Engineering structure reliability analysis method based on kriging surrogate model

Abstract

The application discloses an engineering structure reliability analysis method based on a Kriging surrogate model, comprising the following steps: sampling from random variables and probability distributions of an object to be analyzed to obtain a candidate sample set and an initial sample set; obtaining an initial experimental design set based on the initial sample set and corresponding real response values, and constructing an initial Kriging surrogate model about the object to be analyzed; obtaining an optimal sample from the candidate sample set through a random weight learning function, and expanding the optimal sample and the corresponding real response values to the initial experimental design set; deleting the optimal sample in the current round and sample data within a preset redundancy distance range of the optimal sample from the candidate sample set before the initial experimental design set enters the next round of data expansion; updating and iterating the initial Kriging surrogate model about the object to be analyzed through the experimental design set; and calculating a reliability index of the object to be analyzed according to a failure probability calculated by the current Kriging surrogate model.

Description

Technical Field

[0001] This invention relates to the field of reliability analysis technology, and specifically to a reliability analysis method for engineering structures based on the Kriging surrogate model. Background Technology

[0002] Structures face various uncertainties during design, manufacturing, and use, including material properties, geometric dimensions, and external loads. These uncertainties can significantly impact structural performance, leading to performance fluctuations or even failure. Random variables can reasonably quantify and model these uncertainties, and reliability analysis can be used to assess the structural performance status.

[0003] For reliability problems involving high-dimensional random variables, implicitly nonlinear limit state functions, and extremely low failure probabilities, traditional methods often face numerous challenges, such as difficult analysis and low computational efficiency. Reliability analysis methods based on surrogate models can effectively address these difficulties. A surrogate model is an approximate mathematical model, also known as a response surface model, approximate model, or meta-model, typically used to replace time-consuming numerical analyses (such as finite element analysis). Currently, various surrogate model methods have been developed, including polynomial response surfaces, Kriging surrogate models, radial basis functions, neural networks, support vector machines, and polynomial chaotic expansions. Among these, the Kriging model, as an interpolation method, can simultaneously provide predicted values ​​and predicted variances of the response, possessing both global and local statistical advantages. Therefore, reliability analysis methods based on Kriging surrogate models have received considerable attention in recent years. To further improve computational efficiency, active learning methods are used to select samples and update the Kriging surrogate model. An initial model is first constructed using a small number of initial samples, and then an expansion sample is selected using a learning function to update the model, thereby achieving a high-accuracy model with fewer samples. Existing learning functions mainly include U, EFF, CCL, REIF, and H. However, for complex and challenging real-world engineering structural problems, reliability analysis methods based on these learning functions may face challenges such as insufficient model accuracy or high computational costs.

[0004] Therefore, how to propose new active learning methods to achieve a more accurate and efficient agent model construction method has become an urgent problem to be solved. Summary of the Invention

[0005] In view of this, embodiments of the present invention provide a reliability analysis method for engineering structures based on the Kriging surrogate model, in order to solve the problems of insufficient accuracy and efficiency in reliability analysis of existing reliability analysis methods based on the Kriging surrogate model, which employ active learning methods.

[0006] This invention provides a method for reliability analysis of engineering structures based on a Kriging surrogate model, comprising:

[0007] Step S10: Sample from the random variables and probability distribution of the object to be analyzed to obtain the candidate sample set and the initial sample set respectively; the object to be analyzed is a civil or mechanical engineering structure.

[0008] Step S20: Obtain the initial experimental design set based on the initial sample set and its corresponding true response values, and construct the initial Kriging surrogate model for the object to be analyzed.

[0009] Step S30: Obtain the best sample from the candidate sample set through a random weight learning function, and expand the best sample and the corresponding true response value to the initial experimental design set.

[0010] Step S40: Before the initial experimental design set enters the next round of data augmentation, the best sample in the current round and the sample data within the preset redundancy distance range of the best sample are deleted from the candidate sample set.

[0011] Repeat steps S30 and S40 until the expanded data reaches the preset quantity to obtain the experimental design set;

[0012] Step S50: Update and iterate the initial Kriging proxy model for the object to be analyzed using the experimental design set;

[0013] If the difference in failure probability output by the Kriging surrogate model between two consecutive updates is within a preset error range, the iteration is terminated.

