Reliability Design Optimization Method for Welding Beam Engineering Based on Kriging and Sparrow Search

Abstract

The present invention relates to the technical field of engineering optimization, and particularly relates to a welding beam engineering reliability design optimization method based on Kriging and sparrow search, including: determining the objective function, design variables and constraint conditions in the reliability design optimization problem of the welding beam engineering, and obtaining the random variables of the influencing factors and the distribution function of the random variables; constructing an initial Kriging model; using the enhanced sparrow search algorithm to optimize the initial Kriging model to obtain the current optimal solution and the minimum performance target point, and solving the offset vector; judging whether the global sampling condition is satisfied according to the trade-off factor, if it is satisfied, perform global sampling and update the Kriging model, otherwise, perform local precise sampling and update the Kriging model; when the global convergence condition, the update times of the decoupling process and the local convergence condition are satisfied, output the optimal solution and the optimal objective function value. The present invention can improve the efficiency and accuracy of the welding beam engineering reliability design process.

Description

Technical Field

[0001] The present invention relates to the technical field of engineering optimization, and more specifically, to a method for optimizing the reliability design of a welded beam project based on Kriging and sparrow search. Background Technique

[0002] With the rapid development of modern engineering technology, the complexity of engineering systems has been continuously increasing, and the number of design variables and constraint conditions has been growing day by day, making the reliability-based design optimization problem (RBDO) particularly complex. RBDO aims to find the optimal objective function value and optimal solution under the influence of uncertain factors. However, traditional RBDO methods often face challenges such as high computational costs, slow convergence rates, and the possibility of falling into local optimal solutions when dealing with high-dimensional, non-linear, and multi-constraint problems.

[0003] As an efficient surrogate model, the Kriging model can significantly reduce computational costs while ensuring a certain level of accuracy. However, in the RBDO process, how to effectively establish and maintain the Kriging model to balance global and local accuracy remains an urgent problem to be solved. At the same time, heuristic optimization algorithms, such as the Sparrow Search Algorithm (SSA), perform well in global search and local exploration, but there is still room for improvement in the convergence speed and stability of the original SSA algorithm.

[0004] Therefore, how to improve the efficiency and accuracy of RBDO by combining the advantages of the adaptive Kriging model and the enhanced sparrow search algorithm is an urgent problem for those skilled in the art. Summary of the Invention

[0005] In view of this, the present invention provides a method for optimizing the reliability design of a welded beam project based on Kriging and sparrow search, which can improve the efficiency and accuracy of the reliability design process of the welded beam project.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A method for optimizing the reliability design of a welded beam project based on Kriging and sparrow search, comprising the following steps:

[0008] S1. Determine the objective function, design variables, and constraint conditions in the reliability design optimization problem of the welded beam project, and obtain the random variables of the influencing factors and the distribution function of the random variables;

[0009] S2. Use the Latin hypercube sampling method to generate initial sample points, and construct an initial Kriging model based on the initial sample points and their corresponding true responses;

[0010] S3. Optimize the initial Kriging model using the enhanced sparrow search algorithm to obtain the current optimal solution;

[0011] S4. Calculate the current minimum performance target point, and solve the offset vector based on the current optimal solution and the minimum performance target point;

[0012] S5. Judge whether the global sampling condition is satisfied according to the trade-off factor. If it is satisfied, execute S6; otherwise, execute S7;

[0013] S6. Generate a global candidate sample set using the global sampling algorithm, calculate the corresponding responses, and update the Kriging model;

[0014] S7. Generate a local candidate sample set using the local exact sampling algorithm, calculate the corresponding responses, and update the Kriging model;

[0015] S8. Judge whether the global convergence condition is satisfied. If it is not satisfied, execute S9; otherwise, execute S10;

[0016] S9. Judge whether the number of updates in the decoupling process satisfies the preset value. If it is satisfied, execute S10; otherwise, return to S5;

[0017] S10. Judge whether the local convergence condition is satisfied. If it is satisfied, output the optimal solution and the optimal objective function value; otherwise, return to S4.

