First-order reliability method suitable for AK-ISSO of sheet composite material

Abstract

The invention discloses an AK-ISSO first-order reliability method suitable for a thin-plate composite material, which adopts a mixed strategy combining a first-order reliability method and active Kriging, integrates an improved sparrow search optimization method, and performs local dynamic search by taking the global optimal position of particles as prior position information. According to the method, reliability indexes are searched by using ISSO, an augmented Lagrangian penalty function in FORM is processed, an optimization model used for reliability index approximation in the ISSO is enhanced, and finally, an AK model corresponding to a stop criterion in Kriging model training is used for improving the effective calculation amount. According to the method, the robustness and the globality of FORM are enhanced by searching the reliability index of the thin plate composite material, a more reliable thin plate composite material reliability analysis result can be obtained under limited computing resources, the method is suitable for reliability evaluation of complex engineering, the analysis precision is guaranteed, and the computing efficiency can be improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of structural reliability analysis, and particularly relates to a first-order reliability method of AK-ISSO applicable to thin-plate composite materials. Background Art

[0002] The structural reliability analysis of thin-plate composite materials is an important task in the engineering field, which aims to evaluate the ability of thin-plate composite materials to resist failure under specific conditions. This analysis is crucial for ensuring the safety, stability and durability of thin-plate composite materials. However, for complex thin-plate composite material structures, their reliability analysis often faces challenges such as high computational cost and complex analysis process. The First-Order Reliability Method (FORM) is a commonly used method in structural reliability analysis. It approximately calculates the failure probability by finding the Most Probable Point (MPP). However, the existing FORM methods have limitations in some cases, especially for reliability problems with a high degree of nonlinearity, and their computational efficiency and stability may be affected. In addition, the existing FORM methods usually rely on gradient information, which may be difficult to obtain or calculate in some complex cases.

[0003] The Kriging model is an efficient surrogate model, which can predict the response of unknown points by learning the information of known sample points. In structural reliability analysis, the Kriging model is widely used to construct an approximate model of the limit state function, thus significantly reducing the computational cost. The Active Kriging (AK) model is an improved model of the Kriging model. By introducing an active learning mechanism and training through dynamically selecting sample points, it can obtain more information during the training process, improving the computational efficiency and prediction ability. The Sparrow Search Optimization (SSO) is a newly emerging heuristic optimization algorithm, which mimics the behavioral characteristics of sparrows during foraging. However, the original SSO algorithm may have the risk of local convergence in some cases. The Improved Sparrow Search Optimization (ISSO) algorithm adopts a local normal resampling strategy, using normal random data as the global and local positions of local search, improving the flexibility and adaptability of the search. At the same time, by introducing a dynamic adjustment mechanism and an improved search strategy, the global convergence ability and search efficiency of the algorithm are improved.

[0004] In summary, there is a need to study a first-order reliability method for thin-plate composite materials to improve the computational efficiency and accuracy of the FORM method in the reliability analysis of complex engineering structures. Summary of the Invention

[0005] To solve the above technical problems, the present invention provides a first-order reliability method of AK-ISSO applicable to thin-plate composite materials, which improves the accuracy and stability of the reliability analysis of thin-plate composite materials, while improving efficiency, reducing costs, and can provide more reliable theoretical support for the design and evaluation of engineering structures, and is used for the reliability analysis of actual engineering.

[0006] The technical solution adopted by the present invention is as follows: a first-order reliability method of AK-ISSO applicable to thin-plate composite materials, and the specific steps are as follows:

[0007] S1. Perform parameter initialization settings and establish the current Kriging model according to the experimental design.

[0008] S2. Based on step S1, establish an ALPF fitness function, and use the ISSO optimization algorithm to optimize the fitness function constructed based on the augmented Lagrangian penalty function ALPF in the first-order reliability method FORM to obtain the position information of the current MPP.