[0014] Step S60: Calculate the reliability index of the object to be analyzed based on the failure probability calculated by the current Kriging surrogate model.

[0015] Optionally, it also includes:

[0016] If the difference in failure probability output between two consecutive Kriging surrogate model updates exceeds a preset range, the latest experimental design set will be used as the new initial experimental design set, and a new Kriging surrogate model will be constructed and updated using the latest candidate sample set.

[0017] Optionally, step S10 involves sampling from the random variables and probability distributions of the object to be analyzed to obtain a candidate sample set and an initial sample set, including: generating N random samples z:{z1, z2, ..., z...} using Monte Carlo random sampling. N}, as the candidate sample set; n initial samples x:{x1, x2, ..., xn} are generated using Latin hypercube sampling. n}, which serves as the initial sample set; where the sample size of the candidate sample set is much larger than that of the initial sample set.

[0018] Optionally, step S30 involves obtaining the optimal sample from the candidate sample set using a random weight learning function, and expanding the optimal sample and its corresponding true response value into the initial experimental design set, including:

[0019] Normalize the mean of the predicted values ​​for each sample in the candidate sample set:

[0020]

[0021] in,

[0022]

[0023] Normalize the standard deviation of the predicted value for each sample in the candidate sample set:

[0024]

[0025] in,

[0026]

[0027] A random weight learning function W is constructed based on the normalized mean and standard deviation of the predicted values:

[0028]

[0029] Obtaining the best sample:

[0030]

[0031] Where k = 1, 2, ..., N; Represents sample z k The mean of the predicted values, Represents sample z k The standard deviation of the predicted value; the range of the random weight w is [w min w max ].

[0032] Optionally, step S40 involves deleting the best sample in the current round and sample data within the preset redundancy distance range of the best sample from the candidate sample set before the initial experimental design set enters the next round of data augmentation, including:

[0033] Calculate the Euclidean distance d between the other sample data and the best sample. <z*,z k >;

[0034] If d is satisfied <z*,z k ><d min If so, then delete the corresponding sample data;

[0035] Among them, the preset redundancy distance

[0036] X l ∈X, X=[X1, X2, ..., X s ] T Let σ(X) be a random variable representing the object to be analyzed. l ) represents the l-th dimension random variable X l The standard deviation.

[0037] Optionally, the Kriging surrogate model calculates the failure probability by including:

[0038]

[0039] in, This represents the failure probability of the Kriging agent model output during the i-th update. This indicates that the predicted response value of the k-th candidate sample is obtained using the current Kriging surrogate model.

[0040] Optionally, the preset error range is [-2×10]. -5 2×10 -5 ].

[0041] Optionally, the lower bound w of the random weights w min The value range is 0.8 to 0.9; the upper limit is w. max The value is 1.

[0042] The beneficial effects of this invention are:

[0043] 1. This embodiment provides a reliability analysis method for engineering structures based on the Kriging surrogate model. By constructing a random weight learning function, the best sample is selected from the candidate samples to expand the data of the initial experimental design set. At the same time, redundant distance is introduced to prevent the expanded samples from being too dense, avoid the waste of computing resources caused by redundant samples, and improve computing efficiency.

[0044] 2. The Kriging surrogate model based on a stochastic weighted learning function provided in this embodiment performs reliability analysis on engineering structures. The optimal samples are selected using the stochastic weighted learning function, taking into account samples near the limiting state and samples with high uncertainty. These selected samples expand the experimental design set and update the Kriging surrogate model, improving model accuracy until the accuracy requirements are met. The samples determined by this function are more diverse, which can accelerate iterative convergence.

[0045] 3. This embodiment adopts a single-sample augmentation strategy, which can effectively avoid the tediousness of single-sample augmentation, reduce the number of iterations for rebuilding the Kriging model, thereby saving computation time and further improving computational efficiency. Attached Figure Description

[0046] The features and advantages of the invention will be more clearly understood by referring to the accompanying drawings, which are schematic and should not be construed as limiting the invention in any way. In the drawings:

[0047] Figure 1 A flowchart of an engineering structure reliability analysis method based on the Kriging surrogate model is shown in an embodiment of the present invention.

