CN103646166A - Power station high-temperature pipe system maintenance method based on non-probability reliability theory - Google Patents

Abstract

The invention relates to a power station high-temperature pipe system maintenance method based on the non-probability reliability theory. The power station high-temperature pipe system maintenance method includes the steps of conducting finite element calculation on the strength of a power station high-temperature pipe system, determining key detection parts of the power station high-temperature pipe system, determining creep damage parameters with the non-probability reliability theory, building a creep damage probability model by determining the creep damage parameters, calculating structural failures according to the creep damage probability model, building a maintenance method model based on reliability analysis according to detected data, materials of the power station high-temperature pipe system and structure test results, and determining the optimum maintenance time of the high-temperature pipe system according to the maintenance method model and the actual engineering maintenance cost. The non-probability reliability maintenance method is achieved through the power station high-temperature pipe system, the structural probability reliability is efficiently and accurately determined, maintenance plans can be accurately determined, the maintenance method can solve similar problems of high-temperature pipes in other fields, and therefore the application range is wide.

Description

A kind of High temperature pipe of power station road system maintenance method based on non-probabilistic reliability theory

Technical field

The present invention relates to a kind of High temperature pipe of power station road system maintenance method, especially relate to a kind of High temperature pipe of power station road system maintenance method based on non-probabilistic reliability theory.

Background technology

The maintenance of High temperature pipe of power station road system is the major issue that firepower power station and heat energy factory pay close attention to, because the general cost of high temperature and high pressure steam pipeline in modern firepower power station and heat energy factory is high, deterioration factor complexity due to material under high temperature and high pressure environment is difficult to prediction in addition, once High temperature pipe of power station road system easily breaks down. and break down, will bring tremendous influence to economy and the social safety of enterprise.

In view of this, the maintenance for high-temperature pipe just seems very important.In the sixties in last century, first the U.S. proposed the method for maintaining based on reliability, set up comprehensive production maintenance subsequently concentrate with reliability the maintenance system combining in American and Britain, Deng developed country.Develop into again later take that the influence factors such as infringement that may cause set up into consideration after accident occurs based on Risk Monitoring technology.The ASME of ASME " gas line integrity management system " for example; The oil and gas pipes Study on Risk Assessment that the Pas-petrol Pipeline Risk Assessment steering committee (PRASC) that Canada Deng Qige group of energy conduit association forms carries out etc. is all used widely in engineering reality.From documents and materials, developed countries has been carried out a large amount of analytical works based on risk detection technique, has accumulated a large amount of data.

In China, safety guarantee technology for High temperature pipe of power station road has many-sided demand, Yi Shi China is just greatly developing supercritical generating technology, the raising of temperature and pressure has increased the operation risk of factory widely, and wherein the operation life of high-temperature pipe parts does not also accumulate how many experiences at present; The main steam line of the many power plant of Er Shi China progresses into the aged phase, has generally reached 200,000 hours above (100,000 hours designed lives) working time, nearly 400,000 hours of the longest accumulation active time; High-temperature and high-pressure technique is more and more applied in many high-tech sectors simultaneously, has also proposed new demand.Obviously, setting up a High temperature pipe of power station road method for maintaining based on Applications In Risk Technique that is suitable for China's national situation is very important.

If set up the method for maintaining based under Applications In Risk Technique of an applicable China's national situation, the major issue that must solve is:

(1) first due to China, to carry out this respect working time short, and the data of accumulation is few, how to utilize a small amount of effective information to set up Reliability Maintenance method and be one and ask a question before very important.

(2) secondly, obtaining under the statistical distribution character of different parameters, the probability distribution function that how can determine impairment parameter is also a major issue.

(3) also having, draw method for maintaining model, according to the models coupling risk assessment of gained, obtain High temperature pipe of power station road system best servicing time of programme, is also the important content that belongs to method for maintaining.

(4) be finally how to adopt modern method for maintaining to determine the problem of suitable method for maintaining, this problem has had the technology of comparative maturity, does not do emphasis herein.

Summary of the invention

Technical matters to be solved by this invention, be just to provide a kind of only utilize a small amount of information just can predict comparatively accurately piping system reliability, can be efficiently and determine exactly structural reliability, accurately determine maintenance program, the scope of application High temperature pipe of power station road system maintenance method based on non-probabilistic reliability theory comparatively widely.

Solve the problems of the technologies described above, the technical solution used in the present invention is as follows:

A High temperature pipe of power station road system maintenance method based on non-probabilistic reliability theory, is characterized in that: comprise the following steps:

S1 carries out the FEM (finite element) calculation of High temperature pipe of power station road system, selects the place of 1-5 place maximum stress, as emphasis monitoring position;

S2 arranges fixation of sensor at keypoint part, and the detection data of high temperature pipe system are obtained in the method collection of employing infrared thermal imaging monitoring instrument complete detection system;

S3 is theoretical according to non-probabilistic reliability, determines the stray parameter of the creep impairment of High temperature pipe of power station road system;

S4 sets up the creep impairment probability model of High temperature pipe of power station road system; Calculate the structural failure probability of high temperature pipe system;

S5 is according to the creep damage failure probability of High temperature pipe of power station road system, computation structure fail result;

S6, according to the detection data of the result of calculation of step (5), pipeline, material and structural test result, sets up the method for maintaining model based on fail-safe analysis;

S7 is according to the method for maintaining models coupling risk assessment of gained, obtains High temperature pipe of power station road system best servicing time.

Described step S3 comprises following content:

According to the non-probability model of following Formula creep impairment:

$\stackrel{\·}{D}={\mathrm{Bt}}^{-m}\frac{{\mathrm{\σ}}_{\mathrm{eq}}^r}{{(1-D)}^k};$

Wherein, t is the time; B, m, k, r be under fixed temperature by experiment determined material constant; σ _eqfor equivalent stress, and above-mentioned each parameter is stochastic variable;

To adopt the method in non-probabilistic reliability to define above-mentioned stochastic variable below:

First according to engineering reality, easily determine the minimum and maximum value of above-mentioned parameter, therefore can obtain following interval number: $[\underset{\_}{B},\stackrel{\_}{B}],[\underset{\_}{m},\stackrel{\_}{m}],[\underset{\_}{k},\stackrel{\_}{k}],[\underset{\_}{r},\stackrel{\_}{r}],[{\underset{\_}{\mathrm{\σ}}}_{\mathrm{eq}},{\stackrel{\_}{\mathrm{\σ}}}_{\mathrm{eq}}];$

As follows according to the average of interval number defined parameters and standard deviation and the coefficient of variation:

$B_c=\frac{\stackrel{\_}{B}+\underset{\_}{B}}{2},B_D=\frac{\stackrel{\_}{B}-\underset{\_}{B}}{2},{\mathrm{cov}}_B=\frac{B_D}{B_c};$

$m_c=\frac{\stackrel{\_}{m}+\underset{\_}{m}}{2},m_D=\frac{\stackrel{\_}{m}-\underset{\_}{m}}{2},{\mathrm{cov}}_m=\frac{m_D}{m_c};$

$k_c=\frac{\stackrel{\_}{k}+\underset{\_}{k}}{2},k_D=\frac{\stackrel{\_}{k}-\underset{\_}{k}}{2},{\mathrm{cov}}_k=\frac{K_D}{k_c};$

$r_c=\frac{\stackrel{\_}{r}+\underset{\_}{r}}{2},r_D=\frac{\stackrel{\_}{r}-\underset{\_}{r}}{2},{\mathrm{cov}}_r=\frac{r_D}{r_c};$

${\mathrm{\σ}}_{\mathrm{eqc}}=\frac{{\stackrel{\_}{\mathrm{\σ}}}_{\mathrm{eq}}+{\underset{\_}{\mathrm{\σ}}}_{\mathrm{eq}}}{2},{\mathrm{\σ}}_{\mathrm{eqD}}=\frac{{\stackrel{\_}{\mathrm{\σ}}}_{\mathrm{eq}}-{\underset{\_}{\mathrm{\σ}}}_{\mathrm{eq}}}{2},{\mathrm{cov}}_{\mathrm{\σ}}=\frac{{\mathrm{\σ}}_{\mathrm{eqD}}}{{\mathrm{\σ}}_{\mathrm{eqc}}};$