[0009] S3. Based on step S2, determine whether the current Kriging model meets the preset accuracy requirements. If not, go to step S4; if so, update the penalty factor and augmented Lagrangian operator included in ALPF, increment the iteration count by one, and then determine whether the iterative optimization result is stable.

[0010] Among them, if the iterative optimization result is stable, go to step S5; if it is not stable, return to step S2 to run again.

[0011] S4. Based on step S3, perform the training of the active Kriging model, that is, use the AK model corresponding to the stopping criterion in the Kriging model training to increase the effective calculation amount.

[0012] S5. According to the position information of the current MPP point, calculate the reliability index and failure probability, and then output the results to complete the current reliability analysis.

[0013] Further, the specific steps of step S1 are as follows:

[0014] Perform parameter initialization, including: setting the penalty factor and Lagrangian operator in ALPF, setting the population size and maximum iteration number of the ISSO optimization algorithm, setting the initial values and statistical information of the random variables included in the limit state function LSF; setting the initial iteration period as k = 1 and the call count of LSF as N call = 0.

[0015] Then use Latin hypercube sampling LHS to generate the initial experimental design as {(x1, y1)|y1 = g(x1)}.

[0016] Among them, x1 represents the initial value of the random variable, y1 represents the corresponding response variable, g(x1) represents the initial limit state function, and g(·) represents the limit state function.

[0017] Then, according to the experimental design (x k , y k ), the current Kriging model is established And the U function is used to guide the learning process of the Kriging model, and the expression is as follows:

[0018]

[0019] Among them, represents the average value of the responses obtained by the Kriging model from the candidate sample set; represents the standard deviation of each sample point obtained by calculating the candidate sample set through the Kriging model.

[0020] The formula for updating the sample points of the Kriging model is as follows:

[0021] x * = argmin(U) (2)

[0022] Among them, x * represents the selected update point.

[0023] Furthermore, the specific steps of step S2 are as follows:

[0024] S21. Use the Kriging model to replace the LSF and establish the fitness function ALPF;

[0025] Replace the LSF with the current Kriging model Establish ALPF as the fitness function, and the expression is as follows:

[0026]

[0027] Among them, x represents the vector set of random variables in the limit state function, u represents the vector obtained by transforming x to the standard normal space, β represents the reliability index, v represents the update speed of the Lagrange operator, and ρ represents the penalty factor. And set v as v k+1 = v k + g(x k+1 ) / ρ, and the update of ρ is set as The initial value v0 = 0, ρ0 = 1.

[0028] S22. Use the ISSO optimization algorithm to process the fitness function constructed by ALPF in FORM to obtain the position information x mpp of the current MPP, that is, perform local dynamic search through the previous position information of the most probable point MPP;

[0029] Among them, the ISSO optimization algorithm adopts a local normal resampling strategy and uses normal random data to search for the global and local positions locally. The global position is adjusted through a random process, and the expression is as follows:

[0030]

[0031] where the trade-off factor γ = 1 - k / NI, NI represents the number of particles in the population, and k represents the number of iterations; r1 represents a random number between [0, 1); p represents the participation factor, and its value range is [0.2, 1); norm represents a number generated by a normal distribution, with an average value of μ = 0 and a standard deviation of σ = 1. After global adjustment, the local search for the optimal position is applied, and the expression is as follows:

[0032]

[0033] where, represents the current optimal position, r2 represents a random number between [0, 1); C represents the consideration factor of the global optimal particle, and its value range is [0, 0.09].

[0034] Furthermore, the specific steps of step S3 are as follows:

[0035] S31. Determine whether the current Kriging model meets the pre-set accuracy requirements, that is, whether it meets the stopping criterion. If it meets the accuracy requirements, go to step S32; if it does not meet the accuracy requirements, set the number of updated points aa selected in the k-th loop optimization process to 0 and jump to execute step S4;

[0036] The ESC stopping criterion is used to stop the update of the Kriging model, and its expression is as follows:

[0037]

[0038] where ε r represents the tolerance value in the stopping criterion, and P f represents the actual failure probability; represents the approximate failure probability obtained by the Kriging model; represents the approximate failure probability obtained under the Monte Carlo method; N MCS represents the number of sample points in the candidate sample set to be evaluated; N f represents the number of failure sample points obtained by evaluating through the limit state function; represents the number of failure sample points evaluated by the current Kriging model. The interval represents the number of failure sample points of the current Kriging model, represents the upper limit of the number of sample points located in the safe area but classified as the failure area by the Kriging model. represents the upper limit of the number of sample points located in the failure area but classified as the safe area by the Kriging model.

