CN103115748A - Fiber-optic gyroscope light source reliability detecting method based on Bayesian theory - Google Patents

Abstract

The invention relates to a fiber-optic gyroscope light source reliability detecting method based on Bayesian theory and aims to solve the problem that the existing fiber-optic gyroscope light source reliability detecting methods are long in detecting time and low in accuracy, and wastes resources. The method includes the steps of firstly, using an Er-doped fiber-optic light source to analyze structure and principle of a fiber-optic gyroscope, and determine work principle of each component; secondly, using the fiber-optic gyroscope to perform failure model effectiveness analysis to the fiber-optic gyroscope to obtain a reliability model of the Er-doped fiber-optic light source; thirdly, using the Bayesian theory to estimate failure rate of the Er-doped fiber-optic light source; fourthly, using the reliability model of the Er-doped fiber-optic light source for estimating to obtain reliability indexes; and fifthly, using formula (15), (16) and (17) as parameters for judging whether the Er-doped fiber-optic light source fails or not. The fiber-optic gyroscope light source reliability detecting method is applicable to the field of reliability detecting.

Description

Optical fibre gyro light source reliability checking method based on bayesian theory

Technical field

The present invention relates to the detection method of optical fibre gyro light source reliability.

Background technology

Along with the rapid raising of Technology for Modern Equipment reliability level, long-life, high reliability product proportion are increasing, how to verify that the problem of the index of aging of this series products and reliability index is more and more outstanding.Inertial technology is the core technology that realizes all kinds of weaponry navigation, guidance, positioning and directing, rapid reaction, precision strike and information processing.Therefore, inertia production being carried out reliability consideration is an important research topic.

Optical fibre gyro (FOG) is a kind of angular-rate sensor based on optics Sagnac effect.In recent years, optical fibre gyro is all solid state with it, need not rotatable parts and friction means, the advantages such as the life-span is long, dynamic range is large, instantaneous starting, progressively replaced traditional mechanical gyro, be applied gradually in the equipments such as guided missile, panzer, oil logging tool and spacecraft and product, become the main flow gyro in inertial technology field.

As time goes on the main optical device of optical fibre gyro and electron device can produce the failure modes such as performance drift, deterioration.Light source is as one of Primary Component of optical fibre gyro, and its failure rate accounts for 57% of optical fibre gyro fault, is the highest part of failure rate in optical fibre gyro, and therefore, the research of optical fibre gyro light source reliability is significant to the reliability design of optical fibre gyro system.Along with the continuous expansion of optical fibre gyro application and its vital role in every field, the indexs such as its serviceable life, reliability are known that demand is day by day urgent.The detection of optical fibre gyro light source reliability has become problem demanding prompt solution.But the time of detecting in reliability checking method at present is long, and accuracy rate is low, and the wasting of resources is very serious.The present invention utilizes bayesian theory to carry out reliability to optical fibre gyro with Er-Doped superfluorescent fiber source and detects, obtained the expression formula of Er-Doped superfluorescent fiber source reliability index, thereby for carrying out of Er-Doped superfluorescent fiber source reliability consideration provides theoretical foundation, for the life tests of optical fibre gyro provides useful suggestion.

Summary of the invention

The present invention is that will to solve the time of detecting in the detection method process of optical fibre gyro light source reliability long, and accuracy rate is low, the problem of the wasting of resources, and optical fibre gyro light source reliability checking method based on bayesian theory is provided.

Optical fibre gyro light source reliability checking method based on bayesian theory of the present invention is realized according to the following steps:

Step 1, optical fibre gyro is carried out structure and principle analysis with Er-Doped superfluorescent fiber source;

Step 2, employing Weibull distribution are analyzed as the failure mode of Er-Doped superfluorescent fiber source;

Step 3, employing bayes method are estimated the crash rate of Er-Doped superfluorescent fiber source;

Described employing bayes method estimates that to the crash rate of Er-Doped superfluorescent fiber source concrete grammar is: the density function form of Bayesian formula is:

$h\left(\mathrm{\θ}\right|x_1,...,x_n)=\frac{\mathrm{\π}\left(\mathrm{\θ}\right)p(x_1,...,x_n|\mathrm{\θ})}{\∫\mathrm{\π}\left(\mathrm{\θ}\right)p(x_1,...,x_n|\mathrm{\θ})\mathrm{d\θ}}\mathrm{\θ}$

Wherein θ is solve for parameter, the prior distribution density of π (θ) expression θ, p (x ₁..., x _n| θ) be likelihood function, and h (θ | x ₁..., x _n) be the posteriority distribution of θ;

A, determine the prior distribution of Er-Doped superfluorescent fiber source crash rate:

Under Weibull distribution, suppose that the Er-Doped superfluorescent fiber source life-span is t, have the life-span distribution function to be:

F(t，m，η)＝1-exp(-t ^m/η)，t＞0 (1)

Wherein m is form parameter, weighs the dispersion degree in life-span, and η is scale parameter, claims again characteristics life, by (1) can get Er-Doped superfluorescent fiber source at any time the crash rate of t be λ (t):

