CN103412986A - Plane periodic inspection content optimizing method based on fault-free data analysis - Google Patents

Abstract

The invention relates to a plane periodic inspection content optimizing method based on fault-free data analysis, and aims to effectively solve the problem of excessive maintenance during periodic inspection work and reduce the grounding time of a plane. The method comprises four parts of plane periodic inspection content optimizing target analysis, periodic inspection troubleshooting fault distribution type analysis, fault-free data analysis based on an optimal confidence estimation method and failure distribution parameter equation solving based on nonlinear programming, wherein the plane periodic inspection content optimizing target analysis adopts WinQSB software to construct a network planning diagram, obtain a key route and a key work and select a periodic inspection content optimizing target; and the periodic inspection troubleshooting fault distribution type analysis comprises two manners of fault distribution type list analysis and fault distribution type process analysis. The optimal confidence estimation method is adopted for fault-free data analysis, so that lower confidence limit of reliability of the plane, an engine and airborne equipment is given, and a fault distribution parameter equation is established and solved with a nonlinear programming method. The method can meet requirements for high efficiency and high engineering operability.

Description

A kind of aircraft regular inspection content optimization method of analyzing based on failure-free data

Technical field

The invention belongs to the aeronautical maintenance field, relate to the application of failure-free data analysis in aircraft regular inspection content optimization, efficient solution determines the excessive problem of maintenance in inspection work, under the prerequisite that guarantees reliability, reduces aircraft grounding time and maintenance cost.

Background technology

Aircraft is made regular check on and is safeguarded that (periodic inspection and maintenance is called for short regular inspection) is to use at the aeronautical technology equipment the periodic maintenance work of implementing after a specified time (number of times), is to guarantee often important means in shape of aeronautical technology equipment.The technology status of its to the effect that testing in depth testing aeronautical technology equipment, find in time parts, particularly early stage abrasion and the damage of parts inside, thoroughly get rid of the accident defect of finding, and the maintenance work such as adjust, clean, lubricate.Aircraft regular inspection content optimization is to integrate the technology such as fail-safe analysis, computing machine, nonlinear programming, is intended to solve the excessive problem of maintenance in the regular inspection content.The research of aircraft regular inspection content optimization starts from the eighties in 20th century.Both at home and abroad the customary regular inspection of the aircraft of airline is divided into A, B, C, D inspection according to the pilot time number/number of times that rises and falls usually, carries out after generally the A inspection being placed on to boat, does not need special maintenance downtime; B inspection is in reality and seldom adopt, and often can cancel the B inspection, and B inspection work is adjusted to A inspection and C completes to reduce unnecessary aircraft in examining and stop field time.The U.S. has carried out large quantity research to the age exploration of military aircraft.The problems such as the military aircraft of China exists the regular inspection content reasonable not, and the maintenance number of times is too much, and the scope of examination of offing normal in prophylactic repair is too much, result cause aircraft maintenance grounding overlong time, and serviceability rate is low.Therefore it is all significant that the regular inspection content optimization is operated in the maintenance field of civil and military aircraft.

The gordian technique of aircraft regular inspection content optimization is divided into again failure-free data analytical approach and nonlinear equation method of value solving.Existing failure-free data analytical approach is broadly divided into following a few class: classical way, Bayes method, multi-layer Bayes Method etc.Classical way mainly contains: partition cloth curve method, minimum χ ²-Fa, method of equivalent failure number, optimum confidence limit method, revised Maximum Likelihood function method, generalized linear model method, transformation CLASS-K method and MLR(monotone likelihood ratio) lower limit etc. of family of distributions fiduciary level.

Iterative numerical approach solves nonlinear equation and mainly contains dichotomy, Newton method, process of iteration and quadratic factor algorithm, and these methods are mainly for the monadic algebra equation.Indicial equation algebraic method commonly used can only solve the simplest indicial equation; The integral equation approximate solution has numerical integration method, approximate kernel method, process of iteration and the variational method etc.And fault distribution parameter equation is monobasic indicial equation and binary nonlinear integral equation.Said method all is difficult to solve fault distribution parameter equation.