[0039] S32. Update the penalty factor and augmented Lagrangian operator included in ALPF, and let k = k + 1;

[0040] S33. Based on step S32, determine whether the iterative optimization result is stable. If it is not stable, that is, the requirement for stopping iteration is not satisfied, return to step S2 to run again. If it is stable, that is, the requirement for stopping iteration is satisfied, jump to execute step S5;

[0041] The expression for determining whether it is stable is as follows:

[0042] |β k -β k-1 | < ε t (7)

[0043] where ε t represents the upper tolerance limit of the reliability index β in the k - th and (k - 1)-th iterations.

[0044] Furthermore, the specific steps of step S4 are as follows:

[0045] First, calculate the current trade - off factor γ, and the expression is as follows:

[0046] γ = mod(aa, k + 1) (8)

[0047] where mod represents the remainder algorithm. When γ is not 0, a candidate sample set is established within 0.618σ of the MPP; when it is 0, a sample set is established in the entire sampling space of the optimization problem. aa represents the number of update points selected in the k - th round of optimization.

[0048] Establish the current global or local candidate sample set {X} through LHS sampling, and then predict {X} through the Kriging model to obtain the candidate sample set Search for sample points in the candidate sample set to update the experimental design (x k , y k ), let the current N corresponding to the LSF call = N call + 1, aa = aa + 1.

[0049] Then use the updated experimental design (x k , y k ) to update the existing Kriging model, and determine whether the accuracy of the current Kriging model meets the accuracy requirement, that is, the ESC stopping criterion, or whether aa = aa max, if one of the conditions is met, return to execute step S2; otherwise, return to execute step S3, recalculate the trade-off factor, and re-evaluate the candidate sample set for re-evaluation.

[0050] Among them, aa max represents the number of maximum selection update points in the k-th round of optimization process.

[0051] Furthermore, the specific steps of step S5 are as follows:

[0052] According to the current MPP point position information, define the basic reliability problem, and transform the reliability problem solved by FORM into an unconstrained optimization problem, that is, calculate the reliability index β, and the expression is as follows:

[0053]

[0054] Among them, x represents the random variable in the LSF applied to g(x), u represents the vector obtained by transforming x into the standard normal phase space, and T represents the transpose operation.

[0055] Then calculate the failure probability through the relationship between the failure probability P f and the reliability index β, and the expression is as follows:

[0056]

[0057] Among them, Φ(β) represents solving the failure probability after transforming the reliability index β into the standard normal distribution.

[0058] The beneficial effects of the present invention: The method of the present invention adopts a hybrid strategy combining the first-order reliability method and active Kriging, and at the same time incorporates an improved sparrow search optimization method. The global optimal position of the particle is used as the prior position information for local dynamic search. ISSO is used to search for the reliability index, and by processing the augmented Lagrangian penalty function in FORM, the optimization model used for reliability index approximation in ISSO is enhanced. Finally, the AK model corresponding to the stopping criterion in Kriging model training is used to improve the effective calculation amount. The method of the present invention enhances the robustness and globality of FORM by searching for the reliability index of thin plate composite materials, can obtain more reliable reliability analysis results of thin plate composite materials under limited computing resources, is applicable to the reliability assessment of complex engineering, and can not only ensure the accuracy of the analysis but also improve the calculation efficiency. Description of the Drawings

[0059] Figure 1 is a flowchart of a first-order reliability method of AK-ISSO applicable to thin plate composite materials of the present invention.

