CN107844663A - A kind of modeling reliability method based on Cumulative Fatigue Damage - Google Patents
A kind of modeling reliability method based on Cumulative Fatigue Damage Download PDFInfo
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Abstract
A kind of modeling reliability method based on Cumulative Fatigue Damage, the present invention relates to the modeling reliability method based on Cumulative Fatigue Damage.The present invention is in order to solve the problems, such as that existing method is computationally intensive, the determination of enchancement factor distributed constant has difficulties in the long and Reliability Calculation Model that expends the time.The present invention includes：One：Reliability Model based on Cumulative Fatigue Damage is established according to fatigue stress Life method and probability damage tolerance limit；Two：F when determining that structural fatigue accumulated damage is dam according to regression modela(a | dam), pass through fa(a | dam) solve the Reliability Model based on Cumulative Fatigue Damage.The CALCULATION OF FAILURE PROBABILITY error that the inventive method obtains is 1.82%.CA2 groups test specimen is in accumulated damage dam1Failure probability when=1 is 45.73%, calculation error 4.27%.The inventive method has very high computational accuracy.The present invention is used for aircraft fatigue calculation of structure reliability degree field.
Description
Technical field
The present invention relates to the modeling reliability method based on Cumulative Fatigue Damage.
Background technology
Due to bearing random dynamic loads in more structure designs and flight course, fatigue failure is that aircaft configuration fails most
Important way.The appraisal procedure of aircraft structural reliability has been developed more than 30 years, is generally divided into deterministic parsing method and general
Forthright analysis method.More representative in deterministic parsing method is fatigue stress Life method, in probabilistic analysis
Studied in method it is more be probability damage margin method.
Chinese Air Force and USN (Y.Kim et al, Air Force Journal of Logistics, Volume
XXIX, No.3/4.) fatigue life of aircraft is calculated at present still using fatigue stress life approach.It is linear based on Miner
Accumulated damage theorem (A.Palmgren, 1945, Ball and roller bearing engineering, SKF
Industries, Philadelphia.), the load that fatigue stress Life method directly bears structure and lifetime to one
Rise.The fatigue life of aircaft configuration is decided by full machine fatigue test, and during full machine fatigue experiment, the expection of aircraft bears to carry
Lotus is in laboratory environments by simulation of loading to aircraft.The design active time of aircraft is often set as full machine fatigue test
Obtained structure fatigue life divided by 2 (life damage coefficients), life damage coefficient is decided by material character and fatigue load.For
Ensure that aircraft is not above fatigue life limitation during service, be required for the fatigue for calculating the machine to tire out after each execution task
Product damage.When Cumulative Fatigue Damage reaches 1, aircraft reaches the fatigue design life-span upper limit, and aircraft needs repaired, change pass
Key part is retired.The simple and practical of fatigue stress life approach makes it by universal with determining the fatigue of aircaft configuration
Life-span, but due to the presence of life damage coefficient, can usually cause structure not reach the limit of fatigue life also just needs to carry out
Maintenance is retired, and this can cause structural life-time to waste, and reliability of structure can not be provided clearly.
