Civil aircraft minimum risk bomb position structure reliability analysis method

Abstract

The application discloses a civil aircraft minimum risk bomb position structure reliability analysis method, which comprises the following steps: S10, establishing a finite element model of an LRBL structure, and determining dangerous positions of the civil aircraft minimum risk bomb position structure; S20, determining uncertainty input variables of the LRBL structure, and performing explosion simulation and solving in combination with the uncertainty input variables; S30, determining failure criteria of the dangerous positions of the LRBL structure under explosion action, and obtaining a limit state function; S40, determining a failure probability of the dangerous positions of the LRBL structure according to the limit state function; and S50, obtaining reliability of the LRBL structure by using a fault tree analysis. Explosion simulation is used to avoid the work that can be completed only by a large number of real explosion tests, efficient estimation of the failure probability of the civil aircraft minimum risk bomb position structure is realized, and the efficiency of reliability analysis and calculation is improved.

Description

Technical Field

[0001] This invention belongs to the field of aviation transport safety and structural reliability design, and specifically relates to a method for structural reliability analysis of minimum risk bomb locations on civil aircraft. Background Technology

[0002] The Federal Aviation Administration (FAA), in FAR 25-127 amendment and Advisory Circular AC 25.795-6, stipulates that aircraft with a maximum certified passenger capacity greater than 60 or a takeoff gross weight exceeding 100,000 lbs (45,359 kg) must be designed with a "Least Risk Bomb Location (LRBL)" to house any suspected explosive devices discovered. A bomb containment system (or blast-resistant container) can be used to further reduce the impact of an explosion. Therefore, a blast-resistant structure (i.e., a Least Risk Bomb Location (LRBL) structure) can be designed to house suspected explosive devices discovered on civil aircraft, minimizing damage to the aircraft and ensuring the safety of the aircraft and its occupants.

[0003] The LRBL structure, used on aircraft for the rapid placement and disposal of suspected explosive devices, possesses a relatively complex structure, requiring extremely high structural reliability to ensure its normal operation. Considering the numerous uncertainties affecting the LRBL structure, such as the uncertainty of explosive loads, material properties, and geometric dimensions, even if the designed LRBL structure meets the allowable strength requirements, it may still fail during actual operation, thus failing to provide the intended protection. Therefore, to ensure no problems arise in practical use, a reliability analysis of the LRBL structure is necessary.

[0004] Currently, research on the LRBL structure of civil aircraft in China is still in its early stages, and reliability analysis methods for the LRBL structure are lacking and require further research. Furthermore, explosion testing is complex, costly, and difficult to perform, making it unsuitable for large-scale testing. Therefore, to ensure the safety and reliability of the LRBL structure of civil aircraft, an efficient and reliable reliability analysis method is needed to perform reliability analysis on the LRBL structure, ensuring that it meets stringent reliability requirements and does not encounter problems in actual use. Summary of the Invention

[0005] The technical problem to be solved by the present invention is: The present invention aims to provide a method for reliability analysis of the minimum risk bomb location structure of civil aircraft, which can effectively and accurately perform reliability analysis on the minimum risk bomb location structure of civil aircraft.

[0006] The technical solution of this invention is: a method for structural reliability analysis of minimum-risk bomb locations on civil aircraft, specifically including the following steps:

[0007] Step S10: Use explosion simulation software to establish a finite element model of the LRBL structure, conduct stress analysis on the LRBL structure, and determine the dangerous parts of the LRBL structure;

[0008] Step S20: Determine the uncertainty input variables of the LRBL structure, combine the uncertainty variables to perform explosion simulation and obtain the maximum plastic strain value of the dangerous part, which is used as the output variable of the reliability analysis;

[0009] Step S30: Clarify the failure criteria for the dangerous parts of the LRBL structure under the action of an explosion, and determine the limit state function of the LRBL structure;

[0010] Step S40: Calculate the failure probability of each critical part of the LRBL structure based on the limit state function determined in step S30;

[0011] Step S50: Calculate the reliability of the LRBL structure using fault tree analysis.

