CN115828669A - Method for analyzing position structure reliability of civil aircraft minimum risk bomb - Google Patents

Abstract

The invention discloses a method for analyzing the reliability of a position structure of a civil aircraft minimum risk bomb, which comprises the following steps of: s10, establishing a finite element model of an LRBL structure, and determining a dangerous part of a civil aircraft minimum risk bomb position structure; s20, determining an uncertain input variable of the LRBL structure, and performing explosion simulation solution by combining the uncertain input variable; s30, determining a failure criterion of the LRBL structure dangerous part under the action of explosion to obtain a limit state function; s40, determining the failure probability of the dangerous part of the LRBL structure according to the limit state function; and S50, utilizing fault tree analysis to obtain the reliability of the LRBL structure. The work which can be finished only by a large number of real explosion tests is avoided through explosion simulation, the failure probability of the minimum risk bomb position structure of the civil aircraft is efficiently estimated, and the reliability analysis and calculation efficiency is improved.

Description

Method for analyzing position structure reliability of civil aircraft minimum risk bomb

Technical Field

The invention belongs to the field of design of air transportation safety and structural reliability, and particularly relates to a method for analyzing the structural reliability of a minimum risk bomb position of a civil aircraft.

Background

The united states Federal Aviation Administration (FAA) states that in the FAR 25-127 amendment and the advisory notice AC 25.795-6, for an aircraft with a maximum qualified triage passenger size of more than 60 or a total takeoff weight of more than 100000lb (45359 kg), a "Least Risk Bomb Location (LRBL)" must be designed for placing a suspected explosive device to be found, and a bomb Containment System (Containment System), i.e., an anti-explosion container, may be used to further reduce the impact of explosion. Therefore, an anti-explosion structure (namely a minimum risk bomb position structure, called LRBL structure for short) can be designed to place suspicious explosives found on a civil aircraft, so that the damage of explosion to the aircraft is reduced to the maximum extent, and the safety of the aircraft and passengers is ensured.

The LRBL structure is used as a device for rapidly placing and treating suspicious explosives on an airplane, has a complex structure, and has extremely high requirements on the reliability of the structure for ensuring normal work. Considering that the LRBL structure itself is affected by many uncertain factors such as uncertainty of explosive load, uncertainty of material performance, uncertainty of geometric dimensions, etc., even if the structural strength of the designed LRBL structure meets the requirement of allowable strength, the LRBL structure may be damaged in actual operation, and thus the LRBL structure cannot play a due role in protection. In order to ensure that no problem occurs in practical use, reliability analysis research needs to be carried out on the LRBL structure.

At present, the research on the LRBL structure of the civil aircraft just starts in China, and a reliability analysis method for the LRBL structure of the civil aircraft is still lacked and needs to be researched. And explosion test operation is complicated, the cost is higher, the data acquisition is difficult, and the method is not suitable for large sample test. Therefore, in order to ensure the safety and reliability of the LRBL structure of the civil aircraft, an efficient and reliable reliability analysis method is needed, so that the reliability analysis of the LRBL structure of the civil aircraft is realized, the LRBL structure is ensured to meet the strict reliability index requirements, and no problem occurs in the actual use.

Disclosure of Invention

The technical problem to be solved by the invention is as follows: the invention aims to provide a method for analyzing the reliability of the position structure of the minimum risk bomb of the civil aircraft, which can effectively and accurately analyze the reliability of the position structure of the minimum risk bomb of the civil aircraft.

The technical scheme of the invention is as follows: the invention discloses a method for analyzing the reliability of a position structure of a civil aircraft minimum risk bomb, which specifically comprises the following steps:

s10, establishing a finite element model of the LRBL structure by using explosion simulation software, carrying out stress analysis on the LRBL structure, and determining a dangerous part of the LRBL structure;

s20, determining an uncertain input variable of the LRBL structure, performing explosion simulation solving by combining the uncertain variable, and obtaining a maximum plastic strain value of a dangerous part as a reliability analysis output variable;

s30, determining a failure criterion of a dangerous part of the LRBL structure under the action of explosion and determining a limit state function of the LRBL structure;

step S40: calculating the failure probability of each dangerous part of the LRBL structure according to the limit state function determined in the step S30;

step S50: and calculating the reliability of the LRBL structure by using a fault tree analysis method.

