Reliability analysis method and system based on Kriging proxy model

Abstract

The invention discloses a reliability analysis method based on a Kriging agent model. The method comprises the following steps: S1, generating a sample pool based on a random variable related to the structural reliability of a part; s2, selecting a group of initial sample points from the sample pool to form an initial training set; s3, establishing a Kriging agent model according to the initial training set; s4, updating the Kriging agent model based on a weight probability entropy learning strategy so as to obtain an updated Kriging agent model; s5, calculating the average confidence coefficient of the sample pool by using the updated Kriging agent model; and S6, if the average confidence degree meets the confidence degree requirement, the updated Kriging agent model is used for carrying out reliability analysis on the part. Related systems and computer media are also provided.

Description

Technical Field

[0001] The present invention relates to the technical field of reliability assessment, and in particular to a reliability analysis method and system based on a Kriging proxy model. Background Art

[0002] Accurate and efficient analysis of the structural reliability of parts and components is of great significance to ensure the safety of personnel and property. The commonly used method for reliability analysis is the Monte Carlo method. Taking aircraft engine components as an example, when conducting finite element analysis of engine components based on the Monte Carlo method, the randomness of the parameters that affect the structural strength and life of the components is first considered. By modifying the parameters in the finite element model, a large number of finite element analyses are carried out to calculate the probability distribution of structural strength and life, and then analyze the structural reliability. However, the computational cost of reliability analysis based on the Monte Carlo method is very high. A single finite element analysis of aircraft engine components often requires hundreds of cores. If a large number of finite element analyses are carried out, the cost will be unacceptable.

[0003] In view of this, a surrogate model is proposed to solve the above problems. The surrogate model is essentially a function representing the relationship between input parameters and output responses, which has low computational cost and fast speed. Replacing finite element analysis with a surrogate model is the current mainstream reliability analysis method. The Kriging surrogate model is an unbiased estimation model with the smallest estimation variance. It can often achieve a relatively good fitting effect when solving problems with high nonlinearity, so it is widely used in engineering. Active learning is a method of purposefully sampling and updating the surrogate model. Typical active learning strategies / functions of the Kriging surrogate model include the U function method, the EFF (Expected Feasibility Function) function method and its variant function method. However, these learning strategies mainly focus on the reliability prediction results of individual sample points, without considering the fitting of the overall sample, resulting in a large number of redundant calculations, and unable to give full play to the advantage of the surrogate model in reducing the amount of calculation. At the same time, these learning strategies are difficult to describe the overall confidence of their reliability prediction results, and the overall accuracy of the results is not evaluated, so it is difficult to be applied in engineering problems.

[0004] In view of the deficiencies of the prior art, it is desired to provide an improved reliability analysis method and system. Summary of the invention

[0005] A brief summary of one or more aspects is given below to provide a basic understanding of these aspects. This summary is not an exhaustive overview of all conceived aspects, and is neither intended to identify the key or critical elements of all aspects nor to define the scope of any or all aspects. Its only purpose is to give some concepts of one or more aspects in a simplified form as a prelude to a more detailed description that will be given later.

[0006] The present invention provides a reliability analysis method based on a Kriging proxy model, comprising the following steps: S1: generating a sample pool based on random variables related to the structural reliability of a component; S2: selecting a group of initial sample points from the sample pool to form an initial training set; S3: establishing a Kriging proxy model according to the initial training set; S4: updating the Kriging proxy model based on a weighted probability entropy learning strategy to obtain an updated Kriging proxy model; S5: calculating the average confidence of the sample pool using the updated Kriging proxy model; and S6: if the average confidence meets the confidence requirement, performing reliability analysis on the component using the updated Kriging proxy model.

[0007] In some embodiments, step S4 further includes: selecting new sample points from the sample pool based on a weighted probability entropy learning strategy; appending the new sample points to the initial training set to obtain an expanded training set; and using the expanded training set to update the Kriging proxy model to obtain an updated Kriging proxy model.

[0008] In some embodiments, selecting a new sample point from the sample pool based on the weighted probability entropy learning strategy further includes: calculating the weighted probability entropy of each sample point in the sample pool that does not belong to the initial training set; and selecting the sample point with the largest weighted probability entropy as the new sample point.

[0009] In some embodiments, step S5 further includes: calculating the predicted response values ​​of all sample points in the sample pool according to the updated Kriging proxy model; calculating the confidence of each sample point in the sample pool based on the predicted response values ​​and the true response values ​​of all sample points; and averaging the confidences of all sample points to obtain the average confidence of the sample pool.

[0010] In some embodiments, step S6 further includes: if the average confidence does not meet the confidence requirement, returning to execute steps S4 and S5 to continue updating the Kriging proxy model until the average confidence calculated using the updated Kriging proxy model meets the confidence requirement.

[0011] In some embodiments, performing reliability analysis on a component using an updated Kriging proxy model further includes: estimating the structural failure probability of the component using the updated Kriging proxy model to obtain a failure probability estimate; calculating the coefficient of variation of the failure probability estimate; if the coefficient of variation is less than or equal to a preset threshold, completing the reliability analysis of the component; and if the coefficient of variation is greater than the preset threshold, increasing the sample pool and executing steps S2 to S6 based on the increased sample pool.

