Composite material fuselage wallboard structure reliability analysis method based on chaos polynomial expansion
By using a method based on chaotic polynomial expansion, combined with finite element model and Monte Carlo simulation, the problems of low computational efficiency and redundancy of safety margin in the reliability analysis of composite fuselage panel structures are solved, and efficient reliability analysis is achieved.
Patent Information
- Application Number
- CN202511794399.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-12-02
- Publication Date
- 2026-03-03
AI Technical Summary
In the reliability analysis of composite material fuselage panel structures, the failure criteria of the first layer underestimate the load-bearing capacity of the composite material, resulting in redundancy in safety margin and reliability design. At the same time, the Monte Carlo simulation calculation is inefficient and cannot meet engineering requirements.
A chaotic polynomial expansion-based method is adopted, combined with the finite element model and Latin hypercube sampling, to establish a chaotic polynomial surrogate model. The failure probability is calculated by Monte Carlo simulation, the failure path is found by the branch and bound method, and the overall failure probability is calculated by combining the second-order narrow bound theory.
It improves the computational efficiency of reliability analysis of composite material fuselage panel structures, reduces safety margin redundancy, conforms to the actual failure process, and meets engineering accuracy requirements.
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Figure CN121598700A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the aerospace field, specifically relating to a reliability analysis method for composite material fuselage panel structures based on chaotic polynomial expansion. Background Technology
[0002] Composite materials, with their high specific strength, high specific stiffness, light weight, and high design flexibility, have become key materials in modern aircraft manufacturing. As a critical component for aircraft load-bearing and protection, the structural performance of fuselage panels directly affects the safety and reliability of the aircraft. Conducting reliability analysis on composite fuselage panel structures is of significant engineering importance for improving the safety margin and service reliability of aircraft structural design.
[0003] In practical engineering, due to manufacturing defects, damage during transportation, and complex service environments, the material properties and external loads of composite materials are easily affected by various uncertainties. To solve the reliability analysis problem of composite material structures with uncertainties, the failure probability of the structure is usually obtained through Monte Carlo simulation based on the first-layer failure criterion and combined with the finite element method.
[0004] However, the reliability analysis of the above composite material structures has the following problems: First, the actual failure of composite materials is a progressive failure process, and the first-layer failure criterion underestimates the actual load-bearing capacity of composite materials, resulting in redundancy in safety margin and reliability design; Second, aircraft failure is usually a low-probability event, and due to the complexity of the structure, the time cost required for a single finite element calculation is too high, while Monte Carlo simulation requires repeated calls to the finite element calculation to calculate the failure probability, and the calculation efficiency cannot meet the needs of actual engineering. Summary of the Invention
[0005] In view of the above problems, this invention provides a reliability analysis method for composite material fuselage panel structures based on chaotic polynomial expansion, in order to solve the reliability calculation problem of composite material fuselage panel structures with uncertain parameters, improve calculation efficiency and reduce redundancy in reliability design while ensuring that the calculation accuracy meets engineering requirements.
[0006] This invention provides a reliability analysis method for composite material fuselage panel structures based on chaotic polynomial expansion, comprising:
[0007] Step 1: Discretize the composite material fuselage panel structure using a finite element mesh, set loads and boundary conditions to obtain a finite element model of the composite material fuselage panel structure, which includes at least two single-layer plates;
[0008] Step 2: Determine all failure events of the single-layer plate in the composite material fuselage panel structure, and establish the limit state function corresponding to each failure event;
[0009] Step 3: Establish a normal distribution model of the uncertain parameters of the composite material fuselage panel structure, obtain training sample points using Latin hypercube sampling, calculate the maximum value of the limit state function response under the training sample points based on the finite element model, and establish a chaotic polynomial surrogate model based on the training sample points and the corresponding maximum value.
[0010] Step 4: Use the Latin hypercube sampling to obtain new sample points within the range of the uncertain parameters, combine the chaotic polynomial surrogate model to calculate the predicted response value under the new sample points, conduct Monte Carlo simulation to calculate the failure probability of the failure event in the current stage, determine whether there is a failure branch point in the current stage, record the current failure path, and reduce the stiffness of the single-layer plate for the failure branch point in the current stage according to the sudden degradation criterion of material properties.