Further, in the step S10, an LRBL structure finite element model under the action of an explosive load is established by using LS-DYNA finite element software or CATIA three-dimensional software, and the LRBL structure is subjected to stress analysis.

Further, the step S20 specifically includes the following sub-steps:

a substep S201 of determining an uncertainty input variable of the LRBL structure by combining the uncertainty of the explosion load parameter and the material performance parameter;

substep S202: adopting a Latin hypercube method to sample the uncertain input variables determined in the sub-step S201 and determining uncertain variable samples of the LRBL structure;

substep S203: and performing explosion simulation and solving calculation by combining with the uncertain variable sample in the sub-step S202 to obtain the maximum plastic strain value of each dangerous part of the LRBL structure, and obtaining the output response corresponding to the sample point to be used as the reliability analysis output variable.

Further, in the step S30, the failure behavior of the LRBL structure is described by using a Johnson-Cook failure model:

wherein A represents the yield strength in quasi-static state; b-strain hardening coefficient; n-strain hardening coefficient; c-strain rate sensitivity coefficient; epsilon-equivalent plastic strain;

-a strain rate;

-a reference strain rate;

-dimensionless strain rate, satisfying

T ^* -

T _r Taking the lowest temperature 294K of the test as a reference temperature; t is a unit of _m Is the melting point temperature of the material; m-is the temperature sensitivity coefficient;

in the simulation, the plastic failure strain of the material is used as a failure criterion, and the limit state function of the LRBL structure meets the following conditions:

Z(X)＝ε _f -ε _max (X)

z (X) is the extreme state function, ε _f Is the plastic failure strain of the LRBL structure, X is the uncertainty input variable, ε _max (X) is the maximum plastic strain of the LRBL structure danger part corresponding to the uncertainty input variable.

Further, in the step S40, the failure probability of each dangerous part of the LRBL structure is solved by using a method combining a K-S test and a first second moment, or the failure probability of each dangerous part of the LRBL structure is solved by using a proxy model method.

Further, the specific method for solving the failure probability of each dangerous part of the LRBL structure by using the method of combining the K-S inspection and the first second moment in step S40 is as follows:

performing K-S inspection on the output response sample obtained by the simulation calculation in the step S20, and determining the probability distribution characteristics of the output response of the reliability analysis of the LRBL structure, namely the distribution form, the mean value and the standard deviation of the plastic strain of each dangerous part;

and obtaining a reliability index through a first-order second-order moment method, and calculating the failure probability of each dangerous part of the LRBL structure.

Further, the specific method for solving the failure probability of each dangerous part of the LRBL structure by using the proxy model method in the step S40 is as follows:

fitting the uncertain input variable sample of the LRBL structure determined in the step S20 and the output response sample obtained by simulation calculation to obtain a function proxy model of the relationship between the input variable and the output response of each dangerous part of the LRBL structure;

comparing the strain obtained by simulation in different dangerous parts of the LRBL structure with the strain obtained by the proxy model, and selecting a function proxy model with higher precision and better fitting degree;

according to the probability distribution characteristics of random input variables, random sampling is carried out by using a Monte-Carlo method, corresponding random output response is calculated by combining the sampled sample value and the function of the LRBL structure, and the random output response is compared with the allowable value of the failure mode, so that the reliability analysis of each dangerous part of the LRBL structure is completed.

Further, the proxy model adopted in step S40 is a pure quadratic response surface model, a kriging model, an artificial neural network model, or a support vector machine model.