[0012] The present invention also provides a reliability analysis system based on a Kriging proxy model, comprising: a sample pool module, used to execute step S1: generating a sample pool based on random variables related to the structural reliability of a component; an initial training set module, used to execute step S2: selecting a set of initial sample points from the sample pool to form an initial training set; a model building module, used to execute step S3: building a Kriging proxy model according to the initial training set; a model updating module, used to execute step S4: updating the Kriging proxy model based on a weighted probability entropy learning strategy to obtain an updated Kriging proxy model; a confidence module, used to execute step S5: calculating the average confidence of the sample pool using the updated Kriging proxy model; and a reliability analysis module, used to execute step S6: if the average confidence meets the confidence requirement, performing reliability analysis on the component using the updated Kriging proxy model.

[0013] In some embodiments, the model update module is also configured to perform step S4 by the following operations: selecting new sample points from the sample pool based on a weighted probability entropy learning strategy; appending the new sample points to the initial training set to obtain an expanded training set; and using the expanded training set to update the Kriging proxy model to obtain an updated Kriging proxy model.

[0014] In some embodiments, the model update module is also configured to select new sample points from the sample pool based on the weighted probability entropy learning strategy by: calculating the weighted probability entropy of each sample point in the sample pool that does not belong to the initial training set; and selecting the sample point with the largest weighted probability entropy as the new sample point.

[0015] In some embodiments, the confidence module is also configured to perform step S5 by the following operations: calculating the predicted response values ​​of all sample points in the sample pool according to the updated Kriging proxy model; calculating the confidence of each sample point in the sample pool based on the predicted response values ​​and the true response values ​​of all sample points; and averaging the confidences of all sample points to obtain the average confidence of the sample pool.

[0016] In some embodiments, the model updating module is further configured to: if the average confidence does not meet the confidence requirement, return to execute steps S4 and S5 to continue updating the Kriging proxy model until the average confidence calculated using the updated Kriging proxy model meets the confidence requirement.

[0017] In some embodiments, the reliability analysis module is also configured to perform reliability analysis on the component using the updated Kriging proxy model through the following operations: estimating the structural failure probability of the component using the updated Kriging proxy model to obtain a failure probability estimate; calculating the coefficient of variation of the failure probability estimate; if the coefficient of variation is less than or equal to a preset threshold, completing the reliability analysis of the component; and if the coefficient of variation is greater than the preset threshold, increasing the sample pool and executing steps S2 to S6 based on the increased sample pool.

[0018] The present invention also provides a computer-readable storage medium storing a computer program for reliability analysis based on a Kriging proxy model. The computer program can be executed by a processor to perform the aforementioned reliability analysis method based on a Kriging proxy model.

[0019] The technical solution disclosed in the present invention constructs a Kriging proxy model based on a weighted probability entropy learning strategy, which can quickly improve the accuracy of the Kriging proxy model. Compared with the existing learning strategy, it can reduce redundant calculations and improve analysis efficiency. At the same time, the technical solution can better describe the overall prediction accuracy of the prediction results, ensure the efficiency and accuracy of reliability analysis, and has high application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] The features, nature and advantages of the present invention will become more apparent when the detailed description set forth below is understood in conjunction with the accompanying drawings. In the accompanying drawings, the same reference numerals are always used for corresponding identification. It should be noted that the drawings described are only schematic and non-limiting. In the drawings, the sizes of some components may be exaggerated and are not drawn to scale for illustrative purposes.

[0021] Figure 1 The flowchart of the reliability analysis method based on the Kriging surrogate model of the present invention is shown.

[0022] Figure 2 An exemplary process of reliability analysis based on the Kriging surrogate model of the present invention is shown.

[0023] Figure 3 An example of a sample pool and a true performance function of the initial Kriging proxy model of the present invention is shown.

[0024] Figure 4 An example of the locations of sample points in the training set of the present invention is shown.

[0025] Figure 5 An example of the locations of newly added sample points of the present invention is shown.

[0026] Figure 6An example of the changing trend of the average confidence of the sample pool of the present invention is shown.

[0027] Figure 7 An example of the sample point locations and the functional function of the Kriging proxy model after the update is completed is shown.

[0028] Figure 8 A schematic diagram of output value sign prediction of the Kriging proxy model of the present invention is shown.

[0029] Fig. 9 The reliability analysis system based on the Kriging proxy model of the present invention is shown.

[0030] Fig.10 The device block diagram of the reliability analysis system based on the Kriging proxy model of the present invention is shown. DETAILED DESCRIPTION

[0031] In order to make the purpose, technical scheme and advantages of the present invention clearer, the present invention is further described in detail below in conjunction with specific embodiments and with reference to the accompanying drawings. In the following detailed description, many specific details are set forth to provide a thorough understanding of the described exemplary embodiments. However, it is obvious to those skilled in the art that the described embodiments can be practiced without some or all of these specific details. In other exemplary embodiments, well-known structures are not described in detail to avoid unnecessarily obscuring the concepts of the present disclosure. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. At the same time, in the absence of conflict, the various aspects described in the embodiments can be combined arbitrarily.

[0032] In order to solve the problems of large number of sampling times in conventional reliability analysis and long and costly single finite element analysis of structures, the reliability analysis of engine component structures usually uses the adaptive learning Kriging surrogate model method, whose adaptive learning strategies include U function method, EFF function method and its variant function method. However, these methods generally require a large number of training sample points and cannot effectively estimate the overall confidence of the prediction results, resulting in a large number of redundant calculations, making them difficult to be applied in actual engineering.

[0033] In view of this, the present invention proposes a new Kriging proxy model active learning strategy and a corresponding reliability analysis method, which can significantly reduce the amount of calculation, and perform reliability analysis efficiently and accurately, while also being able to evaluate the overall confidence of the reliability results.