Summary of the invention

Technology of the present invention is dealt with problems and is: overcome the deficiencies in the prior art, a kind of aircraft regular inspection content optimization method of analyzing based on failure-free data is provided, energy high efficiency selected regular inspection content optimization target, take full advantage of historical reliability data message and feature and determine the distribution pattern of regular inspection work investigation fault, adopt the optimum confidence lower limit of certain confidence level that the letter estimation technique obtains the fiduciary level of aircraft, engine and airborne equipment of putting, set up fault distribution parameter equation and adopt the Active Set algorithm fast and accurate solution of nonlinear programming approach.

Technical solution of the present invention is:

1, a kind of aircraft regular inspection content optimization method of analyzing based on failure-free data, its step is as follows: 1) carry out the target analysis of aircraft regular inspection content optimization; 2) Distribution Type Analysis of regular inspection investigation fault; 3) based on optimum, put the failure-free data analysis of the letter estimation technique; 4) based on the fault distribution parameter equation solution of nonlinear programming.

2, method of planning Network Based, adopt WinQSB software building network planning figure, obtains critical path and key job, thereby select regular inspection content optimization target.

3, according to fault distribution pattern table analysis or fault distribution pattern process analysis mode, carry out the Distribution Type Analysis of regular inspection investigation fault.

4, adopt optimum to put the letter estimation technique and carry out the failure-free data analysis, according to the confidence lower limit of (1-α) confidence level of the fiduciary level of formula aircraft, engine and airborne equipment (its most common failure is distributed as exponential distribution, Weibull distribution, normal distribution and lognormal distribution), set up fault distribution parameter equation.

5, adopt the Active Set Algorithm for Solving fault distribution parameter equation of nonlinear programming approach.

Principle of the present invention: traditional regular inspection content optimization is carried out Calculation of Reliability for the important parts of the what is called of each specialty, calculated amount is large, optimization efficiency is low, so the present invention is directed to the thought that regular inspection content optimization target is selected in critical path and key job, overcome the blindly deficiency of poor efficiency of traditional regular inspection content optimization method.

When the distribution pattern of regular inspection work investigation fault, look into the more fast convenience of mode of fault distribution pattern table, weak point is being of limited application of distribution pattern table, judgment criterion is fuzzyyer, sometimes is inconvenient to operate; If obtain based on the like product fault data, the present invention judges according to fault Distribution Type Analysis flow process, has improved efficiency and precision that failure-free data is analyzed.

Contrast several failure-free data analytical approachs, partition cloth curve method, minimum χ ²The key of-Fa is to estimate failure probability, classical estimation error to failure probability is larger, method of equivalent failure number need to be estimated equivalent failure number, the calculated amount of revised Maximum Likelihood function method, transformation CLASS-K method is larger, the generalized linear model method is mainly used in the fault free analysis of Weibull distribution, the MLR(monotone likelihood ratio) the lower limit range of application of family of distributions fiduciary level is fewer; Bayes method, multi-layer Bayes Method are mainly used in partition cloth curve method and minimum χ ²The estimation of failure probability in-Fa, method is more loaded down with trivial details; The present invention adopts optimum to put the letter estimation technique to carry out the failure-free data analysis, raise the efficiency the enhancement engineering operability.

The tradition iterative numerical approach solves nonlinear equation and mainly contains dichotomy, Newton method, process of iteration and quadratic factor algorithm, these methods are mainly for the monadic algebra equation, and fault distribution parameter equation is monobasic indicial equation and binary nonlinear integral equation, the present invention adopts the Active Set Algorithm for Solving fault distribution parameter equation of nonlinear programming approach, improves search efficiency, speed and precision.

