Method for rapidly predicting failure probability of composite material structure under dense perforation damage

Abstract

The invention discloses a rapid prediction method for a composite material structure failure probability under dense perforation damage, and relates to the technical field of composite material structure failure mechanism and failure probability prediction. Comprising the steps of determining material and size information and a damage parameter range of a composite material structure; determining a residual strength finite element simulation model and a solving method; establishing a residual intensity distribution parameter data set; training a proxy model for predicting residual intensity distribution parameters by using the data set; testing the prediction precision of the agent model; determining the critical residual strength of the structure failure; calculating the failure probability of the structure under given damage parameters; predicting a structure failure probability considering the uncertainty of the damage parameter; and establishing a failure probability curved surface and the like. According to the method, rapid prediction of the failure probability of the composite material structure in the dense perforation damage mode is achieved through the agent model method, and the problems that in the prediction process of the failure probability of the composite material structure, the failure data obtaining cost is high, and failure probability prediction is difficult are solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of failure mechanism and failure probability prediction of composite material structures, and particularly relates to a rapid prediction method for the failure probability of composite material structures under dense perforation damage. Background Art

[0002] Compared with conventional metals, composite materials have the advantages of high specific strength, high specific stiffness, and strong designability, and are currently widely used in various fields. For example, composite materials such as carbon fiber reinforced composite laminates are widely used in aircraft fuselage, wing, and rudder surface structures. However, research shows that composite materials are more sensitive to impact damage than metals. Therefore, high-speed impact sources generated by explosives are a major threat to aircraft composite structures. In the process of violent actions such as explosion and impact, the failure results of the structure are usually uncertain, and it is often necessary to use the failure probability to evaluate the failure results of the structure.

[0003] In terms of the impact damage of composite materials, at present, scholars in various countries have carried out a large number of studies on the energy absorption principle, delamination damage, connection failure and other damage mechanisms of composite laminate structures under impact loads. However, most of the research stays at the material scale and mainly focuses on the low-speed impact problems of single or a small number of impact sources. There is currently little research on the failure of composite material structures after high-speed impact of multiple impact sources. At the same time, for the remaining load-bearing capacity of composite material structures containing impact damage, that is, the research on the functional failure of the structure, some researchers choose to equivalent the impact damage of the laminate to circular hole damage and use cohesive elements to predict the remaining strength of the laminate containing impact damage. The experimental research on the high-speed impact and post-damage load-bearing capacity of composite material structures is difficult, and currently mainly focuses on simulation research. However, the calculation efficiency of existing simulation methods is difficult to meet the needs of a large number of and rapid calculations. In order to balance the calculation efficiency and calculation accuracy, some researchers use surrogate models to simulate high-precision simulations and prototype tests. Surrogate models are data-driven, and their calculation results are very close to the original model, but the solution cost is lower. At present, the research and engineering applications of surrogate models have developed relatively maturely, but there is no relevant research on using the surrogate model method for predicting the failure probability of aviation composite structures under dense perforation damage mode. On the other hand, most of the current research on evaluating the failure results of structures using probability targets the problems with low experimental costs, large amounts of data, and intuitive and measurable experimental results. However, the failure mechanism of aircraft composite structures under the action of dense impact sources is complex, and the cost of obtaining failure data is high. It is difficult to establish a failure probability model through a large number of experiments.

[0004] Based on this, the present invention proposes a rapid prediction method for the failure probability of composite material structures under dense perforation damage to solve the problems of high cost of obtaining failure data and difficulty in predicting failure probability in the prediction process of the failure probability of aircraft composite material structures under dense perforation damage mode. Summary of the Invention

[0005] To solve the above technical problems, the present invention provides a rapid prediction method for the failure probability of composite material structures under dense perforation damage, which is used to solve the problems of high cost for obtaining failure data and difficulty in predicting the failure probability during the prediction process of the failure probability of aircraft composite material structures under dense perforation damage.

[0006] To achieve the above object, the present invention provides the following technical solutions: A rapid prediction method for the failure probability of composite material structures under dense perforation damage, comprising: Step 1: Determine the composite material structure information and the range of dense perforation damage parameters; Step 2: According to the composite material structure information and the dense perforation damage parameters determined in Step 1, establish a simulation model for the remaining strength of the composite structure and its solution method; Step 3: Conduct a working condition simulation on the simulation model established in Step 2 to obtain a data set of the remaining strength distribution parameters of the composite structure; Step 4: Use the data set of the remaining strength distribution parameters of the composite structure obtained in Step 3 to train a surrogate model, and at the same time, quickly predict the expectation and standard deviation of the remaining strength of the damaged structure according to the dense perforation damage parameters; Step 5: Test the prediction accuracy of the surrogate model trained in Step 4. After the prediction accuracy meets the usage requirements, complete the training of the surrogate model; Step 6: Determine the critical remaining strength for the failure of the composite structure; Step 7: Based on the critical remaining strength, use the surrogate model obtained in Step 5 to calculate the failure probability of the structure under given damage parameters; Step 8: Based on the failure probability calculation method in Step 7, combine the Monte Carlo method to predict the failure probability of the structure considering the uncertainty of damage parameters; Step 9: According to the results of the failure probability prediction in Step 8, establish a failure probability surface.