[0034] Figure 1 A flow chart of a reliability analysis method 100 based on a Kriging surrogate model of the present invention is shown.

[0035] The method 100 begins at step 105. At step 105, a sample pool is generated based on random variables related to structural reliability of components.

[0036] For example, the n-dimensional random variable that affects the reliability of the component structure can be recorded as x, and a sample pool S representing the probability distribution characteristics of x can be generated based on the random sampling method. MC , the total number of samples in the sample pool is recorded as n MC To ensure accuracy, n MC Generally more than 10 5 It should be noted that the above-mentioned method of generating a sample pool is only illustrative and not restrictive. In specific practice, those skilled in the art may adopt different methods to generate sample pools of different sizes according to actual conditions.

[0037] The relationship between the input random variable x and the corresponding true output response value Y in reliability analysis can be described by the following formula:

[0038] Y=G(x)

[0039] Where G(x) is called the performance function.

[0040] In step 110, a group of initial sample points are selected from the sample pool to form an initial training set.

[0041] In some embodiments, the sample pool S MC A group (for example, N 1 ) sample points {x} i (i=1,2,…,N 1 ) as the initial sample point. At the same time, for these N 1 Finite element analysis is used to obtain the corresponding true response value {Y} i (i=1,2,…,N 1 ). This N 1 The corresponding inputs (sample points) and outputs (true response values) form the initial training set (denoted as T in this paper). MC ).

[0042] In step 115, a Kriging proxy model is established based on the initial training set.

[0043] The Kriging surrogate model is an approximation of the performance function G(x) and can be expressed as the sum of a polynomial and a random process, as shown below:

[0044]

[0045] The polynomial F(x, β) represents the overall trend of the Kriging surrogate model in the input parameter distribution space, and the polynomial F(x, β) can be written as:

[0046] F(x, β) = f(x) T β

[0047] where d(x) T ={f 1 (x), …, f k (x)} is the basis function of x, β={β 1 ,…,β k} are regression coefficients to be determined.

[0048] z(x) is a random process with a mean of zero and a variance of σ 2 , σ 2 is a larger preset value. a 、x b For example, z(x a )、z(x b ) is:

[0049] COV(z(x a ), z(x b ))=σ 2 R θ (x a , x b )

[0050] Among them, R θ is the correlation function (also called kernel function). The commonly used kernel function is the Gaussian kernel, as shown below:

[0051]

[0052] in, For x a 、x b The i-th dimension component of θ. i is the i-th related parameter to be fitted. Assume there are m training samples and the input data is composed of vector [x 1 , x 2 ,…,x m ] T , the output data forms a vector Y = [Y 1 ,Y 2 ,…,Y m ] T =[G(x 1 ), G(x 2 ), …, G(x m )] T The Kriging surrogate model is trained based on these m training samples. and They are:

[0053]

[0054]

[0055] Where R represents the correlation matrix, R = [R ij ]=[R θ (x i ,x j )], i, j = 1, 2, ..., m. Based on the maximum likelihood function, the correlation coefficient θ = (θ 1 ,θ 2 ,…,θ i ,…,θ n ) is as follows:

[0056]

[0057] r(x) represents the difference between the sample point to be predicted x and the training sample point [x 1 , x 2 ,…,x m ] T The correlation vector between them is expressed as follows:

[0058] r(x)=[R θ (x,x 1 ),R θ (x,x 2 ),…,R θ (x,x m )] T

[0059] The best linear unbiased estimate of the output value of the sample point x to be predicted is:

[0060]

[0061] The variance of the estimated output value is:

[0062]

[0063] Since the Kriging surrogate model outputs values ​​at the predicted sample points At the same time, we get the estimated variance Therefore, it provides a basis for calculating the confidence of the output value and adding new training points.

[0064] In step 120 , the Kriging proxy model is updated based on the weighted probability entropy learning strategy to obtain an updated Kriging proxy model.

[0065] In some embodiments, updating the Kriging proxy model based on the weighted probability entropy learning strategy to obtain an updated Kriging proxy model further includes: selecting new sample points from the sample pool based on the weighted probability entropy learning strategy; appending the new sample points to the initial training set to obtain an expanded training set; and using the expanded training set to update the initial Kriging proxy model to obtain an updated Kriging proxy model.

[0066] For a sample point x in the sample pool i For , the estimated output value follows a normal distribution

[0067] Sample point x i Function Values ​​in the range The confidence level within is Φ(γ), then the prediction The probability of a positive sign is as follows:

[0068]

[0069] predict The probability of a negative sign is as follows:

[0070]

[0071] Since Φ(2)=97.725%, γ=2 is generally taken.

[0072] Then we can calculate the sample x i The symbolic probability entropy (Probability Entropy) of the corresponding output value is:

[0073] PE(x i )=-(P + (x i )lnP + (x i )+P - (x i )lnP - (x i ))

[0074] Due to x i It obeys the joint probability density function f x Considering the sample density weight, calculate x i Weight Probability Entropy:

[0075] WPE(x i )=-(f x (x i )+ (x i )ln(P + (x i ))+f x (x i ) - (x i )ln(P - (x i )))

[0076] The higher the weighted probability entropy of a sample point, the more difficult it is to distinguish the positive and negative signs of its function value. The better the model training effect will be when using such sample points. Therefore, it is expected that such sample points will be added to the training set. That is, the criterion for adding the training set is to find the sample pool S MC The sample point x with the largest WPE value (except the sample points in the initial training set) u = arg max WPE(x).