Because certainty fatigue analysis method is conservative in terms of life appraisal, and its definition for " high-reliability "
Not very clearly (G.Frank.A stochastic approach to determine lifetimes and
inspection schemes for aircraft components.International Journal of Fatigue,
2008.30:138-149.), and substantial amounts of engineering experience shows, influences the factors of structure fatigue life its dispersed tables
Reveal a kind of statistical regularity (D.A.Virkler, B.M.Hillbery, P.K.Goel.The statistical
nature of fatigue crack propagation.Journal of engineering material and
technology transaction of the ASME,1979,101:148-153.), probability damage tolerance limit is as a kind of energy
Enough handle high-reliability and take into full account that the fatigue analysis method of the probability nature of various factors is obtaining greatly over the past thirty years
Research and development (M.Nicolas, V.Ludovic, H.Francois.A probabilistic the model to of power
predict the formation and propagation of crack networks in thermal
fatigue.International Journal of Fatigue,2009,31:565-574.).In aeronautical engineering field, generally
Rate damage Tolerance Approach has also obtained (Y.Macheret, P.Kpehn, the J.Teuchman and such as research energetically, Macheret
W.Scheuren.Effect of initial defect distribution on accuracy of predicting
aircraft probability of failure,International Conference on Prognostics and
Health Management, Denver, October 2008.) propose to calculate F-18 wings with probability damage margin method
(the K.Y.Lin and A.V.Styuart.Probabilistic approach to such as the crash rate of annex bulkhead, Lin
damage tolerance design of aircraft composite structures.Journal of Aircraft,
2007,44(4):1309-1317.) propose the fatigue failure with probability damage margin method processing Aircraft Composite Structure
Problem.Although many scholars are proposed different probability damage margin methods to handle the Fatigue Failures of aircraft,
Because failure computation model is excessively complicated, lack damage data, the problems such as computational efficiency is low, probability damage margin method is in engineering
Application aspect still suffers from many problems.
With the continuous development of sensor technology, increasing sensor is applied to detect pass in the design of aircraft
Tired information (L.Molent and B.Aktere, the Review of Fatigue Monitoring of Agile at key position
Military Aircraft, Fatigue Fract Engng Mater Struct 23, pp.767-785,2000.), China
Air force also disposes sensor to record the fatigue load information of key position on new type.The fatigue load information of acquisition is big
More is all for being depicted as S-N curves, calculates the Cumulative Fatigue Damage under corresponding load information using Stress-Life method to guard
Estimation fatigue life.
The content of the invention
The invention aims to solve, existing method is computationally intensive, expends in time length and Reliability Calculation Model
The shortcomings that determination of enchancement factor distributed constant has difficulties, and propose a kind of modeling reliability side based on Cumulative Fatigue Damage
Method.
A kind of modeling reliability method based on Cumulative Fatigue Damage comprises the following steps：
Step 1：Reliability mould based on Cumulative Fatigue Damage is established according to fatigue stress Life method and probability damage tolerance limit
Type：
Wherein PoF (dam) represents crash rate when structural fatigue accumulated damage is dam, a | dam represents structural fatigue accumulation
Damage for dam when crack length, a is structural crack length, fa(a | dam) represent structural crack Length Pr Density Distribution letter
Number, acStructure critical crack length, fac(ac) represent structure critical crack length probability density function；
Step 2：F when determining that structural fatigue accumulated damage is dam according to regression modela(a | dam), pass through the f of determinationa
The Reliability Model based on Cumulative Fatigue Damage that (a | dam) solution procedure one is established.
Beneficial effects of the present invention are：
In order to make full use of the fatigue load information that sensor obtains, rather than simple calculate is corresponded under load information
Cumulative Fatigue Damage, the fatigue life of conservative estimation structure, the present invention are analyzing Cumulative Fatigue Damage and crack size point
On the basis of the relation of cloth parameter, it is proposed that the crack size distribution model based on Cumulative Fatigue Damage, and join probability damage is held
Crack propagation life Interference Model in limit method, establishes new reliability model.New reliability model combines fatigue
The advantages of simple and practical and probability damage tolerance limit of stress life can handle high-reliability, and effectively avoid fatigue stress
Life method is overly conservative, and probability damage tolerance limit method model is excessively complicated, random parameter is difficult to estimate in model, computational efficiency is low etc.
Problem.
The CALCULATION OF FAILURE PROBABILITY error obtained by computational methods proposed by the present invention is 1.82%.CA2 groups test specimen is being accumulated
Damage dam1Failure probability when=1 is 45.73%, calculation error 4.27%.Knot of the invention based on Cumulative Fatigue Damage
Structure Reliability Model has very high computational accuracy.
