CN105426692A - Ocean platform multi-stage task system reliability estimation method based on data drive - Google Patents

Abstract

The invention relates to an ocean platform multi-stage task system reliability estimation method based on data drive. The estimation method mainly includes the steps that a multi-stage task process model is established, and a probability density function of task time is estimated; a system degenerative process model is established, and the residual life is estimated; according to the reliability definition of the multi-stage task process model and the system degenerative model, system reliability parameter values are obtained through real-time calculation through the task time estimated value and the system service life estimated value. Through measured sensor data, the relation between historical data of an individual multi-stage task system and current real-time data information is established, reliability parameters of the multi-stage task system under the dynamic condition are accurately estimated in real time, and the problem that an existing method is only suitable for static hypothesis and a specific system is solved. The reliability parameters of the ocean platform multi-stage task system are accurately estimated in real time, the system is effectively maintained in real time, the maintenance cost of the system is reduced, and catastrophic faults are effectively avoided.

Description

Based on the ocean platform phased mission systems reliability estimation methods of data-driven

Technical field

The invention belongs to reliability engineering technique field, specifically, relate to a kind of ocean platform phased mission systems reliability estimation methods.

Background technology

Ocean platform is the complex apparatus system for completing offshore and gas development work, usually, this kind of complication system of ocean platform needs through multiple stage when completing particular task, and the degradation characteristics in each stage is different, in existing literature research achievement, this type systematic is called as phased mission systems.The basic characteristics of phased mission systems are: continuous, each stage non-overlapping in multiple, stage.Within different consecutive hours intervals (i.e. stage), the phased mission that system completes is different, so the structural reliability in system each stage is also different.For ocean platform system, it completes offshore and gas development work need experience several stages such as offshore platform is built, drilling well, pressure break, running casing, oil recovery, only has the Mission Success in all stages reliably to complete finally completing of guarantee system task.

In complication system, reliability is one of of paramount importance index parameter in system, operation and maintaining process, be one for weighing the Important Parameters of engineering system performance.Therefore, the accurate estimation of ocean platform phased mission systems reliability for the maintenance of system and maintenance very important, system maintenance cost can be reduced to a certain extent, effectively the generation of averting a calamity property fault.

For the reliability estimation problem of this kind of phased mission systems of ocean platform, main employing Fault Tree Analysis and the method based on binary decision diagrams (bdds) in existing achievement in research, but the structure that these methods too rely on phased mission systems is known, but in fact, in engineer applied phased mission systems usually due to too complicated and be difficult to the complete structural information of Obtaining Accurate.For ocean platform, ocean platform at sea works, the interference such as random wave, tide, ocean current, floating ice, earthquake, corrosion is many, the non-intellectual in down-hole is strong, working environment is extremely complicated and uncertain, its mechanism dynamic model is difficult to accurately set up in advance, which dictates that its complete structural information can not Obtaining Accurate.Thus, above-mentioned two class main method are very limited in the application, thus are difficult to the reliability effectively accurately estimating system.On the other hand, under existing method is only applicable to static assumed condition, be a kind of off-line method in essence, contacting between reliability and history observation data and current Real-time Monitoring Data cannot be set up, be not useable for the dynamic estimation of system reliability.So, existing method is adopted to be difficult to estimate exactly the reliability of phased mission systems, thus cannot the fault of prognoses system effectively, and any little potential faults all may develop into large accident, cause the accidents such as the blowout of ocean platform, fire, blast, leakage of oil to occur, cause platform to damage, tilt or topple.Therefore, solution is estimated in the urgent need to seeking a kind of new phased mission systems reliability prediction.

Along with the development of infotech, ocean platform great majority are all equipped with data acquisition and transmission system, can physical quantity on Real-time Collection ocean platform, as voltage, electric current, crude oil temperature, the data such as polished rod load and displacement of motor.But these data only for simply detecting and form, lacking the data mining that manufacturing-oriented security monitoring and reliability prediction etc. are profound, thus causing the waste of resource at present.For this reason, these a large amount of sensor data information are that the reliability prediction of ocean platform multistage negotiation task system is estimated to provide a potential solution route.

Summary of the invention

The object of the invention is to the above-mentioned defect and the deficiency that overcome prior art existence, provide a kind of ocean platform phased mission systems reliability estimation methods based on data-driven, the method adopts the sensing data observed, build the relation between historical data information and current real-time information, accurately estimate in real time phased mission systems reliability parameter under dynamic condition, solve the problem that existing method is only applicable to static assumed condition.

According to one embodiment of the invention, provide a kind of ocean platform phased mission systems reliability estimation methods based on data-driven, the steps include:

Detected by the environment of sensor to system, the system environments Monitoring Data that comprehensive utilization sensor is observed, set up contacting between the historical data of individual phased mission systems and current real-time data information, stochastic filtering model is adopted to carry out modeling to stage interval, obtain phased mission system process model, estimate the probability density function of task time, obtain estimated value task time of phased mission systems.

Fusion application historical data information, sets up phased mission systems degenerative process model, estimates the life-span of phased mission systems, obtains the life estimation value of phased mission systems.

According to the reliability definition of phased mission system process model and phased mission systems degenerative process model, comprehensive utilization estimated value task time and life estimation value calculate the reliability reference value of phased mission systems in real time.