It is B that definition above-mentioned parameter is respectively average _c, m _c, k _c, r _c, σ _eqc; Standard deviation is B _d, m _d, k _d, r _d, σ _eqD; The coefficient of variation is cov _b, cov _m, cov _k, cov _r, cov _σstochastic distribution, stochastic distribution character is chosen according to the principle of being partial to security;

Described step S4 comprises following sub-step:

S4-1 selects the corresponding equivalent stress of regional of described High temperature pipe of power station road system as stratified sampling variable;

If the equivalent stress σ that S4-2 is described _eqmeet following formula, this equivalent stress σ _eqfor can there is not the region of creep damage failure in corresponding region:

${\mathrm{\σ}}_{\mathrm{eq}}\≤{\left\{\frac{1-{(1-[D\left]\right)}^{k+1}}{(k+1)B\left(\frac{t^{1-m}}{1-m}\right)}\right\}}^{1/r};$

Wherein, B, D, k are stochastic variable, and:

Average+3 * the standard deviation of B=damage threshold value;

Average+3 * the standard deviation of k=damage threshold value;

Average-3 * the standard deviation of [D]=damage threshold value;

If the equivalent stress σ that S4-3 is described _eqmeet following formula, this equivalent stress σ _eqfor there is the region of creep damage failure in corresponding region:

${\mathrm{\σ}}_{\mathrm{eq}}>{\left\{\frac{1-{(1-[D\left]\right)}^{k+1}}{(k+1)B\left(\frac{t^{1-m}}{1-m}\right)}\right\}}^{1/r};$

S4-4, in there is the region of creep damage failure, utilizes layered sampling method to calculate failure probability P based on Monte Carlo method and by following formula _f:

$P_f=\frac{\mathrm{nf}}{\mathrm{Num}};$

Wherein, Num is test number (TN), and nf is the number of times losing efficacy in test, meets following relation:

The nonlinear degree that needs to reduce data in this method, is specially: data taken the logarithm, thus the nonlinear degree of reduction data.

Described step 5 comprises the following steps:

First adopt the common Weibull of least square fitting, normal state and lognormal probability distribution function, therefrom select the method for immediate probability distribution function, set up the creep impairment probability model of comparatively accurate High temperature pipe of power station road system;

According to following Formula creep impairment probability model:

$\stackrel{\·}{D}={\mathrm{Bt}}^{-m}\frac{{\mathrm{\σ}}_{\mathrm{eq}}^r}{{(1-D)}^k};$

Wherein, t is the time; B, m, k, r be under fixed temperature by experiment determined material parameter; σ _eqfor equivalent stress, above-mentioned parameter is stray parameter.Its random nature defines definite by non-probabilistic reliability interval number.And creep impairment value is also stray parameter.

According to creep impairment probability model, calculate the structural failure probability of High temperature pipe of power station road system and determine failure probability:

If described equivalent stress σ _eqmeet following formula, this equivalent stress σ _eqfor can there is not the region of creep damage failure in corresponding region:

σ _eq≤[σ] _max；

Wherein, B, D, k are interval number, and [σ] _maxfor maximal value in the interval function of following formula equal sign the right:

${\left[\mathrm{\σ}\right]}_{\max }={\left\{\frac{1-{(1-[D\left]\right)}^{k+1}}{(k+1)B\left(\frac{t^{1-m}}{1-m}\right)}\right\}}^{1/r}$

If described equivalent stress σ _eqmeet following formula, this equivalent stress σ _eqfor there is the region of creep damage failure in corresponding region:

σ _eq＞[σ] _max；

In order to obtain immediate creep impairment stochastic distribution, will adopt equation of linear regression from normal state, lognormality and Weibull distribution, to select the method for best distribution;

The step of Weibull Function of determining pipeline creep impairment is as follows:

According to following formula, determine the cumulative risk function of prediction

$\hat{H}\left(t_k\right)=\underset{i=1}{\overset{k}{\mathrm{\Σ}}}\frac{1}{n+1-i};$

Wherein, t _kfor failure event time of origin, n is the total number of times of generation event, wherein also comprises the event that there is no inefficacy, and the inefficacy of each product is t by ascending sequence constantly ₁≤ t ₂≤ ...≤t _n;

According to following formula, in conjunction with the result of calculation of Larson-Miller method, determine the unreliable degree function F (t) based on Weibull probability distribution function:

F(t _rex/t _res)=1-exp{-(t _rex/t _resη) ^m}；

Wherein, t _rex/ t _resfor the ratio of test life with the life-span of using accordingly Larson-Miller method formula to calculate, m is form parameter, and η is scale parameter; Brief note t=t _rex/ t _res, its probability distribution function is designated as:

F(t)=1-R(t)=1-exp{-H(t)}；

According to following formula, determine the regression equation of cumulative risk function:

H(t)=(t/η) ^m；

lnH(t)=mlnt-mlnη

Wherein, m, η are the determined parameter of equation of linear regression;

According to equation of linear regression y _i=a+bx _i, and according to following formula, determine the parameter of Weibull Function:

m=b

$\mathrm{\η}=\exp \{-\frac{a}{m}\};$

Thereby set up corresponding Weibull probability life-span distribution function.

Described step S6 is specially:

According to following Formula periodic plan Maintenance Model:

$C_T=\frac{C_P}{T_P}+C_c\frac{{\∫}_0^{T_P}(1-R\left(t\right))\mathrm{dt}}{T_P{\∫}_0^{T_P}R\left(t\right)\mathrm{dt}};$

Wherein, C _tfor total maintenance cost in the unit interval; C _cexpense for each correction maintenance; C _pexpense for preventive maintenance; Or, according to following Formula preventive maintenance model:

$C_T=C_c\frac{1-R\left(T_p\right)}{{\∫}_0^{T_P}R\left(t\right)\mathrm{dt}}+C_P\frac{R\left(T_p\right)}{{\∫}_0^{T_P}R\left(t\right)\mathrm{dt}};$

Wherein, C _tfor total maintenance cost in the unit interval; C _cexpense for each correction maintenance; C _pexpense for preventive maintenance.

Described step S7 comprises the following steps:

S7-1 determines the risk R (t) of High temperature pipe of power station road system according to following formula:

$R\left(t\right)=\underset{a}{\overset{b}{\∫}}m(x,t)\·f(x,t)\mathrm{dx};$

Wherein, R (t)=P _f(t) C (t), P _f(t) be the failure probability of structure, the consequence of C (t) for losing efficacy and producing, it is all the function of time t; P _f(t) and C (t) separate, and R (t) is fuzzy random variable, f (x, t) is R (t) and P _f(t) the identical probability distribution of obeying, m (x, t) is the identical subordinate function that R (t) has with C (t), f (x, t) and m (x, t) are all continuous;

S7-2 utilizes linear programming algorithm by following formula, to calculate best servicing time of the t of described High temperature pipe of power station road system:

$\underset{s.t}{\min }R\left(t\right)=P_f\left(t\right)\·C\left(t\right);$

Wherein,

the best servicing time of high temperature pipe is obtained in expression with linear programming algorithm to function R (t).

Beneficial effect: high-temperature pipe confucian orthodoxy method for maintaining of the present invention, owing to wherein having adopted non-probabilistic reliability theoretical, therefore can lack in adequate data amount situation, utilize low volume data to determine parameters stochastic distribution, and utilize two kinds of MC methods that high-level efficiency is calculated that have that are applicable to high temperature pipe creep impairment problem, and adopted the method for maintaining of Reliability Maintenance theoretical method in conjunction with the high-temperature pipe damage problem of risk assessment technology, thereby only utilize a small amount of information just can predict comparatively accurately piping system integrity problem, realized and efficiently and exactly determined structural reliability, determine maintenance program, it is specially adapted to enterprise in a series of implementation methods of formulating high-temperature pipe structural reliability maintenanceization, and can solve the method for maintaining of the high temperature pipe phase class problem in other field, thereby the scope of application is comparatively extensive.