Brief description of the drawings
Fig. 1 is that CA1 crack size data are fitted goodness assay figure；
Fig. 2 is that CA2 crack size data are fitted goodness assay figure；
Fig. 3 is CA1 Cumulative Fatigue Damages and the Regression Analysis Result figure of crack size distribution mean value relationship；
Fig. 4 is CA2 Cumulative Fatigue Damages and the Regression Analysis Result figure of crack size distribution mean value relationship；
Fig. 5 is CA1 Cumulative Fatigue Damages and the Regression Analysis Result figure of crack size distribution offset relation；
Fig. 6 is CA2 Cumulative Fatigue Damages and the Regression Analysis Result figure of crack size distribution offset relation；
Fig. 7 is the failure probability result figure under CA1 with CA2 difference accumulated damages.
Embodiment
Embodiment one：A kind of modeling reliability method based on Cumulative Fatigue Damage comprises the following steps：
Due to bearing random dynamic loads in more structure designs and flight course, fatigue failure is that aircaft configuration fails most
Important way.The appraisal procedure of aircraft structural reliability has been developed more than 30 years, is generally divided into deterministic parsing method and general
Forthright analysis method.More representative in deterministic parsing method is fatigue stress Life method, in probabilistic analysis
Studied in method it is more be probability damage margin method.The simple and practical of fatigue stress life approach makes it by universal
With determining the fatigue life of aircaft configuration (D.T.Rusk and P.Hoffman, 5Th Joint NASA/FAA/DoD
Conference on Aging Aircraft, 2001.), but due to the presence of life damage coefficient, structure usually can be caused also
Do not reach fatigue life the limit just need to be repaired or retired, this can cause structural life-time to waste (S.C.Forth et
Al, 6Th Joint NASA/FAA/DoD Conference on Aging Aircraft, 2001.), and structure is reliable
Property can not be provided clearly.Although many scholars are proposed different probability damage margin methods to handle the fatigue of aircraft
Problem of Failure, but because failure computation model is excessively complicated, lack damage data, the problems such as computational efficiency is low, probability damage
Margin method still suffers from many problems (US Department of Transportation and in terms of engineer applied
Federal Aviation Administration.Probabilistic design methodology for
composite aircraft structures.DOT/FAA/AR-99/2,1999.).In view of the above-mentioned problems, the present invention is dividing
On the basis of the relation for having analysed Cumulative Fatigue Damage and crack size distribution parameter, it is proposed that the crackle chi based on Cumulative Fatigue Damage
Very little distributed model, and the crack propagation life Interference Model in join probability damage Tolerance Approach, are established new based on fatigue
The reliability model of accumulated damage.
Step 1：Reliability mould based on Cumulative Fatigue Damage is established according to fatigue stress Life method and probability damage tolerance limit
Type：
Wherein PoF (dam) represents crash rate when structural fatigue accumulated damage is dam, a | dam represents structural fatigue accumulation
Damage for dam when crack length, a is structural crack length, fa(a | dam) represent structural crack Length Pr Density Distribution letter
Number, acStructure critical crack length,Represent structure critical crack length probability density function；
Crack size distribution density function f when structural fatigue accumulated damage is damaWhen (a | dam) can be determined, then
Failure probability of the structure in dam can be obtained by formula (1).Formula (1) be the present invention establish based on Cumulative Fatigue Damage
Model of structural reliability.From formula (5), can be determined by analyzing the crack size distribution under corresponding load cycle number N
fa(a|dam)。
Step 2：F when determining that structural fatigue accumulated damage is dam according to regression modela(a | dam), pass through the f of determinationa
The Reliability Model based on Cumulative Fatigue Damage that (a | dam) solution procedure one is established.