The present invention's advantage compared with prior art is: 1) method of planning Network Based, adopt WinQSB software building network planning figure, obtain critical path and key job, select the method for regular inspection content optimization target, overcome the blindly deficiency of poor efficiency of traditional regular inspection content optimization.2) can be by looking into fault distribution pattern table or according to the sample fault Distribution Type Analysis flow process based on the like product fault data, determining the distribution pattern of regular inspection work investigation fault, utilize fully historical reliability data message and feature, improved efficiency and precision that failure-free data is analyzed.3) adopt optimum to put the letter estimation technique and carry out the failure-free data analysis, provide the confidence lower limit of (1-α) confidence level of the fiduciary level of aircraft, engine and airborne equipment (its most common failure is distributed as exponential distribution, Weibull distribution, normal distribution and lognormal distribution), set up fault distribution parameter equation.Than Bayes method, multi-layer Bayes Method and other classical way, efficiency is higher, and the engineering operability is stronger.4) fault distribution parameter equation solution is changed into to non-linear constrain extreme-value problem, adopt the Active Set algorithm of nonlinear programming approach, more traditional equation numerical method search efficiency is high, speed is fast, solving precision is high.

The accompanying drawing explanation

Fig. 1 is a kind of aircraft regular inspection content optimization flow process of analyzing based on failure-free data of the present invention;

Fig. 2 is that process flow diagram is determined in the fault distribution, and wherein θ is the increment average, S ₂For the increment average, λ (t) is failure rate; If X ₁, X ₂..., X _nA sample from overall X, x ₁, x ₂..., x _nCorresponding sample value, the increment intermediate value $t_n={10}^{\stackrel{\‾}{X}}={10}^{\frac{1}{n}\underset{k=1}{\overset{n}{\mathrm{\Σ}}}{x}_k};$

Fig. 3 is confidence level 1-α=0.8 o'clock, t=800(h) front wheel hub, active margin and brake gear cylinder seat, crack fault, on horizontal tail, the one-sided confidence lower limit of lower wall panels auxiliary box wallboard and back segment honeycomb and inlet lip metal honeycomb structure glue-line fiduciary level solves and arranges and simulation result;

Fig. 4 is confidence level 1-α=0.8 o'clock, and the one-sided confidence lower limit that cockpit pressure t=800(h) is regulated the subsystem fiduciary level solves and arranges and result.

Specific implementation method:

1. aircraft regular inspection content optimization target analysis

Method of planning Network Based, the PERT_CPM module of employing WinQSB software, according to software supplemental instruction book, input service sequence number, work title, preceding activity and run duration, build the network planning figure that has the work of aircraft regular inspection now; Obtain critical path and key job; The key job that the selection duration is grown is as regular inspection content optimization target.

2. regular inspection is investigated the Distribution Type Analysis of fault

Regular inspection content optimization target is carried out to optimize and analyze, can table look-up and determine the distribution pattern of regular inspection work investigation fault according to the scope of application shown in table 1.

Table 1 fault distribution pattern table

If table look-up, can not determine, according to like product historical failure data, carry out the fault Distribution Type Analysis based on the like product fault data according to step as shown in Figure 2.If X ₁, X ₂..., X _nA sample from overall X, x ₁, x ₂..., x _nCorresponding sample value, the increment intermediate value

3. based on optimum, put the failure-free data analysis of the letter estimation technique

In fixed time test, if the cumulative distribution function of life of product T is F (t, θ), θ ∈ Θ is unknown parameter (can be vector), Θ is parameter space, and reliability index (fiduciary level, Q-percentile life, mean lifetime etc.) g (θ) is the generalized real value function of θ.If there be n its life-span of product to be divided into for T ₁, T ₂..., T _n, for given n Censored Test time X ₁, X ₂..., X _n, obtain the observed reading b of characteristic quantity b ₁, b ₂..., b _n, the test figure that can observe under above-mentioned Censored Test is Z=(t ₁, b ₁..., t _n, b _n).T wherein _i=min (T _i, X _i), i=1 ..., n,

$b_i=\left\{\begin{array}{cc}0& (T_i>X_i)\\ 1& (T_i\≤X_i)\end{array}\right.---\left(1\right)$

B when the product non-fault _i=0, Z ⁰=(t ₁, 0 ..., t _n, 0), claim that these class data are failure-free data (Zero-Failure Data), are denoted as (t _i, b _i).Adopt optimum in classical way to put the confidence lower limit of (1-α) confidence level that the letter estimation technique provides the fiduciary level of aircraft, engine and airborne equipment (its most common failure is distributed as exponential distribution, Weibull distribution, normal distribution and lognormal distribution).