λ(t)＝F′(t)/[1-F(t)]＝mt ^m-1/η，t＞0 (2)

By (1) as can be known, Er-Doped superfluorescent fiber source at any time the fiduciary level R of t (t) be:

R(t)＝1-F(t)＝exp(-t ^m/η)，t＞0 (3)

Note G (t)=-lnR (t)=t ^m/ η can get G (t by definition of concave ﹠ convex function _i)/t _i≤ G (t _k)/t _k, i=1,2 ..., k, and then can get

Be light source any time t _iCrash rate p _iSatisfy:

$0\≤p_i\≤1-{(1-p_k)}^{t_i/t_k},$ i＝1，2，…，k (4)

To light source particular moment t _kCrash rate p _kRequirement provide p _kUpper bound λ _k, and get [0, λ _k] on even distribution as p _kPrior distribution, namely

$\mathrm{\&pi;}\left(p_k\right)=\left\{\begin{array}{c}\frac{1}{{\mathrm{\&lambda;}}_k},0<p_k<{\mathrm{\&lambda;}}_k\\ 0,\mathrm{else}\end{array}\right.---\left(5\right)$

Can set up light source at t by (4) formula _iCrash rate p constantly _iWith light source at t _kCrash rate p constantly _kConservative relational expression as follows:

$p_i=1-{(1-p_k)}^{t_i/t_k},$ i＝1，2，…，k (6)

Therefore light source is at t _iFailure probability p constantly _iPrior distribution be:

${\mathrm{\&pi;}}_i\left(p_i\right)={\mathrm{\&pi;}}_k\left(p_k\right)\frac{{\mathrm{dp}}_k}{{\mathrm{dp}}_i}=\frac{t_k}{{\mathrm{\&lambda;}}_k{t}_i}{(1-p_i)}^{\frac{t_k}{t_i}-1},$ 0＜p _i＜λ _i (7)

Wherein ${\mathrm{\&lambda;}}_i=1-{(1-{\mathrm{\&lambda;}}_k)}^{t_i/t_k},$ i＝1，2，…，k；

B, Er-Doped superfluorescent fiber source is carried out Fix-Time Censored Test under normal temperature, obtain the no-failure testing data of life-span;

C, utilize Bayesian formula to carry out Bayesian Estimation to the crash rate of Er-Doped superfluorescent fiber source:

Obtaining likelihood function by the Fix-Time Censored Test data is

$L\left(s_i\right|p_i)=L\left(p_i\right)={(1-p_i)}^{s_i},$ i＝1，2，…，k， (8)

Can get light source at t by Bayesian formula _iCrash rate p constantly _iPosteriority be distributed as:

$\mathrm{\&pi;}\left(p_i\right|s_i)=\frac{{\mathrm{\&pi;}}_i\left(p_i\right)L\left(s_i\right|p_i)}{{\&Integral;}_0^{{\mathrm{\&lambda;}}_i}{\mathrm{\&pi;}}_i\left(p_i\right)L\left(s_i\right|p_i){\mathrm{dp}}_i}=\frac{{(1-p_i)}^{r_i}(r_i+1)}{1-{(1-{\mathrm{\&lambda;}}_i)}^{r_i+1}}---\left(9\right)$

Wherein k represents Fix-Time Censored Test k time, and n represents that corresponding test specimen number is n ₁, n ₂..., n _k, $r_i=s_i+t_k/t_i-1,{\mathrm{\&lambda;}}_i=1-{(1-{\mathrm{\&lambda;}}_k)}^{t_i/t_k},$ If truncation is respectively t constantly ₁, t ₂..., t _k(t ₁＜t ₂＜...＜t _k), s _i=n _i+ n _i+1+ ... + n _kExpression is to t _iConstantly total s _iIndividual sample is participated in test, i=1, and 2 ..., k;

The expectation value that distributes with posteriority is as p _iBayesian Estimation,

${\hat{p}}_i={\&Integral;}_0^{{\mathrm{\&lambda;}}_i}{p}_i{\mathrm{\&pi;}}_i\left(p_i\right|s_i){\mathrm{dp}}_i=\frac{\frac{1}{r_i+2}[1-{(1-{\mathrm{\&lambda;}}_i)}^{r_i+2}]-{\mathrm{\&lambda;}}_i{(1-{\mathrm{\&lambda;}}_i)}^{r_i+1}}{1-{(1-{\mathrm{\&lambda;}}_i)}^{r_i+1}}i=\mathrm{1,2},...,k---\left(10\right)$

According to by the no-failure testing data of life-span in formula (10) and step 3 B, calculate t _iMoment crash rate p _iThe Bayesian Estimation value

Step 4, Er-Doped superfluorescent fiber source reliability model parameter is estimated:

A, the Er-Doped superfluorescent fiber source t that obtains in step 3 C _iMoment crash rate p _iThe Bayesian Estimation value