[0018] Furthermore, in S1, the objective function takes minimizing the welding cost as the optimization goal; the constraint conditions include at least stress and position; the design variables include at least the height and length of the weld, as well as the height and thickness of the beam; the random variables include at least material properties and loads.

[0019] Furthermore, in S1, the objective function is expressed as: f(μ,x), where μ is the design variable vector and x is the random variable vector; the constraint conditions are expressed as g i (μ,x) ≤ 0, i = 1, 2,..., k, where k is the number of constraint conditions.

[0020] Furthermore, S3 includes:

[0021] Initialize the parameters of the enhanced sparrow search algorithm, including at least the population size, the maximum number of iterations, and the leader ratio;

[0022] Taking the minimization of the objective function as the goal, use the enhanced sparrow search algorithm to perform a global search on the design variable vector to obtain the current optimal solution u MPTP .

[0023] Furthermore, S4 includes:

[0024] Convert the reliability requirements in inverse reliability analysis into constraint conditions in the SQP method, transform the deterministic optimization problem into an unconstrained optimization problem, and use the SQP method to solve for the minimum performance target point x MPTP ;

[0025] Calculate the offset vector s i = μ MPTP - x MPTP , where x MPTP represents the current minimum performance target point.

[0026] Furthermore, in S5, if the trade-off factor γ = 0, then execute S6; if the trade-off factor γ ≠ 0, then execute S7; the calculation formula for the trade-off factor is:

[0027] γ = mod(aa, k + 1)

[0028] where aa represents the update iteration number and k represents the number of constraint conditions.

[0029] Furthermore, S6 includes:

[0030] Generate a global candidate sample set {X MCS} according to the global sampling algorithm;

[0031] Select an update point from the global candidate sample set {X MCS} according to the learning function and add it to the initial sample set {X k};

[0032] Update the Kriging model according to the new sample set {X k}.

[0033] Furthermore, S7 includes:

[0034] Generate a local candidate sample set {X MCS} according to the local exact sampling algorithm;

[0035] Select an update point x MCS from the local candidate sample set {X k U , and add it to the initial sample set {X k};

[0036] Update the Kriging model according to the new sample set {X k}.

[0037] Furthermore, in S8, the global convergence condition is expressed as:

[0038]

[0039] where Pf denotes the failure probability calculated using the limit state function, denotes the failure probability obtained using the Kriging model instead of the limit state function; denotes the number of failure sample points obtained using the Kriging model; denotes the upper limit of the number of sampling points located in the safe region but classified as the failure region by the Kriging model; denotes the upper limit of the number of sample points located in the failure region but classified as the safe region by the Kriging model; ε tol2 denotes the maximum stopping index set under the global convergence condition; Dt denotes the specific search range; k denotes the number of constraint conditions.

[0040] Furthermore, in S10, the local convergence condition is expressed as:

[0041] ε r1 = |||f(x k )|| - ||f(x k-1 )||| ≤ ε tol1

[0042] where ε tol1 denotes the maximum stopping index set under the local convergence condition; f(x k ) denotes the objective function value in the current iteration process; f(x k -1) denotes the objective function value in the previous iteration process.

[0043] Through the above technical solutions, it can be seen that compared with the prior art, the present invention has the following beneficial effects:

[0044] (1) By enhancing the sparrow search algorithm, the present invention can improve the convergence speed and stability of the algorithm while ensuring the global search ability.

[0045] (2) By the adaptive Kriging model establishment strategy, the present invention can significantly reduce the calculation cost on the premise of ensuring the accuracy, especially when dealing with high-dimensional and non-linear problems, the effect is particularly obvious.

[0046] (3) By introducing the local exact Kriging model and the trade-off factor, the present invention can perform balanced search in the global and local ranges, effectively avoiding falling into the local optimal solution.