Accompanying drawing explanation

Fig. 1 is the overall flow figure of High temperature pipe of power station of the present invention road system maintenance method;

Fig. 2 is High temperature pipe of power station of the present invention road system finite element model figure.

Embodiment

In order more clearly to understand technology contents of the present invention, especially exemplified by following examples, describe in detail.

Refer to shown in Fig. 1, high temperature pipe system maintenance method of the present invention, comprises the following steps:

1, first carry out the FEM (finite element) calculation of High temperature pipe of power station road system, according to the place of maximum stress, determine that the emphasis of High temperature pipe of power station road system detects position;

2, at keypoint part, arrange fixation of sensor, adopt the method acquisition testing data of infrared thermal imaging monitoring instrument complete detection system;

3, according to the theoretical creep impairment stray parameter of determining High temperature pipe of power station road system of non-probabilistic reliability, comprise the following steps:

(a) according to obtained test, detection data minimum, maximal value, according to interval number define method in non-probabilistic reliability, determine average, standard deviation and the coefficient of variation of stray parameter;

(b) according to inclined to one side principle of sound accounting, the probability distribution function of the relevant stray parameter of definition;

Be specially:

According to the non-probability model of following Formula creep impairment:

$\stackrel{\·}{D}={\mathrm{Bt}}^{-m}\frac{{\mathrm{\σ}}_{\mathrm{eq}}^r}{{(1-D)}^k};$

Wherein, t is the time; B, m, k, r be under fixed temperature by experiment determined material constant; σ _eqfor equivalent stress, and above-mentioned each parameter is stochastic variable;

Above-mentioned stochastic variable will adopt the method in non-probabilistic reliability theory to define:

First according to engineering reality, easily determine the minimum and maximum value of above-mentioned parameter, obtain following interval number:

$[\underset{\_}{B},\stackrel{\_}{B}],[\underset{\_}{m},\stackrel{\_}{m}],[\underset{\_}{k},\stackrel{\_}{k}],[\underset{\_}{r},\stackrel{\_}{r}],[{\underset{\_}{\mathrm{\σ}}}_{\mathrm{eq}},{\stackrel{\_}{\mathrm{\σ}}}_{\mathrm{eq}}];$

As follows according to the average of interval number defined parameters and standard deviation and the coefficient of variation:

$B_c=\frac{\stackrel{\_}{B}+\underset{\_}{B}}{2},B_D=\frac{\stackrel{\_}{B}-\underset{\_}{B}}{2},{\mathrm{cov}}_B=\frac{B_D}{B_c};$

$m_c=\frac{\stackrel{\_}{m}+\underset{\_}{m}}{2},m_D=\frac{\stackrel{\_}{m}-\underset{\_}{m}}{2},{\mathrm{cov}}_m=\frac{m_D}{m_c};$

$k_c=\frac{\stackrel{\_}{k}+\underset{\_}{k}}{2},k_D=\frac{\stackrel{\_}{k}-\underset{\_}{k}}{2},{\mathrm{cov}}_k=\frac{k_D}{k_c};$

$r_c=\frac{\stackrel{\_}{r}+\underset{\_}{r}}{2},r_D=\frac{\stackrel{\_}{r}-\underset{\_}{r}}{2},{\mathrm{cov}}_r=\frac{r_D}{r_c};$

${\mathrm{\σ}}_{\mathrm{eqc}}=\frac{{\stackrel{\_}{\mathrm{\σ}}}_{\mathrm{eq}}+{\underset{\_}{\mathrm{\σ}}}_{\mathrm{eq}}}{2},{\mathrm{\σ}}_{\mathrm{eqD}}=\frac{{\stackrel{\_}{\mathrm{\σ}}}_{\mathrm{eq}}-{\underset{\_}{\mathrm{\σ}}}_{\mathrm{eq}}}{2},{\mathrm{cov}}_{\mathrm{\σ}}=\frac{{\mathrm{\σ}}_{\mathrm{eqD}}}{{\mathrm{\σ}}_{\mathrm{eqc}}};$

It is B that definition above-mentioned parameter is respectively average _c, m _c, k _c, r _c, σ _eqc; Standard deviation is B _d, m _d, k _d, r _d, σ _eqD; The coefficient of variation is cov _b, cov _m, cov _k, cov _r, cov _σstochastic distribution, stochastic distribution character is chosen according to the principle of being partial to security.

4, by determining the probability distribution of described creep impairment parameter, set up the creep impairment probability model of high temperature pipe system.Wherein the probability distribution function of creep impairment, need to relatively obtain by the regression equation of more conventional Weibull, normal state and lognormal distribution.

Regression equation existing definition in reliability theory due to normal state and lognormal distribution, therefore repeats no more, and definition Weibull function comprises the following steps:

(a) according to following formula, determine the cumulative risk function of prediction

$\hat{H}\left(t_k\right)=\underset{i=1}{\overset{k}{\mathrm{\Σ}}}\frac{1}{n+1-i};$

Wherein, t _kfor failure event time of origin, n is the total number of times of generation event, wherein also comprises the event that there is no inefficacy,

The inefficacy of each product is t by ascending sequence constantly ₁≤ t ₂≤ ...≤t _n;

(b) according to following formula, in conjunction with the result of calculation of Larson-Miller method, determine the unreliable degree function F (t) based on Weibull probability distribution function:

F(t _rex/t _res)=1-exp{-}t _rex/t _resη) ^m}；

Wherein, t _rex/ t _resfor the ratio of test life with the life-span of using accordingly Larson-Miller method formula to calculate, m is form parameter, and η is scale parameter; Brief note t=t _rex/ t _res, its probability distribution function is designated as:

F(t)=1-R(t)=1-exp{-H(t)}；

(c) according to following formula, determine the regression equation of cumulative risk function:

H(t)=(t/η) ^m；

lnH(t)=mlnt-mlnη

Wherein, m, η are the determined parameter of equation of linear regression;

(d) according to equation of linear regression y _i=a+bx _i, and according to following formula, determine the parameter of Weibull Function:

m=b

$\mathrm{\η}=\exp \{-\frac{a}{m}\};$

Thereby set up corresponding expectancy life distribution function;

5, the creep damage failure probability that calculates High temperature pipe of power station road system according to described creep impairment probability model, comprises the following steps:

(a) select the corresponding equivalent stress of regional of described High temperature pipe of power station road system as stratified sampling variable;

(b) if described equivalent stress σ _eqmeet following formula, this equivalent stress σ _eqfor can there is not the region of creep damage failure in corresponding region:

${\mathrm{\σ}}_{\mathrm{eq}}\≤{\left\{\frac{1-{(1-[D\left]\right)}^{k+1}}{(k+1)B\left(\frac{t^{1-m}}{1-m}\right)}\right\}}^{1/r};$

Wherein, B, D, k are stochastic variable, and:

Average+3 * the standard deviation of B=damage threshold value;

Average+3 * the standard deviation of k=damage threshold value;

Average-3 * the standard deviation of [D]=damage threshold value;

(c) if described equivalent stress σ _eqmeet following formula, this equivalent stress σ _eqfor there is the region of creep damage failure in corresponding region:

${\mathrm{\σ}}_{\mathrm{eq}}>{\left\{\frac{1-{(1-[D\left]\right)}^{k+1}}{(k+1)B\left(\frac{t^{1-m}}{1-m}\right)}\right\}}^{1/r};$

(d), in there is the region of creep damage failure, utilize layered sampling method to calculate failure probability P based on Monte Carlo method and by following formula _f:

$P_f=\frac{\mathrm{nf}}{\mathrm{Num}};$

Wherein, Num is test number (TN), and nf is the number of times losing efficacy in test, meets following relation:

6, according to the material of described detection data, High temperature pipe of power station road system and structural test result and described structural failure probability, set up the method for maintaining model based on fail-safe analysis, be specially:

According to following Formula periodic plan Maintenance Model:

$C_T=\frac{C_P}{T_P}+C_c\frac{{\∫}_0^{T_P}(1-R\left(t\right))\mathrm{dt}}{T_P{\∫}_0^{T_P}R\left(t\right)\mathrm{dt}};$

Wherein, C _tfor total maintenance cost in the unit interval; C _cexpense for each correction maintenance; C _pexpense for preventive maintenance;

Or, according to following Formula preventive maintenance model:

$C_T=C_c\frac{1-R\left(T_p\right)}{{\∫}_0^{T_P}R\left(t\right)\mathrm{dt}}+C_P\frac{R\left(T_p\right)}{{\∫}_0^{T_P}R\left(t\right)\mathrm{dt}};$

Wherein, C _tfor total maintenance cost in the unit interval; C _cexpense for each correction maintenance; C _pexpense for preventive maintenance;

7, according to following formula, determine the risk R (t) of High temperature pipe of power station road system:

$R\left(t\right)=\underset{a}{\overset{b}{\∫}}m(x,t)\·f(x,t)\mathrm{dx};$

Wherein, R (t)=P _f(t) C (t), P _f(t) be the failure probability of structure, the consequence of C (t) for losing efficacy and producing, it is all the function of time t; P _f(t) and C (t) separate, and R (t) is fuzzy random variable, f (x, t) is R (t) and P _f(t) the identical probability distribution of obeying, m (x, t) is the identical subordinate function that R (t) has with C (t),

F (x, t) and m (x, t) are all continuous;

8, utilize linear programming algorithm by following formula, to calculate best servicing time of the t of described high temperature pipe system:

$\underset{s.t}{\min }R\left(t\right)=P_f\left(t\right)\·C\left(t\right);$

Wherein,

expression adopts linear programming algorithm to obtain the best servicing time of high temperature pipe to function R (t).

In above formula, determine the factor and the structural failure probability P that affect high-temperature pipe structural life-time _f(t) method is as follows:

(1) determine the high-temperature pipe life-span is affected to large factor

For affecting the more feature of high temperature pipe factors of limit life, first to remove high-temperature pipe to the less factor of life-span impact as far as possible, only leave the factor that impact is large.In conventional fail-safe analysis, what usually adopt is parameters sensitivity analysis method, determines in reliability model that impact is large namely to result those parameters of sensitivity comparatively.But this method can not be effectively applied to analyze a large amount of hot test data.

Rough set (Rough Set) theory is a kind of ambiguous and mathematical tool uncertain problem of processing.In the method, the reasoning of decision rule is widely used among the wide spectrum of medicine and pharmacology, business, finance, market survey, Engineering Control and design.Rough set theory is a kind of very effective theory in Copyright Law About Databases excavates, and has obtained significant effect.And had and used the research report of distinguishing material character from material composition.

Therefore, first utilize rough set theory to determine the method for material impact parameter in test figure.Concrete analytical procedure is as follows:

(a) first will manage to reduce the nonlinearity in material test data, the impacts such as enchancement factor, for example, reduce randomness according to cumulative in gray theory or regressive method; For fatigue data, can adopt the method that data are taken the logarithm to reduce nonlinear degree.

(b) then the experimental data after processing is carried out to unified planning processing, so that analyze.

(c) data after processing are carried out to computational analysis according to the computing method of infosystem decision table in rough set theory.

Step can be determined the sensitive parameter that affects material lifetime in test figure effectively according to the above analysis.

(2) determine parameter probability distribution problem

After selecting the stray parameter that influence factor is high, the problem that solve is the probability distribution function problem of the burn-out life of how to confirm power station, chemical plant or construction material.

This problem is one of sixty-four dollar question in design based on reliability and method for maintaining technical know-how.The failure probability function of general definite structure or member need to be determined by fail-test or by a large amount of data that come from engineering reality.But because engineering actual environment or test condition are limit, sometimes can not obtain abundant data.Therefore, can in conjunction with related reliability achievement in research, be easy to define average and the coefficient of variation and the distribution situation of above-mentioned stray parameter according to relevant interval number define method in non-probabilistic reliability theory.

In order to obtain the stochastic distribution of pipeline creep comparatively accurately, the present invention adopts least square regression algorithm, and the method for the fitting result by more conventional Weibull, normal state and lognormal distribution is selected the probability distribution function of immediate reality.Wherein determine Weibull distribution, according to the method for the propositions such as K.Fujiyama, step is as follows:

Suppose to have n product, each product failure by ascending sequence is constantly

t ₁≤t ₂≤...≤t _n；

With formula below, determine the cumulative risk function (Estimate cumulative hazard function) of prediction:

$\hat{H}\left(t_k\right)=\underset{i=1}{\overset{k}{\mathrm{\Σ}}}\frac{1}{n+1-i}......\left(2.1\right)$

Wherein, t _kbe failure event time of origin, n is that the total number of times of generation event comprises the event that there is no inefficacy.

The data in fail data storehouse can be determined the unreliable degree function based on Weibull probability distribution function in conjunction with L-M method (Larson-Miller method) result of calculation, as follows

F(t _rex/t _res)=1-exp{-(t _rex/t _resη) ^m} ……（2.2）

Wherein, t _rex/ t _restest life and corresponding L-M method formula ratio mathematic(al) expectation.M is form parameter, and η is scale parameter.

Brief note t=t _rex/ t _res, its probability distribution function is designated as:

F(t)=1-R(t)=1-exp{-H(t)} ……（2.3）

At hypothesis failure probability function, obey in Weibull distribution situation, as follows for the regression equation of cumulative risk function:

H(t)=(t/η) ^m ……（2.4）

lnH(t)=mlnt-mlnη

Here, m, η are the determined parameters of equation of linear regression.

According to equation of linear regression:

y _i=a+bx _i

The parameter of Weibull Function is determined by following formula:

m=b

$\mathrm{\η}=\exp \{-\frac{a}{m}\}......\left(2.5\right)$

Employing, by the disposal route of formula (2.1)～(2.5), can effectively be set up and become corresponding Weibull probability life-span distribution function according to high-temperature creep injury material test data.Because this expectancy life distribution function both can be expressed test figure stochastic distribution situation within a regular time, can express again under time growth pattern the expectancy life of material creep damage.Therefore profit can directly be determined the Probabilistic damage diagram of high temperature pipe in this way.

(3) accurate high efficiency computing method

Property of probability in the high-temperature creep injury of metal material has obtained material test to be proved, conventionally researchist determines by lot of experiments on the basis of probability statistics character of associated materials parameter, has set up some corresponding creep probability models.Usually adopt at present FOSM, the methods such as Monte Carlo are calculated creep damage failure probability.

Owing to not only only having normal distribution in the probability parameter of creep impairment and also having many kinds of skewed distribution, therefore adopt FOSM more difficult.And Monte Carlo method is because its method is easy, can be easily for the analog simulation problem of the probability model that contains stochastic variable under different distributions, in addition, because the method has feature insensitive to integration dimension and that be easy to application.In engineering, be widely applied.But because its counting yield is lower, therefore, calculating for creep impairment probability model, particularly, for some complicated models, will spend many computing times.Therefore, how improving counting yield is an important problem, and conventional method has selective sampling method and stratified sampling method at present.But these two kinds of method limitation are larger, therefore propose to be applicable to high temperature pipe creep damage failure method for calculating probability below.

