Welded beam engineering reliability design optimization method based on Kriging and sparrow search

Abstract

The invention relates to the technical field of engineering optimization, in particular to a welded beam engineering reliability design optimization method based on Kriging and sparrow search, which comprises the following steps of: determining an objective function, a design variable and a constraint condition of welded beam engineering in a reliability design optimization problem; obtaining a random variable of the influence factor and a distribution function of the random variable; constructing an initial Kriging model; optimizing the initial Kriging model by adopting an enhanced sparrow search algorithm to obtain a current optimal solution and a minimum performance target point, and solving an offset vector; judging whether a global sampling condition is met or not according to the trade-off factor, if yes, executing global sampling and updating the Kriging model, and if not, executing local accurate sampling and updating the Kriging model; and when the global convergence condition, the updating times of the decoupling process and the local convergence condition are met, outputting an optimal solution and an optimal objective function value. The efficiency and the accuracy of the reliability design process of the welded beam engineering can be improved.

Description

Technical Field

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

[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 speeds, 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 engineering reliability design of a welded beam based on Kriging and sparrow search, which can improve the efficiency and accuracy of the engineering reliability design process of the welded beam.

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

[0007] A method for optimizing the engineering reliability design of a welded beam 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 meets 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, and 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, realize the conversion of the deterministic optimization problem into an unconstrained optimization problem, and use the SQP method to solve 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 of 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 the global candidate sample set {X MCS} according to the global sampling algorithm;

[0031] Select the 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 the local candidate sample set {X MCS} according to the local exact sampling algorithm;

[0035] Select the 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] From 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) Through 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 nonlinear problems.

[0046] (3) By introducing the local accurate Kriging model and the trade-off factor, the present invention can perform balanced search in the global and local ranges and effectively avoid 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 Flowchart of the reliability design optimization method for welded beam engineering based on Kriging and sparrow search provided by the present invention;

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

[0051] Figure 3 Reliability index of 30 repeated tests 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] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with 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 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 of protection of the present invention.

[0057] As Figure 1 shown, the embodiments of the present invention disclose 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 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.

[0061] S2. Generate initial sample points using the Latin Hypercube Sampling (LHS) method, 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. Optimize the initial Kriging model using the Enhanced Sparrow Search Algorithm (ESSA) to obtain the current optimal solution; specifically including:

[0063] Initialize the parameters of the Enhanced Sparrow Search Algorithm, including the 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 = [μ 1 , μ 2 , ..., 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, and the goal is to find the design parameters that minimize f by adjusting the design variable μ and considering the influence of the random variable x; 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 shown below:

[0072] find μ = [μ 1 , μ 2 ,..., 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 Kriging model fitting; represents the failure probability P f ; represents the corresponding reliability index in the engineering reliability design of the welded beam.

[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 the offset vector s is calculated 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) to ensure 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. Use the global sampling algorithm to generate a global candidate sample set, calculate the corresponding responses, and update the Kriging model; specifically including:

[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 {XMCS Select 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[d 1 , d 2

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

[0102]

[0103] Among them, Dt represents the sampling range, d 1 represents the lower bound of the sampling range, d 2 represents the upper bound of the sampling range; λ represents the spatial scale control parameter, which is adjusted according to the search domain requirements; x k represents the current optimization result; x k+1 represents the solution updated 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] εtol2 = 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 stop index set under the global convergence condition; Dt represents the 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 meets, 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] Among them, ε tol1 represents the maximum stop 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 by increasing the attention to the optimal sparrow, and improve the convergence speed and stability of the algorithm.

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

[0118] (3) Locally accurate Kriging model: Increase sample points within the local scope to improve the accuracy of the Kriging model near the optimal solution.

[0119] As shown in Table 1 and Figure 2 as shown, it is the construction process of the global adaptive Kriging model of the present invention. As shown in Table 2, it is the construction process of the locally accurate Kriging model of the present invention.

[0120] Table 1 Construction process of global adaptive Kriging model

[0121]

[0122]

[0123]

[0124] Table 2 Construction process of locally accurate Kriging model

[0125]

[0126]

[0127] The performance of the present invention is further verified by two examples below.

[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 random variables with normal distributions, and the constraint conditions are two non-linear inequality constraints. The specific formulas are as follows:

[0130]

[0131] g 1 (x) = -x 1 sin(4x 1 ) - 1.1x 2 sin(2x 2 )

[0132] g 2 (x) = 3 - x 1 +x 2

[0133]

[0134] Among them, the design variables and are the mean values of the normally distributed random variables x 1 and x 2 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 accuracy 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 SORA method assisted by the Kriging model 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. It can be seen from the figure that accurate optimization results can be obtained by different Kriging model construction strategies. Although the new Kriging model establishment strategy greatly improves the efficiency, its stability will inevitably 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 the normal distribution. This example can be represented by a mathematical model as:

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

[0143]

[0144] where the design variable x1 and x 2 and x 3 and x 4 are the weld height and length, and the height and thickness of the beam respectively, and they respectively follow independent normal distributions. d represents the design variable, μ x1 and μ x2 and μ x3 and μ x4 represent the mean values of a design variable respectively; 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, and β t is the target reliability index; g k (x) represents the k-th constraint condition function; k represents the number of constraint conditions; τ(x) and σ(x) are the 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 RBDO

[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 have no obvious constraint effects, they are not shown. It can be seen from Figure 6 that 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 the present specification, the various embodiments are described in a progressive manner. Each embodiment focuses on the differences from other embodiments. For the same or similar parts among the various embodiments, reference can be made to each other. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple. For the relevant parts, reference can be made to the description in the method section.

[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 obvious to those skilled in the art. 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 will be accorded 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 of the welded beam engineering in the reliability design optimization problem, 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 enhanced sparrow search algorithm to optimize the initial Kriging model and obtain the current optimal solution; S4, calculating the current minimum performance target point, and solving the offset vector according to the current optimal solution and the minimum performance target point; S5, judging whether the global sampling condition is met according to the weighing factor, if so, executing S6, otherwise, executing 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 yes, 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 the 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 S6 is executed; if the trade-off factor γ≠0, then S7 is executed; the calculation formula of the trade-off factor is: γ=mod(aa,k+1) Among them, 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 is 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 add 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, from the local candidate sample set {X MCS }Select the update point And add 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 failure 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 represents the maximum stop index set under the global convergence condition; Dt represents the specific search range; k represents the number of constraints.

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( xk )||-||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 previous iteration.

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