Further, the step S50 specifically includes:

analyzing the top event of the fault tree without realizing normal operation of the LRBL structure, establishing the relationship between the failure of the LRBL structure at the top event and the failure of each dangerous part at the bottom event to obtain the fault tree in which the LRBL structure cannot realize normal operation, wherein the top event and each bottom event of the fault tree are in OR gate relationship,

the calculation formula of the reliability of the LRBL structure for realizing normal work is as follows:

advantageous effects

The invention has the beneficial effects that:

1. according to the method for analyzing the reliability of the structure of the minimum risk bomb position of the civil aircraft, a finite element model is established, and the dangerous part of an LRBL structure is obtained by combining the explosion impact characteristic; the Latin hypercube sampling method is adopted to extract samples for explosion simulation, LS-DYNA software is used for explosion simulation, the work which needs a large number of real explosion tests to complete is avoided, and the efficiency of reliability analysis and calculation is improved.

2. Another advantage of the present invention is that conventional structural reliability calculation methods are all based on explicit expressions of functional functions as random variables. The relation between the structure input variable and the output response under the action of the explosion impact load is highly nonlinear or ambiguous, and a conventional reliability calculation method cannot be directly used, but the method of the invention using the K-S test in combination with the reliability index or establishing the proxy model avoids the defects of the traditional reliability analysis method, realizes the high-efficiency estimation of the failure probability of the minimum risk bomb position structure of the civil aircraft, and has great significance for ensuring the normal work of the minimum risk bomb position structure of the civil aircraft.

Drawings

In order to more clearly explain the technical solutions of the embodiments of the present application, the drawings that are required to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present application and therefore should not be considered as limiting the scope, and that for those skilled in the art, other related drawings can be obtained from these drawings without inventive effort.

FIG. 1 is a flow chart of the method for analyzing the structural reliability of the location of minimum risk bombs of civil aircraft according to the present invention;

FIG. 2 is a flow chart of step S20 of the method for analyzing the positional structure reliability of civil aircraft minimum risk bombs of the present invention;

fig. 3 is a flowchart of step S40 of the method for analyzing the positional structure reliability of civil aircraft minimum risk bombs according to the present invention.

Fig. 4 shows a possible LRBL structure scheme according to an embodiment of the present invention.

In the figure, a 1-LRBL structure tank body, a 101-LRBL structure tank body lug boss, a 2-LRBL structure filling end cover,

201-LRBL structure loads end cover boss, 3-LRBL structure drift, 4-LRBL structure shear pin

Detailed Description

Reference will now be made in detail to the embodiments of the present invention, examples of which are illustrated in the accompanying drawings, and the embodiments described below with reference to the accompanying drawings are exemplary and intended to be illustrative of the present invention and should not be construed as limiting the present invention.

The invention discloses a method for analyzing the reliability of a position structure of a civil aircraft minimum risk bomb, which comprises the following steps:

s10, establishing a finite element model of the LRBL structure by using explosion simulation software, carrying out stress analysis on the LRBL structure, and determining a dangerous part of the LRBL structure;

as shown in fig. 4, the present embodiment shows a possible LRBL structure, which is a whole body of a revolving body structure, and includes an LRBL structure can 1, an LRBL structure loading end cap 2, an LRBL structure punch 3, and an LRBL structure shear pin; bosses are uniformly arranged on the outer wall of one end of the LRBL structure tank body 1 in the circumferential direction and are used as bosses 101 of the LRBL structure tank body, bosses matched with the bosses 101 of the LRBL structure tank body are uniformly arranged on the inner wall of one end of the filling end cover 2 of the LRBL structure in the circumferential direction and are used as bosses 201 of the filling end cover of the LRBL structure.

The three-dimensional geometric model of the LRBL structure can be built in three-dimensional software such as CATIA (computer-graphics aided three-dimensional interactive application), and can also be directly built in finite element software such as LS-DYNA, and the like, and the method is not limited herein.

For example, LS-DYNA finite element software is used for establishing an LRBL structure finite element model under the action of an explosion load, high-temperature, high-pressure and high-speed gas generated by explosion in an LRBL structure cavity acts on the whole LRBL structure, and the stress of the LRBL structure is analyzed by combining the analysis result of the explosion simulation finite element to determine the dangerous part of the LRBL structure.