(3.1) Importance Sampling Method

Paper Importance Sampling Method, this method the most important thing is how to choose Importance Sampling Function, to take another kind of distribution to make simulation have some to lay particular stress on (making creep damage failure increased frequency), thisly be distributed in outstanding above formula of when sampling the part to integral contribution maximum in integrand, for fear of deviation is introduced to end product, finally to revise.Computing formula is as follows:

$P_f=\frac{1}{t}{\∫}_0^{t}h\left(a\right)\underset{i=1}{\overset{k}{\mathrm{\Π}}}\frac{f\left(a\right)}{f_i\left(a\right)}{f}_i\left(a\right)\mathrm{da}......\left(3.1\right)$

In formula: f (a) is the probability density function of former problem; f _i(a), (i=1 ..., k) be the probability density function of selective sampling.

So computing formula of selective sampling:

$P_f=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}h\left(a_i\right)\underset{i=1}{\overset{k}{\mathrm{\Π}}}\frac{f\left(a_i\right)}{f_j\left(a_i\right)}......(3.2)$

The selection principle of Importance Sampling Function is that can make has a large amount of observed readings in h (a) value interval.And f (x)/f ₁(x) be compared to different x values, its fluctuation is not too large.

As can be seen from the above, select Importance Sampling Function will meet two conditions:

(1) can in h (a) value interval, there is a large amount of observed readings.

(2) reduce f (x)/f as far as possible ₁(x) fluctuation of ratio under different x values.

From above-mentioned selection Importance Sampling Function principle, the method for choosing Importance Sampling Function is a lot.For convenience's sake, a kind of method using former probability density function to dangerous direction translation as the Importance Sampling Function of creep impairment probability calculation will be adopted below.

For creep impairment probability failure model:

$\stackrel{\·}{D}={\mathrm{Bt}}^{-m}\frac{{\mathrm{\σ}}_{\mathrm{eq}}^r}{{(1-D)}^k}......\left(3.3\right)$

T: expression time; B, m, k, r: be under fixed temperature by experiment determined material constant; σ _eq: equivalent stress.Above-mentioned parameter is stochastic variable.

According to the requirement of above-mentioned selection Importance Sampling Function, in this model, choose equivalent stress as selective sampling variable.By analysis and comparison, can determine the distance to a standard deviation of stress augment direction translation original function, as the average of this Importance Sampling Function, and variance is constant.Result of calculation shows, in the situation that be less than 10% with the relative error of Monte Carlo direct sampling result of calculation, sampling number, by 10000 times of direct sampling Monte Carlo method, is reduced to 1000 simulations of importance Monte Carlo method sampling.That is to say 1/10 workload that only need to use direct sampling method.

(3.2) layered sampling method

Stratified sampling method is that another kind is usually used in improving sampling efficiency method, its basic thought is to make integrated value contribute large territorial sampling more to have more now, its Sampling Strategies is not change original probability distribution, but sampling interval is divided into some minizones, number of sampling points in each minizone determines according to contribution, make to contribute large sampling more to have more to integrated value existing, to improve sampling efficiency.

Consider integration:

$I=\underset{0}{\overset{l}{\∫}}f\left(x\right)\mathrm{dx}......\left(3.4\right)$

By an a for integrating range [0,1] _i(i=0,1,2 ..., m) being divided into m mutually disjoint sub-range, its length is respectively:

l _i=a _i-a _i-1,(i=1,2,…,m;a ₀=0,a _m=1)，

So

$I={\∫}_0^{l}f\left(x\right)\mathrm{dx}=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{\∫}_{a_{i-1}}^{a_i}f\left(x\right)\mathrm{dx}=\underset{i=1}{\overset{m}{\mathrm{\Σ}}}{I}_i......\left(3.5\right)$

By the mean value estimation technique, ask each minizone [a _i-1, a _i] numerical integration value I _i(i=1,2 ..., m).If know the contribution of each minizone sampling to integration I, just can determine frequency in sampling for its contribution, to those, contribute little region to sample less or unsample.Therefore just can reduce frequency in sampling, thereby improve sampling efficiency.

According to creep impairment probability model (3.3), take above-mentioned relevant layered sampling method into consideration.Select equivalent stress as stratified sampling variable, consider different interval different to the contribution of integration.Between some special section, for example, when Critical Damage value appears being greater than in the impairment value that the interval at stress value place calculates, can make this interval sample value needn't participate in calculating, directly making its creep impairment value is 1.It is 0 that otherwise some little stress are far not enough to make structure generation creep impairment to make creep impairment value.So just can effectively reduce frequency in sampling.

The formula that calculates failure probability value in the Monte Carlo method in each region is:

$P_f=\frac{\mathrm{nf}}{\mathrm{Num}};$

In formula: P _f: failure probability; Num: test number (TN).Nf: Failure count in experiment, its expression formula is as follows:

The scope that can not occur creep impairment in order to determine stress, suppose in the situation that the numerical value of other stochastic variable is enough to make the impairment value of creep impairment model enough large, and stress value still can not make impairment value be more than or equal to damage threshold value.

Consider that stochastic variable value is as follows:

Average+3 * the standard deviation of B=damage threshold value

Average+3 * the standard deviation of k=damage threshold value

Average-3 * the standard deviation of [D]=damage threshold value

According to above-mentioned formula, can release, when below equivalent stress is less than during formula value, can not there is the region of creep damage failure in (in small probability situation):

${\mathrm{\σ}}_{\mathrm{eq}}\≤{\left\{\frac{1-{(1-[D\left]\right)}^{k+1}}{(k+1)B\left(\frac{t^{1-m}}{1-m}\right)}\right\};}^{1/r}$

Otherwise, can define the region that equivalent stress (in large probability situation) can make structure generation creep rupture.

By said method, can be calculated under different time, equivalent stress can not surpass maximum (little) value of damage threshold.Therefore, just can the stratified sampling interval of reasonable arrangement to equivalent stress.

Last result of calculation shows, method in this paper can effectively reduce frequency in sampling.For example, when t=400, direct sampling method needs 10000 times, and stratified sampling method is with 4453 times.

(4) preventive maintenance and risk assessment

(4.1) preventive maintenance

In expense least model in maintenance cycle model, can adopt following two kinds of situations.

(a) periodic plan maintenance, the total maintenance cost in the unit interval is:

$C_T=\frac{C_P}{T_P}+C_c\frac{{\∫}_0^{T_P}(1-R\left(t\right))\mathrm{dt}}{T_P{\∫}_0^{T_P}R\left(t\right)\mathrm{dt}}......\left(4.1\right)$

In formula:

C _t: total maintenance cost in the unit interval; C _c: the expense of each correction maintenance; C _p: the expense of preventive maintenance.

(b) preventive maintenance:

$C_T=C_c\frac{1-R\left(T_p\right)}{{\∫}_0^{T_P}R\left(t\right)\mathrm{dt}}+C_P\frac{R\left(T_p\right)}{{\∫}_0^{T_P}R\left(t\right)\mathrm{dt}}......\left(4.2\right)$

The same above formula of parameter (4.1) wherein.

(4.2) venture analysis

High temperature pipe of power station road system reliability method for maintaining based on venture analysis is defined as follows,

R(t)=P _f(t)·C(t)

In above formula, R (t) represents risk; P _f(t) represent the failure probability of structure; C (t) represents the consequence that lost efficacy and produce.They are all the functions of time t.

Known according to above discussion, the failure probability of structure can be determined by the method for probability statistics.

But because C (t) is the assessment about failure consequence, involve the impact of politics, economy, humanistic environment, enterprise development etc. factors.Due to many analyses and the very difficult numeral of using simply of discriminant criterion.Therefore this can not represent with probabilistic method merely.But the consequence because structural failure produces, due to the restriction of objective condition, therefore also can be considered as a kind of uncertain factor, i.e. fuzzy factors.So can adopt in fuzzy mathematics the comprehensively method such as judge, expert judging to define this function.

At this moment risk R (t) is a problem that includes enchancement factor and these two kinds of uncertain factors of fuzzy factors.At hypothesis P _f(t) and in the separate situation of C (t).R (t) is an obedience and P _f(t) identical probability distribution f (x, t), the fuzzy random variable of the subordinate function m (x, t) identical with C (t).

