Method, device and medium for evaluating reliability of multi-section beam structure

Abstract

The present application belongs to the technical field of reliability evaluation, and in particular to a multi-section beam structure reliability evaluation method, device, equipment and medium. For the reliability test data of the multi-section beam structure under the qualitative and quantitative mixed factors, a UD learning function is used to gradually increase the high-quality training samples by comprehensively predicting the uncertainty of the structure performance and the qualitative and quantitative mixed factor distance factor, the Kriging model constructed based on the initial training set is iteratively updated until the set prediction relative error termination criterion is reached, and finally the prediction of the failure probability, a reliability index, is realized. The present application can realize efficient and accurate beam structure reliability evaluation with as few training samples as possible.

Description

Technical Field

[0001] This invention belongs to the field of reliability assessment technology, and in particular to a method, apparatus, equipment and medium for reliability assessment of multi-section beam structures. Background Technology

[0002] Beam structures play a vital role in modern industry, but in practical applications they are susceptible to various complex factors that can lead to malfunctions or failures. Therefore, before applying them, it is essential to conduct a reliability assessment, including the probability of failure (Failure Probability). Failure probability is a key performance indicator. It refers to the probability that a beam structure will lose its intended function under specified conditions and within a specified time, expressed as: (1) In the formula, These are the structural performance values ​​for the beam. It is a structural influencing factor The joint probability density function (PDF) is used to estimate the failure probability. The region containing positive performance factors is the safe region, and the region containing non-positive factors is the failure region. The continuous surface where performance values ​​approach 0 is called the limit state surface (LSS). The key to estimating the failure probability lies in the estimated performance function values ​​near the limit state surface. With the development of modern science and technology, the number of components constituting structures is increasing, the scale of structures is becoming larger, and the costs of research and development and production are rising. This makes the failure problem of beam structures increasingly important. Accurate estimation of the failure probability of beam structures helps to understand the operating status of beam structures in a timely manner and make correct decisions.

[0003] Since the integral solution of equation (1) is relatively complex, statistical methods are commonly used to conduct multiple reliability tests on the beam structure to solve for the failure probability, that is, to use Monte Carlo Simulation (MCS) sampling values. To replace the true value of failure probability ,Right now (2) In the formula, The number of samples for the MCS. The coefficient of variation of the predicted index. It is often used as an evaluation metric for the size of the MCS sample: (3) The MCS approach primarily involves generating a large number of global test points that cover as many combinations of interfering factors as possible. The simulation program then obtains the miss distance values ​​for each test point, replacing the actual values ​​with these values ​​to calculate the failure probability of the beam structure. This process is repeated until the termination condition for the beam structure failure probability evaluation index is met. The relative error of the failure probability... It is often used as an evaluation metric for solving failure probability models. (4) In practical engineering, as structural complexity increases, shortcomings such as increased training ensemble costs and limited solution efficiency arise. Correspondingly improved sampling strategies include subset simulation, importance sampling, and linear sampling, which are applicable to reliability assessment in various scenarios such as high dimensionality, nonlinearity, and low failure probabilities. These methods often introduce surrogate models, establishing a "black box" surrogate model of the "input-output" relationship between a known, finite set of training samples of performance influencing factors and the corresponding performance function values. This model can predict the performance value and estimate the failure probability at any sampling point, reducing the need to solve for the true performance value. Commonly used surrogate models include support vector machines, response surface methodology, artificial neural networks, and Kriging. Among these, the Kriging model directly provides unbiased interpolation estimates of structural performance values ​​and reflects the variance of prediction uncertainty, making it the most widely used.

[0004] Meanwhile, modeling using only the existing initial training sample set cannot adequately account for the limiting state surface. Small differences in the training set can lead to errors in the sign of the predicted performance function, approaching zero, ultimately resulting in a significant deviation in the failure probability estimate. Active Learning (AL) methods, which interact with the external environment to improve understanding of beam structures and models, are often used to correct surrogate models. Within the active learning framework, learning points based on certain addition criteria—that is, combinations of performance influencing factors (new sample points) that significantly improve the failure probability estimate—are added to the training set and the Kriging model is updated. This iterative process is repeated until a certain termination criterion is met. This process is summarized as the Active Learning Kriging (AK) method. The addition criteria are often implemented by setting learning functions, such as the error probability learning function U based on the Kriging surrogate model, and the expected improvement learning functions EFF and information entropy H, with the following expressions: (5) (6) (7) In the formula, and For the Kriging model of sample points The predicted value and the prediction variance represent the performance values. The former characterizes the predictive ability of the Kriging model constructed from the current training set, while the latter characterizes the uncertainty of the prediction. and Let the coefficients represent the cumulative distribution function (CDF) and probability density function of the standard normal distribution, respectively. The regulating factor of the EFF function, and Proportional, usually taken It is evident that different learning functions characterize the addition of training points from their own perspectives, and often consider regions where the predicted value approaches 0 (near the limit state surface), or regions with large prediction variance (i.e., regions with large uncertainty). This can easily cause the range of points added to fall into local clustering regions and become difficult to converge, thus leading to the inadequacy of an excessively large training set.