For example, the following requirements are required to be satisfied for the normal operation of the present embodiment: under the action of explosive impact, the shearing pin is sheared, the punch head pushes the skin to be impacted under the push of the shock wave, the explosive shock wave is guided to the outside of the cabin, and other parts of the LRBL structure except the shearing pin cannot be damaged, so that the explosive shock wave is prevented from harming personnel in the cabin.

Assume that the materials used for the LRBL structure are shown in table 1:

name of component	The materials used	Strain to failure of material
			LRBL structure jar body	Titanium alloy	0.25
Filling end cap	Titanium alloy	0.25
			Punch head	Titanium alloy	0.25
Shear pin	Stainless steel	0.2

TABLE 1

The grid division is directly related to the calculation precision and the calculation time, and the grid type and the unit division size need to be comprehensively considered and analyzed. In the embodiment, for example, the LS-DYNA finite element software is modeled and gridded, the structure is gridded by using a hexahedral grid, the grid size of the LRBL structure tank, the filling end cap and the punch can be 5mm, and the grid size of the shear pin can be 3mm.

The pretreatment of the LRBL structure in LS-DYNA comprises the following steps: setting a metal material model, an explosive and air model and parameters thereof, and setting boundary conditions; and then submitting to calculation and solving to obtain a stress cloud picture.

The dangerous part of the LRBL structure refers to a part which is easy to fail in all components of the LRBL structure under the action of explosive impact. According to simulation data, the LRBL structure can be known to realize shearing of the shearing pin under the action of explosion impact, the punch is punched out, and the dangerous part of the structure is determined as follows: the bottom of the filling end cover of the LRBL structure, the wall of the tank body of the LRBL structure and the hole edge of the tank body of the LRBL structure are arranged.

S20, determining an uncertain input variable of the LRBL structure, performing explosion simulation solving by combining the uncertain variable, and acquiring a maximum plastic strain value of a dangerous part as a reliability analysis output variable;

the method specifically comprises the following steps:

substep S201: determining an uncertainty input variable of the LRBL structure;

considering the uncertainty of the load parameters and the material property parameters, the uncertainty parameters used in this example are shown in table 2:

TABLE 2

Other materials may be used for the LRBL structure, and more uncertainties in the load parameters and material performance parameters may be considered, and this embodiment is intended to illustrate the method of the present disclosure and will not be listed here.

Substep S202: determining uncertainty input variable samples of the LRBL structure;

and (3) performing 30 groups of sampling on the uncertain input variables by using a Latin hypercube method to obtain 30 groups of test sample points.

Suppose X ₁ ,…，X _K Is K input random variables, X, in the probability problem to be solved _i Is X ₁ ,…，X _K The cumulative probability distribution function of any random variable in (2) is:

Y _k ＝F _k (X _i )

and setting N to represent the sampling scale, wherein the sampling method comprises the following steps: curve Y _k ＝F _k (X _i ) Is divided into N equally spaced non-overlapping intervals (due to Y) _k Is in the range of 0 to 1.0, the width of each interval is 1/N), one Y is selected from each interval _k Of the sampling value(s). The sampling values in the intervals can be randomly selected, and the middle point of each interval can also be selected. Then using function Y _k ＝F _k (X _i ) To calculate X _i Of sampled values, i.e. X _i The nth sample value of (d) is:

thus, in conjunction with the uncertainty parameters of table 2, 30 sets of sample points for this example were obtained, as shown in table 3:

TABLE 3

Substep S203: performing explosion simulation and solving calculation by combining with the uncertain variable sample in the sub-step S202 to obtain the maximum plastic strain value of the dangerous part as a reliability analysis output variable;

maximum plastic strain data of all dangerous parts of the LRBL structure are extracted, and output responses corresponding to 30 groups of sample points are obtained, as shown in Table 4:

TABLE 4

S30, determining a failure criterion of a dangerous part of the LRBL structure under the action of explosion to obtain a limit state function of the LRBL structure;

a Johnson-Cook failure model is adopted to describe the failure behavior of the LRBL structure, the plastic failure strain of the material is adopted as a failure criterion in simulation, and the failure of the material unit in simulation is controlled.