[0007] In a preferred embodiment of the present invention, the composite material structure information in Step 1 includes the structural form, material information, and loading conditions of the composite material structure; the dense perforation damage parameters include at least the perforation diameter D and the number of perforations N .

[0008] In a preferred embodiment of the present invention, the process of establishing the simulation model for the remaining strength of the composite structure and its solution method in Step 2 includes: Step 2.1: Establish a simulation model for the remaining strength of the composite structure; Draw the structural geometric model of the composite material, import the structural geometric model into the simulation software, complete the division of the composite material grid and the ply setting according to the composite material type and ply layup information of the structure, and finally insert zero-thickness cohesive elements between each layer to simulate the interlayer connection of the composite material, obtaining the grid model of the undamaged structure; Step 2.2: Preset damage according to the damage parameters; According to the expected damage parameters, preset randomly located perforation damages on the grid model of the undamaged structure established in Step 2.1; Step 2.3: Determine the material constitutive; Step 2.4: Perform the solution setting for the residual strength simulation model; Set the boundary constraints and loading conditions of the grid model, and output the reaction forces of the constrained boundaries of the grid model; and perform simulation solution on the grid model of the residual strength of the damaged composite material structure.

[0009] In a preferred embodiment of the present invention, the process of performing condition simulation on the simulation model in Step 3 to obtain the dataset of the structural residual strength distribution parameters includes: Step 3.1: Determine the simulation sampling conditions; Determine n groups of simulation sampling conditions within the range of damage parameter values U i ; where i = 0, 1, 2, 3,..., n, i When i = 0, it represents the undamaged state of the structure; Step 3.2: Fit the residual strength distribution parameters; For each simulation sampling condition except the undamaged one U i Perform m times of residual strength simulations with randomly located perforation positions to obtain the residual strength simulation results of the damaged composite material structure S 1 i , S 2 i ,…, S m i , and fit the expectation S μ i and the standard deviation : ; ; where, S μ i and are respectively the simulation sampling conditions U iThe expectations and standard deviations of the remaining strength distributions S j i are the simulation sampling conditions U i The remaining strength simulation results with the random perforation position at the j-th time; Step 3.3: Form a data set of the parameters of the structural remaining strength distribution; Considering the uncertainty of the perforation position, the parameters of the remaining strength distribution of the damaged composite material structure under each simulation sampling condition are obtained through Step 3.2 , and a data set of the parameters of the structural remaining strength distribution for training the surrogate model is formed.

[0010] In a preferred embodiment of the present invention, during the process of Step 4 of training the surrogate model using the data set of the parameters of the structural remaining strength distribution, a radial basis neural network model is used as the surrogate model for training. In the radial basis neural network model, the mapping relationship from the input to the output of the neural network is determined by the Gaussian formula as follows: ; where X= D, N ,…] T is the perforation damage parameter and is the input of the model; Y = y 1, y 2] T = S μ , σ] T is the parameter of the remaining strength distribution and is the output of the model; o is the number of hidden nodes; w ik is the weight coefficient; is the basis function; C k is the k center of the i-th node; d k is the k basis width parameter of the i-th node; is the Euclidean distance between the input vector and the node center.

[0011] In a preferred embodiment of the present invention, the process of Step 5 for testing the prediction accuracy of the surrogate model includes: Taking test sample points outside the training data set to test the prediction accuracy of the surrogate model. After the prediction accuracy meets the usage requirements, the training of the surrogate model is completed. Otherwise, increase the training sampling conditions and further train the model.

[0012] In a preferred embodiment of the present invention, during the process of Step 6 for determining the critical remaining strength of structural failure, the undamaged strength of the structure​S Two-thirds of 0 is used as the critical strength for failure after structural damage S limit 。

[0013] In a preferred embodiment of the present invention, when step 7 calculates the failure probability of the structure with given damage parameters using the surrogate model, the distribution parameters of the remaining strength are quickly predicted according to the given damage parameters , and then according to the normal probability distribution, the probability that the remaining strength of the damaged structure is lower than the critical strength S limit is calculated to obtain the failure probability of the structure with given damage parameters P k / h is: Wherein, P k / h is the failure probability of the structure with given damage parameters, S limit is the critical strength for failure after structural damage, S μ and are the expected value and standard deviation of the remaining strength distribution of the structure with given damage parameters, respectively