Embodiment two：Present embodiment is unlike embodiment one：Fatigue should in the step 1
The expression formula of power Life method is：
Miner linear cumulative damage laws are thought under Cyclic Load, fatigue damage and the relation of load cycle number
It is linear, and fatigue damage can be separate and orthogonal with linear, additive, between each stress, when cumulative damage
When wound reaches 1, fatigue rupture just occurs for test specimen.
dami=ni/Ni (3)
Wherein damiTo damage component, D is total accumulated damage amount, niIn stress level it is S for test specimeniIn the presence of work
Make cycle-index, NiIt is test specimen in stress level SiUnder destruction cycle-index.
Based on Miner linear cumulative damage theorems, the load that fatigue stress Life method directly bears structure is closed with the life-span
Connection is together.The fatigue life of aircaft configuration is decided by full machine fatigue test, during full machine fatigue experiment, aircraft it is pre-
Phase bears load in laboratory environments by simulation of loading to aircraft.The design active time of aircraft is often set as full machine
The structure fatigue life divided by 2 (life damage coefficients) that fatigue test obtains, life damage coefficient are decided by material character and tired
Labor load.In order to ensure aircraft is not above fatigue life limitation during service, it is required for calculating after each execution task and is somebody's turn to do
The Cumulative Fatigue Damage of machine.When fatigue accumulation loss reaches 1, aircraft reaches the fatigue design life-span upper limit, and aircraft needs to carry out
Maintenance, change key component or retired.The simple and practical of fatigue stress life approach makes it by universal with determining to fly
The fatigue life of machine structure, but due to the presence of life damage coefficient, can usually cause structure not reach the pole of fatigue life also
Limit is with regard to needing to be repaired or retired, and this can cause structural life-time to waste, and the reliability of structure can not be provided clearly.
Other steps and parameter are identical with embodiment one.
Embodiment three：Present embodiment is unlike embodiment one or two：Probability in described rapid one
Damage tolerance crackle interference life model be：
Damage tolerance is for base with certainty fracture mechanics (Deterministic Fracture Mechanics, DFM)
What plinth was established, its analysis process is respectively provided with the implication of intermediate value with result, and its reliability is removed by using certainty crack propagation life
Ensured with specified splitting factor.Probability damage tolerance analysis method then takes into full account that influence is split on the basis of damage tolerance
Line extends the dispersiveness of life-span each factor, studies its probability nature, and given crack propagation life is calculated so as to accurate quantitative analysis
Corresponding reliability.
Wherein fa(a, t) is crack distribution density function of flight moment when being t, fac(ac) be structure critical crack chi
Very little distribution density function, PoF (t) are the crash rates of flight moment structure when being t.
Because the crash rate computation model represented by formula (3) is excessively complicated, integration method is typically difficult to handle, one in engineering
As solved using Monte-Carlo methods, but calculate failure probability be (10-4~10-6) when, it is ensured that 95% puts
Reliability Monte-Carlo methods need carry out 107-109Secondary simulation, amount of calculation and spent time are very considerable, actually should
Difficulty is usually present in.Due to lacking test data and the tired information data under actual condition, reliability meter can not be obtained
Enchancement factor distributed constant is really permanent in calculation model is commonly present difficulty, therefore probability damage margin method is in terms of engineer applied
Still suffer from many problems.
Other steps and parameter are identical with embodiment one or two.
Embodiment four：Unlike one of present embodiment and embodiment one to three：The step 1
It is middle establish the Reliability Model based on Cumulative Fatigue Damage detailed process be：
Flight moment t cyclic loading number N is obtained by structural healthy monitoring system, foundation Stress-Life method, with reference to
The cyclic loading number N arrived, the Cumulative Fatigue Damage dam of t is obtained, therefore the transformational relation being shown below be present：
Reliability Model based on Cumulative Fatigue Damage is converted to by formula (5) and formula (4).
Other steps and parameter are identical with one of embodiment one to three.