[0012] Furthermore, in step S10, the LS-DYNA finite element software or CATIA three-dimensional software are used to establish a finite element model of the LRBL structure under explosive load, and the stress analysis of the LRBL structure is performed.

[0013] Furthermore, step S20 specifically includes the following sub-steps:

[0014] Sub-step S201: Combine the uncertainties of the explosion load parameters and material property parameters to determine the uncertainty input variables of the LRBL structure;

[0015] Sub-step S202: Use the Latin hypersolution method to sample the uncertain input variables determined in sub-step S201 to determine the uncertain variable samples of the LRBL structure;

[0016] Sub-step S203: Combine the uncertainty variable samples from sub-step S202 to perform explosion simulation and solve the problem, obtain the maximum plastic strain value of each dangerous part of the LRBL structure, and obtain the output response corresponding to the sample point as the output variable for reliability analysis.

[0017] Furthermore, in step S30, the failure behavior of the LRBL structure is described using the Johnson-Cook failure model:

[0018] In the formula, A is the yield strength under quasi-static conditions; B is the strain hardening coefficient; n is the strain hardening coefficient; C is the strain rate sensitivity coefficient; and ε is the equivalent plastic strain. - Strain rate; -Reference strain rate; -Dimensionless strain rate, satisfying T * - T r This is a reference temperature, taken as the lowest temperature tested, 294K; T m It is the melting point temperature of the material; m is the temperature sensitivity coefficient;

[0019] In the simulation, the plastic failure strain of the material is used as the failure criterion. The limit state function of the LRBL structure satisfies:

[0020] Z(X) = ε f -ε max (X)

[0021] Z(X) is the limit state function, ε f Let X be the plastic failure strain of the LRBL structure, X be the uncertainty input variable, and ε be the strain. max (X) represents the maximum plastic strain at the critical location of the LRBL structure corresponding to the uncertain input variable.

[0022] Furthermore, in step S40, the failure probability of each critical part of the LRBL structure is solved by using the KS test combined with the first second moment method, or the failure probability of each critical part of the LRBL structure is solved by using the surrogate model method.

[0023] Furthermore, the specific method for solving the failure probability of each critical part of the LRBL structure in step S40 using the KS test combined with the first second moment is as follows:

[0024] The KS test is performed on the output response samples obtained from the simulation calculation in step S20 to determine the probability distribution characteristics of the output response of the LRBL structural reliability analysis, namely the distribution form, mean and standard deviation of plastic strain in each critical part.

[0025] The reliability index is obtained by using the first second-order moment method, and the failure probability of each critical part of the LRBL structure is calculated.

[0026] Furthermore, the specific method for solving the failure probability of each critical part of the LRBL structure using the surrogate model method in step S40 is as follows:

[0027] For the input variable samples of LRBL structure uncertainty determined in step S20 and the output response samples obtained from simulation calculation, a functional surrogate model of the relationship between input variables and output response of each dangerous part of LRBL structure is fitted.

[0028] By comparing the strain obtained through simulation and the strain obtained through the surrogate model in different dangerous parts of the LRBL structure, the surrogate model with higher accuracy and better fitting is selected.

[0029] Based on the probability distribution characteristics of the random input variables, random sampling is performed using the Monte Carlo method. By combining the sampled values ​​with the functional function of the LRBL structure, the corresponding random output response is calculated and compared with the allowable failure mode value to complete the reliability analysis of each hazardous part of the LRBL structure.

[0030] Furthermore, the surrogate model used in step S40 is a pure quadratic response surface model, a Kriging model, an artificial neural network model, or a support vector machine model.

[0031] Furthermore, step S50 is specifically implemented by including the following steps:

[0032] The analysis takes the failure of the LRBL structure to function properly as the top event of the fault tree. The relationship between the top event (LRBL structure failure) and the bottom events (failure of each critical component) is established, resulting in a fault tree for the LRBL structure's inability to function properly. Each bottom event in the fault tree is connected to the top event via an OR gate relationship.

