

Solving through above, the time that i.e. available optimum is safeguarded is t_R=t+ Δ t_R。