3.1 exponential distribution

If product cumulative distribution function is F (t, θ)=1-e ^{-t/ θ}, θ wherein>and 0 be mean lifetime.If from a collection of product, appointing, get the individual fixed time test (or on-the-spot use) that carries out of n, to the stipulated time, stop test (or use) and do not find that product bug, the working time of product are t ₁≤ t ₂≤ ...≤t _n.The confidence level of fiduciary level R (t, θ) is that the optimum confidence lower limit of 1-α is:

$R_L\left(t\right)=\exp \left(\frac{t\ln \mathrm{\α}}{\underset{t=1}{\overset{n}{\mathrm{\Σ}}}{t}_i}\right)---\left(2\right)$

3.2 Weibull distribution

If life of product is obeyed Weibull distribution, its distribution function is

Form parameter m wherein>0, characteristics life η>the 0th, unknown parameter.Be provided with n product, the outfield working time is t ₁≤ t ₂≤ ...≤t _nThe time do not find fault, the confidence level of fiduciary level R (t) is that the one-sided confidence lower limit of optimum of 1-α is:

If m ₁With m ₂Known, and 0<m ₁≤ m≤m ₂(m ₁<m ₂).

Wherein ${\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="2013103126986100003DEST\_PATH\_IMAGE004.png"\; state="\{\{state\}\}">t</figure-callout>}}_0={\left(\underset{i=1}{\overset{n}{\mathrm{\&Pi;}}}{t}_i\right)}^{\frac{1}{n}},$ t _(n)=max(t ₁,...,t _n)， $a=\frac{{\mathrm{<figure-callout\; id="1"\; label="t\; m"\; filenames="2013103126986100003DEST\_PATH\_IMAGE004.png"\; state="\{\{state\}\}">t</figure-callout>}}^{m_{}}}{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{<figure-callout\; id="1"\; label="t\; i\; m"\; filenames="2013103126986100003DEST\_PATH\_IMAGE004.png"\; state="\{\{state\}\}">t</figure-callout>}}_{i{m}_{}}^{{}_1}},b=\frac{{\mathrm{<figure-callout\; id="2"\; label="t\; m"\; filenames="2013103126986100003DEST\_PATH\_IMAGE004.png"\; state="\{\{state\}\}">t</figure-callout>}}^{m_{}}}{\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{<figure-callout\; id="2"\; label="t\; i\; m"\; filenames="2013103126986100003DEST\_PATH\_IMAGE004.png"\; state="\{\{state\}\}">t</figure-callout>}}_{i{m}_{}}^{{}_2}},$ M ^*It is following equation root

$\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\left(\frac{t_i}{t}\right)}^m\ln \left(\frac{t_i}{t}\right)=0---\left(5\right)$

3.3 normal distribution

If the cumulative distribution function of product normal distribution is

Wherein location parameter μ, also claim average; Scale parameter σ, also claim standard deviation.Location parameter μ=0, the normal distribution of scale parameter σ=1 is called standardized normal distribution, and distribution function is

Obviously have

If n product work time is t ₁, t ₂..., t _nShi Wei breaks down ,-∞<μ<∞, 0<σ<∞.

(1) under restrictive condition, the confidence level of fiduciary level R (t) is the one-sided confidence lower limit of optimum of 1-α

Restrictive condition σ ₁≤ σ≤σ ₂, σ ₁And σ ₂Known, 0<σ ₁<σ ₂<∞.