[0047] (4) By combining the advantages of the enhanced sparrow search algorithm and the adaptive Kriging model, the present invention can provide more accurate and reliable optimization results. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the accompanying drawings required in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can also be obtained based on the provided drawings.

[0049] Figure 1 Flow chart of the reliability design optimization method for welded beam engineering based on Kriging and sparrow search provided by the present invention;

[0050] Figure 2 Flow chart of the establishment process of the global Kriging model provided by the present invention;

[0051] Figure 3 Reliability index of 30 repeated experiments in the mathematical embodiment of the present invention;

[0052] Figure 4 Repeated experiment results of different RBDO methods in the mathematical embodiment of the present invention;

[0053] Figure 5 Welded beam structure in the engineering embodiment of the present invention;

[0054] Figure 6 Comparison chart of reliability indexes of different methods in the engineering embodiment of the present invention;

[0055] Figure 7 Sample points required to compare Kriging model establishment strategies in the engineering embodiment of the present invention. Detailed implementation manners

[0056] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts belong to the scope protected by the present invention.

[0057] As Figure 1 shown, the embodiment of the present invention discloses a reliability design optimization method for welded beam engineering based on Kriging and sparrow search, including the following steps:

[0058] S1. Determine the objective function, design variables, and constraint conditions in the reliability design optimization problem of the welded beam engineering, and obtain the random variables of the influencing factors and the distribution function of the random variables;

[0059] The objective function is expressed as: f(μ,x), where μ is the design variable vector and x is the random variable vector; the constraint condition is expressed as gi (μ, x) ≤ 0, i = 1, 2, ..., k, where k is the number of constraint conditions. The distribution function of the random variable x is denoted as F x (x).

[0060] The objective function aims to minimize the welding cost; the constraint conditions at least include stress and position; the design variables at least include the height and length of the weld, as well as the height and thickness of the beam; the random variables at least include material properties and loads.

[0061] S2. Use the Latin Hypercube Sampling (LHS) method to generate initial sample points, and construct an initial Kriging model based on the initial sample points and their corresponding true responses. Use the LHS method to generate an initial sample point set X init with the number of sample points being n init . For each initial sample point x i ∈ X init , calculate its corresponding true response yi = f(μ, x i ). Use the initial sample point set X init and its corresponding true response set Y init to construct an initial Kriging model.

[0062] S3. Use the Enhanced Sparrow Search Algorithm (ESSA) to optimize the initial Kriging model to obtain the current optimal solution; specifically including:

[0063] Initialize the parameters of the enhanced sparrow search algorithm, including population size, maximum number of iterations, leader ratio, etc.

[0064] Take the initial Kriging model as the objective function, and use the enhanced sparrow search algorithm for global search to solve the following optimization problem to obtain the current optimal solution u MPTP ;

[0065] find μ = [μ1, μ2, ..., μ m

[0066] min f(μ - s i , x)

[0067] s.t. g i (μ - s i , x) ≥ 0

[0068] μ L ≤ μ ≤ μ U , i = 1, 2, ..., k

[0069] ​where the subscript m represents the number of design variables; f(μ - s i , x) represents the objective function. By adjusting the design variable μ and considering the influence of the random variable x, the goal is to find the design parameters that minimize f; s i represents the offset vector; g i (μ - s i , x) represents the i-th constraint condition function; μ L and μ U represent the upper and lower limits of the design variable, respectively.

[0070] S4. Calculate the current minimum performance target point through the inverse reliability analysis method, and solve the offset vector based on the current optimal solution and the minimum performance target point; specifically including:

[0071] S41. By transforming the original limit state function into a Kriging model, obtain the RBDO model assisted by the Kriging model, as follows:

[0072] find μ = [μ1, μ2,..., μ m

[0073] min f(x)

[0074]

[0075] μ L ≤ μ ≤ μ U , i = 1, 2,..., k

[0076] where f(x) represents the optimization objective function; P[·] represents probability; represents the objective function obtained by fitting the Kriging model; represents the failure probability P f ; represents the corresponding reliability index in the reliability design of the welded beam project.