Embodiment five：Unlike one of present embodiment and embodiment one to four：The step 2
Middle f when determining that structural fatigue accumulated damage is dam according to regression modelaThe detailed process of (a | dam) is：
Wherein μ (dam) represents the logarithm normal distribution average of crack length a when structural fatigue accumulated damage is dam, σ
(dam) the logarithm normal distribution deviation of crack length a when structural fatigue accumulated damage is dam is represented；
Regression analysis is carried out to μ (dam) using quadratic regression model：
μ (dam)=a1dam2+b1dam+c1 (7)
Wherein a1、b1、c1For the regression coefficient of quadratic regression model；
Regression analysis is carried out to σ (dam) using Cubic regression model：
σ (x)=a2dam3+b2dam2+c2dam+d2 (8)
Wherein a2、b2、c2、d2For the regression coefficient of Cubic regression model；
It will return and be obtained in obtained μ (dam) and σ (dam) substitution formula (6) when structural fatigue accumulated damage is dam
fa(a|dam)。
(a) fatigue data is analyzed
The fatigue data that the present invention researchs and analyses derives from Wu (W.F.Wu, C.C.Ni.Statistical
aspects of some fatigue crack growth data.Engineering Fracture Mechanics,
2007；74:2952-2963.), these data are the pre-stage test achievements of an aircraft structural reliability research, with the present invention's
Application background can be good at being bonded.The material of fatigue test is 2024-T351 alloy aluminums, is made extensively in the manufacture of aircraft
With.Two groups of constant amplitude loading fatigue datas in Wu are chosen to be analyzed.First group is named as CA1 (constant-
Amplitude loading set 1) include 30 test specimens, test load is sinusoidal loading, peak load ppeak=
4.5kN, valley load ptrough=0.9kN, stress ratio R=ptrough/ppeak=0.2, result of the test is as shown in Figure 1；The
Two groups are named as CA2 (constant-amplitude loading set 2) and include 10 test specimens, and test load carries to be sinusoidal
Lotus, peak load ppeak=6.118kN, valley load ptrough=3.882kN, stress ratio R=ptrough/ppeak=
0.63, result of the test is as shown in Figure 2.
In order to judge which can preferably be fitted determination load cycle time in logarithm normal distribution and Weibull distributions
Crack size data under several, using KS methods CA1 and CA2 crack size data are fitted with goodness inspection.Specific inspection
Test the KS inspections that process obeys logarithm normal distribution using crack size when load cycle number is Cycles=15000 in CA1
Exemplified by, crack data is as shown in table 1.
1) average u=2.9718 during logarithm normal distribution is obeyed using maximum likelihood method estimation table 1 crack size data
With deviations=0.0187, KS statistics D=0.100 is calculated；
2) it is 30 to produce capacity, and the average that gained is calculated in obeying 1) is u=2.9718, and deviation is pair of σ=0.0187
5000, number normal distribution sample；
3) using the average u of 5000 samples in maximum likelihood method estimation 2)iAnd deviationsi(i=1,2 ..., 5000)；
4) D of 5000 increments is calculated respectively by formula 3.1i(i=1,2 .., 5000) value；
5) by Di(i=1,2 .., 5000) according to being ranked up from small to large, the D=0.100 being calculated in determining 1)
Value is in DiIn position be 1899.
Six groups of crack size data determined under load are have chosen from CA1 and CA2 respectively and carry out KS inspections, assay
Respectively as shown in tables 2 and 3.
Crack size data when the load cycle number of table 1 is Cycles=15000
The CA1 of table 2 KS assays
The CA2 of table 3 KS assays
From table 2 and 3, logarithm normal distribution is than Weibull distribution table in the fitting of CA1 crack size distribution data
Existing will get well, and Weibull distributions performance is better than logarithm normal distribution in the fitting of CA2 crack size distribution data.By
There was only 10 in CA2 test specimen number, data volume is too small, and the randomness of crack size distribution can not be showed sufficiently, intends
The confidence level for closing goodness assay is not so good as CA1, therefore according to CA1 test of fitness of fot result, chooses logarithm normal distribution
Model carries out further research as the crack size distribution model determined under load cycle number.