T in formula _(n)=max (t ₁..., t _n);

(μ ₀, σ ₀) be following solution of equations:

$\left\{\begin{array}{c}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&Phi;}}^{\&prime;}(\mathrm{\&mu;}+\frac{1}{\mathrm{\&sigma;}}(t-t_i))}{\mathrm{\&Phi;}(\mathrm{\&mu;}+\frac{1}{\mathrm{\&sigma;}}(t-t_i))}(t-t_i)=0\\ \underset{i=1}{\overset{n}{\mathrm{\&Pi;}}}\mathrm{\&Phi;}(\mathrm{\&mu;}+\frac{1}{\mathrm{\&sigma;}}(t-t_i))=\mathrm{\&alpha;}\end{array}\right.---\left(\text{7}\right)$

If known σ, ask for μ (σ) by following equation

$\underset{i=1}{\overset{n}{\mathrm{\&Pi;}}}\mathrm{\&Phi;}(\mathrm{\&mu;}\left(\mathrm{\&sigma;}\right)+\frac{1}{\mathrm{\&sigma;}}(t-t_i))=\mathrm{\&alpha;}---\left(8\right)$

(2) confidence level of fiduciary level R (t) is the one-sided confidence lower limit of optimum of 1-α

T in formula _(n)=max (t ₁..., t _n), p equals t n the working time in product _(n)The product number;

(μ ₁, σ ₁) be the unique solution of following system of equations:

$\left\{\begin{array}{c}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&Phi;}}^{\&prime;}(\mathrm{\&mu;}+\frac{1}{\mathrm{\&sigma;}}(t-t_i))}{\mathrm{\&Phi;}(\mathrm{\&mu;}+\frac{1}{\mathrm{\&sigma;}}(t-t_i))}(t-t_i)=0\\ \underset{i=1}{\overset{n}{\mathrm{\&Pi;}}}\mathrm{\&Phi;}(\mathrm{\&mu;}+\frac{1}{\mathrm{\&sigma;}}(t-t_i))=\mathrm{\&alpha;}\end{array}\right.---\left(\text{10}\right)$

3.4 lognormal distribution

If product cumulative distribution function is $F\left(t\right)=\frac{1}{\sqrt{2\mathrm{\&pi;}}\mathrm{\&sigma;}}\underset{0}{\overset{t}{\&Integral;}}\frac{1}{x}{e}^{\frac{{(\ln x-\mathrm{\&mu;})}^2}{2{\mathrm{\&sigma;}}^2}}\mathrm{dx}=\mathrm{\&Phi;}\left(\frac{\ln t-\mathrm{\&mu;}}{\mathrm{\&sigma;}}\right),$ Wherein μ claims the logarithm average; σ claims the logarithm standard deviation.If n product work time is t ₁, t ₂..., t _nShi Wei breaks down ,-∞<μ<∞, and 0<σ<∞, the confidence level of fiduciary level R (t) is that the one-sided confidence lower limit of optimum of 1-α is:

T in formula _(n)=max (t ₁..., t _n), p equals t n the working time in product _(n)The product number;

(μ ₁, σ ₁) be the unique solution of following system of equations:

$\left\{\begin{array}{c}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&Phi;}}^{\&prime;}(\mathrm{\&mu;}+\frac{1}{\mathrm{\&sigma;}}\ln \frac{t}{t_i})}{\mathrm{\&Phi;}(\mathrm{\&mu;}+\frac{1}{\mathrm{\&sigma;}}\ln \frac{t}{t_i})}\ln \frac{t}{t_i}=0\\ \underset{i=1}{\overset{n}{\mathrm{\&Pi;}}}\mathrm{\&Phi;}(\mathrm{\&mu;}+\frac{1}{\mathrm{\&sigma;}}\ln \frac{t}{t_i})=\mathrm{\&alpha;}\end{array}\right.---\left(\text{12}\right)$

4. based on the fault distribution parameter equation solution of nonlinear programming

Tradition equation iterative numerical approach, blindness is larger, and search efficiency is low.The present invention adopts nonlinear programming approach, solves as non-linear constrain extreme-value problem.

