CN103115748B - 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

Based on the optical fibre gyro light source reliability checking method of 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 realizing the navigation of all kinds of weaponry, guidance, positioning and directing, rapid reaction, precision strike and information processing.Therefore, carrying out reliability consideration to inertia production 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, without the need to advantages such as rotatable parts and friction means, the life-span is long, dynamic range is large, instantaneous startings, progressively instead of 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 of field of inertia technology.

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

Summary of the invention

The present invention is that will to solve the time detected 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 provides the optical fibre gyro light source reliability checking method based on bayesian theory.

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

Step one, structure and principle analysis are carried out to optical fibre gyro Er-Doped superfluorescent fiber source;

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

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

Described employing bayes method carries out estimating that concrete grammar is to the crash rate of Er-Doped superfluorescent fiber source: 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, and π (θ) represents the prior distribution density of θ, p (x ₁..., x _n| θ) be likelihood function, h (θ | x ₁..., x _n) be the Posterior distrbutionp 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, then have life distribution function to be:

F(t，m，η)＝1-exp(-t ^m/η)，t＞0 (1)

Wherein m is form parameter, and weigh the dispersion degree in life-span, η is scale parameter, and also known as characteristics life, the crash rate that can be obtained Er-Doped superfluorescent fiber source t at any time by (1) is λ (t):

λ(t)＝F′(t)/[1-F(t)]＝mt ^m-1/η，t＞0 (2)

From (1), the fiduciary level R (t) of Er-Doped superfluorescent fiber source t is at any time:

R(t)＝1-F(t)＝exp(-t ^m/η)，t＞0 (3)

Note G (t)=-lnR (t)=t ^m/ η, can obtain G (t by the concavity and convexity of function _i)/t _i≤ G (t _k)/t _k, i=1,2 ..., k, and then can obtain i.e. light source any time t _icrash rate p _imeet:

$0\≤p_i\≤1-{(1-p_k)}^{t_i/t_k},$ 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 be uniformly distributed as p _kprior distribution, namely

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

Light source can be set up at t by (4) formula _ithe crash rate p in moment _iwith light source at t _kthe crash rate p in moment _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 _ithe failure probability p in moment _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, the Fix-Time Censored Test under normal temperature is carried out to Er-Doped superfluorescent fiber source, obtain no-failure testing data of life-span;

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

Obtaining likelihood function by 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)

Light source can be obtained at t by Bayesian formula _ithe crash rate p in moment _iposterior distrbutionp be:

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

Wherein k represents k Fix-Time Censored Test, 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 the truncation moment is respectively t ₁, t ₂..., t _k(t ₁< t ₂< ... < t _k), s _i=n _i+ n _i+1+ ... + n _krepresent to t _imoment has s _itest participated in by individual sample, i=1, and 2 ..., k;

Using the expectation value of Posterior distrbutionp as p _ibayesian Estimation, then

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

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

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

A, the Er-Doped superfluorescent fiber source t obtained in step 3 C _imoment crash rate p _ibayesian Estimation value 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 obtain

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)

Weighted least-squares method is utilized 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 for weight coefficient, i=1,2 ..., k, (n _i, t _i) be non-failure data;

Get and make 's with as the point estimation of m and η, calculate

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

I.e. 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 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 failure rate estimation 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) judge whether Er-Doped superfluorescent fiber source lost efficacy: according to the failure rate estimation of life distribution function, Er-Doped superfluorescent fiber source and the failure dense function of Er-Doped superfluorescent fiber source calculate the life-span distribute, curve plotting after crash rate and failure density, when optical fibre gyro light source power drop to initial power 50% time, judge that Er-Doped superfluorescent fiber source lost efficacy, namely complete the optical fibre gyro light source reliability checking method based on bayesian theory.

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, method of the present invention is adopted to draw based on non-failure data, only need the test period of thousands of hours, greatly reduce detection time.Simultaneously due to price comparison high of this series products of optical fibre gyro light source, can not adopt the test method under large sample, this method can be carried out based on the test figure under sample, can also utilize former Test Information simultaneously, decrease the expense of test.Apply bayesian theory simultaneously and adopt the method for priori data, the detection method more traditional than fault tree prediction method etc. improves the accuracy rate of detection.

The present invention also has the following advantages:

One, the present invention can obtain Er-Doped superfluorescent fiber source dominant 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 the serviceable life of Er-Doped superfluorescent fiber source;

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

Accompanying drawing explanation

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 reliability curves in embodiment one.