According in the method for estimation of the embodiment of the present invention, set up phased mission system process model and estimate that the concrete steps of probability density function of task time are: suppose that ocean platform offshore and gas development task has N number of stage, make stochastic variable X _nrepresent the n-th phase duration, its span is make stochastic variable T _mrepresent the T.T. of completion system overall tasks, and have order for each stage X _n, the probability density function of n=1, L, N, wherein 2≤n≤N; Make Φ _i,nrepresent cut-off current time t _ithe environmental monitoring data information aggregate corresponding with the n-th stage; Adopt probability density function task time in environmental monitoring data estimation of the order 1 ~ N each stage.

According in the method for estimation of the embodiment of the present invention, the n-th phase process modeling and task time PDF estimation step be: suppose to get current time t by sensor _ithe environmental monitoring data information φ in lower n-th stage _i,n, make L _i,nrepresent t _ithe residue continuous time in stage in moment n-th, then through type L _{i+1, n}=L _i,n-(t _i+1-t _i), (if L _i,n> t _i+1-t _i) residue L continuous time of the n-th stage subsequent time can be obtained _{i+1, n}, L _{0, n}represent the residue continuous time of first stage; The consecutive hours area of a room considering task time always on the occasion of, utilize transform Z _i,n=lnL _i,n, obtain a process variable Z _i,n, to ensure L _i,n> 0, adopts a sliding scales parameter to set up φ _i,nand L _i,nstochastic relation model between the two, thus by φ _i,nestimate L _i,n, make φ _i,nbe expressed as Z _i,nfunction, set up the n-th phase process model as follows:

Z _i,n＝lnL _i,n(1)

φ _i,n＝g _n(Z _i,n)+η _i,n

Wherein, g _n(Z _i,n) be a function undetermined, it is described that the relation between task process and the environmental monitoring data corresponding with the stage; η _i,nthe measuring error of a Normal Distribution, and

Adopt extended Kalman filter to estimate or upgrade Z _i,nconditional probability density function, and ask for further residue continuous time L _i,n; Definition Z _i,nand Z _{i+1, n}renewal amount and one-step prediction conditional probability density function amount be respectively Z _i,n| Φ _i,n: N (z _{i|i, n}, P _{i|i, n}) and Z _{i+1, n}| Φ _i,n: N (z _{i+1|i, n}, P _{i+1|i, n}), parameter z here _{i|i, n}, P _{i|i, n}, z _{i+1|i, n}and P _{i+1|i, n}can be calculated by extended Kalman filter algorithm, its computing formula is as follows:

z _i|i,n＝z _i|i-1,n+K _i,n[φ _i,n-g _n(z _i|i-1,n)](2)

Wherein, K _i,nrepresent the gain battle array of Kalman filtering, obtained by following formula:

Wherein

Correspondingly, the renewal equation of state estimation variance matrix can be obtained by following formula:

P _i|i,n＝P _i|i-1,n(1-K _i,ng′ _n(z _i|i-1,n))(4)

The initial parameter z of extended Kalman filter algorithm _{0|0, n}and P _{0|0, n}estimated to obtain by historical data.

Calculation expectation z is needed in the renewal equation of above-mentioned state estimation variance matrix _{i|i-1, n}with variance P _{i|i-1, n}a step estimated value, consider Z _i,n| Φ _i,n: N (z _{i|i, n}, P _{i|i, n}), and Z _i,n=lnL _i,n, obtain these two amounts by lower two formulas:

Consider the transformational relation of normal distribution and lognormal distribution, have L _{i, 1}| Φ _{i, 1}: lnN (z _{i|i, 1}, P _{i|i, 1}), then based on model expression, obtain and expect z _i|i-1,1with amount of variation P _i|i-1,1expression formula:

P _i|i-1,n＝P _i-1|i-1,n(8)

By above-mentioned renewal expression formula, obtain the estimated probability density function that the first stage remains continuous time for

Again because of

Then directly obtain X by correspondent transform _nat t _ithe distribution in moment

Wherein, calculated by formula (9).

Thus, corresponding to t _imoment and X ₁subordinate phase duration probability density function expression formula under condition is

Similarly, corresponding to t _imoment and X _npostorder under condition each phase duration probability density function expression formula is

Wherein s=n+1 ..., N.

Further, have then task time T _mdistribution function be

At moment t _mprobability density function task time formula (14) differential process being obtained to the n-th stage is

So far, the environmental monitoring data information of being correlated with by the current generation obtains estimator task time in this stage.

According in the method for estimation of the embodiment of the present invention, Wiener-Hopf equation is used to set up phased mission systems degenerative process model, the concrete steps setting up phased mission systems degenerative process model are: assuming that the initial reading of degenerative process is Y (0)=0, if initial time is t _i(i=1,2 ..., N), then the monitored parameters evolution process model of time correlation is

Y(t)＝y _i+λ(t-t _i)+σB(t-t _i)(16)

Further, consider fusion application historical data information, in model, λ develops into dynamic parameter, uses λ _i=λ _i-1+ η replaces, and wherein η ~ N (0, Q), then degradation model is reconstructed into

Wherein ε _i~ N (0, t _i-t _i-1), λ _iestimated value can be obtained by Kalman filtering algorithm.