The mathematical model of non-linear constrain extreme-value problem is: ask n-dimensional vector

(T means transposition), make the scalar objective function local minimum, that is:

Meet lower column constraint: non-linear constrain $c\left(\stackrel{\&RightArrow;}{X}\right)\&le;0$ With $\mathrm{ceq}\left(\stackrel{\&RightArrow;}{X}\right)=0;$ Linear restriction $A\stackrel{\&RightArrow;}{X}\&le;b$ With $\mathrm{Aeq}\stackrel{\&RightArrow;}{X}=\mathrm{beq};$ Span $\stackrel{\&RightArrow;}{l}\&le;\stackrel{\&RightArrow;}{X}\&le;\stackrel{\&RightArrow;}{u}.$

Mathematical model or write as updating currently form:

$\left\{\begin{array}{cc}\min f\left(\stackrel{\&RightArrow;}{X}\right)& \\ g_j\left(\stackrel{\&RightArrow;}{X}\right)\&le;0& j=\mathrm{1,2},...,l\end{array}\right.---\left(13\right)$

The Matlab the inside solves non-linear constrain extreme-value problem and mainly adopts Active Set algorithm, i.e. so-called Ku En-Plutarch (Kuhn-Tucher) equation: establish

The local minimum point of nonlinear programming,

With

(j=1,2 ..., l) at point There is single order continuous offset derivative at place, and

, there is Lagrangian in all active constraint gradient linear independences at place

Make

$\left\{\begin{array}{c}\&dtri;f\left({\stackrel{\&RightArrow;}{X}}^{*}\right)+\underset{j=1}{\overset{l}{\mathrm{\&Sigma;}}}{u}_j^{*}\&dtri;g_j\left({\stackrel{\&RightArrow;}{X}}^{*}\right)=0\\ \\ \begin{array}{cc}{u}_j^{*}{g}_j\left({\stackrel{\&RightArrow;}{X}}^{*}\right)=0& j=\mathrm{1,2},...,l\end{array}\\ \begin{array}{cc}{u}_j^{*}\&GreaterEqual;0& j=\mathrm{1,2},...,l\end{array}\end{array}\right.$

Wherein (del) be to scalar Hamiltonian operator,

For vector, namely $\&dtri;g_j\left(\stackrel{\&RightArrow;}{X}\right)=[\frac{\&PartialD;g_j\left(\stackrel{\&RightArrow;}{X}\right)}{\&PartialD;x_1},\frac{\&PartialD;g_j\left(\stackrel{\&RightArrow;}{X}\right)}{\&PartialD;x_2},...,{\frac{\&PartialD;g_j\left(\stackrel{\&RightArrow;}{X}\right)}{\&PartialD;x_n}]}^T.$

5. aircraft specialty regular inspection content optimization is analyzed

If the fiduciary level of aircraft requires: position and the parts with hiding function, fiduciary level that security relationship is great > 85%; The fiduciary level of general parts is 0.7～0.8; Confidence level: 1-α=0.80.

According to regular inspection content optimization flow process shown in Figure 1, can obtain following regular inspection content optimization suggestion: it is that annex flaw detection (16h) and pressure are regulated subsystem inspection (6h) that 200/400 hour regular inspection reduces content.Concrete operations are as follows:

5.1 between accessories cart, 200 hours 4 regular inspection contents can extend to 800 hours

To 24 of aircraft random inspections, flight time is all more than 400 hours, analyzing 2007.2～2013.3 years failure loggings shows, the front wheel hub of one example, active margin and brake gear cylinder seat do not occur, crack fault, lower wall panels auxiliary box wallboard and back segment honeycomb and inlet lip metal honeycomb structure glue-line fault on horizontal tail.In all 2717 faults, only have one be nondestructive flaw detection examination out, and be not 200 hours/400 hours regular inspection contents.According to Fig. 2 step, analyze, front wheel hub, active margin and brake gear cylinder seat, crack fault, obeys logarithm normal distribution lnt～N (μ, σ fault-time of lower wall panels auxiliary box wallboard and back segment honeycomb and inlet lip metal honeycomb structure glue-line on horizontal tail ²).The sample failure free time is 463,684,656.5,850,602.4,952.7,648.9,703,728.6,740.3,843.6,810.2,519.8,550.8,561.6,509.4,529,527.1,483.6,512, and 671,474.3,524,642.2 hours.