[0014] In a preferred embodiment of the present invention, the process of predicting the failure probability of the structure considering the uncertainty of damage parameters by combining the Monte Carlo method based on the failure probability calculation method in step 7 in step 8 includes: Step 8.1: Determine the distribution form of the perforation damage parameters; Step 8.2: Determine the expected perforation damage parameters; Estimate the expected damage parameters of the structure according to the explosive information and intersection conditions ( D e , N e ,…); and combine the distribution form of the damage parameters to determine the probability distribution F of the actual damage parameters ( D e , N e ,…); Step 8.3: Extract the actual perforation damage parameters; Use the Monte Carlo method to perform the i-th sampling in the probability distribution of the actual damage parameters to obtain the i-th set of actual damage parameters ( D i , N i ,…); Step 8.4: Predict the distribution parameters of the remaining strength of the structure under the actual damage parameters; The i-th set of actual damage parameters ( Di , N i , …) Input the proxy model to obtain the predicted results of the corresponding structural remaining strength distribution parameters ; Step 8.5: Calculate the failure probability of the structure under the actual damage parameters; Substitute the predicted results of the structural remaining strength distribution parameters under the i-th group of actual damage parameters into the formula: to calculate the predicted value of the failure probability of the structure under the i-th group of actual damage parameters P k / h i ; wherein, P k / h i is the failure probability of the structure under the i-th group of actual damage parameters, S limit is the critical strength for the structure to fail after being damaged, S μ i and are respectively the expected value and standard deviation of the structural remaining strength distribution under the i-th group of actual damage parameters; Step 8.6: Calculate the failure probability of the structure under the expected perforation damage parameters; Repeat steps 8.3 to 8.5 w times, and then use w the average value of the predicted values of the failure probability of the structure under the P k / h i groups of actual damage parameters as the predicted result of the failure probability of the structure considering the uncertainty of damage parameters under the expected damage parameters.

[0015] In a preferred embodiment of the present invention, the process of establishing the failure probability surface in step 9 includes: Step 9.1: Sampling of expected damage parameters; Densely and uniformly set sampling points within the value range of damage parameters; Step 9.2: Failure probability prediction; According to step 8, complete the failure probability prediction for each sampling point; Step 9.3: Interpolate to establish the failure probability surface; According to the failure probability prediction results of each sampling point, finally interpolate to establish the failure probability surface.

[0016] Compared with the prior art, the present invention provides a fast prediction method for the failure probability of composite material structures under dense perforation damage, having the following beneficial effects: The present invention realizes the rapid prediction of the failure probability of aircraft composite material structures under the dense perforation damage mode through the surrogate model method, which can provide reference for weapon equipment design and mission decision-making, and save the engineering simulation analysis and test costs.

[0017] The present invention not only considers the uncertainty of the perforation position distribution of the dense impact sources on the structure, but also considers the uncertainty of the perforation damage parameters themselves, making the research on the structural failure probability more refined and reasonably characterizing the influence of the uncertainty of the damage process on the structural failure probability.

[0018] The composite material progressive damage finite element simulation method and failure probability calculation method used in the present invention can be applied to the damage and failure problems of various composite material structures. Compared with the failure prediction engineering algorithms that are only applicable to specific structural forms, the present invention has a wider scope of use.

[0019] The present invention establishes a component functional failure criterion by using the surrogate model method, which can greatly reduce the cost and provide basic data for the failure assessment of complex equipment systems. Brief Description of the Drawings

[0020] Figure 1 is the architecture diagram of the rapid prediction method for the failure probability of composite material structures under the dense perforation damage mode of the present invention; Figure 2 is the schematic diagram of the geometric shape and dimensions of the typical carbon fiber reinforced composite (CFRP) stiffened panel test piece in the embodiment of the present invention; Figure 3 is the schematic diagram of the finite element simulation model of the remaining strength of the stiffened plate established in the embodiment of the present invention; Figure 4 is the comparison diagram of the shear remaining strength simulation and verification test of the damaged composite material stiffened plate in the embodiment of the present invention; Figure 5 is the schematic diagram of the structure of the radial basis function (RBF) neural network model of the present invention; Figure 6 is the response surface of the rapid prediction surrogate model of the remaining strength distribution of the composite material stiffened plate finally established in the embodiment of the present invention; Figure 7 is the flow chart of the structural failure probability prediction considering the uncertainty of the perforation damage parameters of the present invention; Figure 8 is the schematic diagram of the failure probability surface established by interpolation in the embodiment of the present invention. Detailed Embodiment

[0021] The present invention will be further described below in conjunction with the drawings and specific embodiments.

[0022] Please refer to Figures 1-8As shown, a method for quickly predicting the failure probability of a composite material structure under dense perforation damage is used. This embodiment uses a carbon fiber reinforced composite (CFRP) stiffened wall panel as a test piece for verification. The specific process includes: Step 1: Determine the composite material structure information and the range of dense perforation damage parameters; According to the structural characteristics of typical composite material stiffened panels on aircraft wings, this embodiment designs a carbon fiber reinforced composite (CFRP) stiffened panel as a test piece. The test piece structure is as follows: Figure 2 As shown. The test piece is mainly composed of three parts: panel, rib and clamping section. The material of the reinforced wall panel is T300 / QY8911. All parts of the wall panel are laid with unidirectional tapes, and the laying angle of the panel and rib is [45 / 0 / -45 / 90] 7s , the thickness of single layer molding is 0.125mm. This example selects the in-plane four-side shear as the load form of the reinforced plate to study the change of shear residual strength of the composite reinforced plate under the dense perforation damage mode. This example focuses on the number of perforations N and perforation diameter D Two perforation damage parameters, among which the number of perforations N The research range is 5 to 100, and the perforation diameter D The research range is 10 to 30 mm. The information of composite material structure includes parameters such as its structural form, material information and loading conditions.