Under the continuous condition of f (x, t), m (x, t), for a given time t, the calculation expression of risk is:

$R\left(t\right)=\underset{a}{\overset{b}{\∫}}m(x,t)\·f(x,t)\mathrm{dx}$

Above formula can adopt the integral algorithm of Fuzzy Reliability to solve.

But in the ordinary course of things, work as P _f(t) and C (t) be in the situation of known function, obtain the best servicing time based on risk assessment, be to solve an optimization problem,

$\underset{s.t}{\min }R\left(t\right)=P_f\left(t\right)\·C\left(t\right)$

Due to for different engineering problems, its C (t) difference, therefore will analyze as the case may be.

About above technical know-how knowledge, also can be with reference to Publication about Document:

(1) Zhang Xuhong. the Life Design of High Temperature High Pressure pipeline and the research of forecasting techniques. the Master's thesis .2002 of Nanjing University of Technology;

(2) Tu Shandong. high temperature structural integrity principle. Science Press .2003:369～423;

(3) Zhao Jie etc., based on R6 containing defect pressure piping fracture failure venture analysis system system – theory and method (I). petrochemical complex institution of higher education, 2002(15) 4:50～53;

(4) Zhao Jie etc., based on R6 containing defect pressure piping fracture failure venture analysis system system – theory and method (II). petrochemical complex institution of higher education, 2002(16) 5:61～64;

(5) Xie Yujun etc., containing the system – of defect pressure piping fracture failure venture analysis system based on PD6493 (I). petrochemical equipment .2002 (31) 4:4～7;

Power station piping system in Yi Mou company is that example describes method of the present invention below:

The steam line of certain steam turbine is carried out to stress analysis.This part pipeline connects boiler, steam turbine and ignition tube, ignition tube leads to steam turbine and steam main, and to the main steam line of ignition tube, (Φ 273 * 28, elbow radius R=1370mm), (Φ 133 * 14.2 to the connecting tube of ignition tube and partial firing pipe for main steam line, elbow radius R=600mm) and the female pipe of part (Φ 366.5 * 36, elbow radius R=1500mm).

Table 1 pipe design parameter and material parameter

1, high-temperature pipe structure creep Damage Analysis

First carry out finite element analysis, finite element model as shown in Figure 2.According to result of finite element, the most heavily stressed applied stress that there is no to surpass pipeline material at 540 ℃ of pipeline, therefore can safe operation.Match (place that needs to install creep monitoring point in design drawing) that the position part that wherein stress is higher and design drawing provide, the stress of pipe bent position is generally higher in addition, and creep monitoring point should be separately set.Note: the stress at support point place is higher is to be mainly reduced to point load because analyze the load at medium-height trestle place, and what actual conditions will be good is many.

By the high-temerature creep test findings of high-temperature pipe material 10CrMo910, can determine following creep impairment formula again:

${\stackrel{\·}{\mathrm{\ϵ}}}_c=B{\mathrm{\σ}}^n......\left(6.1\right)$

With:

$\stackrel{\·}{D}=A{\left(\frac{\mathrm{\σ}}{1-D}\right)}^P......\left(6.2\right)$

In material parameter.

B:7.488×10 ^-22；n:8.3704；A:2.071×10 ^-19；p:7.27166；

σ: equivalent stress, according to FEM (finite element) calculation, determine.Wherein, the maximum stress of bend pipe is 35.2MPa.

And according to the calculating of structure creep stress, the equivalent stress of bend pipe is 28.16MPa.

2, the CALCULATION OF FAILURE PROBABILITY of high temperature pipe

According to above-mentioned analysis, in conjunction with reference to pertinent literature, can determine the distribution situation of stochastic variable, order:

A obeys logarithm normal distribution, the coefficient of variation is 0.05;

P Normal Distribution, the coefficient of variation is 0.05;

σ Normal Distribution, the coefficient of variation is 0.1;

D _crlimit impairment parameter Normal Distribution, average is 0.417, the coefficient of variation is 0.1.

Adopt Monte Carlo direct sampling method to calculate (computing method are shown in that second portion is described above), frequency in sampling is 10 ⁷inferior.Result of calculation is in Table 2.

The failure probability of table 2 bend pipe creep impairment

Year	Failure probability	Year	Failure probability
				1	6.000e-7	9	1.406e-4
2	2.700e-6	10	1.804e-4
				3	7.700e-6	11	2.299e-4

4	1.560e-5	12	2.780e-4
				5	2.830e-5	13	3.390e-4
6	4.830e-5	14	4.037e-4
				7	7.390e-5	15	4.790e-4
8	1.080e-4

For serviceability method for maintaining computing formula more easily, above-mentioned result of calculation is brought in the equation of linear regression of least square method (concrete grammar sees above face portion), can obtain the fitting parameter under Weibull, normal state and lognormal distribution.

Table 3 bend pipe computational data Fitted probability distribution parameter result

Distribution property	Distribution parameter	Related coefficient
			Weibull distribution	M＝2.5288，η＝3.0639e2	0.9994
Normal distribution	μ＝43.3091，σ＝9.2063	0.9583
			Lognormal distribution	μ’＝8.2860，σ’＝1.6755	0.9974

3, Reliability Maintenance method is calculated

In upper table 6.3, maximum with the related coefficient in the fitting result of Weibull distribution, fitting effect is best.The feature good according to Weibull Distribution data, and often adopt in engineering.Therefore, adopt Weibull distribution as this structure creep impairment Reliability Function here,

$R\left(t\right)=\exp (-{\left(\frac{t}{\mathrm{\η}}\right)}^m)......\left(6.3\right)$

In the expense least model in maintenance cycle model, be divided into two kinds of situations.

(1) periodic plan maintenance, the total maintenance cost in the unit interval is:

$C_T=\frac{C_P}{T_P}+C_c\frac{{\∫}_0^{T_P}(1-R\left(t\right))\mathrm{dt}}{T_P{\∫}_0^{T_P}R\left(t\right)\mathrm{dt}}......\left(6.4\right)$

In formula,

C _t: total maintenance cost in the unit interval; C _c: the expense of each correction maintenance; C _p: the expense of preventive maintenance.

(2) preventive maintenance:

$C_T=C_c\frac{1-R\left(T_p\right)}{{\∫}_0^{T_P}R\left(t\right)\mathrm{dt}}+C_P\frac{R\left(T_p\right)}{{\∫}_0^{T_P}R\left(t\right)\mathrm{dt}}......\left(6.5\right)$

The same above formula of parameter (6.4) wherein.

Due to correction maintenance and the unknown of preventive maintenance expense, suppose preventive maintenance expense C below _pwei Yige unit, considers respectively correction maintenance expense and preventive maintenance expense ratio, C _c/ C _pin=6,11,16 situation, the total maintenance cost calculating.

After work 100000 hours, failure probability is 1.804e-4.Use above-mentioned two kinds of methods to calculate, the results are shown in Table 4.

Table 4 is in total maintenance cost of 100,000 hours back elbows of work

C c/C p	Periodic plan maintenance	Preventive maintenance
			1	0.08761	0.08761
6	0.08764	0.08771
			11	0.08767	0.08782
16	0.08797	0.08793

In above-mentioned calculating, all considered the maintenance of pipeline after breaking down and there is no the preventative maintenance situation under a situation arises.But carry out after real time on-line monitoring sensor has been installed, can, the expense of keeping in repair again after breaking down in the past, reduce and become the expense that preventative maintenance will spend.

Namely realized at C _c/ C _p=1 o'clock, repair.By table 4, can be seen, maintenance cost is minimum in all kinds of maintenance costs.

Same according to the calculating of result of finite element and relevant creep stress, the equivalent stress that obtains straight tube is 22MPa, and its coefficient of variation is 0.1.Other parameter is the same, and calculation procedure is identical.The work that finally obtains is after 100000 hours, and failure probability is 4.2e-7.Maintenance cost sees the following form.