[0033] The reliability calculation formula for the LRBL structure to achieve normal operation is as follows:

[0034]

[0035] Beneficial effects

[0036] The beneficial effects of this invention are as follows:

[0037] 1. The present invention provides a method for structural reliability analysis of minimum risk bomb locations on civil aircraft. By establishing a finite element model and combining it with the characteristics of explosive impact, the dangerous parts of the LRBL structure are obtained. The Latin hypercube sampling method is used to extract samples for explosion simulation. The LS-DYNA software is used for explosion simulation, which avoids the need for a large number of real explosion tests and improves the efficiency of reliability analysis calculation.

[0038] 2. Another advantage of this invention is that conventional structural reliability calculation methods are based on the explicit expression of function as a random variable. The relationship between structural input variables and output response under explosive impact loads is highly nonlinear or ambiguous, making it impossible to directly use conventional reliability calculation methods. However, this invention avoids the drawbacks of traditional reliability analysis methods by using the KS test combined with reliability indices or establishing a surrogate model. This achieves efficient estimation of the failure probability of the minimum-risk bomb location structure on civil aircraft, which is of great significance for ensuring the normal operation of the minimum-risk bomb location structure on civil aircraft. Attached Figure Description

[0039] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained from these drawings without creative effort.

[0040] Figure 1 This is a flowchart of the civil aircraft minimum risk bomb location structure reliability analysis method of the present invention;

[0041] Figure 2 This is a flowchart of step S20 of the civil aircraft minimum risk bomb location structure reliability analysis method of the present invention;

[0042] Figure 3 This is a flowchart of step S40 of the civil aircraft minimum risk bomb location structure reliability analysis method of the present invention.

[0043] Figure 4 An embodiment of the present invention provides a possible LRBL structure scheme.

[0044] In the diagram, the 1-LRBL structural tank body, the 101-LRBL structural tank boss, and the 2-LRBL structural filling end cover are shown.

[0045] 201-LRBL structural filling end cap boss, 3-LRBL structural punch, 4-LRBL structural shear pin Detailed Implementation

[0046] The embodiments of the present invention are described in detail below. Examples of the embodiments are shown in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, but should not be construed as limiting the present invention.

[0047] This invention provides a method for structural reliability analysis of minimum-risk bomb locations on civil aircraft, comprising the following steps:

[0048] Step S10: Use explosion simulation software to establish a finite element model of the LRBL structure, conduct stress analysis on the LRBL structure, and determine the dangerous parts of the LRBL structure.

[0049] like Figure 4 As shown, this embodiment provides a possible LRBL structure, which is a rotating structure, including an LRBL structure tank 1, an LRBL structure filling end cap 2, an LRBL structure punch 3, and an LRBL structure shearing pin; the outer wall of one end of the LRBL structure tank 1 is uniformly provided with bosses circumferentially, which are LRBL structure tank bosses 101; the inner wall of one end of the LRBL structure filling end cap 2 is uniformly provided with bosses circumferentially that cooperate with the LRBL structure tank bosses 101, which are LRBL structure filling end cap bosses 201.

[0050] The three-dimensional geometric model of the LRBL structure can be created in 3D software such as CATIA, or it can be created directly in finite element software such as LS-DYNA. There is no limitation here.

[0051] For example, using LS-DYNA finite element software to establish a finite element model of the LRBL structure under explosive load, since the high temperature, high pressure and high speed gas generated by the explosion in the cavity of the LRBL structure will act on the entire LRBL structure, the stress on the LRBL structure can be analyzed by combining the results of the explosion simulation finite element analysis, and the dangerous parts of the LRBL structure can be determined.

[0052] For example, for this embodiment to function properly, the following requirements must be met: under the impact of an explosion, the shear pin will break, and the punch will impact the skin under the push of the shock wave, guiding the explosion shock wave outside the cabin. Except for the shear pin, other components of the LRBL structure must not be damaged to prevent the explosion shock wave from harming the personnel inside the cabin.