[0023] It should be noted that the structural form, material information and loading conditions of the composite material structure in this step, as well as the type and value range of the expected damage parameter, can all be adjusted according to actual engineering needs.

[0024] Step 2: Based on the composite material structure information and dense perforation damage parameters determined in step 1, a composite structure residual strength simulation model and its solution method are established; Step 2.1: Establish a simulation model of the residual strength of the composite structure; Step 2.1.1: Draw a geometric model of the structure in CATIA 3D modeling software according to the shape and geometric dimensions of the structure. In this embodiment, specifically: draw a structural geometric model of the structure in CATIA 3D modeling software according to the shape and geometric dimensions of the stiffened plate of the test piece; Step 2.1.2: Then import the structural geometry model into ABAQUS simulation software, and complete the composite material grid division and layup setting according to the information such as the composite material type and layup method of the structure; Step 2.1.3: Finally, insert interlayer cohesive elements with zero thickness between each layer to simulate the interlayer connection of the composite material and obtain a mesh model of a lossless structure; Step 2.2: Preset damage according to damage parameters; The number of perforations according to the expected damage parameter N and the perforation diameter D , randomly pre-set perforation damages at positions on the mesh model of the undamaged structure established in Step 2.1 by means of secondary development of Python; Among them, the delamination diameter of the interlaminar cohesive element is taken as 1.5 times the perforation diameter; Step 2.3: Determine the material constitutive model; The three-dimensional Hashin criterion and the asymptotic damage constitutive method are adopted to simulate the generation and evolution of internal damage of the composite material. For interlaminar damage, a traction-separation cohesive model is adopted, and the quadratic nominal stress criterion is used as the damage initiation criterion. In the mixed stress mode, the energy-based Benzeggagh-Kenane fracture criterion is applied to describe the damage evolution of the cohesive element. The material constitutive model is implemented in ABAQUS by writing a VUMAT subroutine, and the corresponding material parameters are shown in Table 1.

[0025] Table 1: Material parameters of CFRP and interlaminar cohesive material

[0026] Step 2.4: Perform the solution settings for the remaining strength simulation model; Set the model boundary constraints and loading conditions according to the structural load-bearing characteristics; output the reaction forces of the constrained boundaries of the model; use the Dynamic-Explicit analysis step to perform simulation solution on the mesh model of the remaining strength of the damaged composite material structure.

[0027] Specifically in this embodiment: Set loading reference points on the four sides of the panel and couple them with the nodal points around the mounting holes of the clamping section, and then apply a smooth displacement load at the reference points to simulate four-sided shear loading; output the reaction force curve of the loading reference points; set the Dynamic-Explicit analysis step for the remaining strength simulation model to perform the solution, set the simulation duration to 1 s, and control the minimum time step to be 2e -5 s; The finally established finite element simulation model of the remaining strength of the stiffened panel is as Figure 3 shown.

[0028] Step 2.5: Verify the simulation accuracy through experiments; Process test specimens and carry out ground static explosion tests, and then perform shear remaining strength simulation and loading tests on the stiffened panel test specimens after being impacted by a dense impact source respectively, and compare and verify the consistency between the simulation and the test, and the obtained results are as Figure 4 shown. It can be seen from Figure 4 that the relative error between the remaining strength obtained by the simulation and the test results is 7.7%.

[0029] Step 3: Conduct finite element working condition simulation on the simulation model established in Step 2 to obtain a data set of structural remaining strength distribution parameters; Step 3.1: Determine the simulation sampling working conditions; According to the calculation cost requirement, select an appropriate DOE (Design of Experiments) method to determine n groups of simulation sampling working conditions within the range of damage parameter values U i ( D i , N i ,…)(i = 0, 1, 2, 3,…, n), where i = 0 represents the undamaged state of the structure.

[0030] Specifically in this embodiment: According to the full factorial design (FFD) method, 23 groups of simulation sampling working conditions are determined within the range of damage parameter values U i ( D i , N i )(i = 0, 1, 2, 3,…, 22), where i = 0 represents the undamaged state of the structure; Step 3.2: Fit the remaining strength distribution parameters; For each simulation sampling working condition U i ( D i , N i ,…), conduct m times of remaining strength simulations with randomly located perforations to obtain the remaining strength results of the damaged composite structure ( S 1 i , S 2 i ,…, S m i ), and fit the expectation S μ i and standard deviation of the remaining strength distribution according to the following formula: ; ; where, S μ i and are respectively the expectation and standard deviation of the remaining strength distribution under the simulation sampling working condition U i , S j i is the simulation sampling working conditionU i The simulation results of the remaining strength with the random punching position at the j-th time.

[0031] Specifically in this embodiment: for each simulation sampling condition except for the non-damaged one U i ( D i , N i ), perform 5 simulations of the remaining strength with the random punching position, and obtain the simulation results of the shear remaining strength of the damaged composite stiffened panel ( S 1 i , S 2 i , S 3 i , S 4 i , S 5 i ), and fit the expectation of the remaining strength distribution according to the following formula S μ i and the standard deviation : ; ; Wherein, S μ i and are respectively the expectation and the standard deviation of the remaining strength distribution under the simulation sampling condition U i , and S j i is the simulation result of the remaining strength with the random punching position at the j-th time under the simulation sampling condition U i .