Table 5 is in total maintenance cost of work straight tube after 100,000 hours

C c/C p	Periodic plan maintenance	Preventive maintenance
			1	0.0876002	0.0876002
6	0.0876003	0.0876005
			11	0.0876004	0.0876009
16	0.0876005	0.0876012

4, based on the definite method for maintaining of risk assessment technology

After the related data obtaining by on-the-spot online detection instrument, then by after finite element analysis and above-mentioned method for maintaining computational analysis.Can calculate in certain time period, pipeline has the failure probability value of two place's fault locations.For example at straight tube place, there is individual defective locations 1, in pipe bent position, have individual defect 2.According to related data, can calculate the failure probability value at corresponding site place.

Defect 1 place, failure probability value is 1.2 * 10 ^-6;

Defect 2 places, failure probability value is 1.0 * 10 ^-6.

While using FEM (finite element) calculation again, find that stress concentration phenomenon occurs at this place.

According to the characterizing method of risk:

R=P _f·C

In formula, R is value-at-risk; P _fit is failure probability; C is the consequence that failure event occurs.

Consider the consequence causing due to inefficacy below, will mainly consider (1) economic loss; (2) damage that cause material at this position; (3) impact that corrosion causes.

Consider the economic loss factor that this pipe fitting lost efficacy and causes, give minutes 10 minutes, be divided into unacceptable loss (10～6.5), heavy losses (6.4～3.5) and can accept to lose (3.4～0) three standards.

Material is caused to damage, need to consider whether inside configuration has stress to concentrate and wait energy accelerating structure Failure Factors phenomenon.Be divided into equally Three Estate, major injury (10～6.5), general damage (6.4～3.5), can ignore damage (3.4～0).

Corrosion condition is divided into three grades, seriously corroded (10～6.5), general corrosion (6.4～3.5), slight corrosion (3.4～0).

Definition failure consequence is evaluated as:

C=C ₁·C ₂·C ₃

First the damage at pipeline position is evaluated:

Table 6 straight tube position parameters data

C 1Economic loss	C 2Material damage	C 3Corrosion condition	C
				5	3	1	15

The damage at bend pipe position is evaluated, consider in calculating with finite element simulation and find that there is region of stress concentration, and this defect of finding is just on region of stress concentration by detecting, due to special shape and this pipe fitting external environment condition of bend pipe, discovery corrosion condition is serious.Therefore evaluation situation is as follows.

Table 7 bend pipe position parameters data

C 1Economic loss	C 2Material damage	C 3Corrosion condition	C
				5	10	8	400

Last risk assessment is:

Pipeline place defect: R=P _fc=1.2 * 10 ^-6* 30=3.6 * 10 ^-5

Pipe bent position defect risk assessment:

R=P _f·C=10 ^-6×400=4×10 ^-4

Consider that such Pipeline Failure form mostly shows as toughness and tears inefficacy.According to risk assessment table 6.8, physical construction can be converted into minimax risk criterion failure probability, as shown in the table.

Table 8 physical construction SI recommendation tables

RELIABILITY INDEX	3.71	4.26	4.75
				Probable range	10 -4	10 -5	10 -6
Failure consequence	Not serious	Seriously	Very serious

Because pipeline failure consequence is not serious, therefore can use failure probability 10 ^-4, as the standard of needing repairing.According to above-mentioned result of calculation, the risk assessment of pipe bent position defect is above standard, therefore need to keep in repair immediately.

From above institute's discussion method and example, the method applied in the present invention, can detect the situation that judges high-temperature pipe effectively, in real time, determines whether to need repairing, and therefore can extend round of visits.

Adopted the method for above-mentioned High temperature pipe of power station road system maintenance method, owing to wherein having adopted the method for determining stray parameter in non-probability theory, therefore can be for utilizing low volume data to determine parameters stochastic distribution character lacking in mass data situation, and utilize two kinds of MC methods that high-level efficiency is calculated that have that are applicable to high-temperature pipe creep impairment problem, and adopted the method for maintaining of Reliability Maintenance theoretical method in conjunction with the high-temperature pipe damage problem of risk assessment technology, thereby only utilize a small amount of information just can predict comparatively accurately piping system integrity problem, realized and efficiently and exactly determined structural reliability, accurately determine maintenance program, it is specially adapted to enterprise in a series of implementation methods of formulating high temperature pipe structural reliability maintenanceization, and can solve the method for maintaining of the high temperature pipe phase class problem in other field, thereby the scope of application is comparatively extensive.

Claims (6)

1. the High temperature pipe of power station road system maintenance method based on non-probabilistic reliability theory, is characterized in that: comprise the following steps:

S1 carries out the FEM (finite element) calculation of High temperature pipe of power station road system, according to the place of maximum stress, determines emphasis monitoring position;

S2 arranges fixation of sensor at keypoint part, adopts the collection of infrared thermal imaging monitoring instrument to obtain the detection data of high temperature pipe system;

S3 is theoretical according to non-probabilistic reliability, determines the stray parameter of the creep impairment of High temperature pipe of power station road system;

S4 sets up the creep impairment probability model of High temperature pipe of power station road system, calculates the structural failure probability of high temperature pipe system;

S5 is according to the creep damage failure probability of High temperature pipe of power station road system, computation structure fail result;

S6, according to the detection data of the result of calculation of step (5), pipeline, material and structural test result, sets up the method for maintaining model based on fail-safe analysis;

S7 is according to the method for maintaining models coupling risk assessment of gained, obtains High temperature pipe of power station road system best servicing time.

2. the High temperature pipe of power station road system maintenance method based on non-probabilistic reliability theory according to claim 1, is characterized in that: described step S3 comprises following content:

According to the non-probability model of following Formula creep impairment:

$\stackrel{\·}{D}={\mathrm{Bt}}^{-m}\frac{{\mathrm{\σ}}_{\mathrm{eq}}^r}{{(1-D)}^k};$

Wherein, t is the time; B, m, k, r be under fixed temperature by experiment determined material constant; σ _eqfor equivalent stress, and above-mentioned each parameter is stochastic variable;

Above-mentioned stochastic variable will adopt the method in non-probabilistic reliability theory to define:

First according to engineering reality, easily determine the minimum and maximum value of above-mentioned parameter, obtain following interval number:

$[\underset{\_}{B},\stackrel{\_}{B}],[\underset{\_}{m},\stackrel{\_}{m}],[\underset{\_}{k},\stackrel{\_}{k}],[\underset{\_}{r},\stackrel{\_}{r}],[{\underset{\_}{\mathrm{\σ}}}_{\mathrm{eq}},{\stackrel{\_}{\mathrm{\σ}}}_{\mathrm{eq}}];$

As follows according to the average of interval number defined parameters and standard deviation and the coefficient of variation:

$B_c=\frac{\stackrel{\_}{B}+\underset{\_}{B}}{2},B_D=\frac{\stackrel{\_}{B}-\underset{\_}{B}}{2},{\mathrm{cov}}_B=\frac{B_D}{B_c};$

$m_c=\frac{\stackrel{\_}{m}+\underset{\_}{m}}{2},m_D=\frac{\stackrel{\_}{m}-\underset{\_}{m}}{2},{\mathrm{cov}}_m=\frac{m_D}{m_c};$

$k_c=\frac{\stackrel{\_}{k}+\underset{\_}{k}}{2},k_D=\frac{\stackrel{\_}{k}-\underset{\_}{k}}{2},{\mathrm{cov}}_k=\frac{K_D}{k_c};$

$r_c=\frac{\stackrel{\_}{r}+\underset{\_}{r}}{2},r_D=\frac{\stackrel{\_}{r}-\underset{\_}{r}}{2},{\mathrm{cov}}_r=\frac{r_D}{r_c};$

${\mathrm{\σ}}_{\mathrm{eqc}}=\frac{{\stackrel{\_}{\mathrm{\σ}}}_{\mathrm{eq}}+{\underset{\_}{\mathrm{\σ}}}_{\mathrm{eq}}}{2},{\mathrm{\σ}}_{\mathrm{eqD}}=\frac{{\stackrel{\_}{\mathrm{\σ}}}_{\mathrm{eq}}-{\underset{\_}{\mathrm{\σ}}}_{\mathrm{eq}}}{2},{\mathrm{cov}}_{\mathrm{\σ}}=\frac{{\mathrm{\σ}}_{\mathrm{eqD}}}{{\mathrm{\σ}}_{\mathrm{eqc}}};$

It is B that definition above-mentioned parameter is respectively average _c, m _c, k _c, r _c, σ _eqc; Standard deviation is B _d, m _d, k _d, r _d, σ _eqD; The coefficient of variation is cov _b, cov _m, cov _k, cov _r, cov _σstochastic distribution, stochastic distribution character is chosen according to the principle of being partial to security.