λ is obtained by Gaussian distribution hypothesis and Bayesian filter principle _iprobability density function be

The life-span of equipment is defined by the concept of first-hitting time, when the degradation values Y (t) that formula (16) is determined reaches the failure threshold w preset first, just thinks equipment failure; By the time that the timing definition that equipment life stops is degenerative process Y (t) First excursion failure threshold w, then equipment t _ithe remaining life S in moment _ibe defined as:

S _i＝inf{s _i:Y(s _i+t _i)≥w|Y _i}(19)

Order for the cumulative distribution function of remaining life, predict t by degradation model formula (17) _ithe degeneration probability density function in moment consideration model profile is normal distribution, has Y (s _i+ t _i) | Y _i: then t _iprobability density function and the cumulative distribution function of the life expectancy of moment phased mission systems are respectively:

According in the method for estimation of the embodiment of the present invention, obtain λ by Kalman filtering algorithm _ithe step of estimated value be:

Initialization p ₀;

T _ithe state estimation in moment is

P _i|i-1＝P _i-1|i-1+Q

K _i＝(t _i-t _i-1) ²P _i|i-1+σ ²(t _i-t _i-1)；

Upgrade

According in the method for estimation of the embodiment of the present invention, obtain the life-span probability density function of task system with probability density function task time after, according to the reliability definition of phased mission system process model and phased mission systems degenerative process model, estimate t _ithe reliability of moment phased mission systems, the probability obtaining the reliability parameter of the n-th stage fill is

The estimation of the reliability parameter value of ocean platform complex phased mission systems can be completed based on formula (21) and (22).

The ocean platform phased mission systems reliability estimation methods based on data-driven that the present invention proposes, adopt observe sensing data, by setting up contacting between the historical data of individual phased mission systems and current real-time data information, accurately estimate in real time the reliability parameter of phased mission systems under dynamic condition, not only solve the reliability estimation problem of individual phased mission systems, the reliability also completing system under dynamic condition is estimated.Existing method cannot utilize real-time information, be only applicable to static assumed condition and particular system, compared with the conventional method, by the ocean platform phased mission systems reliability estimation methods based on data-driven according to the embodiment of the present invention, accurately can estimate the reliability parameter of this kind of phased mission systems of dynamic condition Offshore Platform Under, solve the problem that existing method is only applicable to static assumed condition, thus can effectively safeguard system in time, for the maintenance of system and the determination of repair part ordering strategy provide theoretical foundation and the technical support of power, reduce the maintenance cost of system, the effectively generation of averting a calamity property fault, engineer applied is worth high.

Embodiment

Embodiments of the present invention is further illustrated below.

In order to without loss of generality, for ocean platform three stage fill, according to a kind of ocean platform reliability estimation methods based on data-driven of the embodiment of the present invention, the steps include:

Step one: detected by the environment of sensor to system, the system environments Monitoring Data that comprehensive utilization sensor is observed, set up contacting between the historical data of individual three stage fill and current real-time data information, stochastic filtering model is adopted to carry out modeling to stage interval, obtain three phased mission process models, estimate the probability density function of task time, obtain estimated value task time of three stage fill further.

Suppose that ocean platform offshore and gas development task has 3 stages, make stochastic variable X _nrepresent (n=1,2, the 3) duration in the n-th stage, its span is make stochastic variable T _mrepresent the T.T. of completion system overall tasks, and have order for each phase duration X _n, n=1, the probability density function of 2,3; Make Φ _i,nrepresent cut-off current time t _ithe environmental monitoring data information aggregate corresponding with the n-th stage, adopts environmental monitoring data to estimate probability density function task time in each stage.

(1) first stage process model building and task time PDF estimation

Suppose to get current time t by sensor _ithe environmental monitoring data information φ of lower first stage _{i, 1}, make L _{i, 1}represent t _itime inscribe residue continuous time of first stage, then through type L _i+1,1=L _{i, 1}-(t _i+1-t _i), (if L _i+1,1> t _i+1-t _i) residue L continuous time of first stage subsequent time can be obtained _i+1,1.Further, the consecutive hours area of a room considering task time always on the occasion of, thus, transform Z can be utilized _{i, 1}=lnL _{i, 1}, obtain a process variable Z _{i, 1}, to ensure L _{i, 1}> 0, adopts a sliding scales parameter to set up φ _{i, 1}and L _{i, 1}stochastic relation model between the two, thus by φ _{i, 1}estimate L _{i, 1}, make φ _{i, 1}be expressed as Z _{i, 1}function, set up first stage process model as follows:

Z _i,1＝lnL _i,1(23)

φ _i,1＝g ₁(Z _i,1)+η _i,1

Wherein, g ₁(Z _{i, 1}) be a function undetermined, it is described that the relation between task process and the environmental monitoring data corresponding with the stage; η _{i, 1}the measuring error of a Normal Distribution, and

Extended Kalman filter (hereinafter referred to as EKF) is adopted to estimate/upgrade Z _{i, 1}conditional probability density function, and ask for further residue continuous time L _{i, 1}.Definition Z _{i, 1}renewal amount and one-step prediction conditional probability density function amount be respectively Z _{i, 1}| Φ _{i, 1}: N (z _{i|i, 1}, P _{i|i, 1}) and Z _i+1,1| Φ _{i, 1}: N (z _{i+1|i, 1}, P _{i+1|i, 1}), parameter z here _{i|i, 1}, P _{i|i, 1}, z _{i+1|i, 1}and P _{i+1|i, 1}can be calculated by EKF algorithm, its computing formula is as follows:

z _i|i,1＝z _i|i-1,1+K _i,1[φ _i,1-g ₁(z _i|i-1,1)](24)

Wherein, K _{i, 1}represent the gain battle array of Kalman filtering, obtained by following formula

Wherein

Correspondingly, the renewal equation of state estimation variance matrix can be obtained by following formula:

P _i|i,1＝P _i|i-1,1(1-K _i,1g′ ₁(z _i|i-1,1))(26)