(b) crack size distribution model parameter models
Using CA1 and CA2 test datas, according to Cumulative Fatigue Damage theorem, different fatigue accumulating injuring value can be obtained
Under crack size obey the mean data of logarithm normal distribution, table 4 and table 5 are respectively that fatigue load is tired when be CA1 and CA2
The data statistics result of accumulating injuring value and crack size distribution average.
The data statistics result of the CA1 Cumulative Fatigue Damages value of table 4 and crack size distribution average
The data statistics result of the CA2 Cumulative Fatigue Damages value of table 5 and crack size distribution average
By finding that crack size distribution average is with the change of Cumulative Fatigue Damage value to the data analysis in table 4 and 5
Trend comparison it is good submit to secondary model and exponential model relation, therefore secondary model and exponential model is respectively adopted to crackle
The average and Cumulative Fatigue Damage value of size logarithm normal distribution carry out regression analysis, and secondary model and exponential model difference are as follows
Shown in formula, wherein a, b, c are regression coefficient.
Y=ax2+bx+c (9)
Y=aebx+c (10)
Regression Analysis Result is as shown in table 6 and Fig. 3 and 4.From Fig. 3 and 4, quadratic regression model and Exponential Regression Model
Crack distribution average under real CA1 and CA2 fatigue loads can be returned well with Cumulative Fatigue Damage relation
Return.In order to further analyze the regression result of two kinds of regression models, the coefficient of determination of two kinds of regression models is calculated respectively
R2, shown in calculation formula such as formula (11).
Wherein, yiTo need the True Data returned,Expression needs to be fitted the average of data,Represent to use
The value that regression model is calculated.
R2Result of calculation is as shown in table 7, by R2Bigger regression effect it is better understand, crack size logarithm normal distribution it is equal
Relation more index of coincidence model between value and Cumulative Fatigue Damage.
The R of the crack size distribution model mean regression of table 72Statistical result
Using CA1 and CA2 test datas, according to Cumulative Fatigue Damage theorem, different fatigue accumulating injuring value can be obtained
Under crack size obey the deviation data of logarithm normal distribution, table 8 and table 9 are respectively that fatigue load is tired when be CA1 and CA2
The data statistics result of accumulating injuring value and crack size distribution deviation.
The data statistics result of the CA1 Cumulative Fatigue Damages value of table 8 and crack size distribution deviation
The data statistics result of the CA2 Cumulative Fatigue Damages value of table 9 and crack size distribution deviation
By finding that crack size distribution deviation is with the change of Cumulative Fatigue Damage value to the data analysis in table 8 and 9
Trend comparison it is good submit to quadratic regression model, Cubic regression model and Exponential Regression Model relation, therefore be respectively adopted two
Secondary regression model, Cubic regression model and Exponential Regression Model damage to the average and fatigue accumulation of crack size logarithm normal distribution
Wound value carry out regression analysis, quadratic regression model, Cubic regression model and Exponential Regression Model respectively as formula (9), (12) and
(10) shown in, wherein a, b, c and d are regression coefficient.
Y=ax3+bx2+cx+d (12)
Regression Analysis Result is as shown in table 10 and Fig. 5 and 6.From Fig. 5 and 6, three kinds of regression models can be to true
CA1 and CA2 fatigue loads under crack distribution average returned well with Cumulative Fatigue Damage relation.In order to more enter one
The regression result of three kinds of regression models of analysis of step, the coefficient of determination R of three kinds of regression models is calculated respectively2, as a result such as table 11
Shown, from result of calculation, the relation between the deviation and Cumulative Fatigue Damage of crack size logarithm normal distribution more meets
Model three times.
CA1 the and CA2 crack size distribution model bias Regression Analysis Results of table 10
The R that the crack size distribution model bias of table 11 returns2Statistical result
Other steps and parameter are identical with one of embodiment one to four.