[0077] Therefore, selecting new sample points from the sample pool based on the weighted probability entropy learning strategy can further include: calculating the weighted probability entropy of each sample point in the sample pool that does not belong to the initial training set; and selecting the sample point with the largest weighted probability entropy as the new sample point.

[0078] For the sample point x found in the above way u , the true response value Y can be calculated by conducting finite element analysis u =G(x u ). Then you can put (x u ,Y u ) is added to the initial training set T MC , to obtain the expanded training set. By expanding the training set, the initial Kriging surrogate model K 0 Update (i.e., use the expanded training set to update the model K 0 Retraining) to obtain the updated Kriging proxy model K 1 .

[0079] At step 125, the average confidence of the sample pool is calculated using the updated Kriging proxy model.

[0080] In some embodiments, calculating the average confidence of the sample pool using the updated Kriging proxy model further includes: calculating the predicted response values ​​of all sample points in the sample pool according to the updated Kriging proxy model; calculating the confidence of each sample point in the sample pool based on the predicted response values ​​and the true response values ​​of all sample points; and averaging the confidences of all sample points to obtain the average confidence of the sample pool.

[0081] Specifically, according to the Kriging surrogate model K 1 Calculate the sample pool S MC The predicted response values ​​of all sample points in are obtained and the confidence of each sample point is calculated.

[0082] For a sample point x in the sample pool i For , the estimated output value follows a normal distribution Then the sample point x i Function The value and the true value G(x i ) has the same sign as

[0083] The average confidence can then be calculated as follows:

[0084]

[0085] Average confidence Φ avr Reflects the Kriging surrogate model K 1 For sample pool S MC The overall prediction accuracy of all sample points in .

[0086] In step 130, it is determined whether the average confidence obtained in step 125 meets the confidence requirement.

[0087] In some embodiments, the confidence requirement may be a preset threshold (e.g., 99.9999%). In such cases, if the average confidence is greater than or equal to the threshold, the average confidence may be considered to meet the confidence requirement. If the average confidence is less than the threshold, the average confidence may be considered to not meet the confidence requirement.

[0088] If the average confidence does not meet the confidence requirement (decision box 130 is "No"), it is considered that the Kriging proxy model has not yet reached the accuracy requirement and needs to be updated. At this time, the method 100 can return to step 120 and continue to update the Kriging proxy model based on the weighted probability entropy learning strategy.

[0089] Specifically, the next new sample point can be selected based on the weighted probability entropy learning strategy, and the new sample point is added to the training set of the previous round to obtain a new training set (which is expanded compared to the training set of the previous round), and the Kriging proxy model is updated based on the new training set. This process can be repeated until the average confidence calculated using the updated Kriging proxy model meets the confidence requirement.

[0090] If the average confidence meets the confidence requirement (decision box 130 is "yes"), it is considered that the Kriging proxy model has met the accuracy requirement and does not need to be updated. At this point, the method 100 can proceed to step 135: perform reliability analysis on the component using the updated Kriging proxy model.

[0091] In step 135, performing reliability analysis on the component using the updated Kriging proxy model may further include: estimating the structural failure probability of the component using the updated Kriging proxy model to obtain a failure probability estimate; calculating the coefficient of variation of the failure probability estimate; if the coefficient of variation is less than or equal to a preset threshold, completing the reliability analysis of the component; if the coefficient of variation is greater than the preset threshold, increasing the sample pool and repeating step 110 and subsequent steps based on the increased sample pool.

[0092] Specifically, assuming that the updated Kriging proxy model is model K 1 (That is, the Kriging surrogate model K 0 The average confidence obtained after one update meets the confidence requirement), calculate S MC The predicted response values ​​of all sample points in , and the number of sample points n whose predicted response values ​​are less than or equal to 0 G≤0 , then the estimated value of the structural failure probability is:

[0093]

[0094] Then, the coefficient of variation (COV) of the failure probability estimate can be calculated according to the following formula:

[0095]

[0096] If COV is less than or equal to the preset threshold (e.g., ≤5%), the reliability analysis is completed; otherwise, it indicates that the sample pool S MC The sample size is insufficient and the sample pool needs to be increased and analyzed again.

[0097] Specifically, the total number of samples in the sample pool can be increased by a certain amount, and step 110 and subsequent steps thereof can be repeated based on the increased sample pool. The number of samples increased can be set according to actual conditions. For example, the same number of samples can be increased each time, the number of samples increased each time decreases, the number of samples increased each time increases, the amount of each increase is determined based on other criteria, and the like. Those skilled in the art can determine how to increase the sample pool according to actual conditions.

[0098] Therefore, method 100 can realize structural reliability analysis based on weighted probability entropy active learning strategy. By constructing a Kriging proxy model based on the weighted probability entropy learning strategy, and selecting sample points with the highest positive and negative signed entropy in the probability density maximum area to update the model, the model accuracy can be quickly improved. Compared with the existing Kriging proxy model learning strategy, the learning strategy of the present invention can reduce redundant calculations, significantly reduce the amount of calculations, and improve analysis efficiency. At the same time, the technical solution of the present invention can evaluate the overall prediction accuracy of the proxy model, and can converge faster than methods such as U learning strategy and EFF learning strategy, and better describe the accuracy of the prediction results. The reliability analysis method of the present invention is easy to operate, and ensures the accuracy and efficiency of reliability analysis. It has high engineering application value in the fields of reliability design of aircraft engine components.