The initial parameter z of EKF algorithm _0|0,1and P _0|0,1estimated to obtain by historical data, in the renewal equation of above-mentioned state estimation variance matrix, need calculation expectation z _i|i-1,1with variance P _i|i-1,1a step estimated value, consider Z _{i, 1}| Φ _{i, 1}: N (z _{i|i, 1}, P _{i|i, 1}), and Z _{i, 1}=lnL _{i, 1}, these two amounts can be obtained by lower two formulas:

Consider the transformational relation of normal distribution and lognormal distribution, have L _{i, 1}| Φ _{i, 1}: lnN (z _{i|i, 1}, P _{i|i, 1}), then based on model expression, obtain and expect z _i|i-1,1with variance P _i|i-1,1expression formula:

P _i|i-1，1＝P _i-1|i-1，1(30)

By above-mentioned renewal expression formula, obtain the estimated probability density function that the first stage remains continuous time for

Again because of

X ₁|Φ _i,1＝L _i,1+t _i(32)

Then by X that correspondent transform directly obtains ₁probability density function

Here calculated by formula (31).

Corresponding to t _imoment and X ₁the probability density function expression formula of the subordinate phase duration under condition is

Similarly, corresponding to t _imoment and X ₁duration phase III probability density function expression formula under condition is

Further, if make T _m| Φ _{i, 1}=(X ₁+ X ₂+ X ₃) | Φ _{i, 1}, then task time T _mdistribution function be

At moment t _mthe probability density function task time process of above formula differential being obtained to the first stage is

(2) subordinate phase process model building and task time PDF estimation

Subordinate phase process model is as follows:

Z _i,2＝lnL _i,2(38)

φ _i,2＝g ₂(Z _i,2)+η _i,2

Wherein, g ₂(Z _{i, 2}) be a function undetermined; η _{i, 2}the measuring error of a Normal Distribution, and

Obtain t _ithe environmental monitoring data information φ in moment _{i, 2}after, based on Monitoring Data set Φ _{i, 2}, adopt EKF estimation/update condition L _{i, 2}probability density function, make Z _{i, 2}| Φ _{i, 2}: N (z _{i|i, 2}, P _{i|i, 2}), Z _i+1,2| Φ _{i, 2}: N (z _{i+1|i, 2}, P _{i+1|i, 2}), then Z _{i, 2}have

z _i|i,2＝z _i|i-1,2+K _i,2[φ _i,2-g ₂(z _i|i-1,2)](39)

P _i|i,2＝P _i|i-1,2(1-K _i,2g′ ₂(z _i|i-1,2))(41)

Wherein

Further, z is expected _i|i-1,2with amount of variation P _i|i-1,2expression formula:

P _i|i-1,2＝P _i-1|i-1,2(43)

By above-mentioned renewal expression formula, obtain the estimated probability density function of subordinate phase residue continuous time for

Based on X ₂with L _{i, 2}relation, have

X ₂|Φ _i,2＝L _i,2+(t _i-x ₁)(45)

Wherein, x ₁obtained by first stage task process according to model specification.Thus, by variable transitions, directly X can be write out ₂distribution and expression formula

Wherein can be obtained by formula (44).

Corresponding to t _itime the duration phase III probability density function expression formula of inscribing be

Then task time T _mdistribution function be

Further, at moment t _mthe probability density function task time process of above formula differential being obtained to subordinate phase is

(3) phase III process model building and task time PDF estimation

Phase III process model is as follows:

Z _i,3＝lnL _i,3(50)

φ _i,3＝g ₃(Z _i,3)+η _i,3

Wherein, g ₃(Z _{i, 3}) be a function undetermined; η _{i, 3}the measuring error of a Normal Distribution, and

Obtain t _ithe environmental monitoring data information φ in moment _{i, 3}after, based on Monitoring Data set Φ _{i, 3}, adopt EKF estimation/update condition L _{i, 3}probability density function, then Z _{i, 3}have

z _i|i,3＝z _i|i-1,3+K _i,3[φ _i,3-g ₃(z _i|i-1,3)](51)

P _i|i,3＝P _i|i-1,3(1-K _i,3g′ ₃(z _i|i-1,3))(53)

Wherein

Further, z is expected _i|i-1,3with amount of variation P _i|i-1,3expression formula be:

P _i|i-1,3＝P _i-1|i-1,3(55)

By above-mentioned renewal expression formula, obtain the estimated probability density function that the phase III remains continuous time for

Based on X ₃with L _{i, 3}relation, have

X ₃|Φ _i,3＝L _i,3+(t _i-x ₁-x ₂)(57)

Wherein, x ₁and x ₂the amount obtained in the first two phase process, based on this, directly

Therefore, task time T _mdistribution and expression formula be

Further, at moment t _mthe process of above formula differential is obtained to probability density function task time of phase III:

So far, complete based on relevant environment Monitoring Data information task time probability density function estimation.

Step 2: fusion application historical data information, sets up phased mission systems degenerative process model, estimates the life-span of phased mission systems, obtains the life estimation value of phased mission systems.

(1) Wiener-Hopf equation is used to set up the degenerative process of phased mission systems

For without loss of generality, assuming that the initial reading of degenerative process is Y (0)=0, if initial time is t _i(i=1,2,3), then the monitored parameters evolution process model of time correlation is

Y(t)＝y _i+λ(t-t _i)+σB(t-t _i)(60)

Further, consider fusion application historical data information, in model, λ develops into dynamic parameter, uses λ _i=λ _i-1+ η replaces, and wherein η ~ N (0, Q), then degradation model is reconstructed into

Wherein ε _i~ N (0, t _i-t _i-1), λ _iestimated value can be obtained by Kalman filter algorithm.

