Efficient Adaptive Method Based on Kriging Model

Abstract

The present invention relates to an efficient adaptive method based on the Kriging model. This method is mainly implemented through three steps: First, a certain number of samples are generated by the Latin hypercube method to construct an initial Kriging model; Second, a certain number of candidate samples are screened from the candidate samples through the current Kriging model, and two samples are determined; Third, the candidate samples and the experimental design samples are updated and the Kriging model is reconstructed, and it is judged whether the requirements are met. If not, jump to the second step. If met, the current Kriging model is used to replace the original model for reliability analysis. The present invention continuously increases the number of sample points near the limit state through adaptive iteration, and determines the added samples by maximizing the minimum distance, so that the iteratively updated samples are approximately evenly distributed near the limit state, the sample points are more fully utilized, and the result of the reliability analysis is more accurate.

Description

[0001] This application is a divisional application of the application with the application number 201810109316.2, the application date of February 5, 2018, and the invention name "An Efficient Adaptive Method for Reliability Analysis of Aircraft Cabin Door Lock Mechanisms". Technical Field

[0002] The present invention belongs to the field of reliability analysis and design, and particularly relates to an efficient adaptive method based on the Kriging model. Background Art

[0003] In engineering, mechanical problems often involve more and more complex calculations, and the evaluation of the failure probability may require very time-consuming calculations. How to minimize the number of calculations of the numerical model of the mechanical structure or mechanism while ensuring a certain result accuracy has become an important problem to be solved urgently. At present, the common method to solve this problem is to use a surrogate model to replace the original engineering model with a large amount of calculation to evaluate the failure probability of the model. The common reliability evaluation methods based on surrogate models include the response surface method, the neural network method, the support vector machine method, and the Kriging method, etc. Since the Kriging model not only has both local and global statistical characteristics, but also generally requires a small number of samples for constructing the model, the application of the Kriging model in the field of reliability analysis and design is becoming more and more extensive.

[0004] From the emergence of the mathematical idea of Kriging in the early 20th century, to the French geoscientist D.G. Krige applying this idea to practical work in the 1950s, and then to the application of Kriging technology in many fields, as a semi-parametric interpolation technology, Kriging technology has been well developed and optimized in the past few decades. Kriging technology is to simulate the unknown information at a certain point through some known information. Its basic principle is that Kriging needs to rely on the information of the known points around this point when making a prediction at a certain point, that is, to estimate the unknown information at this point through the linear combination of the information weighted within a certain range around this point.

[0005] Applying the Kriging model to evaluate reliability problems has the characteristics of simple calculation and strong versatility, and is suitable for calculating complex high-dimensional reliability analysis and reliability optimization problems. However, when applying the Kriging model to reliability analysis, generally, the measures adopted are to first use the experimental design method to construct a series of representative sample points, and then construct the Kriging model to replace the original implicit and complex analysis model for reliability analysis. However, the Kriging model constructed by this method has the following two defects: 1) The determination of the point-taking method or the number of points in the experimental design may be unreasonable, resulting in insufficient accuracy and precision of the constructed Kriging model; 2) Since the position of the limit state of the analyzed model in the design space cannot be determined, the point-taking position in the experimental design generally has globality. The constructed Kriging model can meet the global fitting accuracy, but cannot meet the fitting accuracy near the limit state of the structure, resulting in a large deviation in the reliability analysis results. Therefore, in engineering reliability analysis and its optimization, a reliability analysis method that is insensitive to the point-taking method or the number of points in the experimental design, can improve the local fitting accuracy near the limit state, and is easy to apply is needed. Summary of the Invention

[0006] Aiming at reliability analysis and optimization problems, especially for the reliability analysis and design links in the R & D process, the present invention provides a set of feasible and effective reliability analysis methods. The purpose of this method is to overcome the phenomenon that the sample points selected in the experimental design of the existing reliability analysis method based on the Kriging model are unreasonable, resulting in poor accuracy of the Kriging model near the limit state, and to improve the distribution quantity and uniformity of the experimental sample points near the limit state to obtain more accurate reliability analysis results.