[0048] Figure 2 A flowchart of another engineering structure reliability analysis method based on the Kriging surrogate model is shown in an embodiment of the present invention;

[0049] Figure 3 Example 1 illustrates a learning function based on U (N) p A schematic diagram of the sample expansion process for the Kriging agent model with =1);

[0050] Figure 4 Example 1 illustrates a learning function based on W (N) p A schematic diagram of the sample expansion process for the Kriging agent model with =1);

[0051] Figure 5 Example 1 illustrates a learning function based on W (N) p A schematic diagram of the sample expansion process for the Kriging agent model (=3);

[0052] Figure 6 Example 1 illustrates a learning function based on W (N) p A schematic diagram of the sample expansion process for the Kriging agent model (=5);

[0053] Figure 7 Example 1 illustrates a learning function based on W (N) p A schematic diagram of the sample expansion process for the Kriging agent model (=7);

[0054] Figure 8 Example 1 illustrates a learning function based on W (N) p A schematic diagram of the sample expansion process for the Kriging agent model (=9);

[0055] Figure 9 Example 1 illustrates a learning function based on W (N) p The failure probability convergence curve of the Kriging agent model with =1);

[0056] Figure 10 Example 1 illustrates a learning function based on W (N) p The failure probability convergence curve of the Kriging agent model (=3) is shown.

[0057] Figure 11 Example 1 illustrates a learning function based on W (N) p The failure probability convergence curve of the Kriging agent model with 5) is shown.

[0058] Figure 12 Example 1 illustrates a learning function based on W (N) p The failure probability convergence curve of the Kriging agent model with 7) is shown.

[0059] Figure 13 Example 1 illustrates a learning function based on W (N) p The failure probability convergence curve of the Kriging agent model with =9) is shown.

[0060] Figure 14 A schematic diagram of a nonlinear oscillator in Example 2 is shown;

[0061] Figure 15 Example 2 illustrates a learning function based on the W learning function (N). p The failure probability convergence curve of the Kriging agent model with =1);

[0062] Figure 16 Example 2 illustrates a learning function based on the W learning function (N). p The failure probability convergence curve of the Kriging agent model (=2) is shown.

[0063] Figure 17 Example 2 illustrates a learning function based on the W learning function (N). p The failure probability convergence curve of the Kriging agent model with 4) is shown.

[0064] Figure 18 Example 2 illustrates a learning function based on the W learning function (N). p The failure probability convergence curve of the Kriging agent model with 6) is shown.

[0065] Figure 19 Example 2 illustrates a learning function based on the W learning function (N). p The failure probability convergence curve of the Kriging agent model (=8). Detailed Implementation

[0066] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0067] like Figure 1 As shown, this embodiment of the invention provides a method for reliability analysis of engineering structures based on a Kriging surrogate model, including:

[0068] Step S10: Sample from the random variables and probability distribution of the object to be analyzed to obtain the candidate sample set and the initial sample set respectively; the object to be analyzed is a civil or mechanical engineering structure.

[0069] In this embodiment, based on the random variable X = [X1, X2, ..., X...] of the object to be analyzed... s ] T The probability distribution is determined by generating N random samples z:{z1, z2, ..., z...} using the Monte Carlo random sampling method. N As a candidate sample set, n initial samples x:{x1, x2, ..., xn} are generated using Latin hypercube sampling. n}, as the initial sample set.

[0070] In a specific embodiment, N is 10. 5 n is 12.

[0071] Step S20: Obtain the initial experimental design set based on the initial sample set and its corresponding true response values, and construct the initial Kriging surrogate model for the object to be analyzed.

[0072] In this embodiment, the initial sample x: {x1, x2, ..., x} is calculated. n The corresponding true response values ​​G(x) are: {G(x1), G(x2), ..., G(x...} n Let the initial experimental design set D be {x, G(x)}, and the number of function calls in the current step be N. call =n, and the number of iterations in the current step is i=0.

[0073] Step S30: Obtain the best sample from the candidate sample set through a random weight learning function, and expand the best sample and the corresponding true response value to the initial experimental design set.