[0060] Figure 2It is the flow chart of the population update position of the ISSO method in the embodiment of the present invention.

[0061] Figure 3 It is the schematic diagram of the laminate model in the embodiment of the present invention.

[0062] Figure 4 It is the schematic diagram of the result comparison of different reliability analysis methods in the embodiment of the present invention. Detailed implementation manners

[0063] The method of the present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0064] As Figure 1 shown, the flow chart of the first-order reliability method of AK-ISSO applicable to thin plate composite materials of the present invention is as follows:

[0065] S1. Perform parameter initialization settings and establish the current Kriging model according to the experimental design;

[0066] S2. Based on step S1, establish the ALPF fitness function, and use the ISSO optimization algorithm to optimize the fitness function constructed based on the Augmented Lagrangian Penalty Function (ALPF) in the first-order reliability method FORM to obtain the position information of the current MPP;

[0067] S3. Based on step S2, judge whether the current Kriging model meets the preset accuracy requirements. If not, go to step S4; if so, update the penalty factor and augmented Lagrangian operator included in the ALPF, increment the iteration count by one, and then judge whether the iterative optimization result is stable;

[0068] Among them, if the iterative optimization result is stable, go to step S5; if it is unstable, return to step S2 to run again.

[0069] S4. Based on step S3, perform the training of the active Kriging model, that is, use the AK model corresponding to the stopping criterion in the Kriging model training to improve the effective calculation amount;

[0070] S5. According to the position information of the current MPP point, calculate the reliability index and failure probability, and then output the results to complete the current reliability analysis.

[0071] In this embodiment, the specific steps of step S1 are as follows:

[0072] Perform parameter initialization, including: setting the penalty factor and Lagrange operator in ALPF, setting the population size and maximum number of iterations of the ISSO optimization algorithm, setting the initial values and statistical information of the random variables included in the Limit State Function (LSF); setting the initial iteration cycle as k = 1 and the number of calls to the LSF as N call = 0.

[0073] Then use Latin Hypercube Sampling (LHS) to generate the initial experimental design as {(x1, y1)|y1 = g(x1)}.

[0074] Wherein, x1 represents the initial value of the random variable, y1 represents the corresponding response variable, g(x1) represents the initial limit state function, and g(·) represents the limit state function.

[0075] Then, based on the experimental design (x k , y k ), establish the current Kriging model And use the U function to guide the learning process of the Kriging model. The expression is as follows:

[0076]

[0077] Wherein, represents the average value of the responses obtained by the Kriging model from the candidate sample set; represents the standard deviation of each sample point obtained by calculating the candidate sample set through the Kriging model.

[0078] The formula for updating the sample points of the Kriging model is as follows:

[0079] x * = argmin(U) (2)

[0080] Wherein, x * represents the selected update point.

[0081] In this embodiment, the step S2 is specifically as follows:

[0082] S21. Replace the LSF with the Kriging model and establish the fitness function ALPF;

[0083] Replace the LSF with the current Kriging model Establish ALPF as the fitness function. The expression is as follows:

[0084]

[0085] Among them, \(x\) represents the vector set of random variables in the limit state function, \(u\) represents the vector obtained by transforming \(x\) into the standard normal space, \(\beta\) represents the reliability index, \(v\) represents the update speed of the Lagrange operator, and \(\rho\) represents the penalty factor. And set \(v\) as \(v\) k+1 = \(v\) k + \(g(x\) k+1 ) / \(\rho\), and the update of \(\rho\) is set as The initial value \(v_0 = 0\), \(\rho_0 = 1\).