[0011] Step 5: Repeat Step 3 and Step 4 until all failure events occur, obtain all possible failure paths of the composite material fuselage panel structure, calculate the failure probability of each failure path using the second-order narrow-limit theory, and calculate the overall failure probability of the composite material fuselage panel structure based on the failure probabilities of the failure paths.
[0012] In some possible embodiments, the failure path search of the composite fuselage panel structure is carried out based on the branch and bound method, and the overall failure of the composite fuselage panel structure is confirmed after all the failure events have occurred.
[0013] In some possible embodiments, the failure paths are connected in a series logical relationship, the upper bound of the overall failure probability of the fuselage panel structure is the sum of the failure probabilities of each failure path, and the lower bound of the overall failure probability of the fuselage panel structure is the maximum failure probability of each failure path.
[0014] In some possible embodiments, the maximum response value is obtained through a global search algorithm.
[0015] In some possible embodiments, establishing a chaotic multinomial surrogate model based on the training sample points and the corresponding maximum values includes:
[0016] The training sample points and the maximum value are normalized and merged into a dataset;
[0017] The dataset is divided into a training set and a test set;
[0018] Using Hermite polynomials as an orthogonal basis, a chaotic polynomial is established. The maximum value is expanded, and the undetermined coefficients in front of the orthogonal basis are calculated using the least squares principle in combination with the training set, thus obtaining the closed-form solution of the chaotic polynomial surrogate model.
[0019] The test set is substituted into the chaotic polynomial surrogate model, and the average relative error between the response value obtained by the chaotic polynomial surrogate model and the corresponding real response value is calculated. When the average relative error meets the error threshold, the chaotic polynomial surrogate model is retained; otherwise, the orthogonal basis order is changed or resampling and training are performed.
[0020] The reliability analysis method for composite material fuselage panel structures based on chaotic polynomial expansion provided in this invention has at least the following advantages:
[0021] (1) The analysis method in this embodiment of the invention uses the branch and bound method to complete the search for the failure path of the composite material fuselage panel structure, which is more consistent with the real failure physical process and effectively reduces the redundancy of safety margin and reliability analysis.
[0022] (2) The analysis method in this embodiment of the invention completes the Monte Carlo simulation by training the chaotic polynomial expansion, which effectively reduces the number of times the finite element calculation is called, and greatly improves the calculation efficiency while meeting the accuracy requirements.
[0023] (3) The analysis method in this embodiment of the invention uses the Latin hypercube sampling method to perform Monte Carlo simulation, which accelerates the convergence speed of calculating the failure probability. Attached Figure Description
[0024] Figure 1 This is a flowchart of the reliability analysis method for composite material fuselage panel structure based on chaotic polynomial expansion in an embodiment of the present invention;
[0025] Figure 2 This is a simplified flowchart of the reliability analysis method for composite material fuselage panel structure based on chaotic polynomial expansion in an embodiment of the present invention.
[0026] Figure 3 This is a schematic diagram of the composite material fuselage panel structure in an embodiment of the present invention.
[0027] Explanation of reference numerals in the attached figures:
[0028] 1-Fixed boundary;
[0029] 2-Free boundary. Detailed Implementation
[0030] To make the above-mentioned objectives, features, and advantages of the embodiments of the present invention more readily understood, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are merely some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0031] refer to Figure 1 and Figure 2 This invention provides a reliability analysis method for composite material fuselage panel structures based on chaotic polynomial expansion, comprising the following steps:
[0032] Step 1: Discretize the composite fuselage panel structure using a finite element mesh, set loads and boundary conditions to obtain a finite element model of the composite fuselage panel structure, which includes at least two single-layer plates.
[0033] In this embodiment of the invention, the composite material fuselage panel structure refers to a composite material laminate structure formed by m layers of single-layer plates, where m is a positive integer greater than or equal to 2. A geometric model of the composite material fuselage panel structure is established, and this model is discretized using a finite element mesh. Each single-layer plate has n integration points, which are the positions within each element used for numerical integration in the finite element calculation. Loads and boundary conditions are set to obtain the finite element model of the composite material fuselage panel structure. The finite element model is used to simulate the actual service environment and set the operating conditions to conduct static analysis of the aforementioned structure.