Embodiment

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

Step one, structure and principle analysis are carried out to optical fibre gyro Er-Doped superfluorescent fiber source;

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

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

Described employing bayes method carries out estimation concrete grammar to the crash rate of Er-Doped superfluorescent fiber source:

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, and π (θ) represents the prior distribution density of θ, p (x ₁..., x _n| θ) be likelihood function, h (θ | x ₁..., x _n) be the Posterior distrbutionp 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, then have life distribution function to be:

F(t，m，η)＝1-exp(-t ^m/η)，t＞0 (1)

Wherein m is form parameter, and weigh the dispersion degree in life-span, η is scale parameter, and also known as characteristics life, the crash rate that can be obtained Er-Doped superfluorescent fiber source t at any time by (1) is λ (t):

λ(t)＝F′(t)/[1-F(t)]＝mt ^m-1/η，t＞0 (2)

From (1), the fiduciary level R (t) of Er-Doped superfluorescent fiber source t is at any time:

R(t)＝1-F(t)＝exp(-t ^m/η)，t＞0 (3)

Note G (t)=-lnR (t)=t ^m/ η, can obtain G (t by the concavity and convexity of function _i)/t _i≤ G (t _k)/t _k, i=1,2 ..., k, and then can obtain i.e. light source any time t _icrash rate p _imeet: $0\&le;p_i\&le;1-{(1-p_k)}^{t_i/t_k},$ 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 be uniformly distributed as p _kprior distribution, namely

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

Light source can be set up at t by (4) formula _ithe crash rate p in moment _iwith light source at t _kthe crash rate p in moment _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 _ithe failure probability p in moment _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, the Fix-Time Censored Test under normal temperature is carried out to Er-Doped superfluorescent fiber source, obtain no-failure testing data of life-span;

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

Obtaining likelihood function by 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)

Light source can be obtained at t by Bayesian formula _ithe crash rate p in moment _iposterior distrbutionp be:

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

Wherein k represents k Fix-Time Censored Test, 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 the truncation moment is respectively t ₁, t ₂..., t _k(t ₁< t ₂< ... < t _k), s _i=n _i+ n _i+1+ ... + n _krepresent to t _imoment has s _itest participated in by individual sample, i=1, and 2 ..., k;

Using the expectation value of Posterior distrbutionp as p _ibayesian Estimation, then

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

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

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

A, the Er-Doped superfluorescent fiber source t obtained in step 3 C _imoment crash rate p _ibayesian Estimation value 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 obtain

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)

Weighted least-squares method is utilized 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 for weight coefficient, i=1,2 ..., k, (n _i, t _i) be non-failure data;

Get and make 's with as the point estimation of m and η, calculate

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

I.e. 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 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 failure rate estimation 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) judge whether Er-Doped superfluorescent fiber source lost efficacy: according to the failure rate estimation of life distribution function, Er-Doped superfluorescent fiber source and the failure dense function of Er-Doped superfluorescent fiber source calculate the life-span distribute, curve plotting after crash rate and failure density, when optical fibre gyro light source power drop to initial power 50% time, judge that Er-Doped superfluorescent fiber source lost efficacy, namely complete the optical fibre gyro light source reliability checking method based on bayesian theory.

The Er-Doped superfluorescent fiber source of present embodiment forms primarily 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 one: 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, a light part after amplification directly exports, and another part is reflected back toward output terminal and exports after reverberator 5; The optical isolator 4 of output terminal allows Unidirectional light to pass through, and stops the reflected light from optical fibre gyro, to prevent because 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, using spectral bandwidth, mean wavelength stability, output power as Testing index;

In described step 2, analyze the failure mode of Er-Doped superfluorescent fiber source: according to structure and the composition of Er-Doped superfluorescent fiber source, its components and parts are primarily of optical device and electron device two class composition, 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 device prerequisite of good performance itself, the inefficacy one of active device is because electric reason (electrostatic or power supply surge etc.) causes device damage or inefficacy; Two is because technological reason causes device be subject to mechanical damage and even fracture and lost 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; Two is owing to losing efficacy by physical shock and vibrations make device impaired;

In described step 2, according to structure and the principle of work of Er-Doped superfluorescent fiber source, in conjunction with its failure mode, the reliability block diagram of Er-Doped superfluorescent fiber source can be obtained as shown in Figure 3.Its reliability block diagram is a cascaded structure, and the impact of element more forward in cascaded structure on total is larger.The reliability of Er-Doped superfluorescent fiber source is mainly by the impact of optical active device, and namely pump laser diode has the greatest impact to it.Laser diode belongs to electron device, at present still reliability model is not accurately had for electron device, in the reliability consideration of electric product, its invalid cost type of hypothesis is single-parameter exponential distribution mostly, but the failure type of some some electric product of research display is distributed as Weibull distribution, and Weibull Distribution data capability is strong, failure rate estimation has three kinds of shapes, corresponds respectively to the three phases of tub curve, 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, and obtain the reliability data of light source, method is as follows:

In k Fix-Time Censored Test, if the truncation moment 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 result all samples, claims (t _i, n _i), i=1,2 ..., k is non-failure data.Note s _i=n _i+ n _i+1+ ... + n _krepresent to t _imoment, total s _itest participated in by individual sample, and all do not lose efficacy, and therefore fail data also can be designated as (t _i, s _i), i=1,2 ..., k;

8 cover Er-Doped superfluorescent fiber sources normal work respectively at normal temperatures in test, detect to 1000 little 2 cover light sources of taking out constantly in work, 2000 littlely take out 1 cover constantly and detect from remaining light source, 3000 little 2 covers of taking out again constantly detect, 4000 little 1 covers of taking out constantly detect, 5000 little overlapping remaining 2 are constantly detected, and all light sources of result did not all lose efficacy in the detection moment.Therefore the test figure as table 1 is obtained:

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 in described step 3 C, get λ k ₌0.01 (i.e. the crash rate upper bound of 5000 hours), calculates each moment crash rate p _ibayesian Estimation value as shown in table 2:

The Bayesian Estimation value of table 2 crash rate

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

The optical doped fiber source reliability curves that present embodiment obtains as shown in Figure 4.