The basis on, utilize least square method to carry out parameter fitting, estimate model parameter,

By p _i=P (T≤t _i)=1-exp (t _i ^m/ η), T is the optical fiber source life-span, can get

ln[-ln(1-p _i)]＝mlnt _i-lnη (11)

Make y _i=ln[-ln (1-p _i)], x _i=lnt _i,

y _i＝mx _i-lnη (12)

Utilize weighted least-squares method to carry out parameter fitting, order:

$Q(m,\mathrm{\&eta;})=\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_i{[{\mathrm{mx}}_i-\ln \mathrm{\&eta;}-y_i]}^2$

(13)

Wherein

Be weight coefficient, i=1,2 ..., k, (n _i, t _i) be the no-failure data;

Get and make

With

Point estimation as m and η calculates

$\hat{m}=0.9997,$ $\widehat{\mathrm{\&eta;}}=9.945\&times;{10}^5$

Be being estimated as of Er-Doped superfluorescent fiber source fiduciary level:

$\hat{R}\left(t\right)=\exp \left(\frac{-t^{\hat{m}}}{\widehat{\mathrm{\&eta;}}}\right)=\exp \left(\frac{-t^{0.9997}}{9.945\&times;{10}^5}\right)---\left(14\right)$

B, each reliability index of estimation Er-Doped superfluorescent fiber source

The life-span distribution function of Er-Doped superfluorescent fiber source is:

$F(t,m,\mathrm{\&eta;})=1-R\left(t\right)=1-\exp \left(\frac{-t^{0.9997}}{9.945\&times;{10}^5}\right),$ t＞0 (15)

The crash rate function of Er-Doped superfluorescent fiber source is:

$\mathrm{\&lambda;}\left(t\right)=F^{\&prime;}\left(t\right)/[1-F\left(t\right)]=\frac{{0.9997t}^{0.9997-1}}{9.945\&times;{10}^5},$ t＞0 (16)

The failure dense function of Er-Doped superfluorescent fiber source is:

$f\left(t\right)=F^{\&prime;}\left(t\right)=1+\frac{{0.9997t}^{0.9997-1}}{9.945\&times;{10}^5}\exp \left(\frac{{-t}^{0.9997}}{9.945\&times;{10}^5}\right)---\left(17\right)$

Step 5, adopt formula (15), (16) and (17) to judge whether Er-Doped superfluorescent fiber source lost efficacy: to calculate curve plotting after life-span distribution, crash rate and failure density according to the failure dense function of the crash rate function of life-span distribution function, Er-Doped superfluorescent fiber source and Er-Doped superfluorescent fiber source, when the power of optical fibre gyro light source drop to initial power 50% the time, judge that Er-Doped superfluorescent fiber source lost efficacy, and had namely completed the optical fibre gyro light source reliability checking method based on bayesian theory.

The invention effect:

Optical fibre gyro light source reliability checking method testing process based on bayesian theory provided by the invention is fast and accuracy rate is high, method is simple, the optical fibre gyro light source that the present invention studies is a kind of fiber products of high reliability, its theoretical life-span is more than 50000 hours, adopting method of the present invention to be based on the no-failure data draws, only need the test period of thousands of hours to get final product, greatly reduced detection time.Simultaneously high due to the price comparison of this series products of optical fibre gyro light source, can not adopt the test method under large sample, and this method can be carried out based on the test figure under sample, can also utilize former Test Information simultaneously, has reduced the expense of test.Use simultaneously the method that bayesian theory adopts priori data, improved than traditional detection methods such as fault tree prediction methods the accuracy rate that detects.

The present invention also has the following advantages:

One, the present invention can obtain Er-Doped superfluorescent fiber source main failure mode in use from principle;

Two, technology of the present invention can provide theoretical foundation for the calculating of the dependability parameters such as serviceable life of Er-Doped superfluorescent fiber source;

Three, technology of the present invention can for optical fibre gyro even the reliability of inertial navigation system detect basic data and reference be provided, the method reliability of also may be used on the other equipments such as optical fibre gyro detects simultaneously.

Description of drawings

Fig. 1 is the process flow diagram in embodiment one;

Fig. 2 is Er-Doped superfluorescent fiber source structural drawing in embodiment one; Wherein, 1 is pump laser diode, and 2 is wave division multiplex coupler, and 3 is Er-doped fiber, and 4 is optical isolator, and 5 is reverberator;

Fig. 3 is Er-Doped superfluorescent fiber source reliability block diagram in embodiment one;

Fig. 4 is Er-Doped superfluorescent fiber source fiduciary level curve in embodiment one.