[0086] S22. Use the ISSO optimization algorithm to process the fitness function constructed by ALPF in FORM to obtain the position information \(x\) of the current MPP mpp , that is, perform local dynamic search through the previous position information of the Most Probable Point (MPP);

[0087] Among them, the ISSO optimization algorithm adopts a local normal resampling strategy and uses normal random data as the global and local positions for local search. The global position is adjusted through a random process, and the expression is as follows:

[0088]

[0089] Among them, the trade-off factor \(\gamma = 1 - k / N_I\), \(N_I\) represents the number of particles in the population, \(k\) represents the number of iterations; \(r_1\) represents a random number between \([0, 1)\); \(p\) represents the participation factor, and its value range is \([0.2, 1)\); norm represents a number generated by a normal distribution, with an average value of \(\mu = 0\) and a standard deviation of \(\sigma = 1\). After global adjustment, the local search optimal position is applied, and the expression is as follows:

[0090]

[0091] Among them, represents the current optimal position, \(r_2\) represents a random number between \([0, 1)\); \(C\) represents the consideration factor of the global optimal particle, and its value range is \([0, 0.09]\).

[0092] The population update position process of the ISSO method in this embodiment is as Figure 2 shown, and the subscripts in the figure only represent the differences in the population particle updates of the SSO method and the ISSO method.

[0093] In this embodiment, the specific steps of step S3 are as follows:

[0094] S31. Judge whether the current Kriging model meets the preset accuracy requirements, that is, whether it meets the stopping criterion. If it meets the accuracy requirements, go to step S32; if it does not meet the accuracy requirements, set the number \(aa\) of updated points selected in the \(k\)th loop optimization process to 0 and jump to execute step S4;

[0095] Stop the update of the Kriging model according to the ESC stopping criterion, and its expression is as follows:

[0096]

[0097] where ε r represents the tolerance value in the stopping criterion, and P f represents the actual failure probability; represents the approximate failure probability obtained by the Kriging model; represents the approximate failure probability obtained under the Monte Carlo method; N MCS represents the number of sample points in the candidate sample set to be evaluated; N f represents the number of failed sample points obtained by evaluating through the limit state function; represents the number of failure sample points evaluated by the current Kriging model. Since N f is difficult to obtain, the interval is used to represent the number of failure sample points of the current Kriging model, represents the upper limit of the number of sample points located in the safe area but classified as the failure area by the Kriging model, represents the upper limit of the number of sample points located in the failure area but classified as the safe area by the Kriging model.

[0098] S32. Update the penalty factor and augmented Lagrangian operator included in the ALPF, and let k = k + 1;

[0099] S33. Based on step S32, judge whether the iterative optimization result is stable. If it is not stable, that is, it does not meet the requirement of stopping iteration, return to step S2 to run again. If it is stable, that is, it meets the requirement of stopping iteration, jump to execute step S5;

[0100] The expression for judging whether it is stable is as follows:

[0101] |β k -β k-1 | < ε t (7)

[0102] where ε t represents the upper limit of the tolerance value of the reliability index β in the k-th and (k - 1)-th iterations.

[0103] In this embodiment, step S4 is specifically as follows:

[0104] First, calculate the current trade-off factor γ (used to determine whether to select an update point in the global range or a local update point near the MPP) in the current iteration, and its expression is as follows:

[0105] γ = mod(aa, k + 1) (8)

[0106] Among them, mod represents the modulo algorithm. When γ is not 0, a candidate sample set is established within 0.618σ of the MPP; when it is 0, a sample set is established in the entire sampling space of the optimization problem. aa represents the number of update points selected during the k-th round of optimization.

[0107] A current global or local candidate sample set {X} is established through LHS sampling, and then the candidate sample set is obtained by predicting {X} through the Kriging model. In the candidate sample set search for sample points to update the experimental design (x k , y k ), let N corresponding to the current LSF call = N call + 1, aa = aa + 1.

[0108] Then use the updated experimental design (x k , y k ) to update the existing Kriging model, and determine whether the accuracy of the current Kriging model meets the accuracy requirements, that is, the ESC stopping criterion, or whether aa = aa max . If one of them is satisfied, return to execute step S2; otherwise, return to execute step S3, recalculate the trade-off factor, and re-evaluate the candidate sample set .

[0109] Among them, aa max represents the maximum number of update points selected during the k-th round of optimization. In this embodiment, aa max = 10.