[0074] In this embodiment, the candidate samples z:{z1, z2, ..., z...} are obtained using the Kriging surrogate model. N The predicted response value corresponding to}, sample z k The predicted values ​​at (k = 1, 2, ..., N) follow a normal distribution:

[0075]

[0076] In the formula, Represents sample z k The mean of the predicted values, Represents sample z kThe standard deviation of the predicted values. This reflects the sample z k The degree of closeness to the limiting state G=0, This reflects the sample z k The degree of uncertainty at the location. The smaller (i.e.) The closer the z value is to 0, the better the sample z is. k The closer to G=0; The larger the value of sample z, the greater its value. k The greater the uncertainty, the better.

[0077] Normalize the mean of the predicted values ​​for each sample in the candidate sample set:

[0078]

[0079] in,

[0080]

[0081] Normalize the standard deviation of the predicted value for each sample in the candidate sample set:

[0082]

[0083] in,

[0084]

[0085] A random weight learning function W is constructed based on the normalized mean and standard deviation of the predicted values:

[0086]

[0087] Obtaining the best sample:

[0088]

[0089] Where k = 1, 2, ..., N; the range of the random weight w is [w min w max ]. W(z) k This comprehensively reflects the sample z k The degree of closeness to the limiting state G=0 and the sample z k The degree of uncertainty at the location.

[0090] In a specific implementation, the lower bound w of the random weight w is... min The value range is 0.8 to 0.9; the upper limit is w. maxThe value is 1. In a specific embodiment, the random weight w ranges from [0.9, 1]. The random weight learning function W uses large weights to favor samples near the limit state G=0, while using small weights to take into account samples with high uncertainty.

[0091] Step S40: Before the initial experimental design set enters the next round of data expansion, the best sample in the current round and the sample data within the preset redundancy distance range of the best sample are deleted from the candidate sample set.

[0092] In this embodiment, the Euclidean distance d between the sample data near the best sample and the best sample is calculated. <z*,z k >:

[0093] If d is satisfied <z*,z k ><d min If so, then delete the corresponding sample data;

[0094] Among them, the preset redundancy distance

[0095] X l ∈X, X=[X1, X2, ..., X s ] T Let σ(X) be a random variable representing the object to be analyzed. l ) represents the l-th dimension random variable X l The standard deviation.

[0096] Repeat steps S30 and S40 until the expanded data reaches the preset quantity, thus obtaining the experimental design set.

[0097] In this embodiment, if the initial experimental design set data expansion is used for the previous iteration number j less than the preset iteration number N, p If the iteration continues, the expansion will continue; otherwise, the iteration will stop.

[0098] Step S50: Update and iterate the initial Kriging proxy model for the object to be analyzed using the experimental design set;

[0099] If the difference in failure probability output by the Kriging surrogate model between two consecutive updates is within a preset error range, the iteration is terminated.

[0100] Step S60: Calculate the reliability index of the object to be analyzed based on the failure probability calculated by the current Kriging surrogate model.

[0101] In this embodiment, the Kriging surrogate model calculates the failure probability as follows:

[0102]

[0103] in, This represents the failure probability of the Kriging agent model output during the i-th update. This indicates that the predicted response value of the k-th candidate sample is obtained using the current Kriging surrogate model.

[0104] In a specific embodiment, if the difference in failure probability output by the Kriging proxy model in two adjacent iterations is... If the condition is met, the iteration terminates, and the failure probability calculated by the current Kriging surrogate model is output. In a specific embodiment, ε is taken as 2 × 10⁻⁶. -5 .

[0105] like Figure 2 As shown, the reliability analysis method for the Kriging surrogate model based on a random weighted learning function provided in this embodiment is explained as follows: First, an initial Kriging surrogate model is constructed using an initial experimental design set D, and the failure probability of the initial Kriging model is calculated. Then, the optimal sample expansion iteration process begins. After the iteration terminates, the Kriging surrogate model is updated using the expanded experimental design set D, and the updated failure probability is calculated. The difference in failure probabilities between the two Kriging surrogate models before and after the update is calculated. If the difference is within an acceptable range, the iterative update stops; otherwise, the current experimental design set D is used as the new initial design set, and the Kriging model is reconstructed.

[0106] This embodiment provides a reliability analysis method for engineering structures based on the Kriging surrogate model. By constructing a random weight learning function, the best sample is selected from the candidate samples to augment the initial experimental design set. At the same time, redundant distance is introduced to prevent the augmented samples from being too dense, avoid the waste of computational resources caused by redundant samples, and improve computational efficiency.