[0099] Figure 2 The exemplary process 200 of reliability analysis based on the Kriging proxy model of the present invention is shown. For the convenience of explanation, a typical four-link calculation example of engine structure reliability is used as an example for explanation. Figure 3-Figure 8 2. The exemplary process 200 is described. It should be noted that although the technical solution of the present invention is mainly explained in conjunction with the reliability analysis of aircraft engines in the specification, the present invention is not limited thereto and the technical solution of the present invention can be applied to the reliability analysis of various components in other fields.

[0100] In this exemplary process, the performance function can be expressed as:

[0101] Let k = 6

[0102] Among them, x 1 、x 2 is a standard normal variable.

[0103] After the process 200 starts, a sample pool of engine component structural reliability variables may be generated first (205). The sample pool capacity (i.e., the number of samples in the sample pool) is n MC .

[0104] In this example, x 1 、x 2 Two random variables that affect the reliability of component structures. To ensure the uniformity of probability, 10 6 A random sample (i.e., n MC =10 6 ), forming a sample pool S MC The first 10 sample points in the sample pool are shown in Table 1.

[0105] Table 1

[0106] Serial number <![CDATA[x 1 ]]> <![CDATA[x 2 ]]> Serial number <![CDATA[x 1 ]]> <![CDATA[x 2 ]]> 1 -0.4594 0.011735 6 -0.02102 -0.74169 2 -0.06961 -0.26239 7 0.439684 -0.03574 3 0.114136 0.886581 8 0.79264 1.653149 4 -1.47669 0.190804 9 -0.3548 -0.16939 5 0.144439 -0.19545 10 0.168385 -0.03735

[0107] The positions of all sample points in the sample pool and the true function curve are as follows: Figure 3 shown.

[0108] Generate sample pool S MC After that, you can MC Select N 1 Sample points, establish training set T MC (210).

[0109] In some embodiments, it is possible to MC In the process 200, sample points are randomly selected. Generally, a dozen initial points can be selected for low-dimensional numerical examples, and dozens to hundreds of initial points can be selected for high-dimensional engineering examples. As an example, 16 sample points are randomly selected in process 200. The sample points are brought into the function to calculate their true response values, and the corresponding input-output (sample point-true response value) thus constitutes the training set T MC .

[0110] Training set T MC The sample points and response values ​​are shown in Table 2.

[0111] Table 2

[0112] Serial number <![CDATA[x 1 ]]> <![CDATA[x 2 ]]> Y Serial number <![CDATA[x 1 ]]> <![CDATA[x 2 ]]> Y 1 1.104244 0.439824 1.952325 9 -0.25122 -1.54277 1.898266 2 0.432156 -2.18955 1.620932 10 -2.28062 0.21139 1.750632 3 -0.62485 -0.96841 1.885198 11 0.139135 0.189698 2.767736 4 0.483657 -1.29307 2.465912 12 2.372916 0.692999 1.114283 5 -0.22307 -0.59095 2.437937 13 0.196595 -1.6099 2.326986 6 -0.35199 -0.89077 2.150264 14 -0.12373 2.715211 1.403704 7 0.125355 0.792325 2.395587 15 0.988976 -0.61689 2.636775 8 0.12236 0.788524 2.400285 16 0.077815 1.381024 2.13828

[0113] Training set T MC The sample point locations are as follows Figure 4 shown. Figure 4 The training set T is shown in MC The positions of the initial 16 sample points (marked as "initial" in the figure). As can be seen from the figure, the positions of these initial sample points are random.

[0114] In establishing the training set T MC Afterwards, according to T MC Establish Kriging surrogate model K 0 (215).

[0115] According to the input-output information in Table 2, the undetermined coefficient θ of the Gaussian kernel in the Kriging proxy model is calculated, and θ = (1.43, 0.506) is obtained by maximum likelihood estimation. 0 . K can then be used 0 Calculate sample pool S MC The estimated value of all sample points in and variance

[0116] Then, new sample points can be selected based on the weighted probability entropy learning strategy. Specifically, the sample pool S can be found MC (except training set T MC The sample point x with the largest WPE (weighted probability entropy) u As a new sample point (220). At the same time, a finite element analysis can be performed on the new sample point to calculate its true response value Y u =G(x u )(225).

[0117] In the example of process 200, the sample point with the maximum WPE value is x u =(-0.88323776,-0.19705346), the corresponding true response value is Y u =G(x u )=2.28320364.

[0118] After that, (x u ,Y u ) is added to the training set T MC To expand the training set, and update the Kriging surrogate model K based on the expanded training set 0 , and obtain the updated Kriging surrogate model K 1 (230). K 1 The unknown coefficient is θ = (1.4, 0.618).

[0119] Then, according to K 1 Calculate sample pool S MC The confidence of each sample point in S MC The average confidence Φ avr .

[0120] As mentioned above, Φ avr Reflects K 1 For S MC The overall prediction accuracy of all sample points in . avr When the confidence requirement is met, the Kriging proxy model is considered to meet the accuracy requirement. At this time, there is no need to update the Kriging proxy model again. Otherwise, the Kriging proxy model needs to be updated again.

[0121] In process 200, as an example, it is assumed that the confidence requirement is Φ avr ≥99.9999%.

[0122] If Φ avr If the confidence requirement is met (decision box 235 is "yes"), the current Kriging proxy model (K 1) to conduct structural reliability analysis.

[0123] If Φ avr If the confidence requirement is not met (decision box 235 is "No"), it is necessary to continue updating the Kriging proxy model. The detailed process of updating the Kriging proxy model has been described above in conjunction with Figure 1 The description has been given and will not be repeated here.