λ is obtained by Kalman filter algorithm _ithe step of estimated value be:

Step 1: initialization p ₀;

Step 2:t _ithe state estimation in moment is

P _i|i-1＝P _i-1|i-1+Q

K _i＝(t _i-t _i-1) ²P _i|i-1+σ ²(t _i-t _i-1)；

Step 3: upgrade

λ is obtained by Gaussian distribution hypothesis and Bayesian filter principle _iprobability density function be

(2) estimate the life-span of phased mission systems, obtain the life estimation value of phased mission systems

The life-span of equipment is defined by the concept of first-hitting time, when the degradation values Y (t) that formula (60) is determined reaches the failure threshold w preset first, just thinks equipment failure.By the time that the timing definition that equipment life stops is degenerative process Y (t) First excursion failure threshold w, then equipment t _ithe remaining life S in moment _ibe defined as:

S _i＝inf{s _i:Y(s _i+t _i)≥w|Y _i}(63)

Order for the cumulative distribution function of remaining life, predict t by degradation model formula (61) _ithe degeneration probability density function in moment consideration model profile is normal distribution, has Y (s _i+ t _i) | Y _i: then t _iprobability density function and the cumulative distribution function of the life expectancy of moment phased mission systems are respectively:

Step 3: according to the reliability definition of phased mission system process model and phased mission systems degenerative process model, comprehensive utilization estimated value task time and life estimation value calculate the reliability reference value of phased mission systems in real time.

Obtain the life-span probability density function of task system with probability density function task time after, according to the reliability definition of phased mission system process model and phased mission systems degenerative process model, estimate t _ithe reliability of moment phased mission systems, the probability obtaining the reliability parameter of the n-th stage fill is

The estimation of the reliability parameter value of this kind of complicated phased mission systems of ocean platform can be completed based on formula (65) and (66) two formulas.

Above-described embodiment is used for explaining the present invention, instead of limits the invention, and in the protection domain of spirit of the present invention and claim, any amendment make the present invention and change, all fall into protection scope of the present invention.

Claims (6)

1. the ocean platform phased mission systems reliability estimation methods based on data-driven, it is characterized in that: the steps include: to be detected by the environment of sensor to system, the system environments Monitoring Data that comprehensive utilization sensor is observed, set up contacting between the historical data of individual phased mission systems and current real-time data information, stochastic filtering model is adopted to carry out modeling to stage interval, obtain phased mission system process model, estimate the probability density function of task time, obtain estimated value task time of phased mission systems; Fusion application historical data information, sets up phased mission systems degenerative process model, estimates the life-span of phased mission systems, obtains the life estimation value of phased mission systems;

According to the reliability definition of phased mission system process model and phased mission systems degenerative process model, comprehensive utilization estimated value task time and life estimation value calculate the reliability reference value of phased mission systems in real time.

2. the ocean platform phased mission systems reliability estimation methods based on data-driven according to claim 1, it is characterized in that: set up phased mission system process model and estimate that the concrete steps of probability density function of task time are: suppose that ocean platform offshore and gas development task has N number of stage, make stochastic variable X _nrepresent the n-th phase duration, its span is make stochastic variable T _mrepresent the T.T. of completion system overall tasks, and have order for each phase duration X _n, the probability density function of n=1, L, N, wherein 2≤n≤N; Make Φ _i,nrepresent cut-off current time t _ithe environmental monitoring data information aggregate corresponding with the n-th stage; Adopt probability density function task time in environmental monitoring data estimation of the order 1 ~ N each stage.

3. the ocean platform phased mission systems reliability estimation methods based on data-driven according to claim 2, is characterized in that: the n-th phase process modeling and task time PDF estimation step be: suppose to get current time t by sensor _ithe environmental monitoring data information φ in lower n-th stage _i,n, make L _i,nrepresent t _ithe residue continuous time in stage in moment n-th, then through type L _{i+1, n}=L _i,n-(t _i+1-t _i), (if L _i,n> t _i+1-t _i) residue L continuous time of the n-th stage subsequent time can be obtained _{i+1, n}, L _{0, n}represent the residue continuous time of first stage; The consecutive hours area of a room considering task time always on the occasion of, utilize transform Z _i,n=lnL _i,n, obtain a process variable Z _i,n, to ensure L _i,n> 0, adopts a sliding scales parameter to set up φ _i,nand L _i,nstochastic relation model between the two, thus by φ _i,nestimate L _i,n, make φ _i,nbe expressed as Z _i,nfunction, set up the n-th phase process model as follows:

Z _i,n＝lnL _i,n(1)

φ _i,n＝g _n(Z _i,n)+η _i,n

Wherein, g _n(Z _i,n) be a function undetermined, it is described that the relation between task process and the environmental monitoring data corresponding with the stage; η _i,nthe measuring error of a Normal Distribution, and

Adopt extended Kalman filter to estimate or upgrade Z _i,nconditional probability density function, and ask for further residue continuous time L _i,n; Definition Z _i,nand Z _{i+1, n}renewal amount and one-step prediction conditional probability density function amount be respectively Z _i,n| Φ _i,n: N (z _{i|i, n}, P _{i|i, n}) and Z _{i+1, n}| Φ _i,n: N (z _{i+1|i, n}, P _{i+1|i, n}), parameter z here _{i|i, n}, P _{i|i, n}, z _{i+1|i, n}and P _{i+1|i, n}can be calculated by extended Kalman filter algorithm, its computing formula is as follows:

z _i|i,n＝z _i|i-1,n+K _i,n[φ _i,n-g _n(z _i|i-1,n)](2)