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 present embodiment is adopted to draw based on non-failure data, only need the test period of thousands of hours, greatly reduce detection time.Simultaneously due to price comparison high of this series products of optical fibre gyro light source, can not adopt the test method under large sample, this method can be carried out based on the test figure under sample, can also utilize former Test Information simultaneously, decrease the expense of test.Apply bayesian theory simultaneously and adopt the method for priori data, the detection method more traditional than fault tree prediction method etc. improves the accuracy rate of detection.

Present embodiment also has the following advantages:

One, present embodiment can obtain Er-Doped superfluorescent fiber source dominant 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 the serviceable life of Er-Doped superfluorescent fiber source;

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

Claims (1)

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

Step one, structure and principle analysis are carried out to optical fibre gyro Er-Doped superfluorescent fiber source;

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

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

Described employing bayes method carries out estimation concrete grammar to the crash rate of Er-Doped superfluorescent fiber source:

The density function form of Bayesian formula is:

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

Wherein θ is solve for parameter, and π (θ) represents the prior distribution of θ, A (x ₁..., x _n| θ) be likelihood function, h (θ | x ₁..., x _n) be the Posterior distrbutionp 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, then have life distribution function to be:

F(t,m,η)＝1-exp(-t ^m/η),t>0 (1)

Wherein m is form parameter, and weigh the dispersion degree in life-span, η is scale parameter, and also known as characteristics life, the crash rate that can be obtained Er-Doped superfluorescent fiber source t at any time by (1) is λ (t):

λ(t)＝F′(t)/[1-F(t)]＝mt ^m-1/η,t>0 (2)

From (1), the fiduciary level R (t) of Er-Doped superfluorescent fiber source t is at any time:

R(t)＝1-F(t)＝exp(-t ^m/η),t>0 (3)

Note G (t)=-lnR (t)=t ^m/ η, can obtain G (t by the concavity and convexity of function _i)/t _i≤ G (t _k)/t _k, i=1,2 ..., k, and then can obtain i.e. light source any time t _icrash rate p _imeet:

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

To light source particular moment t _kcrash rate p _krequirement provide p _kupper bound λ _k, and get [0, λ _k] on be uniformly distributed as p _kprior distribution, namely

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

Light source can be set up at t by (4) formula _ithe crash rate p in moment _iwith light source at t _kthe crash rate p in moment _kconservative relational expression as follows:

$p_i=1-{(1-p_k)}^{t_i/t_k},i=\mathrm{1,2},...,k---\left(6\right)$

Therefore light source is at t _ithe crash rate p in moment _iprior distribution be:

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

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

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

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

Obtaining likelihood function by Fix-Time Censored Test data is

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

Light source can be obtained at t by Bayesian formula _ithe crash rate p in moment _iposterior distrbutionp be:

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

Wherein k represents k Fix-Time Censored Test, and n represents that corresponding test specimen number is n ₁, n ₂..., n _k, r _i=sx+t _k/ t _i-1, if the truncation moment is respectively t ₁, t ₂..., t _k(t ₁<t ₂< ... <t _k), s _i=n _i+ n _i+1+ ... + n _krepresent to t _imoment has s _itest participated in by individual sample, i=1, and 2 ..., k;

Using the expectation value of Posterior distrbutionp as p _ibayesian Estimation, then

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

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

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

A, the Er-Doped superfluorescent fiber source t obtained in step 3 C _imoment crash rate p _ibayesian Estimation value 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 obtain

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)

Weighted least-squares method is utilized to carry out parameter fitting, order:

$Q(m,\mathrm{\&eta;})=\underset{i=1}{\overset{k}{\mathrm{\&Sigma;}}}{\mathrm{\&omega;}}_i{[{\mathrm{mx}}_i-\ln \mathrm{\&eta;}-y_i]}^2---\left(13\right)$

Wherein for weight coefficient, i=1,2 ..., k, (n _i, t _i) be non-failure data;

Get and make $Q(\hat{m},\widehat{\mathrm{\&eta;}})=\underset{m>1,\mathrm{\&eta;}>0}{\min }Q(m,\mathrm{\&eta;})$ 's with as the point estimation of m and η, calculate

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

I.e. 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 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 failure rate estimation 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:

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

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