[0053] Assume the materials used in the LRBL structure are as shown in Table 1:

[0054] Component Name Materials used Material failure strain LRBL structure tank Titanium alloy 0.25 Filling end cap Titanium alloy 0.25 punch Titanium alloy 0.25 shear pin Stainless steel 0.2

[0055] Table 1

[0056] Meshing directly affects computational accuracy and time, requiring comprehensive analysis to determine the mesh type and element size. In this embodiment, for example, modeling and meshing are performed using LS-DYNA finite element software. A hexahedral mesh is used to mesh the structure. The mesh size for the LRBL structure tank, filling end cap, and punch can be 5mm, while the mesh size for the shear pin can be 3mm.

[0057] The preprocessing of the LRBL structure is completed in LS-DYNA, including: the metal material model, explosive and air models and their parameter settings, and the setting of boundary conditions; then the calculation is submitted to solve the problem and obtain the stress cloud map.

[0058] The hazardous parts of the LRBL structure refer to the parts among all components of the LRBL structure that are prone to failure under the impact of an explosion. Simulation data shows that under the impact of an explosion, the shear pin of the LRBL structure will break and the punch will be ejected. The hazardous parts of the structure are identified as: the bottom of the LRBL structure filling end cover, the wall of the LRBL structure tank, and the edge of the LRBL structure tank hole.

[0059] Step S20: Determine the uncertainty input variables of the LRBL structure, and combine the uncertainty variables to perform explosion simulation to obtain the maximum plastic strain value of the dangerous part as the reliability analysis output variable;

[0060] Specifically, it includes:

[0061] Sub-step S201: Determine the uncertain input variables for the LRBL structure;

[0062] Considering the uncertainties in load parameters and material property parameters, the uncertainty parameters used in this embodiment are shown in Table 2:

[0063]

[0064] Table 2

[0065] Other materials can also be used in LRBL structures, and more uncertainties in load parameters and material performance parameters can be considered. This embodiment is intended to illustrate the method of this disclosure, and will not be elaborated here.

[0066] Sub-step S202: Determine the uncertain input variable samples for the LRBL structure;

[0067] The Latin hypersolution method was used to sample 30 groups of uncertain input variables, resulting in 30 experimental sample points.

[0068] Assume X1,…,X K Let X be the K input random variables in the probability problem to be solved. i Let X1, ..., X K For any random variable in the set, its cumulative probability distribution function is:

[0069] Y k =F k (X i )

[0070] Let N represent the sampling size, and the sampling method is as follows: [The text abruptly ends here, likely due to an incomplete sentence or a formatting error.] k =Fk (X i The vertical axis of ) is divided into N equally spaced, non-overlapping intervals (due to Y) k If the range is 0 to 1.0, then the width of each interval is 1 / N). Select a Y from each interval. k The sampled values ​​are obtained. The sampled values ​​within the interval can be randomly selected, or the midpoint of each interval can be chosen. Then, the function Y is used... k =F k (X i To calculate X, use the inverse function of ). i The sampled value, i.e., X i The nth sample value is:

[0071]

[0072] Therefore, based on the uncertainty parameters in Table 2, we obtained 30 sets of sample points for this embodiment, as shown in Table 3:

[0073]

[0074]

[0075] Table 3

[0076] Sub-step S203: Combine the uncertainty variable samples in sub-step S202 to perform explosion simulation and solve the problem to obtain the maximum plastic strain value of the dangerous part, which is used as the output variable for reliability analysis;

[0077] The maximum plastic strain data of each critical part of the LRBL structure were extracted, and the output response corresponding to 30 sample points was obtained, as shown in Table 4:

[0078]

[0079]

[0080] Table 4

[0081] Step S30: Determine the failure criteria for the dangerous parts of the LRBL structure under the action of an explosion, and obtain the limit state function of the LRBL structure;

[0082] The Johnson-Cook failure model was used to describe the failure behavior of the LRBL structure. In the simulation, the plastic failure strain of the material was used as the failure criterion to control the failure of the material elements in the simulation.