[0107] This embodiment provides a Kriging surrogate model based on a stochastic weighted learning function for reliability analysis of engineering structures. The optimal samples are selected using the stochastic weighted learning function, taking into account samples near the limiting state and samples with high uncertainty. These selected samples expand the experimental design set and update the Kriging surrogate model, improving model accuracy until the accuracy requirements are met. The samples determined by this function are more diverse, which accelerates iterative convergence.

[0108] This embodiment adopts a single-sample augmentation strategy, which can effectively avoid the tediousness of single-sample augmentation, reduce the number of iterations for rebuilding the Kriging model, thereby saving computation time and further improving computational efficiency.

[0109] Example 1: Four-branch series system.

[0110] The limit state function of a four-branch series system is defined as follows:

[0111]

[0112] Where X = [X1, X2] is a normally distributed random variable, and the specific probability distribution is shown in Table 1.

[0113] Table 1 Probability distribution of random variables in the cascade system

[0114] random variable Distribution type mean Standard deviation <![CDATA[X1]]> normal 0 1 <![CDATA[X2]]> normal 0 1 ;

[0115] Monte Carlo simulation is often used as a benchmark method due to its high accuracy and robustness. The Kriging surrogate model method based on the U learning function is a typical example of an efficient reliability analysis method. Therefore, the two existing methods mentioned above, as well as the Kriging surrogate model method based on the W learning function presented in this invention, are all used to solve this series system problem. The results of different methods are compared as follows: Figures 3 to 13 And as shown in Table 2.

[0116] Table 2 Failure probability results for different methods

[0117]

[0118] As shown in Table 2, the Monte Carlo simulation method is used as the benchmark method, and the calculated failure probability P f =2.17×10 -3 Considered an accurate reference value, the computational accuracy of other reliability methods can be evaluated by the error between this reference value and the actual value. The computational efficiency of each method can be measured by the number of iterations *i* and the total number of function calls *N*. call The performance was evaluated in conjunction with execution time. All analytical calculations were performed on the same computer, which was configured with an Intel(R) Core(TM) i7-10750H processor (2.60GHz) and 16.0GB of memory.

[0119] exist Figures 3 to 8 In the diagram, black triangles represent the initial samples, while blue circles and red squares represent the augmented samples of the Kriging surrogate model method based on the U learning function and the proposed method, respectively. The solid black line represents the true limit state G(X) = 0, and the dashed blue and red lines represent the predicted limit states of the Kriging surrogate model method based on the U learning function and the proposed method, respectively.

[0120] from Figures 3 to 8 It can be seen that the augmented samples of the Kriging surrogate model method based on the U learning function overlap, indicating that the augmented samples are too dense and contain a lot of redundant samples, resulting in wasted computational resources. In contrast, the method provided in this embodiment has a reasonable distribution of augmented samples, avoiding the waste of computational resources caused by redundant samples and improving computational efficiency.

[0121] from Figures 3 to 8 As can be seen from Table 2, the Monte Carlo simulation method first generates N=10 5 A random sample of group X is generated, and the corresponding true response value is calculated. Then, the proportion of failed samples to the total number of samples is counted, which is the failure probability. The total number of function calls for this method is N. call =N=10 5 The Kriging surrogate model method based on the U learning function is an efficient existing approach. It first generates n = 12 initial samples X to construct the initial Kriging surrogate model. Then, the U learning function is used to select augmented samples to update the model, with N samples augmented in a single iteration. p =1, the number of iterations for rebuilding the Kriging proxy model is i=46. The total number of function calls for this method is N. call =n+N p ×i=12+1×46=58. Although the failure probability result P obtained by this method f =2.17×10 -3 It is very accurate, but the execution time is long because the number of iterations and function calls in the proxy model reconstruction is large.