[0032] Step 3.3: Form a data set of the parameters of the structural remaining strength distribution; Considering the uncertainty of the punching position, obtain the parameters of the remaining strength distribution of the damaged composite material structure under each simulation sampling condition obtained in Step 3.2 (i = 0, 1, 2, 3,..., n), and form a data set of the parameters of the structural remaining strength distribution for training the surrogate model.

[0033] Specifically in this embodiment: considering the uncertainty of the punching position, obtain the parameters of the remaining strength distribution of the damaged composite stiffened panel under each simulation sampling condition For (i = 0, 1, 2, 3, …, 22), a dataset of the remaining strength distribution parameters for training the surrogate model is formed as shown in Table 2; Table 2: Dataset of Shear Remaining Strength Distribution of Damaged Composite Stiffened Plates

[0034] Step 4: Use the dataset of the remaining strength distribution parameters of the composite structure obtained in Step 3 to train the surrogate model, and simultaneously quickly predict the expectation and standard deviation of the remaining strength of the damaged structure according to the dense perforation damage parameters; Select the Radial Basis Function (RBF) neural network model as the surrogate model. The structure of the RBF neural network model is as Figure 5 shown. Use the dataset of the remaining strength distribution parameters formed by the simulation in Step 3 to train the RBF neural network model to achieve a quick prediction of the remaining strength distribution of the composite stiffened plate under the dense perforation damage mode. Among them, in the RBF neural network model, the mapping relationship from the input to the output of the neural network can be determined by the Gaussian formula as follows: ; where X= D, N , …] T are the perforation damage parameters and are the inputs of the model; Y = y 1, y 2] T = S μ , σ] T are the remaining strength distribution parameters and are the outputs of the model; o is the number of hidden nodes; w ik is the weight coefficient; is the basis function; C k is the k th node center; d k is the k th node's basis width parameter; is the Euclidean distance between the input vector and the node center.

[0035] Step 5: Test the prediction accuracy of the surrogate model trained in Step 4. After the prediction accuracy meets the usage requirements, complete the training of the surrogate model; Take another test sample point outside the training dataset to test the prediction accuracy of the surrogate model. After the prediction accuracy meets the usage requirements, complete the training of the surrogate model. Otherwise, increase the training sampling conditions and further train the model to improve the prediction accuracy.

[0036] ​Among them, both the training data set and the test sample points are taken from the data set of the structural remaining strength distribution parameters, and the test sample points do not participate in the training of the surrogate model.

[0037] Specifically in this embodiment: outside the training data set, test sample points ( D = 25 mm, N = 25) are additionally selected, and the shear remaining strength of the stiffened panel under 5 different perforation position distributions is obtained through simulation and the distribution parameter N(793.6, 72.0 2 ) is fitted. Comparing the predicted result N(728.7, 67.5 2 ) of the remaining strength distribution parameter of the test sample points by the surrogate model with the distribution parameter obtained based on finite element simulation, the relative prediction errors of the surrogate model for the expected value and standard deviation of the remaining strength are 8.2% and 6.3% respectively, and the prediction accuracy meets the usage requirements, completing the training of the surrogate model.

[0038] Step 6: Determine the critical remaining strength of the composite structure failure; According to the aircraft structure design theory, the design safety factor of aircraft structural components is usually 1.5. Therefore, 2 / 3 of the non-destructive strength S 0 of the structure is used as the critical strength for failure after the structure is damaged S limit , where the non-destructive strength S 0 is obtained through the remaining strength simulation of the non-destructive structure.

[0039] Specifically in this embodiment: according to the aircraft structure design theory, the design safety factor of aircraft structural components is usually 1.5. Therefore, 2 / 3 of the non-destructive shear strength S 0 = 1401.1 KN of the stiffened panel is used as the critical remaining strength for the failure of the damaged stiffened panel S limit = 934.1 KN. The response surface of the fast prediction surrogate model for the remaining strength distribution of the composite material stiffened panel finally established is as shown in the appendix Figure 6 . Figure 6 shows the response surface of three typical values of the remaining strength prediction of the damaged stiffened panel, and S μ , S μ + 2 × σ and S μ - 2 × σ can be determined according to the damage parameters, where S μ and σ are the expected value and standard deviation of the remaining strength distribution respectively. The critical failure section of the response surface contains three response surfaces and the critical failure strengthS limit = 934.1 KN plane's intersection line divides the plane into four regions. From bottom to top, they are the extremely low probability failure region (blue, P k / h <2.275%), the low probability failure region (green, 2.275% < P k / h <50%), the high probability failure region (light red, 50% < P k / h <97.725%), and the extremely high probability failure region (dark red, 97.725% < P k / h ). According to the critical failure cross-section, the critical damage parameters corresponding to the four types of failure regions can be determined. For example, when the number of perforations is 30, the perforation diameter needs to reach at least 18.7 mm to cause extremely high probability shear failure of the stiffened plate.