Under the action of explosive load, the LRBL structure is subjected to huge impact load in a short time, the structure is likely to deform greatly, for the complex nonlinear dynamic response process, the failure behavior of the LRBL structure is described by adopting a Johnson-Cook failure model, and the formula is as follows:

wherein, A represents the yield strength in quasi-static state; b-strain hardening coefficient; n-strain hardening coefficient; c-strain rate sensitivity coefficient; ε -equivalent plastic strain;

-a strain rate;

-a reference strain rate;

-dimensionless strain rate, satisfying

T ^* ——

T _r Is a reference temperature, and the lowest temperature 294K of the test is taken; t is _m Is the melting point temperature of the material; m-is the temperature sensitivity coefficient.

The strain at which the structure breaks is given by:

when injury factor

When the value of D is more than or equal to 1, the structure is considered to be damaged, the formula is deformed, and the failure criterion is obtained

Wherein

The strain at a certain position of the structure is designated as ε (X).

In conclusion, the plastic failure strain control failure of the material is used in the simulation as the failure criterion;

the limit state function of the LRBL structure satisfies the following relation:

Z(X)＝ε _f -ε _max (X)

wherein Z (X) is the extreme state function, ε _f Is the plastic failure strain of the LRBL structure, X is the uncertainty input variable, ε _max And (X) is the maximum plastic strain of the LRBL structure dangerous part corresponding to the uncertainty input variable.

The limit state function of the LRBL structure satisfies the following relation:

Z(X)＝ε _f -ε _max (X)

wherein Z (X) is the extreme state function, ε _f Is the plastic failure strain of the LRBL structure, X is the uncertainty input variable, ε _max And (X) is the maximum plastic strain of the LRBL structure dangerous part corresponding to the uncertainty input variable.

And if the Z (X) is less than zero, the maximum plastic strain of the dangerous part of the LRBL structure is greater than the plastic failure strain of the material, and the dangerous part of the LRBL structure is judged to be failed.

And S40, determining the failure probability of each dangerous part of the LRBL structure according to the limit state function.

Method S40a: the method for solving the failure probability of each dangerous part of the LRBL structure by combining the K-S inspection with the primary second moment specifically comprises the following steps:

and performing K-S inspection on the output response sample obtained by simulation calculation, determining the probability distribution characteristics of the output response of reliability analysis of the LRBL structure, namely the distribution form, the mean value and the standard deviation of plastic strain of each dangerous part, and then obtaining a reliability index through a first-order second-order moment method to calculate the failure probability of each dangerous part of the LRBL structure.

And performing K-S inspection on the extracted strain data of each dangerous part of the LRBL structure:

H ₀ : observations from populations subject to specific distribution patterns

H ₁ : observations come from populations that do not obey a particular distribution form;

arranging given sample data in a sequence from small to large, and setting F _n (x) Empirical distribution function for simple subsamples of capacity n, i.e. event x<The probability of X, then:

f (x) is the theoretical distribution function of the assumed population, let statistic D _n Comprises the following steps:

D _n ＝sup|F(x)-F _n (x)|

according to the Kohr Mo Ge Loff theorem:

multiply both sides of the above formula by

The following can be obtained:

it can be seen that when n is large, the distribution on the left side of the above formula tends to be θ (y). After a certain significance level alpha is given, the critical value D of the confidence coefficient alpha _n,α The following formula is satisfied:

P(D _n ＞D _n,α )＝1-θ(y)＝α

if D is _n ＞D _n,α Then the hypothesis H is rejected ₀ Otherwise, accept H ₀ 。

By Y _i The output variable representing the reliability of the LRBL structure, i.e., the plastic strain of each dangerous site. For the original hypothesis H ₀ : total Y _i Obeying a normal distribution N (mu, sigma) ² ) Checking, and calculating to obtain statistic D of 30 groups of LRBL structure output variable samples _n And critical value D thereof _n,α As shown in table 5:

TABLE 5

According to the K-S test results of the LRBL structure output variables in Table 5, at the significance level of 5%, the statistic D of 30 groups of output variable samples is shown _n Less than its critical value D _n,α Therefore, accept the assumption H ₀ That is, the plastic strain of each dangerous part of the LRBL structure is considered to follow a normal distribution, and the specific probability distribution characteristics are shown in table 6:

TABLE 6

If the output variable Y of the LRBL structure reliability analysis obeys normal distribution N (mu, sigma) ² ) Then, the failure probability calculation formula of each dangerous part of the LRBL structure is:

in the formula: lambda-the failure equivalent plastic strain of the LRBL structural material; f (Y) -the density distribution function of the output variable Y (plastic strain) of the reliability analysis of the LRBL structure; μ — mean of the variable Y; σ -the standard deviation of the variable Y.

The failure probability of each dangerous part of the LRBL structure under the implosion action can be obtained as follows:

method S40b: estimating failure probability by using a proxy model method and combining a Monte-Carlo method, and performing reliability analysis;

solving the failure probability of each dangerous part of the LRBL structure by using a proxy model method: and (3) obtaining agent model functions of each dangerous part by utilizing input and output sample point fitting, verifying that the precision meets the requirement, and estimating the failure probability by using a Monte-Carlo method based on the finally established agent model.

And fitting by adopting a proxy model of a response surface method according to the input variable data in the table 3 and the strain data of each dangerous part of the LRBL structure extracted in the table 4 to obtain a function model of the relation between the input variable and the output response.

Using normalized absolute error mean value MNAE, root mean square error RMSE, decision coefficient R ² And comparing the strain obtained by simulation in different dangerous parts with the strain obtained by the proxy model as an accuracy index for measuring the proxy model fitting function, thereby selecting a function model with higher accuracy and better fitting degree.

Taking the plastic strain data fitted by the pure quadratic response surface proxy model function as an example, calculation analysis is performed to obtain the fitting degree of each dangerous part function model as shown in table 7.

Serial number	Object	Degree of fit/R	Determining coefficient/R 2
				1	Tank body wall	0.97	0.95
2	Tank hole edge	0.92	0.84
				3	Bottom of filling end cap	0.91	0.83
4	Punch hole edge	0.90	0.80

TABLE 7

Of course, other proxy models, such as kriging model, artificial neural network model, support vector machine model, etc. may also be employed; this example is intended to illustrate the method of the present disclosure and is not presented here.

The functions of the tank body wall, the tank body hole edge, the filling end cover bottom and the punch hole edge obtained by adopting the pure secondary response surface model are respectively as follows:

Y ₁ ＝-0.7992-0.0650X ₁ -0.0093X ₂ +0.0063X ₃ +0.4917X ₄ +0.0082X ₅ +0.0018X ₁ ² +2.7890×10 ^-4 X ₂ ² -3.1357×10 ^-5 X ₃ ² -0.2976X ₄ ² -1.7363×10 ^-5 X ₅ ²

Y ₂ ＝1.0967-0.0746X ₁ -0.0750X ₂ +0.0017X ₃ +0.0647X ₄ +9.8035×10 ^-4 X ₅ +0.0021X ₁ ² +0.0025X ₂ ² -8.6698×10 ^-6 X ₃ ² -0.0731X ₄ ² -2.2750×10 ^-6 X ₅ ²

Y ₃ ＝0.3444-0.0543X ₁ +0.0185X ₂ -9.0587×10 ^-5 X ₃ +0.1304X ₄ +5.5713×10 ^-5 X ₅ +0.0014X ₁ ² -5.1123×10 ^-4 X ₂ ² +1.7890×10 ^-7 X ₃ ² -0.0977X ₄ ² +8.0054×10 ^-7 X ₅ ²

Y ₄ ＝0.0782+0.0726X ₁ +0.0377X ₂ -3.5283×10 ^-4 X ₃ -0.1071X ₄ -0.0056X ₅ -0.0022X ₁ ² -0.0012X ₂ ² -8.6283×10 ^-7 X ₃ ² -0.0281X ₄ ² +1.1512×10 ^-5 X ₅ ²

the mean and standard deviation of the maximum strain of the wall of the can body, the maximum strain of the hole edge of the can body, the maximum strain of the bottom of the filling end cover and the maximum strain of the hole edge of the punch obtained by function model fitting are shown in Table 8