Embodiment

Embodiment one: the optical fibre gyro light source reliability checking method based on bayesian theory of present embodiment is realized according to the following steps:

Step 1, optical fibre gyro is carried out structure and principle analysis with Er-Doped superfluorescent fiber source;

Step 2, employing Weibull distribution are analyzed as the failure mode of Er-Doped superfluorescent fiber source;

Step 3, employing bayes method are estimated the crash rate of Er-Doped superfluorescent fiber source;

Described employing bayes method estimates that to the crash rate of Er-Doped superfluorescent fiber source concrete grammar is:

The density function form of Bayesian formula is:

$h\left(\mathrm{\&theta;}\right|x_1,...,x_n)=\frac{\mathrm{\&pi;}\left(\mathrm{\&theta;}\right)p(x_1,...,x_n|\mathrm{\&theta;})}{\&Integral;\mathrm{\&pi;}\left(\mathrm{\&theta;}\right)p(x_1,...,x_n|\mathrm{\&theta;})\mathrm{d\&theta;}}\mathrm{\&theta;}$

Wherein θ is solve for parameter, the prior distribution density of π (θ) expression θ, p (x ₁..., x _n| θ) be likelihood function, and h (θ | x ₁..., x _n) be the posteriority distribution of θ;

A, determine the prior distribution of Er-Doped superfluorescent fiber source crash rate:

Under Weibull distribution, suppose that the Er-Doped superfluorescent fiber source life-span is t, have the life-span distribution function to be:

F(t，m，η)＝1-exp(-t ^m/η)，t＞0 (1)

Wherein m is form parameter, weighs the dispersion degree in life-span, and η is scale parameter, claims again characteristics life, by (1) can get Er-Doped superfluorescent fiber source at any time the crash rate of t be λ (t):

λ(t)＝F′(t)/[1-F(t)]＝mt ^m-1/η，t＞0 (2)

By (1) as can be known, Er-Doped superfluorescent fiber source at any time the fiduciary level R of t (t) be:

R(t)＝1-F(t)＝exp(-t ^m/η)，t＞0 (3)

Note G (t)=-lnR (t)=t ^m/ η can get G (t by definition of concave ﹠ convex function _i)/t _i≤ G (t _k)/t _k, i=1,2 ..., k, and then can get

Be light source any time t _iCrash rate p _iSatisfy: $0\&le;p_i\&le;1-{(1-p_k)}^{t_i/t_k},$ i＝1，2，…，k (4)

To light source particular moment t _kCrash rate p _kRequirement provide p _kUpper bound λ _k, and get [0, λ _k] on even distribution as p _kPrior distribution, namely

$\mathrm{\&pi;}\left(p_k\right)=\left\{\begin{array}{c}\frac{1}{{\mathrm{\&lambda;}}_k},0<p_k<{\mathrm{\&lambda;}}_k\\ 0,\mathrm{else}\end{array}\right.---\left(5\right)$

Can set up light source at t by (4) formula _iCrash rate p constantly _iWith light source at t _kCrash rate p constantly _kConservative relational expression as follows:

$p_i=1-{(1-p_k)}^{t_i/t_k},$ i＝1，2，…，k (6)

Therefore light source is at t _iFailure probability p constantly _iPrior distribution be:

${\mathrm{\&pi;}}_i\left(p_i\right)={\mathrm{\&pi;}}_k\left(p_k\right)\frac{{\mathrm{dp}}_k}{{\mathrm{dp}}_i}=\frac{t_k}{{\mathrm{\&lambda;}}_k{t}_i}{(1-p_i)}^{\frac{t_k}{t_i}-1},$ 0＜p _i＜λ _i (7)

Wherein ${\mathrm{\&lambda;}}_i=1-{(1-{\mathrm{\&lambda;}}_k)}^{t_i/t_k},$ i＝1，2，…，k；

B, Er-Doped superfluorescent fiber source is carried out Fix-Time Censored Test under normal temperature, obtain the no-failure testing data of life-span;

C, utilize Bayesian formula to carry out Bayesian Estimation to the crash rate of Er-Doped superfluorescent fiber source:

Obtaining likelihood function by the Fix-Time Censored Test data is

$L\left(s_i\right|p_i)=L\left(p_i\right)={(1-p_i)}^{s_i},$ i＝1，2，…，k， (8)

Can get light source at t by Bayesian formula _iCrash rate p constantly _iPosteriority be distributed as:

$\mathrm{\&pi;}\left(p_i\right|s_i)=\frac{{\mathrm{\&pi;}}_i\left(p_i\right)L\left(s_i\right|p_i)}{{\&Integral;}_0^{{\mathrm{\&lambda;}}_i}{\mathrm{\&pi;}}_i\left(p_i\right)L\left(s_i\right|p_i){\mathrm{dp}}_i}=\frac{{(1-p_i)}^{r_i}(r_i+1)}{1-{(1-{\mathrm{\&lambda;}}_i)}^{r_i+1}}---\left(9\right)$

Wherein k represents Fix-Time Censored Test k time, and n represents that corresponding test specimen number is n ₁, n ₂..., n _k, $r_i=s_i+t_k/t_i-1,{\mathrm{\&lambda;}}_i=1-{(1-{\mathrm{\&lambda;}}_k)}^{t_i/t_k},$ If truncation is respectively t constantly ₁, t ₂..., t _k(t ₁＜t ₂＜...＜t _k), s _i=n _i+ n _i+1+ ... + n _kExpression is to t _iConstantly total s _iIndividual sample is participated in test, i=1, and 2 ..., k;