Adopt the analysis method for reliability of failure-free data.

(1) confidence level 1-α=0.8 o'clock, t=200,400, the one-sided confidence lower limit of fiduciary level 600(h)

Separate: because ${\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="2013103126986100003DEST\_PATH\_IMAGE004.png"\; state="\{\{state\}\}">t</figure-callout>}}_0={\left(\underset{i=1}{\overset{24}{\mathrm{\&Pi;}}}{t}_i\right)}^{\frac{1}{24}}=619.8\left(h\right),$ t ₍₂₄₎＝952.7(h)

So 0<t<t ₍₀₎

$R_L\left(200\right)=R_L\left(400\right)=R_L\left(600\right)={0.2}^{\frac{1}{24}}=0.94$

And adopt 200 hours regular inspections and 400 hours regular inspections little to the raising effect of fiduciary level.

(2) confidence level 1-α=0.8 o'clock, the one-sided confidence lower limit of fiduciary level t=800(h)

Because ${\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="2013103126986100003DEST\_PATH\_IMAGE004.png"\; state="\{\{state\}\}">t</figure-callout>}}_0={\left(\underset{i=1}{\overset{24}{\mathrm{\&Pi;}}}{t}_i\right)}^{\frac{1}{24}}=619.8\left(h\right),$ t ₍₂₄₎=952.7（h）

So t ₍₀₎<t<t ₍₂₄₎

Solving equations, ask (μ ₁, σ ₁)

$\left\{\begin{array}{c}\underset{i=1}{\overset{24}{\mathrm{\&Sigma;}}}\frac{{\mathrm{\&Phi;}}^{\&prime;}(\mathrm{\&mu;}+\frac{1}{\mathrm{\&sigma;}}\ln \frac{t}{t_i})}{\mathrm{\&Phi;}(\mathrm{\&mu;}+\frac{1}{\mathrm{\&sigma;}}\ln \frac{t}{t_i})}\ln \frac{t}{t_i}=0\\ \underset{i=1}{\overset{24}{\mathrm{\&Pi;}}}\mathrm{\&Phi;}(\mathrm{\&mu;}+\frac{1}{\mathrm{\&sigma;}}\ln \frac{t}{t_i})=0.2\end{array}\right.$

Adopt the Optimization Toolbox of matlab, select Constrained Nonlinear to optimize solver, Active set algorithm, be constrained to μ ₁∈ (0, ∞), σ ₁(0, ∞), search starting point is [0.1,0.1] to ∈, and iteration 20 steps obtain μ ₁=1.022, σ ₁=0.236, as shown in Figure 3.So R _L(800)=Φ (1.022)=0.85

Therefore suggestion extends to 800 hours by 200 hours regular inspection contents shown in table 2 between accessories cart.

200 hours regular inspection optimize the contents between table 2 accessories cart

5.2 between accessories cart, 400 hours 15 regular inspection contents can extend to 800 hours

24 aircrafts of random inspection, flight time is have 13 more than 600 hours, analyzing 2007.2～2013.3 years failure loggings shows, the front wheel hub of one example, active margin and brake gear cylinder seat do not occur, crack fault, lower wall panels auxiliary box wallboard and back segment honeycomb and inlet lip metal honeycomb structure glue-line fault on horizontal tail.If front wheel hub, active margin and brake gear cylinder seat, crack fault, obeys logarithm normal distribution fault-time of lower wall panels auxiliary box wallboard and back segment honeycomb and inlet lip metal honeycomb structure glue-line on horizontal tail.Suggestion extends to 800 hours by 400 hours regular inspection contents between accessories cart shown in table 3.

400 hours regular inspection optimize the contents between table 3 accessories cart

5.3 between aircraft vehicle, 200/400 hour cockpit pressure is regulated subsystem regular inspection content and can be extended to 800 hours

According to Fig. 2 step, analyze, aircraft cabin pressure is regulated subsystem t fault-time and is met Weibull distribution.The failure free time that 24 airplane sample cockpit pressures are regulated subsystem is 463,684,656.5,850,602.4,952.7,648.9,703,728.6,740.3,843.6,810.2,519.8,550.8,561.6,509.4,529,527.1,483.6,512,671,474.3,524,642.2 hours.