TABLE 8

And randomly sampling the random input variable by using a Monte Carlo method according to the probability distribution characteristics of the random input variable, calculating corresponding random output response by combining the sampling value and the function of the structure, and comparing the random output response with the failure mode allowable value to finish the structural reliability analysis. Then there are:

P _f (Y ₁ )≤10 ^-30

P _f (Y ₂ )＝0.0256

P _f (Y ₃ )≤10 ^-30

P _f (Y ₄ )≤10 ^-30

and S50, establishing a relation between failure of the LRBL structure of the top event and failure of each dangerous part of the bottom event by using a fault tree analysis method to obtain a reliability calculation model of the LRBL structure, and calculating the reliability of the LRBL structure.

And (4) analyzing the top event of the fault tree by using the LRBL structure which does not realize normal work. The reasons for the LRBL structure not working normally include: (1) the wall of the tank body of the LRBL structure is damaged; (2) damaging the hole edge of the LRBL structure tank body; (3) the bottom of a filling end cover of the LRBL structure is damaged; (4) the hole edge of the punch of the LRBL structure is broken.

A fault tree in which the LRBL structure cannot work normally can be obtained, and an or gate relationship exists between each bottom event and a top event of the fault tree, that is, the top event will occur as long as any bottom event occurs. Therefore, the reliability calculation formula for realizing normal operation of the LRBL structure is as follows:

therefore, the reliability of the normal operation of the embodiment is realized by

R＝(1-10 ^-20 )(1-0.0256)(1-10 ^-20 )(1-10 ^-20 )≈0.9744

The invention extracts samples for explosion simulation by establishing an explosion simulation finite element model and combining a Latin hypercube sampling method, and then performs reliability calculation by combining K-S inspection with a reliability index or a method for establishing a proxy model. The method for analyzing the position structure reliability of the minimum risk bomb of the civil aircraft solves the problems of high cost of a real explosion test and time consumption of an explosion simulation test, and realizes efficient estimation of the position structure failure probability of the minimum risk bomb of the civil aircraft.

Although embodiments of the present invention have been shown and described, it will be understood that they are exemplary and not intended to limit the invention, and that various changes, modifications, substitutions and alterations can be made herein by those skilled in the art without departing from the spirit and scope of the invention, which should not be limited to the exact construction and arrangement of parts set forth herein. The embodiments of this specification illustrate the best mode known for carrying out the disclosure and will enable those skilled in the art to utilize the disclosure.

Claims (9)

1. A method for analyzing the reliability of a civil aircraft minimum risk bomb position structure is characterized by comprising the following steps:

s10, establishing a finite element model of the LRBL structure by using explosion simulation software, carrying out stress analysis on the LRBL structure, and determining a dangerous part of the LRBL structure;

s20, determining an uncertain input variable of the LRBL structure, performing explosion simulation solving by combining the uncertain variable, and obtaining a maximum plastic strain value of a dangerous part as a reliability analysis output variable;

s30, determining a failure criterion of a dangerous part of the LRBL structure under the action of explosion and determining a limit state function of the LRBL structure;

step S40: calculating the failure probability of each dangerous part of the LRBL structure according to the limit state function determined in the step S30;

step S50: and calculating the reliability of the LRBL structure by using a fault tree analysis method.

2. The method for analyzing the positional structure reliability of the civil aircraft minimum risk bomb according to claim 1, wherein in the step S10, LS-DYNA finite element software or CATIA three-dimensional software is adopted to establish an LRBL structural finite element model under the action of an explosive load, and the LRBL structure is subjected to stress analysis.