The expectation value that distributes with posteriority is as p _iBayesian Estimation,

${\hat{p}}_i={\&Integral;}_0^{{\mathrm{\&lambda;}}_i}{p}_i{\mathrm{\&pi;}}_i\left(p_i\right|s_i){\mathrm{dp}}_i=\frac{\frac{1}{r_i+2}[1-{(1-{\mathrm{\&lambda;}}_i)}^{r_i+2}]-{\mathrm{\&lambda;}}_i{(1-{\mathrm{\&lambda;}}_i)}^{r_i+1}}{1-{(1-{\mathrm{\&lambda;}}_i)}^{r_i+1}}i=\mathrm{1,2},...,k---\left(10\right)$

According to by the no-failure testing data of life-span in formula (10) and step 3 B, calculate t _iMoment crash rate p _iThe Bayesian Estimation value

Step 4, Er-Doped superfluorescent fiber source reliability model parameter is estimated:

A, the Er-Doped superfluorescent fiber source t that obtains in step 3 C _iMoment crash rate p _iThe Bayesian Estimation value

The basis on, utilize least square method to carry out parameter fitting, estimate model parameter,

By p _i=P (T≤t _i)=1-exp (t _i ^m/ η), T is the optical fiber source life-span, can get

ln[-ln(1-p _i)]＝mlnt _i-lnη (11)

Make y _i=ln[-ln (1-p _i)], x _i=lnt _i,

y _i＝mx _i-lnη (12)

Utilize weighted least-squares method to carry out parameter fitting, order:

$Q(m,\mathrm{\&eta;})=\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_i{[{\mathrm{mx}}_i-\ln \mathrm{\&eta;}-y_i]}^2$

(13)

Wherein

Be weight coefficient, i=1,2 ..., k, (n _i, t _i) be the no-failure data;

Get and make

With

Point estimation as m and η calculates

$\hat{m}=0.9997,$ $\widehat{\mathrm{\&eta;}}=9.945\&times;{10}^5$

Be being estimated as of Er-Doped superfluorescent fiber source fiduciary level:

$\hat{R}\left(t\right)=\exp \left(\frac{-t^{\hat{m}}}{\widehat{\mathrm{\&eta;}}}\right)=\exp \left(\frac{-t^{0.9997}}{9.945\&times;{10}^5}\right)---\left(14\right)$

B, each reliability index of estimation Er-Doped superfluorescent fiber source

The life-span distribution function of Er-Doped superfluorescent fiber source is:

$F(t,m,\mathrm{\&eta;})=1-R\left(t\right)=1-\exp \left(\frac{-t^{0.9997}}{9.945\&times;{10}^5}\right),t>0---\left(15\right)$

The crash rate function of Er-Doped superfluorescent fiber source is:

$\mathrm{\&lambda;}\left(t\right)=F^{\&prime;}\left(t\right)/[1-F\left(t\right)]=\frac{{0.9997t}^{0.9997-1}}{9.945\&times;{10}^5}t>0,---\left(16\right)$

The failure dense function of Er-Doped superfluorescent fiber source is:

$f\left(t\right)=F^{\&prime;}\left(t\right)=1+\frac{{0.9997t}^{0.9997-1}}{9.945\&times;{10}^5}\exp \left(\frac{{-t}^{0.9997}}{9.945\&times;{10}^5}\right)---\left(17\right)$

Step 5, adopt formula (15), (16) and (17) to judge whether Er-Doped superfluorescent fiber source lost efficacy: to calculate curve plotting after life-span distribution, crash rate and failure density according to the failure dense function of the crash rate function of life-span distribution function, Er-Doped superfluorescent fiber source and Er-Doped superfluorescent fiber source, when the power of optical fibre gyro light source drop to initial power 50% the time, judge that Er-Doped superfluorescent fiber source lost efficacy, and had namely completed the optical fibre gyro light source reliability checking method based on bayesian theory.

The Er-Doped superfluorescent fiber source of present embodiment mainly is comprised of pump laser diode 1, wave division multiplex coupler 2, Er-doped fiber 3, optical isolator 4 and reverberator 5, and its structure as shown in Figure 2;

The principle of work of the Er-Doped superfluorescent fiber source in described step 1: during Er-Doped superfluorescent fiber source work, the pump light that pump laser diode 1 pumping produces is coupled into Er-doped fiber 3 by wave division multiplex coupler 2, amplify through spontaneous radiation (ASE) in Er-doped fiber 3, directly output of a light part after amplification, another part is reflected back toward output terminal output after reverberator 5; 4 of the optical isolators of output terminal allow Unidirectional light to pass through, and stop the reflected light from optical fibre gyro, to prevent because the light reflection causes light vibration;

In described step 2, the inefficacy of Er-Doped superfluorescent fiber source refers to that its performance index can not reach requirement, with spectral bandwidth, mean wavelength stability, output power as detecting index;