[0007] In summary, the present invention proposes a high-efficiency adaptive reliability analysis method based on the Kriging model, which is mainly realized through three steps: The first step is to generate a certain number of samples by the Latin hypercube method to construct an initial Kriging model; the second step is to screen out a certain number of candidate samples from the candidate samples through the current Kriging model, and then determine two samples by the maximum minimum distance criterion; the third step is to update the candidate samples and the experimental design samples, and reconstruct the Kriging model, and judge whether the requirements are met. If not, jump to the second step. If so, use the current Kriging model to replace the original model for reliability analysis.

[0008] Specifically, the invention of the present invention includes the following detailed steps:

[0009] 1) Determine the design variables and the limit state function: Determine the design variables x = (x1, x2,..., x n) Functional characteristic quantity H and failure criterion I are used to establish the limit state function G(x), where n represents the number of design variables.

[0010] 2) Determine the design space: According to the distribution type of the design variables and the design requirements, determine the upper and lower limits L i and U i (i = 1, 2,..., n), that is, determine the design space. Generally, for the upper and lower limits of normal design variables, they can be determined according to the "3σ principle", that is, L i = μ i - 3σ i and U i = μ i + 3σ i , where μ i is the mean value of the variable, and σ i is the standard deviation of the variable.

[0011] 3) Generate the candidate sample set and the test sample set: In the design space, use uniform sampling to generate the candidate sample set X C containing T uniform samples and the test sample set X T . It is recommended that the sample quantity T be taken as where the symbol "[·]" is the ceiling operator.

[0012] 4) Create the initial DOE and construct the Kriging model: Apply the Latin hypercube method to generate N0 samples to form the experimental design sample set X D , where N0 = 3n. Call the limit state function G(x) to calculate the function values of these N0 samples, and form the sample point set {(x, G(x))|x ∈ X D}, that is, the initial DOE. Initialize the number of times of constructing the model z = 1, and use the sample point set to construct the Kriging model

[0013] 5) Construct the validation sample set and calculate the classification index of the samples in it: Select the first T0 samples closest to the current Kriging model T limit state from the test sample set X to form the validation sample set X V , that is, the first T0 samples closest to 0, where T0 = [T / 100]. Classify the samples in the validation sample set X V into two categories of "+1" and "-1" according to the positive and negative conditions of their function values, and assign values to the classification index according to formula (1).

[0014]

[0015] 6) Screen the first candidate sample set and determine the first sample: Use the current Kriging model Analyze the current candidate sample set X C , select the first T0 samples closest to the limit state as the first candidate sample set X FC Calculate X using formulas (2) to (4) FC The sample in the middle and the current experimental design sample set X D The maximum and minimum distance L of samples in 1max-min , and then use formula (5) to determine X FC is equal to the "maximum minimum distance" L 1max-min In the method proposed in this paper, the first non-zero k1(i) value corresponding to X is selected. FC The sample in is the first sample x1 added to the current X D middle.

[0016]

[0017]

[0018]

[0019]

[0020] 7) Construct the second candidate sample set and determine the second sample: FC Select all samples with different function values from sample x1 to construct the second candidate sample set X SC ,Right now Calculate X using formulas (6) to (8) SC The sample in the middle and the current experimental design sample set X D The maximum and minimum distance L of samples in 2max-min , and then use formula (9) to determine X SC is equal to the "maximum minimum distance" L 2max-min In the method proposed in this paper, the first non-zero k2(i) value corresponding to X is selected. SC The sample in is the second sample x2 added to the current X D middle.

[0021]

[0022]

[0023]

[0024]

[0025] 8) Update the DOE and remove the corresponding samples: Call the limit state function G(x) to calculate the function values of samples x1 and x2, and then update the sample point set {(x, G(x)) | x ∈ X D}, that is, update the DOE. Subsequently, delete the samples corresponding to x1 and x2 from the candidate sample set X C .