[0083] Under explosive loading, the LRBL structure is subjected to a huge impact load in a short period of time, which may lead to large deformation. For this complex nonlinear dynamic response process, the Johnson-Cook failure model is used to describe the failure behavior of the LRBL structure, and the formula is as follows:

[0084]

[0085] In the formula, A is the yield strength under quasi-static conditions; B is the strain hardening coefficient; n is the strain hardening coefficient; C is the strain rate sensitivity coefficient; and ε is the equivalent plastic strain. —Strain rate; —Reference strain rate; —Dimensionless strain rate, satisfying T * —— T r This is a reference temperature, taken as the lowest temperature tested, 294K; T m is the melting point temperature of the material; m is the temperature sensitivity coefficient.

[0086] The strain at the point of structural failure is given by the following formula:

[0087]

[0088] When damage factors When the value of is 1, that is, when D≥1, the structure is considered to have failed. By modifying this formula, the failure criterion is obtained as follows: in Let ε(X) be the strain at a certain part of the structure.

[0089] In summary, the plastic failure strain of the material is used to control failure in the simulation as a failure criterion;

[0090] The limit state function of the LRBL structure satisfies the following relationship:

[0091] Z(X) = ε f -ε max (X)

[0092] Where Z(X) is the limit state function, ε f Let X be the plastic failure strain of the LRBL structure, X be the uncertainty input variable, and ε be the strain. max (X) represents the maximum plastic strain at the critical location of the LRBL structure corresponding to the uncertain input variable.

[0093] The limit state function of the LRBL structure satisfies the following relationship:

[0094] Z(X) = ε f -ε max (X)

[0095] Where Z(X) is the limit state function, ε fis the plastic failure strain of the LRBL structure, X is the uncertain input variable, and ε max (X) is the maximum plastic strain at the dangerous part of the LRBL structure corresponding to the uncertain input variable.

[0096] If Z(X) is less than zero, the maximum plastic strain at the dangerous part of the LRBL structure is greater than the plastic failure strain of the material, and it is determined that the dangerous part of the LRBL structure fails.

[0097] Step S40: Determine the failure probability of each dangerous part of the LRBL structure according to the limit state function.

[0098] Method S40a: Use the method of combining the K-S test with the first-order second-moment method to solve the failure probability of each dangerous part of the LRBL structure, specifically including:

[0099] Perform a K-S test on the output response samples obtained from the simulation calculation to determine the probability distribution characteristics of the output response of the LRBL structure reliability analysis, that is, the distribution form, mean, and standard deviation of the plastic strain at each dangerous part, and then obtain the reliability index through the first-order second-moment method to calculate the failure probability of each dangerous part of the LRBL structure.

[0100] Perform a K-S test on the strain data of each dangerous part of the extracted LRBL structure:

[0101] H0: The observed results come from a population that follows a specific distribution form

[0102] H1: The observed results come from a population that does not follow a specific distribution form;

[0103] Arrange the given sample data in ascending order, and let F n (x) be the empirical distribution function of a simple subsample with a capacity of n, that is, the probability of the event x < X, then:

[0104]

[0105] F(x) is the theoretical distribution function of the assumed population, and let the statistic D n be:

[0106] D n = sup|F(x) - F n (x)|

[0107] According to the Kolmogorov theorem:

[0108]

[0109] Multiply both sides of the above formula by to obtain:

[0110]

[0111] It can be seen that when n is large, the distribution on the left side of the above equation approaches θ(y). Given a certain significance level α, the critical value D of the confidence level α is... n,α Satisfy the following formula:

[0112] P(D n >D n,α )=1-θ(y)=α

[0113] If D n >D n,α If the hypothesis is true, then reject the hypothesis H0; otherwise, accept H0.