Embodiment one：
The structural reliability mould based on Cumulative Fatigue Damage of the invention established is verified using Crack Extension data CA1
Type.Assuming that a test specimen experienced n altogether1Individual cyclic loading, and destruction cycle-index of the test specimen under the stress level is N1.Root
According to Stress-Life method, Cumulative Fatigue Damage corresponding to structure is dam1=n1/N1.Based on crack size distribution mould derived above
Regression model μ (dam) the and σ (dam) of shape parameter, structure is in dam1When crack size distribution probability density function be：
According to CA1 data, the critical crack size distribution probability density function of structure represents as follows:
According to formula (1), (13) and (14), test specimen is dam in accumulated damage1When CALCULATION OF FAILURE PROBABILITY it is as follows：
According to formula (15), the test specimen of crack Propagation data CA1 and CA2 group is dam in Cumulative Fatigue Damage1∈
Failure probability when [0.5,1] is as shown in Figure 7.
As shown in Figure 7, CA1 groups test specimen is in accumulated damage dam1Failure probability when=1 is 48.18%, and this is with obtaining
Experimental result (about 50% test specimen is broken when accumulated damage reaches 1) matches.Obtained by computational methods proposed by the present invention
CALCULATION OF FAILURE PROBABILITY error be 1.82%, can receive.Similar, CA2 groups test specimen can be obtained in accumulated damage dam1=1
When failure probability be 45.73%, calculation error 4.27%.From the foregoing, it will be observed that the structural reliability based on Cumulative Fatigue Damage
Model has very high computational accuracy.
The present invention can also have other various embodiments, in the case of without departing substantially from spirit of the invention and its essence, this area
Technical staff works as can make various corresponding changes and deformation according to the present invention, but these corresponding changes and deformation should all belong to
The protection domain of appended claims of the invention.
Claims (5)
- A kind of 1. modeling reliability method based on Cumulative Fatigue Damage, it is characterised in that：It is described based on Cumulative Fatigue Damage The detailed process of modeling reliability method is：Step 1：Reliability Model based on Cumulative Fatigue Damage is established according to fatigue stress Life method and probability damage tolerance limit：<mrow> <mi>P</mi> <mi>o</mi> <mi>F</mi> <mrow> <mo>(</mo> <mi>d</mi> <mi>a</mi> <mi>m</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>&Integral;</mo> <mo>&Integral;</mo> <msub> <mi>f</mi> <mi>a</mi> </msub> <mrow> <mo>(</mo> <mi>a</mi> <mo>|</mo> <mi>d</mi> <mi>a</mi> <mi>m</mi> <mo>)</mo> </mrow> <msub> <mi>f</mi> <msub> <mi>a</mi> <mi>c</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>dada</mi> <mi>c</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow>Wherein PoF (dam) represents crash rate when structural fatigue accumulated damage is dam, a | dam represents structural fatigue accumulated damage For dam when crack length, a is structural crack length, fa(a | dam) represent structural crack Length Pr density fonction, ac Structure critical crack length,Represent structure critical crack length probability density function；Step 2：F when determining that structural fatigue accumulated damage is dam according to regression modela(a | dam), pass through the f of determinationa(a| Dam) the Reliability Model based on Cumulative Fatigue Damage that solution procedure one is established.
- A kind of 2. modeling reliability method based on Cumulative Fatigue Damage according to claim 1, it is characterised in that：It is described The expression formula of fatigue stress Life method is in step 1：<mrow> <mi>D</mi> <mo>=</mo> <munder> <mo>&Sigma;</mo> <mi>i</mi> </munder> <msub> <mi>dam</mi> <mi>i</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>dami=ni/Ni (3)Wherein damiTo damage component, D is total accumulated damage amount, niIn stress level it is S for test specimeniIn the presence of work follow Ring number, NiIt is test specimen in stress level SiUnder destruction cycle-index.