[0077] S42. When using the decoupling method to solve RBDO, the inverse reliability analysis process of MPTP is as follows:

[0078] find x MPTP

[0079]

[0080] s.t.: ||x|| = β t

[0081] where x MPTP represents the current minimum performance target point; ​Denote the objective function obtained by fitting the limit state function using the Kriging model; β is the target reliability index. Through this optimization process, x can be obtained MPTP , and then calculate the offset vector s i = μ MPTP - x MPTP .

[0082] The purpose of solving the offset vector is to adjust the deterministic optimization result to a solution that meets the target reliability requirements through inverse reliability analysis. Specifically:

[0083] Adapt to uncertainty: Random variables in the welded beam design (such as material properties, loads) introduce uncertainty. The offset vector is used to adjust the current optimal solution (MPTP point) so that the reliability index (such as the target β value) can still be guaranteed when the random variables fluctuate, thereby reducing the failure risk.

[0084] Transform the optimization problem: Through the offset vector, the originally constrained deterministic optimization problem is transformed into an unconstrained optimization problem, simplifying the solution process. The offset vector quantifies the direction and magnitude of the adjustment required for the design variables to minimize the welding cost while meeting the reliability constraints.

[0085] Balance reliability and cost: The offset vector reflects the corrective effect of the reliability requirements on the design variables, ensuring that the optimization result not only has the lowest cost but also meets the stress, position, and other constraint conditions in a probabilistic sense, achieving a trade-off between engineering reliability and economy.

[0086] S5. Judge whether the global sampling condition is satisfied according to the trade-off factor. If it is satisfied, execute S6; otherwise, execute S7; Select update points in the local and global ranges through the trade-off factor to balance the global and local accuracies of the Kriging model.

[0087] Specifically, the calculation formula for the trade-off factor is:

[0088] γ = mod(aa, k + 1)

[0089] where aa represents the update iteration number, and k represents the number of constraint conditions.

[0090] If the trade-off factor γ = 0, execute S6; if the trade-off factor γ ≠ 0, execute S7.

[0091] S6. Generate a global candidate sample set using the global sampling algorithm, calculate the corresponding responses, and update the Kriging model; Specifically include:

[0092] Generate a global candidate sample set {X MCS} according to the global sampling algorithm;

[0093] According to the learning function, from the global candidate sample set {X MCSSelect update points from and add them to the initial sample set {X k};

[0094] Update the Kriging model according to the new sample set {X k}.

[0095] S7. Generate a local candidate sample set using the local exact sampling algorithm, calculate the corresponding responses, and update the Kriging model, including:

[0096] Generate a local candidate sample set {X MCS} according to the local exact sampling algorithm;

[0097] Select update points from the local candidate sample set {X MCS} according to the learning function and add them to the initial sample set {X k};

[0098] Update the Kriging model according to the new sample set {X k}.

[0099] Among them, the generation range of the local candidate sample set is determined by the sampling range formula, and the sampling range formula is expressed as:

[0100] Dt = max[d1, d2]

[0101] d1 = λ·max[β i , i = 1, 2,..., m

[0102]

[0103] Among them, Dt represents the sampling range, d1 represents the lower bound of the sampling range, d2 represents the upper bound of the sampling range; λ represents the spatial scale control parameter, which is adjusted according to the search domain; x k represents the current optimization result; x k+1 represents the updated solution after the next iteration; || ||2 represents the two-norm operation, for example

[0104] S8. Judge whether the global convergence condition is satisfied. If not, execute S9; otherwise, execute S10; the global convergence condition is called the stopping criterion ε r2 , which is expressed as:

[0105]

[0106] ε tol2 = 0.05·Dt·k

[0107] Among them, P f represents the failure probability calculated using the limit state function, represents the failure probability obtained using the Kriging model instead of the limit state function; represents the number of failure sample points obtained using the Kriging model; represents the upper limit of the number of sampling points located in the safe region but classified as the failure region by the Kriging model; represents the upper limit of the number of sample points located in the failure region but classified as the safe region by the Kriging model; ε tol2 represents the maximum stopping index set under the global convergence condition; Dt represents a specific search range; k represents the number of constraint conditions.