[0114] Use Y i The output variable representing the structural reliability of the LRBL is the plastic strain at each critical location. For the null hypothesis H0: the overall Y... i Follows a normal distribution N(μ,σ) 2 The test was performed, and the statistic D for the 30 groups of LRBL structured output variable samples was calculated. n and its critical value D n,α As shown in Table 5:

[0115]

[0116] Table 5

[0117] According to the KS test results of the LRBL structure output variables in Table 5, at a significance level of 5%, the statistical measure D of the 30 output variable samples is... n Less than its critical value D n,α Therefore, we accept hypothesis H0, which means that the plastic strain of each critical part of the LRBL structure follows a normal distribution, and its specific probability distribution characteristics are shown in Table 6:

[0118]

[0119] Table 6

[0120] If the output variable Y of the LRBL structural reliability analysis follows a normal distribution N(μ,σ) 2 If the failure probability of each critical part of the LRBL structure is calculated, then the formula is as follows:

[0121]

[0122] In the formula: λ——failure equivalent plastic strain of LRBL structural material; f(y)——density distribution function of output variable Y (plastic strain) of LRBL structural reliability analysis; μ——mean value of variable Y; σ——standard deviation of variable Y.

[0123] The failure probabilities of each critical part of the LRBL structure under implosion can be obtained as follows:

[0124]

[0125]

[0126]

[0127]

[0128] Method S40b: Reliability analysis is performed by estimating the failure probability using the surrogate model method combined with the Monte Carlo method;

[0129] The failure probability of each dangerous part of the LRBL structure is solved by using the surrogate model method: the surrogate model function of each dangerous part is obtained by fitting the input and output sample points, and the accuracy is verified to meet the requirements. Based on the finally established surrogate model, the failure probability is estimated by Monte Carlo method.

[0130] Based on the input variable data in Table 3 and the strain data of each critical part of the LRBL structure extracted in Table 4, a surrogate model using the response surface methodology is used to fit the functional model of the relationship between the input variables and the output response.

[0131] The normalized absolute error mean (MNAE), root mean square error (RMSE), and coefficient of determination (R²) were used. 2 As an indicator of the accuracy of the fitting function of the surrogate model, the strain obtained by simulation and the strain obtained by the surrogate model in different dangerous parts are compared, so as to select the function model with higher accuracy and better fitting.

[0132] Taking the plastic strain data fitted by the pure quadratic response surface surrogate model function as an example, calculation and analysis were performed, and the fitting degree of the function model for each dangerous part is shown in Table 7.

[0133] Serial Number object goodness of fit / R <![CDATA[Coefficient of determination / R 2 > 1 tank body wall 0.97 0.95 2 edge of the can body hole 0.92 0.84 3 Filling end cap bottom 0.91 0.83 4 punch hole edge 0.90 0.80

[0134] Table 7

[0135] Of course, other proxy models can also be used, such as the Kriging model, artificial neural network model, support vector machine model, etc.; this embodiment is intended to illustrate the method of this disclosure, and will not be listed here.

[0136] The functions for the tank wall, tank hole edge, filling end cap bottom, and punch hole edge obtained using a pure quadratic response surface model are as follows:

[0137] Y1=-0.7992-0.0650X1-0.0093X2+0.0063X3+0.4917X4+0.0082X5+0.0018X1 2 +2.7890×10 -4 X2 2 -3.1357×10 -5 X3 2 -0.2976X4 2 -1.7363×10 -5 X5 2

[0138] Y2=1.0967-0.0746X1-0.0750X2+0.0017X3+0.0647X4+9.8035×10 -4 X5+0.0021X1 2 +0.0025X2 2 -8.6698×10 -6 X3 2 -0.0731X4 2 -2.2750×10 -6 X5 2

[0139] Y3=0.3444-0.0543X1+0.0185X2-9.0587×10 -5 X3+0.1304X4+5.5713×10 -5 X5+0.0014X1 2 -5.1123×10 -4 X2 2 +1.7890×10 -7 X3 2 -0.0977X4 2 +8.0054×10 -7 X5 2

[0140] Y4=0.0782+0.0726X1+0.0377X2-3.5283×10 -4 X3-0.1071X4-0.0056X5-0.0022X1 2 -0.0012X2 2 -8.6283×10 -7 X3 2 -0.0281X4 2 +1.1512×10 -5 X5 2

[0141] The mean and standard deviation of the maximum strain of the tank wall, the maximum strain at the edge of the tank hole, the maximum strain at the bottom of the filling end cap, and the maximum strain at the edge of the punch hole, obtained by fitting the function model, are shown in Table 8.