[0124] For example, if the model meets the requirement after 70 updates, it means that a total of 70 new sample points have been added, and the Kriging proxy model K obtained by the first 69 updates is 1 -K 69 Φ avr Does not meet the confidence requirement, and the Kriging surrogate model K 70 Φ avr Satisfy confidence requirements.

[0125] The locations of all newly added sample points are as follows: Figure 5 As shown in Figure 6 As shown. Figure 5 It can be seen that the newly added sample points (marked as "Add" in the figure) are basically located near the area where the function value is equal to 0. Figure 6 It can be seen that the average confidence fluctuates in the early model update process, but gradually increases and tends to be stable in the later model update process, and finally reaches the confidence requirement (0.999999).

[0126] After the proxy model update is completed (the updated proxy model meets the confidence requirement), the updated Kriging proxy model can be used to perform reliability analysis.

[0127] For the convenience of explanation, assume that the proxy model K 70 (That is, the initial proxy model K 0 The proxy model obtained after 70 updates meets the confidence requirement. Figure 7 The updated Kriging surrogate model K is shown 70 The positions of all sample points in the training set and the functional function curve of their agents. Figure 7 In the figure, the light-colored curve represents the true performance function, and the dark-colored curve represents the approximate performance function (i.e., the proxy model K 70 approximation to the true function). In addition, Figure 7 The initial sample point (initial) and the subsequently added sample points (Add) are also shown.

[0128] According to K 70 S can be calculated MCThe predicted response values ​​of all sample points in , and the number of sample points n whose predicted response values ​​are less than or equal to 0 G≤0 . Figure 8 The K 70 The predicted response value sign prediction results are obtained. The dark points in the figure represent sample points whose predicted response values ​​are greater than 0 (positive sign), and the light points represent sample points whose predicted response values ​​are less than 0 (negative sign).

[0129] From this, the probability of structural failure can be estimated (240):

[0130]

[0131] The coefficient of variation COV of the failure probability estimate is then calculated:

[0132]

[0133] If COV≤5% (decision box 250 is "yes"), the analysis is completed and process 200 ends. Otherwise, the sample pool needs to be expanded (255). After the sample pool is expanded, step 210 and subsequent steps can be repeated based on the expanded sample pool. The specific process of expanding the sample pool has been described above in conjunction with Figure 1 The description has been given and will not be repeated here.

[0134] It should be noted that the above implementation of process 200 is exemplary and not restrictive. In actual implementation, those skilled in the art may adopt different methods to implement the reliability analysis process as needed. For example, sample pools of different capacities, training sets of different sizes, different confidence requirements, etc. may be adopted according to actual conditions.

[0135] The commonly used Monte Carlo method is used as a comparison. The structural failure probability calculated by the embodiment of process 200 using the Monte Carlo method is 4.454×10 -3 , the coefficient of variation of the estimated value of the failure probability is 1.46%, and the error with the calculation result of the method of the present invention is less than 0.03%. It can be seen that the reliability analysis method proposed in the present invention has a very high accuracy, and the calculation amount is only 0.007% of the Monte Carlo method. Compared with other similar learning strategies, the embodiment of process 200 requires 132 samples when using the U learning strategy and 128 samples when using the EFF learning strategy. In contrast, process 200 uses an initial 16 sample points and a subsequent 70 sample points, totaling 86 sample points, which reduces the number of samples and the amount of calculation compared to other conventional learning strategies, thereby reducing redundant calculations and improving analysis efficiency.

[0136] Fig. 9A reliability analysis system 900 based on a Kriging proxy model of the present invention is shown.

[0137] like Fig. 9 As shown, the system 900 may include a sample pool module 905, an initial training set module 910, a model building module 915, a model updating module 920, a confidence module 925, and a reliability analysis module 930. Each of these modules may be directly or indirectly connected or communicated with each other on one or more buses 935.

[0138] In various embodiments of the present invention, the sample pool module 905 may be configured to perform step S1: generating a sample pool based on a random variable related to the structural reliability of a component.

[0139] The initial training set module 910 may be configured to execute step S2: selecting a set of initial sample points from the sample pool to form an initial training set.

[0140] The model building module 915 may be configured to execute step S3: building a Kriging proxy model according to the initial training set.

[0141] The model updating module 920 may be configured to perform step S4: updating the Kriging proxy model based on a weighted probability entropy learning strategy to obtain an updated Kriging proxy model.

[0142] In some embodiments, the model update module 920 is also configured to perform step S4 by the following operations: selecting new sample points from the sample pool based on a weighted probability entropy learning strategy; appending the new sample points to the initial training set to obtain an expanded training set; and using the expanded training set to update the Kriging proxy model to obtain an updated Kriging proxy model.

[0143] In some embodiments, the model updating module 920 is further configured to select new sample points by: calculating the weighted probability entropy of each sample point in the sample pool that does not belong to the initial training set; and selecting the sample point with the largest weighted probability entropy as the new sample point.

[0144] The confidence module 925 may be configured to execute step S5: using the updated Kriging proxy model to calculate the average confidence of the sample pool.

[0145] In some embodiments, the confidence module 925 is also configured to perform step S5 by the following operations: calculating the predicted response values ​​of all sample points in the sample pool according to the updated Kriging proxy model; calculating the confidence of each sample point in the sample pool based on the predicted response values ​​and the true response values ​​of all sample points; and averaging the confidences of all sample points to obtain the average confidence of the sample pool.

[0146] The reliability analysis module 930 may be configured to execute step S6: if the average confidence level meets the confidence level requirement, then use the updated Kriging proxy model to perform reliability analysis on the component.