[0110] In this embodiment, the specific steps of step S5 are as follows:

[0111] According to the current MPP point position information, define the basic reliability problem, and transform the reliability problem solved by FORM into an unconstrained optimization problem (reducing the influence of the penalty factor on the selection of MPP search accuracy), that is, calculate the reliability index β, and the expression is as follows:

[0112]

[0113] Among them, x represents the random variable in the LSF applied to g(x), u represents the vector obtained by transforming x into the standard normal space, and T represents the transpose operation.

[0114] Then calculate the failure probability through the relationship between the failure probability P f and the reliability index β, and the expression is as follows:

[0115]

[0116] Among them, Φ(β) represents the solution of the failure probability after transforming the reliability index β into the standard normal distribution.

[0117] In this embodiment, experimental verification is further carried out. The reliability analysis of a thin plate composite material is carried out, and 9 methods in three major categories of analytical methods, soft computing methods, and hybrid ISSO are compared. They are Hasofer-Lind and Rackwitz-Fiessler (HL-RF), Finite-Step Length (FSL), Directional Stability Transformation Method (DSTM); Subset Simulation Analysis (SSA), Particle Swarm Optimization (PSO), Improved Sparrow Search Optimization (ISSO); U-ISSO, EFF-ISSO, AK-ISSO (the method of the present invention).

[0118] The comparison indicators of this embodiment include: the number of function calls N call , and comparative analysis is carried out on the average, best, worst reliability index β, standard deviation (Std), and error.

[0119] As Figure 3 shown, the analysis object of this embodiment consists of six plates, and the main failure mode is buckling. The size of the six-layer plate is 20 cm × 12.5 cm, the compressive load is N x = 500 kN / m, and the uniformly distributed lateral load is P = 0.2 MPa. The stacking structure is [0° / 45° / 90° / 90° / -4°5 / 0°], and it can be seen from Figure 3 that the thickness of the 0° and 90° laminates is 0.25 mm, and the others are 0.125 mm. The laminating material is epoxy carbon woven (230 GPa) prepreg. Considering the Tsai-Wu failure criterion, the LSF expression of this embodiment is as follows:

[0120] g(x) = 1 - f(ω)

[0121] Among them, ω represents the total stress on the thin plate, and the expression of f(ω) is as follows:

[0122]

[0123] Among them, ωi , where \(i = 1, 2, 3, 4, 5, 6\) represents the stress on each thin plate layer; \(F\) (·) represents a simple expression of the parameters related to the force on the structure, and the calculation expression is as follows:

[0124]

[0125] Among them, \(X\) T represents the longitudinal tensile strength of the material, with an average value of 1150 MPa; \(X\) C represents the longitudinal compressive strength, with an average value of 1150 MPa; \(Y\) T represents the transverse tensile strength, with an average value of 38 MPa; \(Y\) C represents the transverse compressive strength, with an average value of 236 MPa; \(Z\) C represents the vertical compressive strength, with an average value of 170 MPa; \(Z\) T represents the vertical tensile strength, with an average value of 50 MPa; \(S\) YZ \(= S\) XY \(= S\) XZ respectively represent the shear strengths in three directions, and their average values are all 48 MPa. The variance of all random variables is 0.1, and other characteristic parameters are default values.

[0126] The analysis and comparison results of this embodiment under different reliability methods are shown in Table 1.

[0127] Table 1

[0128]

[0129] As can be seen from Table 1, the gradient-based FORM method cannot provide effective analysis results for this case. According to Figure 4 it can be seen that the FORM based on the heuristic algorithm shows promising performance, and the proposed AK-ISSO method of the present invention has a lower computational cost and strong engineering practicability.