[0108] S9. Judge whether the number of updates in the decoupling process meets the preset value. If it meets, execute S10; otherwise, return to S5;

[0109] The formula for judging the number of updates in the decoupling process is:

[0110] aa>aa max = 10.

[0111] S10. Judge whether the local convergence condition is met. If it is met, output the optimal solution and the optimal objective function value; otherwise, return to S4.

[0112] The local convergence condition is called the stopping criterion ε r1 , which is expressed as:

[0113] ε r1 = |||f(x k )|| - ||f(x k-1 )||| ≤ ε tol1

[0114] where ε tol1 represents the maximum stopping index set under the local convergence condition; f(x k ) represents the objective function value in the current iteration process; f(x k -1) represents the objective function value in the previous iteration process.

[0115] It can be seen from S1 - S10 that the present invention adopts three key technologies:

[0116] (1) Enhanced Sparrow Search Algorithm (ESSA): Improve the original SSA algorithm, and improve the convergence speed and stability of the algorithm by increasing the attention to the optimal sparrow.

[0117] (2) Adaptive Kriging model establishment strategy: Select update points in the local and global ranges through the trade - off factor to balance the global and local accuracies of the Kriging model.

[0118] (3) Local Exact Kriging Model: Add sample points within a local range to improve the accuracy of the Kriging model near the optimal solution.

[0119] As shown in Table 1 and Figure 2 illustrated, the construction process of the global adaptive Kriging model of the present invention is shown in Table 2, and the construction process of the local exact Kriging model of the present invention is shown in Table 2.

[0120] Table 1 Construction Process of Global Adaptive Kriging Model

[0121]

[0122]

[0123]

[0124] Table 2 Construction Process of Local Exact Kriging Model

[0125]

[0126]

[0127] Next, the performance of the present invention is further verified with two examples.

[0128] Example 1: Verification by Mathematical Example

[0129] Taking a typical RBDO mathematical example as an example, the objective function is to minimize a certain combination of design variables, the design variables are two normally distributed random variables, and the constraint conditions are two non-linear inequality constraints. The specific formulas are as follows:

[0130]

[0131] g1(x) = -x1sin(4x1) - 1.1x2sin(2x2)

[0132] g2(x) = 3 - x1 + x2

[0133]

[0134] Among them, the design variables and are the means of the normally distributed random variables x1 and x2 respectively.

[0135] Next, the method of the present invention is compared with the traditional double-loop method, the decoupling method based on the original SSA, and the decoupling method based on the global Kriging model, as shown in Table 3.

[0136] Table 3 Results of Different RBDOs

[0137]

[0138] The results show that the method of the present invention performs excellently in terms of the accuracy of the optimization results. Especially when dealing with high-dimensional and non-linear problems, the method of the present invention can significantly reduce the computational cost and improve the accuracy of the optimization results. Further, Figure 3 The precision of reliability is compared with the optimal solution of repeated experiments. Through calculation, the reliability indices of constraint function 2 of different RBDO methods are all higher than the target reliability index. It can be seen that the reliability index obtained by the decoupling method is closer to the target reliability index than that obtained by the double-loop optimization method. The optimal solution obtained by the Kriging model-assisted SORA method is also very close to the target reliability index constraint.