[0122] Unlike the two methods mentioned above, the method proposed in this embodiment constructs a W-weighted learning function, introduces redundant distance, and combines it with a single-instance multi-sample augmentation strategy. Table 2 shows the number of samples N augmented in a single iteration. p The calculation results are shown for cases N = 1, 3, 5, 7, and 9. The results show that as the number of samples N expanded in a single iteration increases... p As the value increases, the number of iterations i decreases, and the total number of function calls N increases. call Increase, failure probability P f Increased computational accuracy leads to increased execution time. When N p When the value is 1, the method first generates n = 12 initial samples of X to construct the initial Kriging surrogate model. Then, the W learning function is used to select augmented samples to update the model, with N being the number of augmented samples per iteration. p =1, the number of iterations for rebuilding the Kriging proxy model is i=13. The total number of function calls in this case is N. call =n+N p ×i = 12 + 1 × 13 = 25. This is because the number of iterations for surrogate model reconstruction is i = 13 and the number of function calls is N. call =25 are both very small, therefore the execution time is very short, about one-tenth of the Kriging surrogate model method based on the U learning function. When N p When the value is 9, although the number of iterations for surrogate model reconstruction (i=6) is small, the number of function calls (N) is large. call=66, which is not significantly different from the Kriging surrogate model method based on the U learning function. Even so, the execution time is only about one-third of the latter. It can be seen that, for all cases, the Kriging surrogate model method based on the W learning function proposed in this embodiment is superior to the Kriging surrogate model method based on the U learning function in terms of computational efficiency. The error of this method is less than 3% in all cases, which is sufficient to prove that the proposed method also performs well in terms of computational accuracy. In summary, the method proposed in this invention can perform reliability analysis accurately and efficiently.

[0123] Example 2: Nonlinear oscillator.

[0124] Figure 14 For a nonlinear undamped single-degree-of-freedom system involving six random variables, its limit state function is expressed as follows:

[0125]

[0126] Where X = [r, F1, m, c1, c2, t1] is a normally distributed random variable, and the relevant probability distribution is shown in Table 3.

[0127] Table 3 Probability distribution of random variables for nonlinear oscillators

[0128] random variable Distribution type mean Standard deviation r normal 0.5 0.05 <![CDATA[F1]]> normal 1 0.2 m normal 1 0.05 <![CDATA[c1]]> normal 1 0.1 <![CDATA[c2]]> normal 0.1 0.01 <![CDATA[t1]]> normal 1 0.2 ;

[0129] Reliability was evaluated using Monte Carlo simulation, a Kriging surrogate model based on a U-learning function, and the Kriging surrogate model based on a W-learning function as presented in this invention. The results of these methods are as follows: Figures 15 to 19 And as shown in Table 4.

[0130] from Figures 15 to 19 As shown in Table 4, in the Monte Carlo simulation method, it is necessary to generate N=10 5 The function takes a random sample from group X and calculates the response value. The total number of function calls is N. call =N=10 5 Failure probability P f =0.02834 was used as a benchmark for results obtained by other methods. Based on the probability distribution of X, the Kriging surrogate model method based on the U learning function first constructs an initial Kriging surrogate model using n=12 initial samples. Subsequently, the U learning function is used to select augmented samples to update the model, with N being the number of augmented samples per iteration. p =1, the number of iterations for rebuilding the Kriging proxy model is i=317. The total number of function calls for this method is N. call =n+N p×i=12+1×317=329. Although the failure probability result P obtained by this method f =0.02834 is very accurate, but the execution time is long because the number of iterations and function calls in the proxy model reconstruction is large.

[0131] Table 4 Failure probability results for different methods

[0132]

[0133] In this embodiment, the number of sample augmentations N in a single iteration is given. p The calculation results are shown for cases N = 1, 2, 4, 6, and 8. It can be seen that as the number of samples expanded in a single iteration N increases... p As the value increases, the number of iterations i decreases, and the total number of function calls N increases. call Increase, failure probability P f Increased computational accuracy leads to increased execution time. When N p When the value is 8, the method first generates n=12 initial samples of X to construct the initial Kriging surrogate model. Then, the W learning function is used to select augmented samples to update the model, with N being the number of augmented samples per iteration. p =8, the number of iterations for rebuilding the Kriging proxy model is i=19. In this embodiment, the total number of function calls in this case is N. call =n+N p ×i=12+8×19=164. Compared with the Kriging surrogate model method based on the U learning function, the proposed method has a lower failure probability P in all cases. f The errors are all less than 5%, the number of iterations i, and the total number of function calls N. call Both the computational accuracy and execution time are smaller, indicating that the proposed method exhibits superior performance in terms of both computational accuracy and computational efficiency.