In described step 2, analyze the failure mode of Er-Doped superfluorescent fiber source: according to the structure and composition of Er-Doped superfluorescent fiber source, its components and parts mainly are comprised of optical device and electron device two classes, and its failure mode mainly contains two kinds: optical active device lost efficacy and optical passive component lost efficacy.The optical active device of Er-Doped superfluorescent fiber source is pump laser diode 1.Under the well behaved prerequisite of device itself, the inefficacy one of active device is because electric reason (static or power supply surge etc.) causes device damage or inefficacy; The 2nd, because technological reason causes that device is subject to mechanical damage and even fractures losing efficacy.The optical passive component of Er-Doped superfluorescent fiber source has Er-doped fiber 3, wave division multiplex coupler 2, optical isolator 4, reverberator 5 etc.The inefficacy one of passive device is that optical fiber causes hydraulic performance decline even to lose efficacy because fractureing owing to being subject to stress; The 2nd, owing to being subjected to physical shock and vibrations to make that device is impaired to lose efficacy;

In described step 2, according to structure and the principle of work of Er-Doped superfluorescent fiber source, in conjunction with its failure mode, can obtain the reliability block diagram of Er-Doped superfluorescent fiber source as shown in Figure 3.Its reliability block diagram is a cascaded structure, and element more forward in cascaded structure is larger on the impact of total.The reliability of Er-Doped superfluorescent fiber source mainly is subjected to the impact of optical active device, and namely pump laser diode has the greatest impact to it.Laser diode belongs to electron device, still there is no reliability model accurately for electron device at present, its inefficacy distribution pattern of hypothesis is the one-parameter exponential distribution mostly in the reliability consideration of electric product, but some studies show that the failure type of some electric product is distributed as Weibull distribution, and the Weibull Distribution data capability is strong, the crash rate function has three kinds of shapes, corresponds respectively to the three phases of tub curve, and is more realistic.Therefore select Weibull distribution as the reliability distribution models of Er-Doped superfluorescent fiber source here;

Described step 3 B adopts the Fix-Time Censored Test under normal temperature, obtains the reliability data of light source, and method is as follows:

In k Fix-Time Censored Test, establish truncation and constantly be respectively t ₁, t ₂..., t _k(t ₁＜t ₂＜...＜t _k), corresponding test specimen number is n ₁, n ₂..., n _k, none inefficacy of all samples as a result claims (t _i, n _i), i=1,2 ..., k is the no-failure data.Note s _i=n _i+ n _i+1+ ... + n _kExpression is to t _iConstantly, total s _iIndividual sample is participated in test, and all less than inefficacy, so fail data also can be designated as (t _i, s _i), i=1,2 ..., k;

8 cover Er-Doped superfluorescent fiber sources normal operation respectively at normal temperatures in test, taking out 2 cover light sources when working by 1000 hours detects, taking out 1 cover in the time of 2000 hours from remaining light source detects, taking out again 2 covers in the time of 3000 hours detects, taking out 1 cover in the time of 4000 hours detects, in the time of 5000 hours, 2 remaining covers are detected, all light sources are detecting constantly all inefficacies as a result.Therefore obtain the test figure as table 1:

Table 1 no-failure testing data of life-span

Sequence number	t i(hour)	n i(individual)	s i(individual)
				1	1000	2	8
2	2000	1	6
				3	3000	2	5

4	4000	1	3
				5	5000	2	2

By the test figure in formula (10) and table 1, get λ k in described step 3 C ₌0.01 (the crash rate upper bounds of namely 5000 hours) calculate each crash rate p constantly _iThe Bayesian Estimation value As shown in table 2:

The Bayesian Estimation value of table 2 crash rate

In described step 4, each estimated value of crash rate constantly of the Er-Doped superfluorescent fiber source that is obtained by table 2 utilizes parameter fitting that Er-Doped superfluorescent fiber source reliability model parameter is estimated.And then can obtain the mathematic(al) representation of each reliability index of Er-Doped superfluorescent fiber source according to the relation between each reliability index;

Present embodiment obtains optical doped fiber source fiduciary level curve as shown in Figure 4.

The present embodiment effect:

The optical fibre gyro light source reliability checking method testing process based on bayesian theory that present embodiment provides is fast and accuracy rate is high, method is simple, the optical fibre gyro light source that present embodiment is studied is a kind of fiber products of high reliability, its theoretical life-span is more than 50000 hours, the method of employing present embodiment is based on the no-failure data and draws, only need the test period of thousands of hours to get final product, greatly reduced detection time.Simultaneously high due to the price comparison of this series products of optical fibre gyro light source, can not adopt the test method under large sample, and this method can be carried out based on the test figure under sample, can also utilize former Test Information simultaneously, has reduced the expense of test.Use simultaneously the method that bayesian theory adopts priori data, improved than traditional detection methods such as fault tree prediction methods the accuracy rate that detects.