[0040] Step 7: Based on the critical remaining strength, use the surrogate model obtained in Step 5 to calculate the failure probability of the structure under the given damage parameters; Using the surrogate model trained in Step 5, the distribution parameters of the remaining strength can be quickly predicted according to the given damage parameters and then, according to the normal probability distribution, calculate the probability that the remaining strength of the damaged structure is lower than the critical strength S limit to obtain the failure probability of the structure under the given damage parameters P k / h which is: ; where, P k / h is the failure probability of the structure under the given damage parameters, S limit is the critical strength for the structure to fail after being damaged, S μ and s are the expected value and standard deviation of the remaining strength distribution of the structure under the given damage parameters respectively.

[0041] Specifically in this embodiment: Using the trained surrogate model, the distribution parameters of the remaining strength can be quickly predicted according to the given damage parameters and then, according to the normal probability distribution, calculate the probability that the remaining strength of the damaged structure is lower than the critical strength S limit = 934.1 KN. For example, under the damage parameters ( D = 15 mm, N = 30), the prediction results of the surrogate model for the distribution parameters of the remaining strength are ( S μ = 949.9, = 74.7), and then calculate the failure probability of the stiffened panel under this damage parameter P k / h = 41.6%, and the calculation process is as follows: .

[0042] Step 8: Based on the failure probability calculation method in Step 7, combine the Monte Carlo method to predict the structural failure probability considering the uncertainty of damage parameters; Based on the surrogate model established in Step 5, use the Monte Carlo random sampling method to realize the prediction of the structural failure probability considering the uncertainty of damage parameters. The flow chart is as Figure 7 shown, and the specific process is as follows: Step 8.1: Determine the distribution form of the perforation damage parameters; According to the explosive information and intersection conditions, select the appropriate distribution form F of the perforation damage parameters of the dense impact source ( D , N , …) to characterize the uncertainties existing in the processes of explosion, shock source propagation, and structural shock response.

[0043] In this embodiment, specifically: Select the following truncated normal distribution to describe the uncertainty of the damage parameters: The perforation diameter D obeys the normal distribution N ( D e, σ D 2 , D min , D max ), where: D e is the expected value of the perforation diameter, and the standard deviation of the perforation diameter σ D = 0.05 D e , the lower limit of the distribution D min = 0.85 D e , the upper limit of the distribution D max = 1.15 D e ; The number of perforations N obeys the normal distribution N ( N e, σ N 2 , N min , N max ),N e is the expected value of the number of perforations, and the standard deviation of the number of perforations σ N = 0.05 N e , and the lower limit of the distribution N min =0.85 N e , and the upper limit of the distribution N max = 1.15 N e .

[0044] Step 8.2: Determine the expected perforation damage parameters; Estimate the expected perforation damage parameters based on the explosive information and explosion conditions ( D e , N e , …), and combine the distribution form of the perforation damage parameters to determine the probability distribution F of the actual perforation damage parameters ( D e , N e , …).

[0045] Specifically in this embodiment: Taking the expected damage parameters ( D e =15mm, N e =30) as an example, considering the uncertainty of the damage parameters, the failure probability prediction process based on the surrogate model and the Monte Carlo method is demonstrated.

[0046] Step 8.3: Extract the actual perforation damage parameters; Use the Monte Carlo method to conduct the i-th sampling in the probability distribution of the actual damage parameters to obtain the i-th set of actual damage parameters ( D i , N i ); Step 8.4: Predict the remaining strength distribution parameters of the structure under the actual perforation damage parameters; Input the i-th set of actual damage parameters ( D i , N i ) into the surrogate model to obtain the prediction result of the corresponding remaining strength distribution parameters of the structure ; Step 8.5: Calculate the failure probability of the structure under the actual perforation damage parameters; The prediction result of the remaining strength distribution parameters of the structure under the i-th set of actual damage parameters Substitute into the formula: to calculate the predicted value of the failure probability of the structure under the actual damage parameters of the i-th group P k / h i ; where, P k / h i is the failure probability of the structure under the actual damage parameters of the i-th group, S limit is the critical strength at which the structure fails after being damaged, S μ i and are the expected value and standard deviation of the remaining strength distribution of the structure under the actual damage parameters of the i-th group respectively; Step 8.6: Calculate the failure probability of the structure under the expected perforation damage parameters; Repeat Steps 8.3 to 8.5 w times, and then take the average value of the predicted values of the failure probability of the structure under the w groups of actual damage parameters P k / h i (i = 1, 2,..., w ) as the predicted result of the failure probability of the structure considering the uncertainty of damage parameters under the expected damage parameters ( D e , N e ,...).

[0047] In this embodiment, specifically: Repeat Steps 8.3 to 8.5 10 times (here, for the convenience of display, the number of repeated samplings can be increased in actual applications), and then take the average value of the predicted values of the failure probability of the structure under 10 groups of actual damage parameters P k / h i (i = 1, 2,..., 10) as the predicted result of the failure probability of the structure considering the uncertainty of damage parameters under the expected damage parameters ( D e = 15mm, N e = 30), and the detailed calculation process is shown in Table 3.