[0034] In one possible example, the composite fuselage panel structure consists of four single-layer panels, with fiber lay-up angles from the inside out of [0° / -45° / 45° / 90°]. Figure 3 As shown, the geometric model of the above structure has a circular cross-section with a radius of 2.5 meters and an axial length of 1 meter.
[0035] The geometric model of the above structure was discretized using a finite element mesh. Specifically, a 4-node shell element was used to mesh the geometric model, with 39,250 elements per plate. A fixed support boundary was set on the fixed boundary 1 on the right side of the geometric model, and axial force, shear force, bending moment, and torque were applied to the free boundary 2 on the left side of the geometric model to obtain the finite element model of the composite material fuselage panel structure.
[0036] Step 2: Determine all failure events of a single layer in the composite material fuselage panel structure, and establish the limit state function corresponding to each failure event.
[0037] In this embodiment of the invention, a single-layer plate is used as the basic unit. It is assumed that each single-layer plate has t failure events, where t is a positive integer greater than or equal to 2. The composite material fuselage panel structure has a total of t×m basic failure events. Combining common single-layer plate failure criteria, a limit state function corresponding to each failure event is established, which is a function representing the boundary between the two states of failure and non-failure.
[0038] In one possible example, each single-layer plate considers two failure modes: fiber failure and matrix failure. The matrix-related term in the Tsai-Wu criterion is chosen as the matrix failure criterion, and the Tan criterion is chosen as the fiber failure criterion. The limit state function for each failure event of the single-layer plate is established, expressed as:
[0039]
[0040] in σ1, σ2, σ3 represent the failure criteria response values for the i-th fiber layer and the matrix, respectively. A value greater than 0 indicates that the corresponding failure event has occurred; 12 These represent the normal stress along the fiber direction, the in-plane normal stress perpendicular to the fiber direction, and the in-plane shear stress of a single-layer plate, respectively; f1, f2, f 11 ,f 12 ,f 22 ,f 66 For the strength parameter item, the specific form is:
[0041]
[0042] Where x t ,x c These represent the fiber tensile strength and fiber compressive strength, respectively; y t ,y c Let represent the matrix tensile strength and matrix compressive strength, respectively, and s represent the in-plane shear strength. Specific values can be calculated using the normal distribution model of the uncertain parameters from step three.
[0043] Step 3: Establish a normal distribution model of uncertain parameters of composite material fuselage panel structure, obtain training sample points using Latin hypercube sampling, calculate the maximum value of the limit state function response under the training sample points based on the finite element model, and establish a chaotic polynomial surrogate model based on the training sample points and the corresponding maximum value.
[0044] In some possible implementations, the uncertain parameters of the composite fuselage panel structure are determined, and a normal distribution model of the uncertain parameters is established. Multiple sets of training sample points are obtained through Latin hypercube sampling, and the limit state function response value corresponding to each training sample point is calculated using a finite element model. The maximum response value is obtained through a global search algorithm, and the training sample points and the maximum value are normalized and merged into a dataset. The dataset is then divided into training and test sets in a 4:1 ratio. A chaotic polynomial is established using Hermite polynomials as an orthogonal basis. The maximum value is expanded, and the undetermined coefficients before the orthogonal basis are calculated using the least squares principle in conjunction with the training set to obtain the closed-form solution of the chaotic polynomial surrogate model. The accuracy of the surrogate model is verified using the test set, enabling rapid prediction.
[0045] Specifically, the stiffness coefficient, strength coefficient, geometric dimensions, and external loads of the composite fuselage panel structure are considered as uncertain parameters, all of which follow a normal distribution. Within the distribution domain of these uncertain parameters, a group of training sample points is randomly selected. Based on the finite element model, the response value of a certain failure event is obtained layer by layer. The maximum response value of a single-layer plate is obtained through a global search method, expressed as:
[0046]
[0047] in This represents the response value at the nth integration point of failure event A at level i.
[0048] The training sample points and the maximum value are normalized and merged into a dataset. The dataset is then divided into a training set and a test set in a 4:1 ratio.
[0049] Constructing chaotic polynomials using Hermite polynomials as an orthogonal basis, the maximum value is expanded and expressed as:
[0050]
[0051] Where X is an uncertain parameter; c i There are P-1 undetermined coefficients, of which p is the order of the orthogonal basis; φ i (X) is an orthogonal basis composed of Hermite polynomials; the closed-form solution of the above formula, i.e., the undetermined coefficients C = (c1, c2, ..., c P-1 ) T The following can be obtained by combining the training set data and using the least squares method:
[0052]
[0053] Where Y train This is the normalized result of the maximum response value corresponding to each training sample point in the training set.