3. The method for analyzing the structural reliability of the civil aircraft minimum risk bomb position according to claim 1, wherein the step S20 specifically comprises the following substeps:

the substep S201 is that uncertainty of the explosion load parameter and the material performance parameter is combined to determine uncertainty input variables of the LRBL structure;

substep S202: adopting a Latin hypercube method to sample the uncertain input variables determined in the sub-step S201 and determining uncertain variable samples of the LRBL structure;

substep S203: and performing explosion simulation and solving calculation by combining with the uncertain variable sample in the sub-step S202 to obtain the maximum plastic strain value of each dangerous part of the LRBL structure, and obtaining the output response corresponding to the sample point to be used as the reliability analysis output variable.

4. The method for analyzing the reliability of the location structure of the civil aircraft minimum risk bomb according to claim 1, wherein in the step S30, the failure behavior of the LRBL structure is described by using a Johnson-Cook failure model:

wherein A-yield strength at quasi-static state; b-strain hardening coefficient; n-strain hardening coefficient;

c-strain rate sensitivity coefficient; epsilon-equivalent plastic strain;

-a strain rate;

-a reference strain rate;

-dimensionless strain rate, satisfying

T _r Is a reference temperature, and the lowest temperature 294K of the test is taken; t is _m Is the melting point temperature of the material; m-is the temperature sensitivity coefficient;

in the simulation, the plastic failure strain of the material is used as a failure criterion, and the limit state function of the LRBL structure meets the following conditions:

Z(X)＝ε _f -ε _max (X)

z (X) is the extreme state function, ε _f Is the plastic failure strain of the LRBL structure, X is the uncertainty input variable, ε _max (X) is the uncertaintyAnd entering the maximum plastic strain of the dangerous part of the LRBL structure corresponding to the variable.

5. The method as claimed in claim 1, wherein in step S40, the K-S test is combined with the first second moment to solve the failure probability of each dangerous part of the LRBL structure, or the surrogate model is used to solve the failure probability of each dangerous part of the LRBL structure.

6. The method for analyzing the positional structure reliability of the civil aircraft minimum risk bomb according to claim 3 or 5, wherein the specific method for solving the failure probability of each dangerous part of the LRBL structure by using the method of combining the K-S test and the first secondary moment in the step S40 is as follows:

performing K-S inspection on the output response sample obtained by the simulation calculation in the step S20, and determining the probability distribution characteristics of the output response of the reliability analysis of the LRBL structure, namely the distribution form, the mean value and the standard deviation of the plastic strain of each dangerous part;

and obtaining a reliability index through a first-order second-order moment method, and calculating the failure probability of each dangerous part of the LRBL structure.

7. The method for analyzing the positional structure reliability of the civil aircraft minimum risk bomb according to claim 3 or 5, wherein the concrete method for solving the failure probability of each dangerous part of the LRBL structure by using the surrogate model method in the step S40 is as follows:

fitting the uncertain input variable sample of the LRBL structure determined in the step S20 and the output response sample obtained by simulation calculation to obtain a function proxy model of the relationship between the input variable and the output response of each dangerous part of the LRBL structure;

comparing the strain obtained by simulation in different dangerous parts of the LRBL structure with the strain obtained by the proxy model, and selecting a function proxy model with higher precision and better fitting degree;

according to the probability distribution characteristics of random input variables, random sampling is carried out by using a Monte-Carlo method, corresponding random output response is calculated by combining the sampling value and the function of the LRBL structure, and the random output response is compared with the failure mode allowable value, so that the reliability analysis of each dangerous part of the LRBL structure is completed.

8. The method for analyzing the structural reliability of the civil aircraft minimum risk bomb position according to claim 7, wherein the proxy model adopted in the step S40 is a pure quadratic response surface model, a Krigin model, an artificial neural network model or a support vector machine model.

9. The method for analyzing the positional structure reliability of the civil aircraft minimum risk bomb according to claim 1, wherein the step S50 is implemented by:

analyzing the top event of the fault tree without realizing normal operation of the LRBL structure, establishing the relationship between the failure of the LRBL structure at the top event and the failure of each dangerous part at the bottom event to obtain the fault tree in which the LRBL structure cannot realize normal operation, wherein the top event and each bottom event of the fault tree are in OR gate relationship,

the calculation formula of the reliability of the LRBL structure for realizing normal work is as follows:

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