[0142]

[0143] Table 8

[0144] Based on the probability distribution characteristics of the random input variables, the Monte Carlo method is used to randomly sample them. Combining the sampled values ​​with the structural function, the corresponding random output response is calculated and compared with the allowable failure mode values ​​to complete the structural reliability analysis. Therefore:

[0145] P f (Y1)≤10 -30

[0146] P f (Y2) = 0.0256

[0147] P f (Y3)≤10 -30

[0148] P f (Y4)≤10 -30

[0149] Step S50: Using the fault tree analysis method, establish the relationship between the top event LRBL structural failure and the failure of each dangerous part in the bottom event, obtain the reliability calculation model of the LRBL structure, and calculate the reliability of the LRBL structure.

[0150] The analysis uses the failure of the LRBL structure to function properly as the top event in the fault tree. The reasons for the LRBL structure's failure to function properly include: ① damage to the LRBL structure tank wall; ② damage to the LRBL structure tank hole edge; ③ damage to the bottom of the LRBL structure filling end cover; ④ damage to the LRBL structure punch hole edge.

[0151] A fault tree can be obtained indicating that the LRBL structure cannot function properly. Each bottom event in the fault tree is connected to the top event via an OR gate; that is, if any bottom event occurs, the top event will also occur. Therefore, the reliability calculation formula for the LRBL structure to function properly is as follows:

[0152]

[0153] Therefore, the reliability of this embodiment in achieving normal operation is:

[0154] R = (1-10) -20 (1-0.0256)(1-10) -20 (1-10) -20 )≈0.9744

[0155] This invention establishes an explosion simulation finite element model and uses the Latin hypercube sampling method to extract samples for explosion simulation. Reliability calculations are then performed using the KS test combined with reliability indices or by establishing a surrogate model. This invention provides a reliability analysis method for the minimum-risk bomb location structure of civil aircraft, solving the problems of high costs associated with real explosion tests and time-consuming explosion simulation tests, and achieving efficient estimation of the failure probability of the minimum-risk bomb location structure on civil aircraft.

[0156] Although embodiments of the present invention have been shown and described above, it is to be understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the invention. The present invention is not limited to the detailed structure and arrangement of the components presented in this specification. The embodiments in this specification illustrate the best known mode for carrying out this disclosure and will enable those skilled in the art to utilize this disclosure.

Claims

1. A method for structural reliability analysis of minimum-risk bomb placement on civil aircraft, characterized in that, Specifically, the following steps are included: Step S10: Use explosion simulation software to establish a finite element model of the LRBL structure, perform stress analysis on the LRBL structure, and determine the critical parts of the LRBL structure; Step S20: Determine the uncertainty input variables of the LRBL structure, combine the uncertainty variables to perform explosion simulation and obtain the maximum plastic strain value of the dangerous part, which is used as the output variable of the reliability analysis; Step S30: Define the failure criteria for the critical parts of the LRBL structure under explosion and determine the limit state function of the LRBL structure; this step describes the failure behavior of the LRBL structure using the Johnson-Cook failure model: In the formula, A represents the yield strength under quasi-static conditions; B represents the strain hardening coefficient; and n represents the strain hardening coefficient. C - Strain rate sensitivity coefficient; - Equivalent plastic strain; - Strain rate; -Reference strain rate; -Dimensionless strain rate, satisfying ; -Normalized temperature= , This is a reference temperature, taken as the lowest temperature of the test, 294K; It is the melting point temperature of the material; —This is the temperature sensitivity coefficient; In the simulation, the plastic failure strain of the material is used as the failure criterion. The limit state function of the LRBL structure satisfies: Let be the limit state function. Let X be the plastic failure strain of the LRBL structure, and let X be the uncertainty input variable. The maximum plastic strain at the critical location of the LRBL structure corresponding to the uncertain input variable; Step S40: Calculate the failure probability of each critical part of the LRBL structure based on the limit state function determined in step S30; Step S50: Calculate the reliability of the LRBL structure using fault tree analysis.