[0054] Substituting the test set data into the constructed chaotic multinomial surrogate model, the average relative error between the surrogate model's predicted response value and the actual response value of the test set is calculated and expressed as:
[0055]
[0056] in Y test (X) represent the surrogate model's predicted response value and the actual value in the test set, respectively, for a given failure event's maximum response value. When the average relative error satisfies the error threshold ε... tol At that time, i.e., e MRE <ε tol If necessary, retain the surrogate model; otherwise, change the orthogonal basis order or resample and train.
[0057] In one possible example, in a composite fuselage panel structure formed by four single-layer plates, the stiffness coefficient, strength coefficient, and fiber layup angle of each single-layer plate are uncertain parameters, that is, the above parameters are uncertain and are used as input parameters.
[0058] The stiffness coefficient includes the stiffness E of the single-layer plate along the fiber direction. 11 Stiffness E of single-layer plate along the direction perpendicular to the fiber 22 and the shear stiffness G of a single-layer plate 12 The strength coefficient of a single-layer board includes the fiber tensile strength x t Fiber compressive strength x c Matrix tensile strength y t Matrix compressive strength y c , and in-plane shear strength s; fiber layup angles α1, α2, α3, α4 of each single-layer board, i.e., fiber layup angles in each single-layer board from the inside to the outside.
[0059] The aforementioned uncertain parameters follow a normal distribution, as shown in Table 1 below:
[0060] Table 1. Normal Distribution Model for Uncertain Parameters
[0061]
[0062] For a specific failure event in a single-layer plate, 500 sets of training sample points are generated by random sampling, and the response values of each failure event are obtained through a finite element model. The maximum response value of the failure event in the single-layer plate is then selected through a global search algorithm.
[0063] The training sample points and the maximum value are normalized and merged into a dataset, which is then divided into a training set and a test set. The training set contains 400 training sample points, and the test set contains 100 training sample points. The undetermined coefficients are solved using the least squares method on the training set to obtain the closed-form solution of the polynomial. Predictions are then made for the test set sample points. Taking the failure of the first layer matrix as an example, the average relative error is calculated as follows:
[0064]
[0065] Where E = (E 11 E 22 G 12 ) is the stiffness parameter; X = (x t ,x c ,y t ,y c ,s) is the strength parameter; θ=(α1,α2,α3,α4) is the fiber layup angle. Take ε tol If the average relative error is within the acceptable range and the error is 5%, then the chaotic polynomial surrogate model is retained.
[0066] Based on the above process, the chaotic polynomial surrogate model of each failure event of each single-layer plate is obtained in sequence.
[0067] Step 4: Use Latin hypercube sampling to obtain new sample points within the range of uncertain parameter values, combine the chaotic polynomial surrogate model to calculate the predicted response value under the new sample points, carry out Monte Carlo simulation to calculate the failure probability of the failure event in the current stage, determine whether there is a failure branch point in the current stage, record the current failure path, and reduce the stiffness of the single-layer plate for the failure branch point in the current stage according to the sudden degradation criterion of material properties.
[0068] New sample points are obtained within the range of uncertain parameters using Latin hypercube sampling. These new sample points are then input into a chaotic polynomial surrogate model to quickly predict the maximum response value of a single failure event. The failure probability of the failure event is calculated using Monte Carlo simulation. Assuming b sets of new sample points are drawn in each round, for a total of N rounds, the probability of failure event A occurring in the i-th layer is expressed as:
[0069]
[0070] in Indicates that the predicted value is satisfied in n rounds. The number of new sample points. When the failure probability satisfies:
[0071]
[0072] in Let represent the failure probabilities calculated in the (n+1)th and nth rounds of sampling, respectively. ε is used as the criterion for convergence of the failure probabilities. Once the above equation is satisfied, the failure probability of the failure event is considered converged, and the Monte Carlo simulation stops. The failure probabilities of other failure events are calculated using the same method, which will not be elaborated here.