[0139] In addition, Figure 4 The optimization results obtained by different proposed RBDO methods in repeated experiments are compared. As can be seen from the figure, accurate optimization results can be obtained by different Kriging model construction strategies. Although the new Kriging model construction strategy greatly improves the efficiency, its stability will necessarily be slightly worse when the Kriging model is updated more frequently.

[0140] Example 2: Verification of the welded beam engineering example

[0141] The welded beam structure is as Figure 5 shown. Its design goal is to minimize the welding cost while satisfying the constraints such as stress and position. The design variables are the height and length of the weld and the height and thickness of the beam, and the random variables are material properties (such as elastic modulus, yield strength, etc.) and loads (such as bending moment, torque, etc.), and these random variables all follow a normal distribution. What can be represented by a mathematical model in this example is:

[0142] s.t.Pr(g k (x)≥0)≥Φ(β t ),k = 1,2,3,4,5

[0143]

[0144] where the design variables x1, x2, x3, and x4 are the height and length of the weld and the height and thickness of the beam respectively, and they respectively follow an independent normal distribution. d represents the design variable, μ x1 , μ x2 , μ x3 , μ x4 respectively represent the mean of a design variable; Pr(g k (x)≥0)≥Φ(βt) is the probability constraint condition to ensure that the design meets the reliability requirements; P r represents probability, Φ is the cumulative distribution function of the standard normal distribution, βt is the target reliability index; g k (x) represents the k-th constraint function; k represents the number of constraints; τ(x) and σ(x) are stress-related functions respectively; and are the distributions of the design variables respectively.

[0145] To verify the effectiveness of the present invention in engineering practical problems, the method of the present invention is compared with the traditional Monte Carlo simulation method. Under the same computing resources, the computing costs and the accuracy of the optimization results of different methods are compared, and the results are shown in Table 4.

[0146] Table 4 Results of different RBDOs

[0147]

[0148] The results show that the method of the present invention is superior to the Monte Carlo simulation method in terms of the accuracy of the optimization results.

[0149] As Figure 6 shown, it is the reliability analysis of the optimization results in the above table. Among them, Constraints 1, 2, and 3 play important constraint roles. Since Constraints 4 and 5 do not have obvious constraint effects, they are not shown. As can be seen from Figure 6 , the reliability analysis results meet the target reliability index constraints of the example, indicating that the proposed method is accurate.

[0150] Figure 7 shows the number of LSF calls required to establish different Kriging models, indicating the efficiency of the method proposed by the present invention.

[0151] The results show that the method of the present invention is superior to the Monte Carlo simulation method in terms of both efficiency and accuracy of the optimization results. Especially when dealing with complex engineering problems, the method of the present invention can significantly reduce the computing cost and improve the accuracy of the optimization results.

[0152] In this specification, each embodiment is described in a progressive manner. The key point of each embodiment is to illustrate the differences from other embodiments. For the same or similar parts among the embodiments, reference can be made to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the description of the method part.

[0153] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A reliability design optimization method for welded beam engineering based on Kriging and sparrow search, characterized in that: The following steps are involved: S1. Determine the objective function, design variables, and constraints in the reliability design optimization problem of the welded beam project, and obtain the random variables of the influencing factors and the distribution function of the random variables; S2, using the Latin hypercube sampling method to generate initial sample points, and constructing an initial Kriging model based on the initial sample points and their corresponding true responses; S3, using the enhanced sparrow search algorithm to optimize the initial Kriging model and obtain the current optimal solution; S4. Calculate the current minimum performance target point and solve the offset vector based on the current optimal solution and the minimum performance target point; S5. Determine whether the global sampling condition is met based on the weighing factor. If so, execute S6; otherwise, execute S7. S6. Generate a global candidate sample set using a global sampling algorithm, calculate the corresponding response, and update the Kriging model; S7, using a local precise sampling algorithm to generate a local candidate sample set, calculating the corresponding response, and updating the Kriging model; S8, determine whether the global convergence condition is met, if not, execute S9, otherwise execute S10; S9, determine whether the number of updates in the decoupling process meets the preset value, if so, execute S10, otherwise return to S5; S10. Determine whether the local convergence condition is met. If so, output the optimal solution and the optimal objective function value. Otherwise, return to S4.