[0147] In some embodiments, the model updating module 920 is further configured to: if the average confidence does not meet the confidence requirement, return to execute steps S4 and S5 to continue updating the Kriging proxy model until the average confidence calculated using the updated Kriging proxy model meets the confidence requirement.

[0148] In some embodiments, the reliability analysis module 930 is also configured to perform reliability analysis on the component by the following operations: using an updated Kriging proxy model to estimate the structural failure probability of the component to obtain a failure probability estimate; calculating the coefficient of variation of the failure probability estimate; if the coefficient of variation is less than or equal to a preset threshold, completing the reliability analysis of the component; and if the coefficient of variation is greater than the preset threshold, increasing the sample pool and executing steps S2 to S6 based on the increased sample pool.

[0149] It should be understood that Fig. 9 Only one exemplary structure of the reliability analysis system 900 is shown. In other examples, the reliability analysis system of the present invention can be implemented in different ways. For example, one or more modules can be added or omitted, or multiple modules can be merged or integrated. For example, the model building module 915 and the model updating module 920 can be merged into a single module.

[0150] Fig.10 The block diagram of the device 1000 including the reliability analysis system based on the Kriging surrogate model of the present invention is shown.

[0151] The apparatus illustrates a general hardware environment in which the present invention may be applied according to its exemplary embodiments.

[0152] Now refer to Fig.10 Device 1000 is described, which is an exemplary embodiment of a hardware device that can be applied to various aspects of the present invention. Device 1000 can be any machine configured to perform processing and / or computing, and can be, but is not limited to, a workstation, a server, a desktop computer, a laptop computer, a tablet computer, a personal digital assistant (PDA), a smart phone, or any combination thereof. The above system can be implemented in whole or in part by device 1000 or similar devices or systems.

[0153] The device 1000 may include components that may be connected to or in communication with the bus 1030 via one or more interfaces. For example, the device 1000 may include the bus 1000, a processor 1005, a memory 1010, an input device 1020, and an output device 1025, among others.

[0154] Processor 1005 may be any type of processor, and may include, but is not limited to, a general purpose processor and / or a dedicated processor (e.g., a special processing chip), an intelligent hardware device (e.g., a general purpose processor, a DSP, a CPU, a microcontroller, an ASIC, an FPGA, a programmable logic device, a discrete gate or transistor logic component, a discrete hardware component, or any combination thereof). In some cases, processor 1005 may be configured to operate a memory array using a memory controller. In other cases, a memory controller (not shown) may be integrated into processor 1005. Processor 1005 may be responsible for managing the bus and general processing, including executing software stored on the memory. Processor 1005 may also be configured to perform various functions described herein related to reliability analysis based on the Kriging proxy model. For example, processor 1005 can be configured to: generate a sample pool based on random variables related to the structural reliability of the component; select a set of initial sample points from the sample pool to constitute an initial training set; establish a Kriging proxy model based on the initial training set; update the Kriging proxy model based on a weighted probability entropy learning strategy to obtain an updated Kriging proxy model; use the updated Kriging proxy model to calculate the average confidence of the sample pool; and if the average confidence meets the confidence requirement, use the updated Kriging proxy model to perform reliability analysis on the component.

[0155] The memory 1010 may be any storage device that can implement data storage. The memory 1010 may include, but is not limited to, a disk drive, an optical storage device, a solid-state memory, a floppy disk, a floppy disk, a hard disk, a magnetic tape or any other magnetic medium, an optical disk or any other optical medium, a ROM (read-only memory), a RAM (random access memory), a cache memory and / or any other memory chip or box, and / or any other medium from which a computer can read data, instructions and / or codes. The memory 1010 may store computer executable software 1015 including computer readable instructions that, when executed, cause the processor to perform various functions described herein related to reliability analysis based on the Kriging proxy model.

[0156] Input device 1020 may be any type of device that can be used to input information.

[0157] Output device 1025 may be any type of device for outputting information. In one embodiment, output device 1025 may be any type of output device that can display information.

[0158] The technical solution of the present invention constructs and updates the Kriging proxy model based on the weighted probability entropy learning strategy, which can quickly improve the accuracy of the proxy model, significantly reduce the amount of calculation compared to the existing learning strategy, and improve the analysis efficiency. At the same time, it also solves the defect that the existing learning strategy cannot describe the overall confidence of the sample pool, which is conducive to practical application in engineering problems.

[0159] The detailed description described above in conjunction with the accompanying drawings describes examples and does not represent all examples that can be implemented or fall within the scope of the claims. The terms "example" and "exemplary" when used in this specification mean "used as an example, instance or illustration" and do not mean "better or better than other examples".

[0160] Reference throughout this specification to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, use of these phrases may refer to more than just one embodiment. Furthermore, the described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0161] The previous description is provided to enable any person skilled in the art to practice the various aspects described herein. Various modifications to these aspects will be readily apparent to those skilled in the art, and the universal principles defined herein may be applied to other aspects. Therefore, the claims are not intended to be limited to the aspects shown herein, but should be granted the full scope consistent with the claims in language, wherein the singular reference to the elements is not intended to mean "there is and only one", but "one or more", unless otherwise specifically stated. Unless otherwise specifically stated, the term "some" refers to one or more. The elements of the various aspects described throughout the present invention are all structurally and functionally equivalent schemes currently or hereafter known to those of ordinary skill in the art and are expressly incorporated herein by reference, and are intended to be covered by the claims.