[0073] In real-world failures, there may be situations where the most probable failure event does not occur, while the second most probable failure event does. Therefore, based on the branch and bound method, a branch criticality coefficient α is introduced. critical To obtain the structural failure branch points at each stage, define:
[0074]
[0075] Where P max This represents the maximum probability of failure for each failure event at each layer. Failure events that satisfy the above formula are all possible and are set as failure branch points. That is, failure events corresponding to failure branch points are all possible and the current failure path is recorded.
[0076] Establish corresponding sudden degradation criteria for material properties based on different failure events, and reduce the stiffness of the single-layer plate that has failed at the branch point identified in the current stage according to the degradation criteria.
[0077] In one possible example, for ease of description, the failure events are first numbered, such as 1M representing the failure of the first matrix layer, 2F representing the failure of the second fiber layer, and in the Monte Carlo simulation, ε = 0.01, with a branching critical coefficient α. critical =0.3, calculate the failure probability of all failure events, and determine whether there is a failure branch point in the current stage. Take the failure events of the first and second stages as examples:
[0078] Table 2 Failure Probability of Each Failure Event in Phase 1
[0079]
[0080] Where P max =max{0.791,0.137,0}=0.791, with Since the failure branch point has been identified, the stage assumes that failure event 1M occurs first.
[0081] Table 3 Failure Probability of Each Failure Event in Phase 2
[0082]
[0083] P max =max{0.864,0.386,0.848,0}=0.864, with Once the failure branch point is identified, then 2M, 3M, and 4M are all failure branch points in this stage, and all three events may fail in this stage.
[0084] Therefore, in the second stage of the failure analysis, there were a total of 3 failure path records: (1) 1M, 2M; (2) 1M, 3M; (3) 1M, 4M;
[0085] The criteria for sudden degradation of material properties are established as follows:
[0086] (1) Fiber failure: E 11 =0;
[0087] (2) Matrix failure: E 22 =0,G 12 =0;
[0088] If the first stage branch point is 1M, then the stiffness E in the first single-layer plate will be... 22 G 12 The stiffness E in the second layer of the single-layer plate is reduced to 0. The second stage has three branch points. Taking 2M as an example, in this path, it is assumed that 2M fails in the second stage while 3M and 4M do not. Therefore, the stiffness E in the second layer of the single-layer plate is reduced to 0. 22 G 12 If the stiffness is reduced to 0, the stiffness of the remaining layers is not reduced at this stage. The same logic applies to other paths, which will not be elaborated here.
[0089] Step 5: Repeat steps 3 and 4 until all failure events occur, obtain all possible failure paths of the composite fuselage panel structure, calculate the failure probability of each failure path using the second-order narrow-limit theory, and calculate the overall failure probability of the composite fuselage panel structure based on the failure path failure probabilities.
[0090] Repeat steps three and four until all failure events occur, confirming the overall failure of the composite fuselage panel structure, and record all possible failure paths of the composite fuselage panel structure.
[0091] For a specific failure path among all possible failure paths, and using the second-order narrow-bound theory, the failure probability of a failure path is calculated as the minimum of the joint failure probabilities of any two failure events in the path, expressed as:
[0092]
[0093] in Let P represent the probability of the k-th path failing, min[P] i≠j (E i ∩E jThe ] represents the minimum combined failure probability of the two failure events in the path. The corresponding failure probability for each failure path is obtained using the method described above, which will not be repeated here.
[0094] Each failure path is considered to follow a cascade failure logic. Taking into account the correlation between failure paths, the overall failure probability of the fuselage panel structure can be expressed as:
[0095]
[0096] in Let be the overall failure probability of the composite fuselage panel structure. If the failure paths are completely independent, an upper bound is used; if the failure paths are completely correlated, a lower bound is used. A more conservative estimate uses the upper bound of this approach for the overall failure probability of the composite fuselage panel structure, expressed as:
[0097]
[0098] In one possible example, steps three and four are repeated until all failure events occur. In this embodiment, there are a total of 12 failure paths, represented as follows:
[0099] Table 4: All possible failure paths in the embodiments
[0100]
[0101] Based on the second-order narrow-bound theory, assuming that the probability of a failure path is calculated by the minimum joint failure probability of any two failure events in that path, and considering failures as approximately independent, we find that all failure paths are determined by failure events 4F and 1F. Therefore, the failure probability of each path is:
[0102] P(E 4F ∩E 1F = 0.015 × 0.112 = 0.00168
[0103] The formula for calculating the overall failure probability of the composite material fuselage panel structure is as follows:
[0104]
[0105] The final overall structural failure probability is:
[0106]
[0107] The overall failure probability of the composite fuselage panel structure is conservatively estimated to be...