[0026] 9) Reconstruct the Kriging model and calculate the number of misclassifications: Let the number of times of constructing the model z = z + 1, then reconstruct the Kriging model with the current DOE sample point set, and use the reconstructed Kriging model to calculate the function values of the samples in the verification sample set X V . Classify them into two categories of "+1" and "-1" according to the positive and negative situations of the function values, and assign values to the classification index according to formula (1), and calculate the number of misclassifications through formula (10) That is, the number of misclassifications of the z-th Kriging model relative to the (z - 1)-th Kriging model for the verification sample set X V . The misclassification index is used to reflect the difference degree of the failure boundaries of these two models.

[0027]

[0028] 10) Judge the stability of the model output: Calculate the stability index of the z-th Kriging model through formula (11) It is used to characterize the number of misclassifications of the z-th Kriging model whether it meets the allowable value N mis0 , generally N mis0 = [T0 × 5%]. To reduce the influence of accidental events, the model convergence stability index is defined as the situation where the number of misclassifications of two consecutive models does not exceed the allowable value, and is obtained by calculating through formula (12). If it is considered that the constructed Kriging model has been stable, and the algorithm immediately proceeds to step 11), otherwise it returns to step 5).

[0029]

[0030]

[0031] 11) Generate the Monte Carlo sample set and evaluate the failure probability: Generate a Monte Carlo sample set X mcs consisting of N MCS samples through Monte Carlo random sampling. The number of samples N mcsThere is no specific requirement for the value, and 10,000 can be taken as the initial value. Then, calculate its function value using the Kriging model constructed last time, and evaluate the failure probability through formulas (13) and (14).

[0032]

[0033]

[0034] 12) Determine whether the estimated value of the failure probability is stable: Calculate the coefficient of variation cov of the failure probability through formula (15) to judge the number of Monte Carlo samples N mcs For whether the estimated failure probability is sufficient. If cov is less than its allowable value Δcov (generally taken as 5%), the calculated failure probability is the final result, and the algorithm ends; otherwise, let N mcs = 10×N mcs , and then go back to step 11).

[0035]

[0036] In the present invention, the initially selected sample points are fewer. By means of adaptive iteration, the number of sample points near the limit state is continuously increased, and the added samples are determined by maximizing the minimum distance, so that the iteratively updated samples are approximately evenly distributed near the limit state, making the sample points more fully utilized. In the case of the same number of experimental samples, the obtained Kriging model classification is more accurate, thus making the result of the reliability analysis more accurate; moreover, the method of the present invention is easy to be programmed, simple and easy to implement, and is applicable to the field of engineering reliability analysis and optimization design with huge computational workloads, such as the reliability optimization design of complex multi-body dynamics mechanical mechanisms, and the multi-disciplinary reliability analysis and optimization design of complex engineering systems such as aircraft, automobiles, and ships. Description of the Drawings

[0037] Att Figure 1 is the flow chart of the efficient adaptive method for mechanism reliability analysis described in the present invention Att Figure 2 is the schematic diagram of the composition of the locking mechanism

[0038] Att Figure 3 is the schematic diagram of the force on the locking mechanism

[0039] 1 - Lock body; 2 - Piston; 3 - Rocker arm; 4 - Piston connecting rod; 5 - Lock hook connecting rod; 6 - Lock hook Detailed Embodiment

[0040] The following will describe the embodiments in detail with reference to the accompanying drawings. Taking the reliability problem of the unlocking function of an aircraft cabin door lock mechanism as an example, a comparative study is carried out on the proposed adaptive method and the Kriging method based on the direct Latin hypercube experimental design. In the example, the reliability results calculated by using the same Monte Carlo samples for the constructed Kriging model and the original model are compared to verify the practicability and efficiency of the Kriging model constructed by the proposed method in reliability estimation.