[0048] Table 3: Calculation process of failure probability considering the uncertainty of damage parameters (example)

[0049] Step 9: Establish a failure probability surface according to the failure probability prediction method in Step 8; To facilitate the analysis of the changing trend of the structural failure probability, this step further establishes a failure probability surface, and the specific process is as follows: Step 9.1: Sampling of expected damage parameters; Within the value range of the damage parameters, 10,000 sampling points are densely and evenly set; Step 9.2: Prediction of failure probability; According to Step 8, the failure probability prediction for each sampling point is completed; Step 9.3: Interpolation to establish the failure probability surface; Based on the failure probability prediction results of each sampling point, the failure probability surface is finally established by interpolation as shown in Figure 8 From Figure 8 it can be seen that: as the perforation diameter and the number of perforations increase, the failure probability of the composite stiffened panel monotonically increases from 0 to 1, and the growth rate of the failure probability with the number of perforations is faster under a large perforation diameter.

[0050] Therefore, combined with the above results, it can be seen that the rapid prediction method for the failure probability of composite structures under dense perforation damage proposed in this embodiment has the following advantages: 1. The composite structure failure probability prediction method based on the residual strength finite element analysis and surrogate model method proposed in this embodiment can realize the failure assessment and failure probability prediction of aircraft composite structures considering the uncertainty during the damage process in the dense perforation damage mode; it can provide a reference for weapon equipment design and mission decision-making, and save the engineering simulation analysis and test costs.

[0051] 2. The prediction method proposed in this embodiment not only considers the uncertainty of the perforation position distribution on the impact source structure, but also considers the uncertainty of the dense perforation damage parameters themselves, making the research on the structural failure probability more refined, and reasonably characterizing the influence of the uncertainty during the damage process on the structural failure probability.

[0052] 3. The composite progressive damage finite element simulation method and failure probability calculation method used in this method can be applied to the damage and failure problems of various composite structures. Compared with the failure assessment engineering algorithms that are only applicable to specific structural forms, the application scope of this embodiment is wider.

[0053] Although the embodiments of the present invention have been shown and described, for those of ordinary skill in the art, it can be understood that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A rapid prediction method for the failure probability of composite material structures under intensive perforation damage, characterized in that: include: Step 1: Determine the composite material structure information and the range of dense perforation damage parameters; Step 2: Based on the composite material structure information and dense perforation damage parameters determined in step 1, a composite structure residual strength simulation model and its solution method are established; Step 3: Perform working condition simulation on the simulation model established in step 2 to obtain a data set of residual strength distribution parameters of the composite structure; Step 4: Use the data set of residual strength distribution parameters of the composite structure obtained in step 3 to train the proxy model, and quickly predict the expected and standard deviation of the residual strength of the damaged structure based on the dense perforation damage parameters; Step 5: Test the prediction accuracy of the proxy model trained in step 4. When the prediction accuracy meets the usage requirements, the training of the proxy model is completed; Step 6: Determine the critical residual strength of the composite structure for failure; Step 7: Based on the critical residual strength, the proxy model obtained in step 5 is used to calculate the failure probability of the structure under given damage parameters; Step 8: Based on the failure probability calculation method in step 7, the Monte Carlo method is used to predict the structural failure probability considering the uncertainty of damage parameters; Step 9: Based on the results of the failure probability prediction in step 8, establish the failure probability surface.

2. The rapid prediction method for the failure probability of a composite material structure under intensive perforation damage according to claim 1, wherein: The composite material structure information in Step 1 includes the structural form, material information, and loading conditions of the composite material structure; the dense perforation damage parameters include at least the perforation diameter D and the number of perforations N .

3. The rapid prediction method for the failure probability of a composite material structure under intensive perforation damage as described in claim 1, wherein: Step 2: The process of establishing the composite structure residual strength simulation model and its solution method includes: Step 2.1: Establish a simulation model of the residual strength of the composite structure; Draw the structural geometric model of the composite material and import it into the simulation software. Complete the mesh division and ply setting of the composite material according to the composite material type and ply method information of the structure. Finally, insert zero-thickness cohesive force units between each layer to simulate the interlayer connection of the composite material and obtain the mesh model of the lossless structure. Step 2.2: Preset damage according to damage parameters; According to the expected damage parameters, randomly set perforation damage on the grid model of the lossless structure established in step 2.1; Step 2.3: Determine the material constitutive structure; Step 2.4: Set up the residual strength simulation model solution; The boundary constraints and loading conditions of the grid model are set, and the support reaction forces of the constraint boundaries of the grid model are output; and the grid model of the residual strength of the damaged composite structure is simulated and solved.

4. The rapid prediction method for the failure probability of a composite material structure under intensive perforation damage as claimed in claim 2, wherein: Step 3: The process of performing working condition simulation on the simulation model to obtain a data set of structural residual strength distribution parameters includes: Step 3.1: Determine the simulation sampling conditions; Determine n groups of simulation sampling conditions within the range of damage parameter values U i ; where \(i = 0, 1, 2, 3,\cdots, n\), i when it is \(0\), it represents the lossless state of the structure; Step 3.2: Fitting the residual intensity distribution parameters; For each simulation sampling condition except the lossless one U i perform m times of remaining strength simulations with randomly located perforations to obtain the remaining strength simulation results of the damaged composite structure S 1 i , S 2 i ,…, S m i , and fit the expectation of the remaining strength distribution S μ i and the standard deviation : ； ； Among them, S μ i and are the mean and standard deviation of the remaining strength distribution under the simulation sampling conditions U i respectively, S j i is the simulation result of the remaining strength with the random piercing position at the j-th time under the simulation sampling conditions U i ; Step 3.3: Form a data set of structural residual strength distribution parameters; Considering the uncertainty of the perforation position, the remaining strength distribution parameters of the composite material structure after damage under each simulation sampling condition are obtained through step 3.2 , and a data set of the remaining strength distribution parameters of the structure for training the surrogate model is formed.