3. the High temperature pipe of power station road system maintenance method based on non-probabilistic reliability theory according to claim 1, is characterized in that: described step S4 comprises following sub-step:

S4-1 selects the corresponding equivalent stress of regional of described High temperature pipe of power station road system as stratified sampling variable;

If the equivalent stress σ that S4-2 is described _eqmeet following formula, this equivalent stress σ _eqfor can there is not the region of creep damage failure in corresponding region:

${\mathrm{\σ}}_{\mathrm{eq}}\≤{\left\{\frac{1-{(1-[D\left]\right)}^{k+1}}{(k+1)B\left(\frac{t^{1-m}}{1-m}\right)}\right\}}^{1/r};$

Wherein, B, D, k are stochastic variable, and:

Average+3 * the standard deviation of B=damage threshold value;

Average+3 * the standard deviation of k=damage threshold value;

Average-3 * the standard deviation of [D]=damage threshold value;

If the equivalent stress σ that S4-3 is described _eqmeet following formula, this equivalent stress σ _eqfor there is the region of creep damage failure in corresponding region:

${\mathrm{\σ}}_{\mathrm{eq}}>{\left\{\frac{1-{(1-[D\left]\right)}^{k+1}}{(k+1)B\left(\frac{t^{1-m}}{1-m}\right)}\right\}}^{1/r};$

S4-4, in there is the region of creep damage failure, utilizes layered sampling method to calculate failure probability P based on Monte Carlo method and by following formula _f:

$P_f=\frac{\mathrm{nf}}{\mathrm{Num}};$

Wherein, Num is test number (TN), and nf is the number of times losing efficacy in test, meets following relation:

The nonlinear degree that reduces data adopts the data mode of taking the logarithm.

4. the High temperature pipe of power station road system maintenance method based on non-probabilistic reliability theory according to claim 1, is characterized in that: described step 5 comprises the following steps:

First adopt the common Weibull of least square fitting, normal state and lognormal probability distribution function, therefrom select the method for immediate probability distribution function, set up the creep impairment probability model of comparatively accurate High temperature pipe of power station road system;

According to following Formula creep impairment probability model:

$\stackrel{\·}{D}={\mathrm{Bt}}^{-m}\frac{{\mathrm{\σ}}_{\mathrm{eq}}^r}{{(1-D)}^k};$

Wherein, t is the time; B, m, k, r be under fixed temperature by experiment determined material parameter; σ _eqfor equivalent stress, above-mentioned parameter is stray parameter.Its random nature defines definite by non-probabilistic reliability interval number.And creep impairment value is also stray parameter.

According to creep impairment probability model, calculate the structural failure probability of High temperature pipe of power station road system and determine failure probability:

If described equivalent stress σ _eqmeet following formula, this equivalent stress σ _eqfor can there is not the region of creep damage failure in corresponding region:

σ _eq≤[σ] _max；

Wherein, B, D, k are interval number, and [σ] _maxfor maximal value in the interval function of following formula equal sign the right:

${\left[\mathrm{\σ}\right]}_{\max }={\left\{\frac{1-{(1-[D\left]\right)}^{k+1}}{(k+1)B\left(\frac{t^{1-m}}{1-m}\right)}\right\}}^{1/r}$

If described equivalent stress σ _eqmeet following formula, this equivalent stress σ _eqfor there is the region of creep damage failure in corresponding region:

σ _eq＞[σ] _max；

In order to obtain immediate creep impairment stochastic distribution, will adopt equation of linear regression from normal state, lognormality and Weibull distribution, to select the method for best distribution;

The Weibull distribution method of wherein determining pipeline creep impairment comprises the following steps:

According to following formula, determine the cumulative risk function of prediction

$\hat{H}\left(t_k\right)=\underset{i=1}{\overset{k}{\mathrm{\Σ}}}\frac{1}{n+1-i};$

Wherein, t _kfor failure event time of origin, n is the total number of times of generation event, wherein also comprises the event that there is no inefficacy, and the inefficacy of each product is t by ascending sequence constantly ₁≤ t ₂≤ ...≤t _n;

According to following formula, in conjunction with the result of calculation of Larson-Miller method, determine the unreliable degree function F (t) based on Weibull probability distribution function:

F(t _rex/t _res)=1-exp{-(t _rex/t _resη) ^m}；

Wherein, t _rex/ t _resfor the ratio of test life with the life-span of using accordingly Larson-Miller method formula to calculate, m is form parameter, and η is scale parameter; Brief note t=t _rex/ t _res, its probability distribution function is designated as:

F(t)=1-R(t)=1-exp{-H(t)}；

According to following formula, determine the regression equation of cumulative risk function:

H(t)=(t/η) ^m；

lnH(t)=mlnt-mlnη

Wherein, m, η are the determined parameter of equation of linear regression;

According to equation of linear regression y _i=a+bx _i, and according to following formula, determine the parameter of Weibull Function:

m=b

$\mathrm{\η}=\exp \{-\frac{a}{m}\};$

Thereby set up corresponding Weibull probability life-span distribution function.

5. the High temperature pipe of power station road system maintenance method based on non-probabilistic reliability theory according to claim 1, is characterized in that: described step S6 is specially:

According to following Formula periodic plan Maintenance Model:

$C_T=\frac{C_P}{T_P}+C_c\frac{{\∫}_0^{T_P}(1-R\left(t\right))\mathrm{dt}}{T_P{\∫}_0^{T_P}R\left(t\right)\mathrm{dt}};$

Wherein, C _tfor total maintenance cost in the unit interval; C _cexpense for each correction maintenance; C _pexpense for preventive maintenance; Or, according to following Formula preventive maintenance model:

$C_T=C_c\frac{1-R\left(T_p\right)}{{\∫}_0^{T_P}R\left(t\right)\mathrm{dt}}+C_P\frac{R\left(T_p\right)}{{\∫}_0^{T_P}R\left(t\right)\mathrm{dt}};$

Wherein, C _tfor total maintenance cost in the unit interval; C _cexpense for each correction maintenance; C _pexpense for preventive maintenance.

6. the High temperature pipe of power station road system maintenance method based on non-probabilistic reliability theory according to claim 1, is characterized in that: described step S7 comprises following sub-step:

S7-1 determines the risk R (t) of High temperature pipe of power station road system according to following formula:

$R\left(t\right)=\underset{a}{\overset{b}{\∫}}m(x,t)\·f(x,t)\mathrm{dx};$

Wherein, R (t)=P _f(t) C (t), P _f(t) be the failure probability of structure, the consequence of C (t) for losing efficacy and producing, it is all the function of time t; P _f(t) and C (t) separate, and R (t) is fuzzy random variable, f (x, t) is R (t) and P _f(t) the identical probability distribution of obeying, m (x, t) is the identical subordinate function that R (t) has with C (t), f (x, t) and m (x, t) are all continuous;

S7-2 utilizes linear programming algorithm by following formula, to calculate best servicing time of the t of described High temperature pipe of power station road system:

$\underset{s.t}{\min }R\left(t\right)=P_f\left(t\right)\·C\left(t\right);$

Wherein,

the best servicing time of high temperature pipe is obtained in expression with linear programming algorithm to function R (t).

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