Wherein, K _i,nrepresent the gain battle array of Kalman filtering, obtained by following formula:

$K_{i,n}=\[P_{i|i-1,n}{g}_i^{\′}\left(z_{i|i-1,n}\right)\]{\[g_i^{\′}{\left(z_{i|i-1,n}\right)}^2{P}_{i|i-1,n}+{\mathrm{\σ}}_n^2\]}^{-1}---\left(3\right)$

Wherein $g_n^{\′}\left(z_{i|i-1,n}\right)={\mathrm{dg}}_n\left(z_{i,n}\right)/{\mathrm{dz}}_{i,n}{|}_{z_{i,n}=z_{i|i-1,n}};$

Correspondingly, the renewal equation of state estimation variance matrix can be obtained by following formula:

P _i|i,n＝P _i|i-1,n(1-K _i,ng′ _n( _zi|i-1,n))(4)

The initial parameter z of extended Kalman filter algorithm _{0|0, n}and P _{0|0, n}estimated to obtain by historical data; Calculation expectation z is needed in the renewal equation of above-mentioned state estimation variance matrix _{i|i-1, n}with variance P _{i|i-1, n}a step estimated value, consider Z _i,n| Φ _i,n: N (z _{i|i, n}, P _{i|i, n}), and Z _i,n=lnL _i,n, obtain these two amounts by lower two formulas:

$E\[L_{i,n}|{\mathrm{\Φ}}_{i,n}\]=e^{z_{i|i,n}+0.5P_{i|i,n}}---\left(5\right)$

$\mathrm{var}\[L_{i,n}|{\mathrm{\Φ}}_{i,n}\]=(e^{P_{i|i,n}}-1)e^{2z_{i|i,n}+P_{i|i,n}}---\left(6\right)$

Consider the transformational relation of normal distribution and lognormal distribution, have L _{i, 1}| Φ _{i, 1}: lnN (z _{i|i, 1}, P _{i|i, 1}), then based on model expression, obtain and expect z _i|i-1,1with variance P _i|i-1,1expression formula:

$z_{i|i-1,n}=\ln \[e^{z_{i-1|i-1,n}+0.5P_{i-1|i-1,n}}-(t_i-t_{i-1})\]-0.5\ln (1+\frac{(e^{P_{i-1|i-1,n}}-1)2^{2z_{i-1|i-1,n}+P_{i-1|i-1,n}}}{{\[e^{z_{i-1|i-1,n}+0.5P_{i-1|i-1,n}}-(t_i-t_{i-1})\]}^2})---\left(7\right)$

P _i|i-1,n＝P _i-1|i-1,n(8)

By above-mentioned renewal expression formula, obtain the estimated probability density function that the first stage remains continuous time for

$p_{L_{i,n}|{\mathrm{\Φ}}_{i,n}}\left(l_{i,n}\right|{\mathrm{\Φ}}_{i,n})=\frac{1}{l_{i,n}\sqrt{2{\mathrm{\πP}}_{i|i,n}}}{e}^{-{\left(2P_{i|i,n}\right)}^{-1}{({\mathrm{lnl}}_{i,n}-z_{i|i,n})}^2}---\left(9\right)$

Again because of

$X_n|{\mathrm{\Φ}}_{i,n}=L_{i,n}+t_i-\underset{j=1}{\overset{n-1}{\Σ}}{x}_j---\left(10\right)$

Then directly obtain X by correspondent transform _nat t _ithe distribution in moment

$p_{X_n|{\mathrm{\Φ}}_{i,n}}\left(x_n\right|{\mathrm{\Φ}}_{i,n})=p_{L_{i,n}|{\mathrm{\Φ}}_{i,n}}(x_n+\underset{j=1}{\overset{n-1}{\Σ}}{x}_j-t_i|{\mathrm{\Φ}}_{i,n})---\left(11\right)$

Wherein, $p_{L_{i,n}|{\mathrm{\Φ}}_{i,n}}(x_n+{\mathrm{\Σ}}_{j=1}^{n-1}{x}_j-t_i|{\mathrm{\Φ}}_{i,n})$ Calculated by formula (9);

Thus, corresponding to t _imoment and X ₁subordinate phase duration probability density function expression formula under condition is

$p_{X_{n+1}|{\mathrm{\Φ}}_{i,n}}\left(x_{n+1}\right|{\mathrm{\Φ}}_{i,n})=\∫p_{X_{n+1}|X_n}\left(x_{n+1}\right|x_n)p_{L_{i,n}|{\mathrm{\Φ}}_{i,n}}(x_n+{\mathrm{\Σ}}_{j=1}^{n-1}{x}_j-t_i|{\mathrm{\Φ}}_{i,n}){\mathrm{dx}}_n---\left(12\right)$

Similarly, corresponding to t _imoment and X _npostorder under condition each phase duration probability density function expression formula is