[0130] In summary, compared with SSO, the ISSO of the method of the present invention has stronger global search ability and local development ability in multi-distribution and complex situations, and can provide higher accuracy and stability. Using the AK-ISSO strategy of the method of the present invention to construct a Kriging model usually requires less computational cost. The AK-ISSO strategy can reduce unnecessary limit state function calls on the premise of ensuring the accuracy of the calculation results. Thus, it improves the reliability analysis ability of engineering cases including complex finite element cases. The FORM framework of the method of the present invention combining the ISSO algorithm and a new Kriging model construction strategy can accurately and stably obtain the position of the MPP, showing high efficiency and accuracy in the reliability analysis of thin plate composites, and can improve the efficiency in the reliability analysis of thin plate composites.

[0131] The above are only the preferred specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, according to the technical solution and inventive concept of the present invention, making equivalent substitutions or changes should be covered within the protection scope of the present invention.

Claims

1. A first-order reliability method of AK-ISSO applicable to thin plate composite materials, the specific steps are as follows: S1, perform parameter initialization settings and establish the current Kriging model according to the experimental design; S2. Based on step S1, an ALPF fitness function is established, and the ISSO optimization algorithm is used to optimize the fitness function constructed based on the augmented Lagrangian penalty function ALPF in the first-order reliability method FORM to obtain the position information of the current MPP; S3, based on step S2, determine whether the current Kriging model meets the preset accuracy requirements, if not, go to step S4, if yes, update the penalty factor and augmented Lagrangian operator included in ALPF, increase the number of iterations by one, and then determine whether the iterative optimization result is stable; in, If the iterative optimization result is stable, go to step S5; if it is unstable, go back to step S2 and run again; S4, based on step S3, training the active Kriging model, that is, using the AK model corresponding to the stopping criterion in the Kriging model training to increase the effective calculation amount; S5. According to the current MPP point location information, calculate the reliability index and failure probability, and then output the results to complete the current reliability analysis.

2. The first-order reliability method of AK-ISSO for thin plate composite materials according to claim 1, characterized in that: The step S1 is specifically as follows: Initialize parameters, including: Set the penalty factor and Lagrangian operator in ALPF, set the population size and maximum number of iterations of the ISSO optimization algorithm, set the initial value and statistical information of the random variables included in the limit state function LSF; set the initial iteration period to k = 1 and the number of calls to LSF to N call =0; Then Latin hypercube sampling LHS is used to generate the initial experimental design as {(x1,y1)|y1=g(x1)}; Where x1 represents the initial value of the random variable, y1 represents the corresponding response variable, g(x1) represents the initial limit state function, and g(·) represents the limit state function; According to the experimental design (x k ,y k ) Establish the current Kriging model The U function is used to guide the learning process of the Kriging model, and the expression is as follows: in, represents the average value of the responses obtained by the Kriging model from the candidate sample set; Represents the standard deviation of each sample point obtained by calculating the candidate sample set through the Kriging model; The sample point formula for updating the Kriging model is as follows: x * =argmin(U) (2) Among them, x * Indicates the selected update point.

3. The first-order reliability method of AK-ISSO for thin plate composite materials according to claim 1, characterized in that: The step S2 is specifically as follows: S21, use the Kriging model to replace LSF and establish the fitness function ALPF; Replace LSF with the current kriging model ALPF is established as the fitness function, and the expression is as follows: Where x represents the vector set of random variables in the limit state function, u represents the vector obtained by transforming x into the standard normal phase space, β represents the reliability index, v represents the update speed of the Lagrangian operator, and ρ represents the penalty factor; and v is set to v k+1 =v k +g(x k+1 ) / ρ, the update of ρ is set to Initial values ​​v0=0, ρ0=1; S22. Use the ISSO optimization algorithm to process the fitness function constructed by ALPF in FORM to obtain the current MPP position information x mpp , that is, local dynamic search is performed through the previous position information of the most likely point MPP; The ISSO optimization algorithm adopts a local normal resampling strategy, using normal random data as the local search for global and local positions; the global position Adjustment is done through a random process, and the expression is as follows: Among them, the trade-off factor γ = 1-k / NI, NI represents the number of particles in the population, k represents the number of iterations; r1 represents a random number between [0,1); p represents the participation factor, and its value interval is [0.2,1); norm represents the number generated by the normal distribution, with an average value of μ = 0 and a standard deviation of σ = 1; after global adjustment, the local search for the optimal position is applied, and the expression is as follows: in, represents the current optimal position, r2 represents a random number between [0,1); C represents the consideration factor of the global optimal particle, and its value range is [0,0.09].