[0108] In summary, the reliability analysis method for composite fuselage panel structures based on chaotic polynomial expansion provided in this invention comprehensively considers various failure modes of composite fuselage panel structures, offering greater precision compared to macroscopic failure calculation models. For individual failure events, a chaotic polynomial surrogate model is established to achieve rapid prediction of response extrema, and Monte Carlo simulation is combined to calculate the failure probability, significantly reducing the number of finite element method calls and greatly improving computational efficiency while meeting engineering accuracy requirements. By employing a branch-and-bound approach to find multiple branch points and obtain multiple possible failure paths for the structure, the method better reflects the actual failure process of composite materials and avoids redundancy in reliability design. This method can systematically solve the structural reliability analysis problem of composite fuselage panel structures, effectively improving computational efficiency and reducing redundancy in reliability design while ensuring computational accuracy meets engineering requirements.
[0109] The embodiments or implementation methods described in this specification are presented in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. In this specification, the terms "one embodiment," "some embodiments," "illustrative embodiment," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with an embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described can be combined in any suitable manner in one or more embodiments or examples.
[0110] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.
Claims
1. A reliability analysis method for composite material fuselage panel structures based on chaotic polynomial expansion, characterized in that, include: Step 1: Discretize the composite material fuselage panel structure using a finite element mesh, set loads and boundary conditions to obtain a finite element model of the composite material fuselage panel structure, which includes at least two single-layer plates; Step 2: Determine all failure events of the single-layer plate in the composite material fuselage panel structure, and establish the limit state function corresponding to each failure event; Step 3: Establish a normal distribution model of the uncertain parameters of the composite material fuselage panel structure, obtain training sample points using Latin hypercube sampling, calculate the maximum value of the limit state function response under the training sample points based on the finite element model, and establish a chaotic polynomial surrogate model based on the training sample points and the corresponding maximum value. Step 4: Use the Latin hypercube sampling to obtain new sample points within the range of the uncertain parameters, combine the chaotic polynomial surrogate model to calculate the predicted response value under the new sample points, conduct Monte Carlo simulation to calculate the failure probability of the failure event in the current stage, determine whether there is a failure branch point in the current stage, record the current failure path, and reduce the stiffness of the single-layer plate for the failure branch point in the current stage according to the sudden degradation criterion of material properties. Step 5: Repeat Step 3 and Step 4 until all failure events occur to obtain all possible failure paths of the composite material fuselage panel structure. Calculate the failure probability of each failure path using the second-order narrow-limit theory, and calculate the overall failure probability of the composite material fuselage panel structure based on the failure probabilities of the failure paths.
2. The method according to claim 1, characterized in that, The failure path search of the composite material fuselage panel structure is carried out based on the branch and bound method. After all the failure events have occurred, the overall failure of the composite material fuselage panel structure is confirmed.
3. The method according to claim 1, characterized in that, The failure paths are connected in a series and are related. The upper bound of the overall failure probability of the fuselage panel structure is the sum of the failure probabilities of each failure path, and the lower bound of the overall failure probability of the fuselage panel structure is the maximum failure probability of each failure path.
4. The method according to claim 1, characterized in that, The maximum response value is obtained through a global search algorithm.
5. The method according to claim 1, characterized in that, The step of establishing a chaotic multinomial surrogate model based on the training sample points and the corresponding maximum values includes: The training sample points and the maximum value are normalized and merged into a dataset; The dataset is divided into a training set and a test set; Using Hermite polynomials as an orthogonal basis, a chaotic polynomial is established. The maximum value is expanded, and the undetermined coefficients in front of the orthogonal basis are calculated using the least squares principle in combination with the training set, thus obtaining the closed-form solution of the chaotic polynomial surrogate model. Substitute the test set into the chaotic polynomial surrogate model, calculate the average relative error between the response value obtained by the chaotic polynomial surrogate model and the corresponding real response value. When the average relative error meets the error threshold, retain the chaotic polynomial surrogate model; otherwise, change the orthogonal basis order or resample and train.