[0041] An efficient adaptive reliability analysis method based on the Kriging model proposed by the present invention will be described below with reference to Figure 1 the following flow chart to illustrate the specific implementation steps of the proposed method:

[0042] 1) Determine the design variables and the limit state function: Determine the design variables x = (x1, x2, …, x n ) of the problem to be processed, the functional characteristic quantity H, and the failure criterion I, so as to establish the limit state function G(x), where n represents the number of design variables.

[0043] 2) Determine the design space: According to the distribution type of the design variables and the design requirements, determine the upper and lower limits L i and U i (i = 1, 2, …, n) of each design variable, that is, determine the design space. Generally, for the upper and lower limits of normal design variables, they can be determined according to the "3σ principle", that is, L i = μ i - 3σ i and U i = μ i + 3σ i , where μ i is the mean value of the variable, and σ i is the standard deviation of the variable.

[0044] 3) Generate the candidate sample set and the test sample set: In the design space, use uniform sampling to generate the candidate sample set X C containing T uniform samples and the test sample set X T respectively. The sample quantity T is recommended to be taken as where the symbol "[·]" is the ceiling operator.

[0045] 4) Create the initial DOE and construct the Kriging model: Apply the Latin hypercube method to generate N0 samples to form the experimental design sample set X D , where N0 = 3n, call the limit state function G(x) to calculate the function values of these N0 samples, and form the sample point set {(x, G(x))|x ∈ X D}, that is, the initial DOE. Initialize the number of times of constructing the model \(z = 1\), and use the sample point set to construct the Kriging model

[0046] 5) Construct a validation sample set and calculate the classification index of the samples in it: Select the first \(T_0\) samples closest to the current Kriging model T from the test sample set \(X\) to form the validation sample set \(X\) V , that is the first \(T_0\) samples closest to 0, where \(T_0=[T / 100]\). Classify the samples in the validation sample set \(X\) V into two categories of “+1” and “-1” according to the positive and negative conditions of their function values, and assign values to the classification index according to formula (1).

[0047]

[0048] 6) Screen the first candidate sample set and determine the first sample: Use the current Kriging model to analyze the current candidate sample set \(X\) C , and screen out the first \(T_0\) samples closest to the limit state as the first candidate sample set \(X\) FC . Calculate the maximum and minimum distances \(L\) FC between the samples in \(X\) D and the samples in the current experimental design sample set \(X\) 1max-min through formulas (2) - (4), and then use formula (5) to determine all the samples in \(X\) FC that are equal to the “maximum and minimum distance” \(L\) 1max-min . In the method proposed in this paper, select the sample in \(X\) FC corresponding to the first non-zero \(k_1(i)\) value as the first sample \(x_1\) and add it to the current \(X\) D .

[0049]

[0050] [[ID=5l]]

[0051]

[0052]

[0053] 7) Construct the second candidate sample set and determine the second sample: Select all the samples in the first candidate sample set \(X\) FC whose function value signs are different from that of the sample \(x_1\) to construct the second candidate sample set \(X\) SC , that is Calculate X through formulas (6) to (8). SC The maximum and minimum distance L between the samples in and the current experimental design sample set X D of the samples in 2max-min , and then use formula (9) to determine X SC in which are equal to the "maximum and minimum distance" L 2max-min of all samples. In the method proposed in this paper, select the sample in X corresponding to the first non-zero k2(i) value SC as the second sample x2 and add it to the current X D .

[0054]

[0055]

[0056]

[0057]

[0058] 8) Update DOE and remove the corresponding samples: Call the limit state function G(x) to calculate the function values of samples x1 and x2, and then update the sample point set {(x, G(x))|x ∈ X D}, that is, update DOE. Subsequently, delete the samples corresponding to x1 and x2 in the candidate sample set X C .