$\begin{array}{c}{p}_{X_s|{\mathrm{\Φ}}_{i,n}}\left(x_s\right|{\mathrm{\Φ}}_{i,n})\\ =\∫...\∫p_{L_{i,n}|{\mathrm{\Φ}}_{i,n}}(x_n+{\mathrm{\Σ}}_{j=1}^{n-1}{x}_j-t_i|{\mathrm{\Φ}}_{i,n})p_{X_{n+1}|X_n}\left(x_{n+1}\right|x_n)...p_{X_s|X_n,X_{n\mathrm{+1}},...,X_{s-1}}\left(x_s\right|x_n,x_{n+1},...,x_{s-1}){\mathrm{dx}}_n{\mathrm{dx}}_{n\mathrm{+1}}...{\mathrm{dx}}_{s-1}\end{array}---\left(13\right)$

Wherein s=n+1 ..., N;

Further, have then task time T _mprobability distribution function be

$\begin{array}{c}Pr(T_M\≤t_m|{\mathrm{\Φ}}_{i,n})\\ ={\∫}_0^{t_m-\underset{j=1}{\overset{n-1}{\mathrm{\Σ}}}{x}_j}{p}_{X_n|{\mathrm{\Φ}}_{i,n}}\left(x_n\right|{\mathrm{\Φ}}_{i,n}){\∫}_0^{t_m-\underset{j=1}{\overset{n-1}{\mathrm{\Σ}}}{x}_j-x_n}{p}_{X_{n+1}|X_n}\left(x_{n+1}\right|x_n)...{\∫}_0^{t_m-\underset{j=1}{\overset{n-1}{\mathrm{\Σ}}}{x}_j-\underset{k=n}{\overset{N-2}{\mathrm{\Σ}}}{x}_k}{p}_{X_{N-1}|X_n,X_{n\mathrm{+1}},...,X_{N-2}}\left(x_{N-1}\right|x_n,x_{n\mathrm{+1}},...,x_{N-2})\\ \×{\mathrm{Pr}}_{X_N|X_n,X_{n\mathrm{+1}},...,X_{N-1}}(t_m-\underset{j=1}{\overset{n-1}{\mathrm{\Σ}}}{x}_j-\underset{k=n}{\overset{N-2}{\mathrm{\Σ}}}{x}_k|x_n,x_{n+1},...,x_{N-1}){\mathrm{dx}}_n{\mathrm{dx}}_{n\mathrm{+1}}...{\mathrm{dx}}_{N-1}\end{array}---\left(14\right)$

At moment t _mprobability density function task time formula (14) differential process being obtained to the n-th stage is

$\begin{array}{c}{p}_{T_M|{\mathrm{\Φ}}_{i,n}}\left(t_m\right|{\mathrm{\Φ}}_{i,n})\\ ={\∫}_0^{t_m-\underset{j=1}{\overset{n-1}{\mathrm{\Σ}}}{x}_j}{p}_{X_n|{\mathrm{\Φ}}_{i,n}}\left(x_n\right|{\mathrm{\Φ}}_{i,n}){\∫}_0^{t_m-\underset{j=1}{\overset{n-1}{\mathrm{\Σ}}}{x}_j-x_n}{p}_{X_{n+1}|X_n}\left(x_{n+1}\right|x_n)...{\∫}_0^{t_m-\underset{j=1}{\overset{n-1}{\mathrm{\Σ}}}{x}_j-\underset{k=n}{\overset{N-2}{\mathrm{\Σ}}}{x}_k}{p}_{X_{N-1}|X_n,X_{n\mathrm{+1}},...,X_{N-2}}\left(x_{N-1}\right|x_n,x_{n\mathrm{+1}},...,x_{N-2})\\ \×p_{X_N|X_n,X_{n\mathrm{+1}},...X_{N-1}}(t_m-\underset{j=1}{\overset{n-1}{\mathrm{\Σ}}}{x}_j-\underset{k=n}{\overset{N-2}{\mathrm{\Σ}}}{x}_k|x_n,x_{n+1},...,x_{N-1}){\mathrm{dx}}_n{\mathrm{dx}}_{n\mathrm{+1}}...{\mathrm{dx}}_{N-1}\end{array}---\left(15\right)$

So far, the environmental monitoring data information of being correlated with by the current generation obtains estimator task time in this stage.

4. the ocean platform phased mission systems reliability estimation methods based on data-driven according to claim 1 or 3, it is characterized in that: use Wiener-Hopf equation to set up phased mission systems degenerative process model, the concrete steps setting up phased mission systems degenerative process model are: assuming that the initial reading of degenerative process is Y (0)=0, if initial time is t _i(i=1,2 ..., N), then the monitored parameters evolution process model of time correlation is

Y(t)＝y _i+λ(t-t _i)+σB(t-t _i)(16)

Further, consider fusion application historical data information, in model, λ develops into dynamic parameter, uses λ _i=λ _i-1+ η replaces, and wherein η ~ N (0, Q), then degradation model is reconstructed into

$\left\{\begin{array}{c}{\mathrm{\λ}}_i={\mathrm{\λ}}_{i-1}+\mathrm{\η}\\ y_i=y_{i-1}+{\mathrm{\λ}}_{i-1}(t_i-t_{i-1})+{\mathrm{\σ\ϵ}}_i\end{array}\right.---\left(17\right)$

Wherein ε _i~ N (0, t _i-t _i-1), λ _iestimated value obtained by Kalman filtering algorithm,

λ is obtained by Gaussian distribution hypothesis and Bayesian filter principle _iprobability density function be

$f_{{\mathrm{\λ}}_i|Y_i}\left({\mathrm{\λ}}_i\right|Y_i)=\frac{1}{\sqrt{2{\mathrm{\πP}}_{i|i}}}\exp \[-{({\mathrm{\λ}}_i-{\widehat{\mathrm{\λ}}}_i)}^2/2P_{i|i}\]---\left(18\right)$