[0134] Although embodiments of the invention have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the invention, and such modifications and variations all fall within the scope defined by the appended claims.

Claims

1. A reliability analysis method for engineering structures based on a Kriging surrogate model, characterized in that, include: Step S10: Sample from the random variables and probability distribution of the object to be analyzed to obtain the candidate sample set and the initial sample set, respectively; The object to be analyzed is a civil or mechanical engineering structure; Step S20: Based on the initial sample set and its corresponding real response values, obtain the initial experimental design set and construct the initial Kriging proxy model for the object to be analyzed. Step S30: Obtain the best sample from the candidate sample set through a random weight learning function, and expand the best sample and the corresponding real response value to the initial experimental design set; Step S40: Before the initial experimental design set enters the next round of data expansion, the best sample in the current round and the sample data within the preset redundancy distance range of the best sample are deleted from the candidate sample set. Repeat steps S30 and S40 until the expanded data reaches the preset quantity to obtain the experimental design set; Step S50: Update and iterate the initial Kriging proxy model for the object to be analyzed using the experimental design set; If the difference in failure probability output by the Kriging surrogate model between two consecutive updates is within a preset error range, the iteration is terminated. Step S60: Calculate the reliability index of the object to be analyzed based on the failure probability calculated by the Kriging surrogate model.

2. The engineering structure reliability analysis method based on the Kriging surrogate model according to claim 1, characterized in that, Also includes: If the difference in failure probability output by the Kriging surrogate model between two consecutive updates exceeds the preset error range, then the latest experimental design set is used as the new initial experimental design set, and a new Kriging surrogate model is obtained by reconstructing and updating it with the latest candidate sample set.

3. The engineering structure reliability analysis method based on the Kriging surrogate model according to claim 1, characterized in that, Step S10: Sample from the random variables and probability distributions of the object to be analyzed to obtain the candidate sample set and the initial sample set, including: generating N random samples z:{z1, z2, ..., z...} using Monte Carlo random sampling. N }, as the candidate sample set; n initial samples x:{x1, x2, ..., xn} are generated using Latin hypercube sampling. n }, which serves as the initial sample set; wherein the sample size of the candidate sample set is much larger than the sample size of the initial sample set.

4. The engineering structure reliability analysis method based on the Kriging surrogate model according to claim 3, characterized in that, Step S30 involves obtaining the optimal sample from the candidate sample set using a random weight learning function, and expanding the optimal sample and its corresponding true response value into the initial experimental design set, including: The mean of the predicted values ​​for each sample in the candidate sample set is normalized: in, The standard deviation of the predicted value for each sample in the candidate sample set is normalized: in, A random weight learning function W is constructed based on the normalized mean and standard deviation of the predicted values: Obtain the optimal sample: Where k = 1, 2, ..., N; Represents sample z k The mean of the predicted values, Represents sample z k The standard deviation of the predicted value; the range of the random weight w is [w min w max ].

5. The engineering structure reliability analysis method based on the Kriging surrogate model according to claim 4, characterized in that, Step S40, before the initial experimental design set enters the next round of data augmentation, deletes the best sample in the current round and the sample data within the preset redundancy distance range of the best sample from the candidate sample set, including: Calculate the Euclidean distance d between the other sample data and the best sample. <z * , z k >; If d is satisfied <z * ,z k >d min If so, then delete the corresponding sample data; Wherein, the preset redundancy distance X l ∈X, X=[X1,X2,…,X s ] T Let σ(X) be the random variable of the object to be analyzed. l ) represents the l-th dimension random variable X l The standard deviation.

6. The engineering structure reliability analysis method based on the Kriging surrogate model according to claim 1, characterized in that, The Kriging surrogate model calculates the failure probability as follows: in, This represents the failure probability of the Kriging agent model output during the i-th update. This indicates that the predicted response value of the k-th candidate sample is obtained using the Kriging proxy model described above.

7. The engineering structure reliability analysis method based on the Kriging surrogate model according to claim 1, characterized in that, The preset error range is [-2×10]. -5 2×10 -5 ].

8. The engineering structure reliability analysis method based on the Kriging surrogate model according to claim 4, characterized in that, The lower bound w of the random weight w min The value range is 0.8 to 0.9; the upper limit is w. max The value is 1.

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