[0059] 9) Reconstruct the Kriging model and calculate the number of misclassifications: Let the number of times of constructing the model z = z + 1, then reconstruct the Kriging model with the current DOE sample point set, and use the reconstructed Kriging model to calculate the function values of the samples in the verification sample set X V Classify them into two categories of "+1" and "-1" according to the positive and negative conditions of the function values, and assign values to the classification index according to formula (1), and calculate the number of misclassifications through formula (10) That is, the number of misclassifications of the z-th Kriging model relative to the (z - 1)-th Kriging model for the verification sample set X . The misclassification index is used to reflect the difference degree of the failure boundaries of these two models. V

[0060]

[0061] 10) Judge the stability of the model output: Calculate the stability index of the z-th Kriging model through formula (11) It is used to characterize the number of misclassifications of the z-th Kriging model whether it meets the allowable value N mis0 , generally N​mis0 = [T0 × 5%]. To reduce the influence of accidental events, the model convergence stability index is defined as the situation where the number of model misclassifications in two consecutive times does not exceed the permitted value, and is obtained by calculating with formula (12). If it is considered that the constructed Kriging model has been stable, the algorithm immediately transfers to step 11), otherwise it returns to step 5).

[0062]

[0063]

[0064] 11) Generate Monte Carlo sample set and evaluate the failure probability: Generate a Monte Carlo sample set X mcs composed of N MCS samples through Monte Carlo random sampling. There is no specific requirement for the value of the sample number N mcs . 10000 can be taken as the initial value, and then use the Kriging model constructed last time to calculate its function value, and evaluate the failure probability through formula (13) and formula (14)

[0065]

[0066]

[0067] 12) Judge whether the estimated value of the failure probability is stable: Calculate the coefficient of variation cov of the failure probability through formula (15) to judge whether the Monte Carlo sample number N mcs is sufficient for the estimated failure probability. If cov is less than its permitted value Δcov (generally take 5%), the calculated failure probability is the final result and the algorithm ends; otherwise, let N mcs = 10 × N mcs , and then transfer to step 11).

[0068]

[0069] Note: In the proposed method, the parameter settings not specified are as follows: the starting number of misclassifications the starting stability index the starting model convergence stability index

[0070] such as Figure 2 and Figure 3The composition diagram and force diagram of the lock mechanism shown. The lock mechanism mainly includes six components, namely the lock body 1, the piston 2, the rocker arm 3, the piston connecting rod 4, the lock hook connecting rod 5, and the lock hook 6. All hinges in the lock mechanism are revolute pairs (a total of six, namely R0, R1, R2, R3, R4, and R5). The rocker arm and the lock hook are connected by a spring. During the unlocking process, due to the influence of some internal factors in the lock mechanism, the resistance may be too large, and the lock mechanism cannot be unlocked smoothly under the condition of the existing maximum driving force, resulting in the failure of the unlocking function of the lock mechanism. Then the failure domain D of insufficient driving force for the unlocking function of the lock mechanism F is

[0071] D F ={x|F>[F]}

[0072] where F is the actual driving force required on the piston, and this force is assumed to vary linearly with time. After the lock hook is opened, this force returns to a smaller value. [F] is the magnitude of the maximum driving force that the piston can provide, and [F]=900N. Through the dynamic analysis of the lock mechanism, the mechanical parameters that have an impact on the unlocking function of the lock mechanism include: the damping coefficient of the piston movement during the opening process of the lock mechanism, the maximum contact pressure between the lock hook and the lock ring, the friction coefficient between the lock hook and the lock ring, the decoupling angle between the lock hook and the lock ring, the stiffness coefficient of the spring, and the maximum contact angle between the lock hook and the lock ring. Assuming that all input variables follow independent normal distributions, Table 1 lists their distribution parameters

[0073] Table 1 Distribution types and parameters of random variables of the lock mechanism

[0074]

[0075] The implementation steps of the reliability analysis of the proposed method are as follows

[0076] 1) Determine the design variables and the limit state function: The design variables are x=[x1 x2 x3 x4 x5 x6], and each of its components is a random variable that follows an independent normal distribution, with a mean of μ=[5000 7500 0.25 49 7000 58] and a standard deviation of σ=[200 100 0.025 1 200 0.5].