The life-span of equipment is defined by the concept of first-hitting time, when the degradation values Y (t) that formula (16) is determined reaches the failure threshold w preset first, just thinks equipment failure; By the time that the timing definition that equipment life stops is degenerative process Y (t) First excursion failure threshold w, then equipment t _ithe remaining life S in moment _ibe defined as:

S _i＝inf{s _i:Y(s _i+t _i)≥w|Y _i}(19)

Order for the cumulative distribution function of remaining life, predict t by degradation model formula (17) _ithe degeneration probability density function in moment consideration model profile is normal distribution, has $Y(s_i+t_i)|Y_i:N(y_i+{\widehat{\mathrm{\λ}}}_i{s}_i,P_{i|i}{s}_i^2+{\mathrm{\σ}}^2{s}_i),$ Then t _iprobability density function and the cumulative distribution function of the life expectancy of moment phased mission systems are respectively:

$\begin{array}{c}{f}_{T_d|Y_i}\left(t_d\right|Y_i)=\frac{w-y_i}{\sqrt{2\mathrm{\π}{(t_d-t_i)}^3\left(P_{i|i}\right(t_d-t_i)+{\mathrm{\σ}}^2)}}\exp (-\frac{{(w-y_i-{\widehat{\mathrm{\λ}}}_i(t_d-t_i\left)\right)}^2}{2(t_d-t_i)\left(P_{i|i}\right(t_d-t_i)+{\mathrm{\σ}}^2)}),t_d>t_i\\ f_{T_d|Y_i}\left(t_d\right|Y_i)=1-\mathrm{\Φ}\left(\frac{w-y_i-{\widehat{\mathrm{\λ}}}_i(t_d-t_i)}{\sqrt{P_{i|i}(t_d-t_i)+{\mathrm{\σ}}^2(t_d-t_i)}}\right)\\ +\exp (\frac{2{\widehat{\mathrm{\λ}}}_i(w-y_i)}{{\mathrm{\σ}}^2}+\frac{2P_{i|i}{(w-y_i)}^2}{{\mathrm{\σ}}^4})\mathrm{\Φ}(-\frac{2P_{i|i}(w-y_i)(t_d-t_i)+{\mathrm{\σ}}^2\left({\widehat{\mathrm{\λ}}}_i\right(t_d-t_i)+w-y_i)}{{\mathrm{\σ}}^2\sqrt{P_{i|i}{(t_d-t_i)}^2+{\mathrm{\σ}}^2(t_d-t_i)}})\end{array}---\left(20\right).$

5. the ocean platform phased mission systems reliability estimation methods based on data-driven according to claim 4, is characterized in that: obtain λ by Kalman filtering algorithm _i(i=1,2 ..., N) the step of estimated value be:

Initialization p ₀;

T _ithe state estimation in moment is

P _i|i-1＝P _i-1|i-1+Q

K _i＝(t _i-t _i-1) ²P _i|i-1+σ ²(t _i-t _i-1)；

${\widehat{\mathrm{\λ}}}_i={\widehat{\mathrm{\λ}}}_{i-1}+P_{i|i-1}(t_i-t_{i-1})K_i^{-1}(y_i-y_{i-1}-{\widehat{\mathrm{\λ}}}_{i-1}(t_i-t_{i-1}\left)\right)$

Upgrade $P_{i|i}=P_{i|i-1}-P_{i|i-1}{(t_i-t_{i-1})}^2{K}_i^{-1}{P}_{i|i-1}.$

6. the ocean platform phased mission systems reliability estimation methods based on data-driven according to claim 4, is characterized in that: the life-span probability density function obtaining task system with probability density function task time after, according to the reliability definition of phased mission system process model and phased mission systems degenerative process model, estimate t _ithe reliability of moment phased mission systems, the probability obtaining the reliability parameter of the n-th stage fill is

$\mathrm{Pr}(T_d\≥T_M|{\mathrm{\Φ}}_{i,n},Y_i)={\∫}_{t_m>0}{p}_{T_M|{\mathrm{\Φ}}_{i,n}}\left(t_m\right|{\mathrm{\Φ}}_{i,n})\left({\∫}_{t_d\≥t_m}{f}_{T_d|Y_i}\left(t_d|Y_i\right){\mathrm{dt}}_d\right){\mathrm{dt}}_m---\left(21\right)$

$\mathrm{Pr}(T_M\&le;R|T_M\&le;T_d,{\mathrm{\&Phi;}}_{i,n},Y_i)=\frac{{\&Integral;}_{0<t_m\&le;R}{p}_{T_M|{\mathrm{\&Phi;}}_{i,n}}\left(t_m\right|{\mathrm{\&Phi;}}_{i,n})\left({\&Integral;}_{t_d\&GreaterEqual;t_m}{f}_{T_d|Y_i}\left(t_d|Y_i\right){\mathrm{dt}}_d\right){\mathrm{dt}}_m}{{\&Integral;}_{t_m>0}{p}_{T_M|{\mathrm{\&Phi;}}_{i,n}}\left(t_m\right|{\mathrm{\&Phi;}}_{i,n})\left({\&Integral;}_{t_d\&GreaterEqual;t_m}{f}_{T_d|Y_i}\left(t_d|Y_i\right){\mathrm{dt}}_d\right){\mathrm{dt}}_m}---\left(22\right)$

The estimation of the reliability parameter value of ocean platform complex phased mission systems can be completed based on formula (21) and (22).