[0162] It should also be noted that these embodiments may be described as a process depicted as a flow chart, flow diagram, structure diagram, or block diagram. Although the flow chart may describe the operations as sequential processes, many of these operations can be performed in parallel or concurrently. In addition, the order of these operations can be rearranged.

[0163] Although various embodiments have been illustrated and described, it should be understood that the embodiments are not limited to the precise configuration and components described above. Various modifications, substitutions and improvements obvious to those skilled in the art may be made in the arrangement, operation and details of the devices disclosed herein without departing from the scope of the claims.

Claims

1. A reliability analysis method based on Kriging surrogate model, The following steps are involved: S1: Generate a sample pool based on random variables related to the structural reliability of the components; S2: Selecting a set of initial sample points from the sample pool to form an initial training set; S3: Establishing a Kriging proxy model based on the initial training set; S4: updating the Kriging proxy model based on a weighted probability entropy learning strategy to obtain an updated Kriging proxy model; S5: Calculate the average confidence of the sample pool using the updated Kriging proxy model; as well as S6: If the average confidence level meets the confidence level requirement, reliability analysis of the component is performed using the updated Kriging proxy model.

2. The method according to claim 1, It is characterized in that Step S4 further comprises: Selecting new sample points from the sample pool based on the weighted probability entropy learning strategy; Appending the new sample points to the initial training set to obtain an expanded training set; and The Kriging proxy model is updated using the augmented training set to obtain the updated Kriging proxy model.

3. The method according to claim 2, It is characterized in that Selecting new sample points from the sample pool based on the weighted probability entropy learning strategy further includes: Calculating the weighted probability entropy of each sample point in the sample pool that does not belong to the initial training set; and The sample point with the largest weighted probability entropy is selected as the new sample point.

4. The method according to claim 1, It is characterized in that Step S5 further comprises: Calculate the predicted response values ​​of all sample points in the sample pool according to the updated Kriging proxy model; Calculating the confidence of each sample point in the sample pool based on the predicted response values ​​and the true response values ​​of all sample points; and The confidences of all sample points are averaged to obtain the average confidence of the sample pool.

5. The method according to claim 1, It is characterized in that Step S6 further comprises: If the average confidence does not meet the confidence requirement, the process returns to step S4 and step S5 to continue updating the Kriging proxy model until the average confidence calculated using the updated Kriging proxy model meets the confidence requirement.

6. The method according to claim 1, It is characterized in that Performing reliability analysis on the component using the updated Kriging proxy model further includes: estimating the structural failure probability of the component using the updated Kriging surrogate model to obtain a failure probability estimate; calculating a coefficient of variation of the failure probability estimate; If the coefficient of variation is less than or equal to a preset threshold, completing the reliability analysis of the component; and If the coefficient of variation is greater than the preset threshold, the sample pool is enlarged and steps S2 to S6 are performed based on the enlarged sample pool.

7. A reliability analysis system based on Kriging surrogate model, include: A sample pool module, configured to execute step S1: generating a sample pool based on a random variable related to the structural reliability of a component; The initial training set module is used to execute step S2: select a group of initial sample points from the sample pool to form an initial training set; A model building module, used to execute step S3: building a Kriging proxy model according to the initial training set; A model updating module, configured to execute step S4: updating the Kriging proxy model based on a weighted probability entropy learning strategy to obtain an updated Kriging proxy model; A confidence module, used to execute step S5: using the updated Kriging proxy model to calculate the average confidence of the sample pool; as well as The reliability analysis module is used to execute step S6: if the average confidence meets the confidence requirement, then use the updated Kriging proxy model to perform reliability analysis on the component.

8. The system according to claim 7, It is characterized in that The model updating module is further configured to perform step S4 by: Selecting new sample points from the sample pool based on a weighted probability entropy learning strategy; Adding the new sample points to the initial training set to obtain an expanded training set; as well as The Kriging proxy model is updated using the augmented training set to obtain the updated Kriging proxy model.

9. The system according to claim 8, It is characterized in that The model updating module is further configured to select new sample points from the sample pool based on a weighted probability entropy learning strategy by performing the following operations: Calculating the weighted probability entropy of each sample point in the sample pool that does not belong to the initial training set; and The sample point with the largest weighted probability entropy is selected as the new sample point.

10. The system according to claim 7, It is characterized in that The confidence module is further configured to perform step S5 by: Calculate the predicted response values ​​of all sample points in the sample pool according to the updated Kriging proxy model; Calculating the confidence of each sample point in the sample pool based on the predicted response values ​​and the true response values ​​of all sample points; as well as The confidences of all sample points are averaged to obtain the average confidence of the sample pool.

11. The system according to claim 7, It is characterized in that The model updating module is further configured to: If the average confidence does not meet the confidence requirement, the process returns to step S4 and step S5 to continue updating the Kriging proxy model until the average confidence calculated using the updated Kriging proxy model meets the confidence requirement.

12. The system according to claim 7, It is characterized in that The reliability analysis module is further configured to perform reliability analysis on the component using the updated Kriging proxy model by: estimating the structural failure probability of the component using the updated Kriging surrogate model to obtain a failure probability estimate; calculating a coefficient of variation of the failure probability estimate; If the coefficient of variation is less than or equal to a preset threshold, completing the reliability analysis of the component; as well as If the coefficient of variation is greater than the preset threshold, the sample pool is enlarged and steps S2 to S6 are performed based on the enlarged sample pool. 13 . A computer-readable storage medium storing a computer program for reliability analysis based on a Kriging surrogate model, wherein the computer program can be executed by a processor to perform the method according to claim 1 .

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