Present embodiment also has the following advantages:

One, present embodiment can obtain Er-Doped superfluorescent fiber source main failure mode in use from principle;

Two, the technology of present embodiment can provide theoretical foundation for the calculating of the dependability parameters such as serviceable life of Er-Doped superfluorescent fiber source;

Three, the technology of present embodiment can for optical fibre gyro even the reliability of inertial navigation system detect basic data and reference be provided, the method reliability of also may be used on the other equipments such as optical fibre gyro detects simultaneously.

Claims (1)

1. based on the optical fibre gyro light source reliability checking method of bayesian theory, it is characterized in that realizing according to the following steps based on the optical fibre gyro light source reliability checking method of bayesian theory:

Step 1, optical fibre gyro is carried out structure and principle analysis with Er-Doped superfluorescent fiber source;

Step 2, employing Weibull distribution are analyzed as the failure mode of Er-Doped superfluorescent fiber source;

Step 3, employing bayes method are estimated the crash rate of Er-Doped superfluorescent fiber source;

Described employing bayes method estimates that to the crash rate of Er-Doped superfluorescent fiber source concrete grammar is:

The density function form of Bayesian formula is:

$h\left(\mathrm{\&theta;}\right|x_1,...,x_n)=\frac{\mathrm{\&pi;}\left(\mathrm{\&theta;}\right)p(x_1,...,x_n|\mathrm{\&theta;})}{\&Integral;\mathrm{\&pi;}\left(\mathrm{\&theta;}\right)p(x_1,...,x_n|\mathrm{\&theta;})\mathrm{d\&theta;}}\mathrm{\&theta;}$

Wherein θ is solve for parameter, the prior distribution density of π (θ) expression θ, p (x ₁..., x _n| θ) be likelihood function, and h (θ | x ₁..., x _n) be the posteriority distribution of θ;

A, determine the prior distribution of Er-Doped superfluorescent fiber source crash rate:

Under Weibull distribution, suppose that the Er-Doped superfluorescent fiber source life-span is t, have the life-span distribution function to be:

F(t，m，η)＝1-exp(-t ^m/η)，t＞0 (1)

Wherein m is form parameter, weighs the dispersion degree in life-span, and η is scale parameter, claims again characteristics life, by (1) can get Er-Doped superfluorescent fiber source at any time the crash rate of t be λ (t):

λ(t)＝F′(t)/[1-F(t)]＝mt ^m-1/η，t＞0 (2)

By (1) as can be known, Er-Doped superfluorescent fiber source at any time the fiduciary level R of t (t) be:

R(t)＝1-F(t)＝exp(-t ^m/η)，t＞0 (3)

Note G (t)=-lnR (t)=t ^m/ η can get G (t by definition of concave ﹠ convex function _i)/t _i≤ G (t _k)/t _k, i=1,2 ..., k, and then can get Be light source any time t _iCrash rate p _iSatisfy:

$0\&le;p_i\&le;1-{(1-p_k)}^{t_i/t_k},$ i＝1，2，…，k (4)

To light source particular moment t _kCrash rate p _kRequirement provide p _kUpper bound λ _k, and get [0, λ _k] on even distribution as p _kPrior distribution, namely

$\mathrm{\&pi;}\left(p_k\right)=\left\{\begin{array}{c}\frac{1}{{\mathrm{\&lambda;}}_k},0<p_k<{\mathrm{\&lambda;}}_k\\ 0,\mathrm{else}\end{array}\right.---\left(5\right)$

Can set up light source at t by (4) formula _iCrash rate p constantly _iWith light source at t _kCrash rate p constantly _kConservative relational expression as follows:

$p_i=1-{(1-p_k)}^{t_i/t_k},$ i＝1，2，…，k (6)

Therefore light source is at t _iFailure probability p constantly _iPrior distribution be:

${\mathrm{\&pi;}}_i\left(p_i\right)={\mathrm{\&pi;}}_k\left(p_k\right)\frac{{\mathrm{dp}}_k}{{\mathrm{dp}}_i}=\frac{t_k}{{\mathrm{\&lambda;}}_k{t}_i}{(1-p_i)}^{\frac{t_k}{t_i}-1},$ 0＜p _i＜λ _i (7)

Wherein ${\mathrm{\&lambda;}}_i=1-{(1-{\mathrm{\&lambda;}}_k)}^{t_i/t_k},$ i＝1，2，…，k；

B, Er-Doped superfluorescent fiber source is carried out Fix-Time Censored Test under normal temperature, obtain the no-failure testing data of life-span;

C, utilize Bayesian formula to carry out Bayesian Estimation to the crash rate of Er-Doped superfluorescent fiber source:

Obtaining likelihood function by the Fix-Time Censored Test data is

$L\left(s_i\right|p_i)=L\left(p_i\right)={(1-p_i)}^{s_i},$ i＝1，2，…，k， (8)

Can get light source at t by Bayesian formula _iCrash rate p constantly _iPosteriority be distributed as:

$\mathrm{\&pi;}\left(p_i\right|s_i)=\frac{{\mathrm{\&pi;}}_i\left(p_i\right)L\left(s_i\right|p_i)}{{\&Integral;}_0^{{\mathrm{\&lambda;}}_i}{\mathrm{\&pi;}}_i\left(p_i\right)L\left(s_i\right|p_i){\mathrm{dp}}_i}=\frac{{(1-p_i)}^{r_i}(r_i+1)}{1-{(1-{\mathrm{\&lambda;}}_i)}^{r_i+1}}---\left(9\right)$

Wherein k represents Fix-Time Censored Test k time, and n represents that corresponding test specimen number is n ₁, n ₂..., n _k, $r_i=s_i+t_k/t_i-1,{\mathrm{\&lambda;}}_i=1-{(1-{\mathrm{\&lambda;}}_k)}^{t_i/t_k},$ If truncation is respectively t constantly ₁, t ₂..., t _k(t ₁＜t ₂＜...＜t _k), s _i=n _i+ n _i+1+ ... + n _kExpression is to t _iConstantly total s _iIndividual sample is participated in test, i=1, and 2 ..., k;

The expectation value that distributes with posteriority is as p _iBayesian Estimation,

${\hat{p}}_i={\&Integral;}_0^{{\mathrm{\&lambda;}}_i}{p}_i{\mathrm{\&pi;}}_i\left(p_i\right|s_i){\mathrm{dp}}_i=\frac{\frac{1}{r_i+2}[1-{(1-{\mathrm{\&lambda;}}_i)}^{r_i+2}]-{\mathrm{\&lambda;}}_i{(1-{\mathrm{\&lambda;}}_i)}^{r_i+1}}{1-{(1-{\mathrm{\&lambda;}}_i)}^{r_i+1}}i=\mathrm{1,2},...,k---\left(10\right)$

According to by the no-failure testing data of life-span in formula (10) and step 3 B, calculate t _iMoment crash rate p _iThe Bayesian Estimation value

Step 4, Er-Doped superfluorescent fiber source reliability model parameter is estimated:

A, the Er-Doped superfluorescent fiber source t that obtains in step 3 C _iMoment crash rate p _iThe Bayesian Estimation value The basis on, utilize least square method to carry out parameter fitting, estimate model parameter,

By p _i=P (T≤t _i)=1-exp (t _i ^m/ η), T is the optical fiber source life-span, can get

ln[-ln(1-p _i)]＝mlnt _i-lnη(11)

Make y _i=ln[-ln (1-p _i)], x _i=lnt _i,

y _i＝mx _i-lnη (12)

Utilize weighted least-squares method to carry out parameter fitting, order:

$Q(m,\mathrm{\&eta;})=\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_i{[{\mathrm{mx}}_i-\ln \mathrm{\&eta;}-y_i]}^2$

Wherein Be weight coefficient, i=1,2 ..., k, (n _i, t _i) be the no-failure data;

Get and make

With

Point estimation as m and η calculates

$\hat{m}=0.9997,$ $\widehat{\mathrm{\&eta;}}=9.945\&times;{10}^5$

Be being estimated as of Er-Doped superfluorescent fiber source fiduciary level:

$\hat{R}\left(t\right)=\exp \left(\frac{-t^{\hat{m}}}{\widehat{\mathrm{\&eta;}}}\right)=\exp \left(\frac{-t^{0.9997}}{9.945\&times;{10}^5}\right)---\left(14\right)$

B, each reliability index of estimation Er-Doped superfluorescent fiber source

The life-span distribution function of Er-Doped superfluorescent fiber source is:

$F(t,m,\mathrm{\&eta;})=1-R\left(t\right)=1-\exp \left(\frac{-t^{0.9997}}{9.945\&times;{10}^5}\right),t>0---\left(15\right)$

The crash rate function of Er-Doped superfluorescent fiber source is:

$\mathrm{\&lambda;}\left(t\right)=F^{\&prime;}\left(t\right)/[1-F\left(t\right)]=\frac{{0.9997t}^{0.9997-1}}{9.945\&times;{10}^5}t>0,---\left(16\right)$

The failure dense function of Er-Doped superfluorescent fiber source is:

$f\left(t\right)=F^{\&prime;}\left(t\right)=1+\frac{{0.9997t}^{0.9997-1}}{9.945\&times;{10}^5}\exp \left(\frac{{-t}^{0.9997}}{9.945\&times;{10}^5}\right)---\left(17\right)$

Step 5, adopt formula (15), (16) and (17) to judge whether Er-Doped superfluorescent fiber source lost efficacy: to calculate curve plotting after life-span distribution, crash rate and failure density according to the failure dense function of the crash rate function of life-span distribution function, Er-Doped superfluorescent fiber source and Er-Doped superfluorescent fiber source, when the power of optical fibre gyro light source drop to initial power 50% the time, judge that Er-Doped superfluorescent fiber source lost efficacy, and had namely completed the optical fibre gyro light source reliability checking method based on bayesian theory.

Images