[0077] Use the LMS Virtual.Lab simulation analysis software to establish the dynamic model of the lock mechanism, obtain the calculation result F(x) of the driving force required for unlocking, and thus the limit state function can be obtained as

[0078] G(x)=[F]-F(x)

[0079] 2) Determine the design space: According to the "3σ principle", determine the upper and lower limits of each design variable L = [4400 7200 0.17546 6400 56.5], U = [5600 7800 0.325 52 7600 59.5].

[0080] 3) Generate the candidate sample set and the test sample set: In the design space, use uniform sampling to generate a candidate sample set X with C samples and a test sample set X T .

[0081] 4) Create the initial DOE and construct the Kriging model: Apply the Latin hypercube method to generate an experimental design sample set X D consisting of N0 = 3×6 = 18 samples, call the limit state function G(x) to calculate the function values of these 18 samples, and form a sample point set {(x, G(x))|x ∈ X D}, as shown in Table 2, which is the initial DOE. Initialize the number of times of constructing the model z = 1, and use the sample point set to construct the Kriging model

[0082] Table 2 Initial DOE

[0083]

[0084] 5) Construct the validation sample set and calculate the classification index of the samples in it: Select the first T0 = [T / 100] = 245 samples closest to the current Kriging model T limit state from the test sample set X to form the validation sample set X V , that is the first 245 samples closest to 0. Classify the samples in the validation sample set X V into two categories of "+1" and "-1" according to the positive and negative of their function values, and assign values to the classification index according to formula (1). Table 3 gives the calculation results when z = 1.

[0085] Table 3 Calculation results of the validation sample set X V when z = 1

[0086]

[0087] 6) Screen the first candidate sample set and determine the first sample: Use the current Kriging model to analyze the current candidate sample set X C , and screen out the first 245 samples closest to the limit state as the first candidate sample set X FCCalculate X through formulas (2) to (4). FC The maximum and minimum distance L between the samples in D and the current experimental design sample set X 1max-min Then use formula (5) to determine X FC All samples in which are equal to the "maximum and minimum distance" L 1max-min Select the sample corresponding to the first non-zero k1(i) value in X FC as the first sample x1 and add it to the current X D Table 4 gives the calculation results of the first candidate sample set X when z = 1 FC and the first sample is

[0088] Table 4 First candidate sample set X when z = 1 FC Calculation results

[0089]

[0090] 7) Construct the second candidate sample set and determine the second sample: Select all samples in the first candidate sample set X FC whose function value signs are different from that of the sample x1 to construct the second candidate sample set X SC That is Calculate the maximum and minimum distance L between the samples in X SC and the samples in the current experimental design sample set X D Then use formula (9) to determine X 2max-min All samples in which are equal to the "maximum and minimum distance" L SC Select the sample corresponding to the first non-zero k2(i) value in X 2max-min as the second sample x2 and add it to the current X SC Table 5 gives the calculation results of the second candidate sample set X when z = 1 D and the first sample is SC Table 5 Second candidate sample set X when z = 1

[0091]

[0092] Calculation results SC Table 5 Second candidate sample set X when z = 1

[0093]

[0094]

[0095] 8) Update the DOE and remove the corresponding samples: Call the limit state function G(x) to calculate the function values of the samples x1 and x2, and then update the sample point set {(x, G(x))|x ∈ XD}, that is, update the DOE. Subsequently, delete the samples corresponding to x1 and x2 in the candidate sample set X C . Table 6 shows the updated DOE when z = 1.