2. The method for structural reliability analysis of minimum-risk bomb placement on a civil aircraft according to claim 1, characterized in that, In step S10, the LS-DYNA finite element software or CATIA 3D software is used to establish a finite element model of the LRBL structure under explosive load, and the stress analysis of the LRBL structure is performed.

3. The method for structural reliability analysis of minimum-risk bomb placement on a civil aircraft according to claim 1, characterized in that, Step S20 specifically includes the following sub-steps: Sub-step S201: Combine the uncertainties of the explosion load parameters and material property parameters to determine the uncertainty input variables of the LRBL structure; Sub-step S202: Use the Latin hypersolution method to sample the uncertain input variables determined in sub-step S201 to determine the uncertain variable samples of the LRBL structure; Sub-step S203: Combine the uncertainty variable samples from sub-step S202 to perform explosion simulation and solve the problem, obtain the maximum plastic strain value of each dangerous part of the LRBL structure, and obtain the output response corresponding to the sample point as the output variable for reliability analysis.

4. A method for analyzing the structural reliability of a minimum-risk bomb location on a civil aircraft, as described in claim 1, is characterized in that... In step S40, the failure probability of each critical part of the LRBL structure is solved by combining the KS test with the first second moment method, or the failure probability of each critical part of the LRBL structure is solved by the surrogate model method.

5. The method for structural reliability analysis of minimum-risk bomb placement on a civil aircraft according to claim 4, characterized in that, The specific method for solving the failure probability of each critical part of the LRBL structure in step S40 using the KS test combined with the first second moment method is as follows: The KS test is performed on the output response samples obtained from the simulation calculation in step S20 to determine the probability distribution characteristics of the output response of the LRBL structural reliability analysis, namely the distribution form, mean and standard deviation of plastic strain in each critical part. The reliability index is obtained by using the first second-order moment method, and the failure probability of each critical part of the LRBL structure is calculated.

6. The method for structural reliability analysis of minimum-risk bomb placement on a civil aircraft according to claim 4, characterized in that, The specific method for solving the failure probability of each dangerous part of the LRBL structure using the surrogate model method in step S40 is as follows: For the input variable samples of LRBL structure uncertainty determined in step S20 and the output response samples obtained from simulation calculation, a functional surrogate model of the relationship between input variables and output response of each dangerous part of LRBL structure is fitted. By comparing the strain obtained through simulation and the strain obtained through the surrogate model in different dangerous parts of the LRBL structure, the surrogate model with higher accuracy and better fitting is selected. Based on the probability distribution characteristics of the random input variables, random sampling is performed using the Monte Carlo method. By combining the sampled values ​​with the functional function of the LRBL structure, the corresponding random output response is calculated and compared with the allowable failure mode value to complete the reliability analysis of each hazardous part of the LRBL structure.

7. A method for analyzing the structural reliability of a minimum-risk bomb location on a civil aircraft according to claim 6, characterized in that, The surrogate model used in step S40 is a pure quadratic response surface model, a Kriging model, an artificial neural network model, or a support vector machine model.

8. The method for structural reliability analysis of minimum-risk bomb placement on a civil aircraft according to claim 1, characterized in that, The specific implementation steps of step S50 include: The analysis takes the failure of the LRBL structure to function properly as the top event of the fault tree. The relationship between the top event (LRBL structure failure) and the bottom events (failure of each critical component) is established, resulting in a fault tree for the LRBL structure's inability to function properly. Each bottom event in the fault tree is connected to the top event via an OR gate relationship. The reliability calculation formula for the LRBL structure to achieve normal operation is as follows: 。

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