5. The rapid prediction method for the failure probability of a composite material structure under dense perforation damage according to claim 4, characterized in that: In the process of training the surrogate model using the dataset of the structural remaining strength distribution parameters in Step 4, a radial basis neural network model is used as the surrogate model for training. In the radial basis neural network model, the mapping relationship from the input to the output of the neural network is determined by the Gaussian formula as follows: ; Among them, X= D, N ,…] T is the perforation damage parameter, which is the input of the model; Y = y 1, y 2] T = S μ , σ] T is the remaining strength distribution parameter, which is the output of the model; o is the number of hidden nodes; w ik is the weight coefficient; is the basis function; C k is the k center of the d k is the k basis width parameter of the is the Euclidean distance between the input vector and the node center.​ 6. The rapid prediction method for the failure probability of a composite material structure under intensive perforation damage as claimed in claim 1, characterized in that: Step 5 The process of testing the prediction accuracy of the surrogate model includes: Take test sample points outside the training data set to test the prediction accuracy of the proxy model. When the prediction accuracy meets the use requirements, the training of the proxy model is completed. Otherwise, increase the training sampling conditions and further train the model.

7. The rapid prediction method for the failure probability of a composite material structure under intensive perforation damage as described in claim 5, characterized in that: In the process of determining the critical remaining strength of structural failure in step 6, take 2 / 3 of the non-destructive strength of the structure S 0 as the critical strength of the structure after damage and failure S limit .

8. The rapid prediction method for the failure probability of a composite material structure under dense perforation damage according to claim 7, characterized in that: When calculating the failure probability of the structure with the given damage parameters in step 7 using the surrogate model, the distribution parameters of the remaining strength are quickly predicted according to the given damage parameters , and then, according to the normal probability distribution, the probability that the remaining strength of the damaged structure is lower than the critical strength S limit is calculated to obtain the failure probability of the structure under the given damage parameters P k / h as follows: ; wherein, P k / h is the failure probability of the structure under given damage parameters, S limit is the critical strength at which the structure fails after being damaged, S μ and s are the expected value and standard deviation of the remaining strength distribution of the structure under given damage parameters, respectively.

9. The rapid prediction method for the failure probability of a composite material structure under intensive perforation damage as claimed in claim 8, characterized in that: Step 8 Based on the failure probability calculation method in step 7, the process of predicting the structural failure probability considering the uncertainty of damage parameters by combining the Monte Carlo method includes: Step 8.1: Determine the distribution form of perforation damage parameters; Step 8.2: Determine the expected perforation injury parameters; Estimate the expected damage parameters of the structure based on the explosive information and intersection conditions ( D e , N e ,…); and combine the distribution form of the damage parameters to determine the probability distribution F of the actual damage parameters ( D e , N e ,…); Step 8.3: Extract actual perforation damage parameters; The i-th sampling is carried out in the probability distribution of the actual damage parameters by using the Monte Carlo method to obtain the i-th group of actual damage parameters ( D i , N i ,…); Step 8.4: Predict the remaining strength distribution parameters of the structure under actual damage parameters; Input the actual damage parameters of the i-th group ( D i , N i , …) into the surrogate model to obtain the predicted results of the corresponding structural remaining strength distribution parameters ; Step 8.5: Calculate the failure probability of the structure under actual damage parameters; Substitute the prediction results of the structural remaining strength distribution parameters under the actual damage parameters of the i-th group into the formula: to calculate the predicted value of the failure probability of the structure under the actual damage parameters of the i-th group P k / h i ; Among them, P k / h i is the failure probability of the structure under the actual damage parameters of the i-th group, S limit is the critical strength of the structure after being damaged and failing, S μ i and are respectively the expected value and the standard deviation of the remaining strength distribution of the structure under the actual damage parameters of the i-th group; Step 8.6: Calculate the failure probability of the structure under expected perforation damage parameters; Repeat steps 8.3 to 8.5 w times, and then w the predicted failure probability values of the structure under P k / h i groups of actual damage parameters Take the average value as the predicted result of the structure failure probability considering the uncertainty of damage parameters under the expected damage parameters.

10. The rapid prediction method for the failure probability of a composite material structure under intensive perforation damage according to claim 9, wherein: Step 9 The process of establishing the failure probability surface includes: Step 9.1: Sampling of expected damage parameters; Densely and uniformly set sampling points within the value range of damage parameters; Step 9.2: Failure probability prediction; According to Step 8, complete the failure probability prediction for each sampling point; Step 9.3: Interpolate to establish the failure probability surface; According to the failure probability prediction results of each sampling point, finally interpolate to establish the failure probability surface.

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