[0096] Table 6 Updated DOE when z = 1

[0097]

[0098] 9) Reconstruct the Kriging model and calculate the number of misclassifications: Let the number of times of constructing the model z = z + 1, then reconstruct the Kriging model with the current DOE sample point set, and calculate the sample function values in the verification sample set X V according to the positive and negative situations of the function values Divide them into two categories of "+1" and "-1", and assign values to the classification index according to formula (1), and calculate the number of misclassifications through formula (10)

[0099] 10) Judge the stability of the model output: Calculate the stability index of the z-th Kriging model through formula (11) N in formula (11) mis0 = [T0 × 5%] = 13. Calculate the model convergence stability index through formula (12) If it is considered that the constructed Kriging model has been stable, the algorithm immediately transfers to step 11), otherwise returns to step 5).

[0100] 11) Generate the Monte Carlo sample set and evaluate the failure probability: Generate N mcs (the initial value is taken as 10000) samples to form the Monte Carlo sample set X MCS , then calculate its function values with the last constructed Kriging model, and evaluate the failure probability through formula (13) and formula (14)

[0101] 12) Judge whether the estimated value of the failure probability is stable: Calculate the coefficient of variation cov of the failure probability through formula (15). If cov is less than its allowable value of 5%, the calculated failure probability is the final result and the algorithm ends; otherwise, let N mcs = 10 × N mcs , and then transfer to step 11).

[0102] The proposed method obtains a stable Kriging model when z = 90, and at N mcsThe failure probability was obtained when = 100000, and the result was 1.031×10 . The total number of times the limit state function G(x) was called to calculate the function value during the calculation process was N0 + 2×(z - 1) = 196. Table 7 gives the final DOE. -2 .

[0103] Table 7 Final DOE of the proposed method

[0104]

[0105] To prove the practicability and efficiency of the proposed method, the reliability analysis results and the calculation results of the relative error of reliability of the Kriging models (Kriging1) constructed by Monte Carlo and direct experimental design and the Kriging model (Kriging2) constructed by the proposed method are listed in Table 8.

[0106] Table 8 Comparison of calculation results of examples

[0107]

[0108]

[0109] According to the calculation results in Table 8, it can be seen that the relative errors of the reliability calculated by the Kriging model constructed by direct Latin hypercube experimental design are relatively large, while the relative error of the Kriging model constructed by the method proposed in the present invention is significantly lower. It is worth pointing out that even when 1000 samples are used in the direct Latin hypercube experimental design method, the relative error of the reliability analysis result of the Kriging model constructed by it relative to the analysis result of Monte Carlo is 2.33%, while the relative error of the reliability analysis result of the Kriging model constructed by the proposed method with only 196 samples (18 initial samplings and 196 required for 89 iterative loops) relative to the analysis result of Monte Carlo is 0.19%. According to the results corresponding to Kriging1 in Table 8, it can be found that the method of constructing the Kriging model by direct experimental design has certain blindness and instability. Therefore, this example fully proves the practicability and efficiency of the proposed method.

[0110] The above embodiments are only preferred specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by those skilled in the art within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims

1. An efficient adaptive method based on the Kriging model, characterized in that, The method includes the following steps: Step 1. Determine the design variables a and the limit state function G(x); Step 2, determine the design space; Step 3, generate a candidate sample set XC and a test sample set XT ; Step 4, create an initial DOE and construct a Kriging model; Step 5, construct a validation sample set and calculate the classification indexes of the samples therein; Step 6, screening the first candidate sample set XFC and determining the first sample x 1; Step 7: Construct the second candidate sample set XSC and determine the second sample x 2; Step 8, update the DOE and remove the corresponding samples; Step 9, reconstruct the Kriging model and calculate the number of misclassifications; Step 10, judge the stability of the model output. If it is stable, execute Step 11; otherwise, return to execute Step 5; Step 11, generate a Monte Carlo sample set and evaluate the failure probability; Step 12, judge whether the estimated value of the failure probability is stable. If it is stable, end; otherwise, reset the number of samples in the Monte Carlo sample set and return to execute Step 11; Step 2 specifically includes: determining the lower limit of each design variable according to the distribution type of the design variables and the design requirements Lr and the upper limit Ur ， wherein r = 1, 2, ..., n , and then determining the design space; Lr = μ r - 3 σ r and Ur = μ r + 3 σ r, wherein μ r is the mean of the variable, σ r is the standard deviation of the variable; The specific steps of step 5 include: screening from the test sample set XT the first samples closest to the current Kriging model T limit state to form a validation sample set XV , where the samples in the validation sample set XV are classified into two categories of "+1" and "-1" according to the positive and negative conditions of their function values, and the classification index is assigned values according to formula (1); ； Step 1 specifically includes: determining the design variables of the problem to be processed a = ( a 1, a 2, …, a6 ), functional characteristic quantities H and failure criteria I , and establishing a limit state function G ( x ); a 1 is the damping coefficient of the piston movement; a 2 is the maximum contact pressure between the locking hook and the locking ring; a 3 is the friction coefficient between the locking hook and the locking ring; a 4 is the decoupling angle between the locking hook and the locking ring; a 5 is the stiffness coefficient of the spring; a 6 is the maximum contact angle between the locking hook and the locking ring; Establish a dynamic model of the locking mechanism with simulation analysis software, obtain the calculation result F(x) of the driving force required for unlocking, so that the limit state function can be obtained as G(x) = [F] - F(x); [F] is the maximum driving force magnitude that the piston can provide; The corresponding samples in step 8 are the candidate sample sets X C corresponding to x 1 and x 2; The specific steps of step 4 include: generating N an experimental design sample set consisting of 0 samples X D , where N 0 = 3 n , calling the limit state function G ( x ) to calculate the function values of the N 0 samples, forming a sample point set , obtaining the initial DOE, initializing the number of times of constructing the model z = 1, and constructing a Kriging model using the sample point set .

2. The method according to claim 1, wherein The specific steps of step 3 include: in the design space, using uniform sampling to generate a candidate sample set containing T uniform samples X C and a test sample set X T .

3. The method according to claim 1, wherein Step 6 specifically includes: using the current Kriging model to analyze the current candidate sample set X C , and screening out the top T 0 samples closest to the limit state as the first candidate sample set X FC ; Calculate through formulas (2) to (4) X FC The maximum and minimum distances between the samples in and the current experimental design sample set X D The maximum and minimum distances of the samples in L 1max-min , and then determine using formula (5) X FC All the samples in that are equal to "the maximum and minimum distance" L 1max-min , select the first non-zero k 1( i ) value corresponding to X FC The sample in is the first sample Add to the current X D in; 。 4. The method according to claim 1, wherein The specific steps of step 7 include: selecting all samples in the first candidate sample set X FC whose function value signs are different from those of the samples corresponding to sample x 1 to construct a second candidate sample set X SC , where , calculating the maximum and minimum distances between the samples in X SC and the samples in the current experimental design sample set X D using formulas (6) to (8), and then determining all samples in L 2max-min that are equal to the "maximum and minimum distance" X SC . Select the first non-zero L 2max-min 2( k ) value-corresponding i ) value-corresponding X SC sample in as the second sample X D and add it to the current 。 5. The method according to claim 1, characterized in that The specific steps of step 8 include: calling the limit state function G ( x ) to calculate the function values of samples x 1 and x 2, and then update the sample point set , and update the DOE.

6. The method according to claim 1, wherein The specific steps of step 9 include: setting the number of times of constructing the model z = z + 1, then reconstructing the Kriging model with the current DOE sample point set, and calculating the sample function values in the verification sample set X V using the reconstructed Kriging model ; It is divided into two categories of "+1" and "-1" according to the positive and negative conditions of the function values, and the classification index is assigned according to formula (1). The number of misclassifications is calculated through formula (10). : .

Images