2. The reliability design optimization method for welded beam engineering based on Kriging and sparrow search according to claim 1 is characterized in that: In S1, the objective function takes minimizing welding cost as the optimization goal; the constraints include at least stress and position; the design variables include at least the height and length of the weld, and the height and thickness of the beam; and the random variables include at least material properties and loads.

3. The reliability design optimization method for welded beam engineering based on Kriging and sparrow search according to claim 1 is characterized in that: In S1, the objective function is expressed as: f(μ,x), where μ is the design variable vector and x is the random variable vector; the constraint condition is expressed as g i (μ,x)≤0,i=1,2,...,k, where k is the number of constraints.

4. The reliability design optimization method for welded beam engineering based on Kriging and sparrow search according to claim 3 is characterized in that: S3 includes: Initialize the parameters of the enhanced sparrow search algorithm, including at least the population size, maximum number of iterations, and leader ratio; With the goal of minimizing the objective function, the enhanced sparrow search algorithm is used to perform a global search on the design variable vector to obtain the current optimal solution u MPTP .

5. The reliability design optimization method for welded beam engineering based on Kriging and sparrow search according to claim 4 is characterized in that S4 include: The reliability requirements in the inverse reliability analysis are converted into constraints in the SQP method, which converts the deterministic optimization problem into an unconstrained optimization problem. The SQP method is used to solve the minimum performance target point x MPTP ; Calculate the offset vector s i =μ MPTP -x MPTP , where x MPTP Indicates the current minimum performance target point.

6. The reliability design optimization method for welded beam engineering based on Kriging and sparrow search according to claim 1 is characterized in that: In S5, if the trade-off factor γ = 0, then execute S6; if the trade-off factor γ ≠ 0, then execute S7; the calculation formula of the trade-off factor is: γ=mod(aa,k+1) Where aa represents the number of update iterations and k represents the number of constraints.

7. The reliability design optimization method for welded beam engineering based on Kriging and sparrow search according to claim 1, characterized in that S6 include: According to the global sampling algorithm, a global candidate sample set {X MCS }; According to the learning function, from the global candidate sample set {X MCS }Select the update point And added to the initial sample set {X k }; According to the new sample set {X k }Update the kriging model.

8. The reliability design optimization method for welded beam engineering based on Kriging and sparrow search according to claim 1 is characterized in that S7 include: According to the local precise sampling algorithm, a local candidate sample set {X MCS }; According to the learning function, the local candidate sample set {X MCS }Select the update point And added to the initial sample set {X k }; According to the new sample set {X k }Update the kriging model.

9. The reliability design optimization method for welded beam engineering based on Kriging and sparrow search according to claim 1 is characterized in that: In S8, the global convergence condition is expressed as: Among them, P f represents the failure probability calculated using the limit state function, represents the failure probability obtained using the Kriging model instead of the limit state function; Indicates the number of fault sample points obtained using the Kriging model; represents an upper bound on the number of sampling points that are located in safe areas but classified as trouble areas by the kriging model; represents the upper limit of the number of sample points that are located in the fault area but classified as safe area by the kriging model; ε tol2 Indicates the maximum stopping index set under the global convergence condition.

10. The reliability design optimization method for welded beam engineering based on Kriging and sparrow search according to claim 1 is characterized in that: In S10, the local convergence condition is expressed as: ε r1 =|||f(x k )||-||f(x k-1 )|||≤ε tol1 Among them, ε tol1 Indicates the maximum stop index set under local convergence conditions; f(x k ) represents the objective function value in this iteration; f(x k -1) represents the objective function value in the last iteration.

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