- A kind of 3. modeling reliability method based on Cumulative Fatigue Damage according to claim 2, it is characterised in that：It is described The crackle interference life model of probability damage tolerance limit is in rapid one：<mrow> <mi>P</mi> <mi>o</mi> <mi>F</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>=</mo> <mo>&Integral;</mo> <mo>&Integral;</mo> <msub> <mi>f</mi> <mi>a</mi> </msub> <mrow> <mo>(</mo> <mi>a</mi> <mo>,</mo> <mi>t</mi> <mo>)</mo> </mrow> <msub> <mi>f</mi> <msub> <mi>a</mi> <mi>c</mi> </msub> </msub> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mi>c</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>dada</mi> <mi>c</mi> </msub> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>Wherein fa(a, t) is crack distribution density function of flight moment when being t,It is the Size Distribution of structure critical crack Density function, PoF (t) are the crash rates of flight moment structure when being t.
- A kind of 4. modeling reliability method based on Cumulative Fatigue Damage according to claim 3, it is characterised in that：It is described The detailed process of Reliability Model of the foundation based on Cumulative Fatigue Damage is in step 1：Flight moment t cyclic loading number N is obtained by structural healthy monitoring system, according to Stress-Life method, with reference to what is obtained Cyclic loading number N, the Cumulative Fatigue Damage dam of t is obtained, therefore the transformational relation being shown below be present：Reliability Model based on Cumulative Fatigue Damage is converted to by formula (5) and formula (4).
- A kind of 5. modeling reliability method based on Cumulative Fatigue Damage according to claim 4, it is characterised in that：It is described F when determining that structural fatigue accumulated damage is dam according to regression model in step 2aThe detailed process of (a | dam) is：<mrow> <msub> <mi>f</mi> <mi>a</mi> </msub> <mrow> <mo>(</mo> <mi>a</mi> <mo>|</mo> <mi>d</mi> <mi>a</mi> <mi>m</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mrow> <msqrt> <mrow> <mn>2</mn> <mi>&pi;</mi> </mrow> </msqrt> <mi>&sigma;</mi> <mrow> <mo>(</mo> <mi>d</mi> <mi>a</mi> <mi>m</mi> <mo>)</mo> </mrow> <mi>a</mi> <mrow> <mo>(</mo> <mi>d</mi> <mi>a</mi> <mi>m</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mi>exp</mi> <mo>(</mo> <mo>-</mo> <mfrac> <msup> <mrow> <mo>(</mo> <mi>ln</mi> <mi> </mi> <mi>a</mi> <mo>(</mo> <mrow> <mi>d</mi> <mi>a</mi> <mi>m</mi> </mrow> <mo>)</mo> <mo>-</mo> <mi>&mu;</mi> <mo>(</mo> <mrow> <mi>d</mi> <mi>a</mi> <mi>m</mi> </mrow> <mo>)</mo> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mrow> <mn>2</mn> <msup> <mi>&sigma;</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mi>d</mi> <mi>a</mi> <mi>m</mi> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>Wherein μ (dam) represents the logarithm normal distribution average of crack length a when structural fatigue accumulated damage is dam, σ (dam) table Show the logarithm normal distribution deviation of crack length a when structural fatigue accumulated damage is dam；Regression analysis is carried out to μ (dam) using quadratic regression model：μ (dam)=a1dam2+b1dam+c1 (7)Wherein a1、b1、c1For the regression coefficient of quadratic regression model；Regression analysis is carried out to σ (dam) using Cubic regression model：σ (x)=a2dam3+b2dam2+c2dam+d2 (8)Wherein a2、b2、c2、d2For the regression coefficient of Cubic regression model；It will return in obtained μ (dam) and σ (dam) substitution formula (6) and obtain f when structural fatigue accumulated damage is dama(a| dam)。
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