(1) confidence level 1-α=0.8 o'clock, t=200,400, the one-sided confidence lower limit of fiduciary level 600(h)

Separate: because t ₍₂₄₎=952.7(h), p=1, ${\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="2013103126986100003DEST\_PATH\_IMAGE004.png"\; state="\{\{state\}\}">t</figure-callout>}}_0={\left(\underset{i=1}{\overset{24}{\mathrm{\&Pi;}}}{t}_i\right)}^{\frac{1}{24}}=619.8\left(h\right)$

So 0<t<t ₍₀₎

$R_L\left(200\right)=R_L\left(400\right)=R_L\left(600\right)={0.2}^{\frac{1}{24}}=0.94$

And adopt 200 hours regular inspections and 400 hours regular inspections little to the raising effect of fiduciary level.

(2) confidence level 1-α=0.8 o'clock, the one-sided confidence lower limit of fiduciary level t=800(h)

Because ${\mathrm{<figure-callout\; id="0"\; label="t"\; filenames="2013103126986100003DEST\_PATH\_IMAGE004.png"\; state="\{\{state\}\}">t</figure-callout>}}_0={\left(\underset{i=1}{\overset{24}{\mathrm{\&Pi;}}}{t}_i\right)}^{\frac{1}{24}}=619.8\left(h\right),$ t ₍₂₄₎=952.7（h）

So t ₍₀₎<t<t ₍₂₄₎

Solve an equation, m ^*Following equation root (m ^*0)

$\underset{i=1}{\overset{24}{\mathrm{\&Sigma;}}}{\left(\frac{t_i}{t}\right)}^m\ln \left(\frac{t_i}{t}\right)=0$

Adopt the Optimization Toolbox of matlab, select Constrained Nonlinear to optimize solver, Active set algorithm, be constrained to m ^*(0, ∞), search starting point is [0] to ∈, and iteration 15 steps obtain m ^*=6.593, as shown in Figure 4.

So $R_L\left(800\right)={0.2}^{\left(\frac{t^{6.593}}{\underset{i=1}{\overset{24}{\mathrm{\&Sigma;}}}{t}_i^{6.593}}\right)}=0.86$ 。

Claims (5)

1. an aircraft regular inspection content optimization method of analyzing based on failure-free data, is characterized in that step is as follows: 1) aircraft regular inspection content optimization target analysis; 2) Distribution Type Analysis of regular inspection investigation fault; 3) based on optimum, put the failure-free data analysis of the letter estimation technique; 4) based on the fault distribution parameter equation solution of nonlinear programming.

2. according to a kind of described aircraft regular inspection content optimization method of analyzing based on failure-free data of right 1, it is characterized in that: the optimization aim analysis of described step 1) is divided into network planning figure structure, the critical path of existing aircraft regular inspection work and key job is obtained, three steps of regular inspection content optimization target selection.

3. according to a kind of described aircraft regular inspection content optimization method of analyzing based on failure-free data of right 1, it is characterized in that: the Distribution Type Analysis described step 2) has fault distribution pattern table analysis and two kinds of modes of fault distribution pattern process analysis.

4. according to a kind of described aircraft regular inspection content optimization method of analyzing based on failure-free data of right 1, it is characterized in that: in described step 3), put the confidence lower limit of the failure-free data analysis of the letter estimation technique according to (1-α) confidence level of the fiduciary level of formula aircraft, engine and airborne equipment (its most common failure is distributed as exponential distribution, Weibull distribution, normal distribution and lognormal distribution) based on optimum, set up fault distribution parameter equation.

5. according to a kind of described aircraft regular inspection content optimization method of analyzing based on failure-free data of right 1, it is characterized in that: in described step 4), fault distribution parameter equation solution adopts the Active Set algorithm of nonlinear programming approach.

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