4. The first-order reliability method of AK-ISSO applicable to thin plate composite materials according to claim 1, characterized in that: The step S3 is specifically as follows: S31, judging whether the current Kriging model meets the preset accuracy requirement, that is, whether it meets the stop criterion, if it meets the accuracy requirement, proceeding to step S32, if it does not meet the accuracy requirement, setting the number of update points aa selected in the kth cycle optimization process to 0 and jumping to step S4; The ESC stopping criterion is used to stop the update of the Kriging model, and its expression is as follows: Among them, ε r represents the tolerance value in the stopping criterion, P f represents the actual failure probability; represents the approximate failure probability obtained by the Kriging model; represents the approximate failure probability obtained under the Monte Carlo method; N MCS Represents the number of sample points in the selected sample set to be evaluated; N f Represents the number of failure sample points obtained through the evaluation of the limit state function; Indicates the number of fault sample points evaluated by the current Kriging model; interval Indicates the number of failed sample points in the current Kriging model. represents the upper limit of the number of sample points that are located in the safe area but classified as the fault area by the Kriging model. It represents the upper limit of the number of sample points that are located in the failure area but classified as safe areas by the Kriging model; S32, updating the penalty factor and augmented Lagrangian operator included in ALPF, and setting k=k+1; S33, based on step S32, determine whether the iterative optimization result is stable. If it is not stable, that is, it does not meet the requirement for stopping iteration, return to step S2 and re-run. If it is stable, that is, it meets the requirement for stopping iteration, jump to step S5; The expression for judging whether it is stable is as follows: |b k -b k-1 |<e t (7) Among them, ε t It represents the upper limit of the tolerance value of the reliability index β in the k-th and k-1-th iterations.

5. The first-order reliability method of AK-ISSO applicable to thin plate composite materials according to claim 1, characterized in that: The step S4 is specifically as follows: First, calculate the current trade-off factor γ, which is expressed as follows: γ=mod(aa,k+1) (8) Wherein, mod represents the remainder algorithm; when γ is not 0, the post-selection sample set is established within 0.618σ of the MPP; when it is 0, the sample set is established in the entire sampling space of the optimization problem; aa represents the number of update points selected in the kth round of optimization process; The current global or local candidate sample set {X} is established through LHS sampling, and then the candidate sample set is obtained by predicting {X} through the Kriging model. In the candidate sample set Search for sample points in the experiment to update the experimental design (x k ,y k ), let N corresponding to the current LSF call =N call +1, aa=aa+1; Then use the updated experimental design (x k ,y k ) Update the existing Kriging model and determine whether the accuracy of the current Kriging model meets the accuracy requirements, that is, the ESC stop criterion, or whether aa=aa max If one of the conditions is met, then return to step S2, otherwise return to step S3, recalculate the weight factor, and Conduct a reassessment; Among them, aa max Indicates the maximum number of selected update points during the kth round of optimization.

6. The first-order reliability method of AK-ISSO applicable to thin plate composite materials according to claim 1, characterized in that: The step S5 is specifically as follows: According to the current MPP point location information, the basic reliability problem is defined, and the reliability problem solved using FORM is transformed into an unconstrained optimization problem, that is, the reliability index β is calculated, and the expression is as follows: Where x represents the random variable in the LSF applied to g(x), u represents the vector obtained by transforming x into the standard normal phase space, and T represents the transpose operation; Then the failure probability P f The relationship between the reliability index β and the failure probability is calculated as follows: Among them, Φ(β) means that the reliability index β is transformed into a standard normal distribution and then the failure probability is solved.

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