[0005] In engineering, the requirements for estimating the failure probability of beam structures often include both the accuracy of the estimated failure probability and the efficiency of the solution. The termination criteria corresponding to the aforementioned classic learning functions are mostly based on a threshold value of the learning function itself; for example, the termination criterion for the U learning function is... Existing research has shown that such learning functions often introduce too many unnecessary training points, leading to excessively high training costs. Therefore, the construction of learning functions and more efficient termination criteria need to be improved.

[0006] Furthermore, existing studies have only focused on learning functions based on quantitative structural influence factor data; learning functions for qualitative structural influence factors are currently lacking. However, in practice, the reliability of beam structures often involves a mixture of qualitative and quantitative influence factors. The challenge in efficiently conducting reliability assessments within an active learning framework lies in constructing a Kriging model for mixed qualitative and quantitative factors and measuring the distance between them. Summary of the Invention

[0007] This invention provides a method, apparatus, equipment, and medium for reliability assessment of multi-section beam structures. The key technical problem this invention aims to solve is, based on the initial training set data from reliability tests of multi-section beam structures, how to construct a learning function that integrates qualitative and quantitative factors to guide the selection of high-quality training points, obtain the true performance value of the training point to update the Kriging model, and thus accurately assess the failure probability index with the least possible cost. This invention provides a method, apparatus, equipment, and medium for reliability assessment of multi-section beam structures.

[0008] To achieve the above objectives, the present invention provides the following technical solution: On the one hand, a reliability assessment method for multi-section beam structures is provided, including the following steps: S1, determine the mixed factors affecting the performance of multi-section beam structures. The mixed factors include one or more quantitative factors and one or more qualitative factors, and determine the distribution characteristics of each factor. S2, based on the distribution characteristics of each factor, randomly generate a candidate sample pool containing candidate samples and a test sample dataset containing test samples and their actual performance responses. S3, Based on the Latin hypercube sampling method, an initial training sample containing a mixture of qualitative and quantitative factors is generated to construct a training set of the mixture of qualitative and quantitative factors; S4. Obtain the true performance response corresponding to the qualitative and quantitative mixed factor training set and construct the training set. S5, based on the training set, constructs a Kriging proxy model under a mixture of qualitative and quantitative factors; S6. Use the constructed Kriging surrogate model to predict the performance response of the test sample dataset, calculate the predicted failure probability of the multi-section beam structure, and determine whether the relative error between the predicted failure probability of the multi-section beam structure and the true failure probability of the multi-section beam structure calculated from the actual response value of the test sample dataset meets the preset termination criterion. If it meets the criterion, proceed to S9; otherwise, proceed to S7. S7, construct the UD learning function to select training samples to be supplemented from the candidate sample pool; S8: Add the selected training samples and their actual performance responses to the qualitative and quantitative mixed factor training set, update the qualitative and quantitative mixed factor training set, and return to S4. S9, calculate the coefficient of variation of the predicted failure probability of the multi-section beam structure based on the test sample dataset, and determine whether it is less than the preset threshold; if yes, proceed to S10; if no, return to S2 and expand the candidate sample pool. S10 outputs the final reliability assessment results, including the final Kriging surrogate model and the predicted failure probability of the multi-section beam structure.

[0009] On the other hand, a reliability assessment device for multi-section beam structures is provided to implement the above-mentioned reliability assessment method for multi-section beam structures, including: The factor configuration module is used to determine the mixed factors that affect the performance of multi-section beam structures. The mixed factors include one or more quantitative factors and one or more qualitative factors, and determine the distribution characteristics of each factor. The sample generation module is used to randomly generate a candidate sample pool containing candidate samples and a test sample dataset containing test samples and their actual performance responses, based on the distribution characteristics of each factor. The initial training sample generation module is used to generate initial training samples containing qualitative and quantitative mixed factors based on the Latin hypercube sampling method, and to construct a qualitative and quantitative mixed factor training set. The training set construction module is used to obtain the true performance response corresponding to the qualitative and quantitative mixed factor training set and construct the training set. The proxy model construction and update module is used to construct a Kriging proxy model with qualitative and quantitative mixed factors based on the training set. The reliability calculation and error judgment module is used to predict the performance response of the test sample dataset using the constructed Kriging surrogate model, calculate the predicted failure probability value of the multi-section beam structure, and judge whether the relative error between the predicted failure probability value of the multi-section beam structure and the true failure probability value of the multi-section beam structure calculated from the actual response value of the test sample dataset meets the preset termination criteria. The active learning and sample selection module is used to select training samples to be supplemented from the candidate sample pool based on the constructed UD learning function when the termination criteria are not met. The training set update module is used to add the selected training samples and their true performance responses to the training set, and trigger the surrogate model construction and update module to rebuild the Kriging surrogate model under the qualitative and quantitative mixed factors. The convergence judgment and result output module is used to further calculate the coefficient of variation of the predicted failure probability value of the multi-section beam structure based on the test sample dataset when the termination criterion is met, and output the final reliability assessment result when the coefficient of variation is less than a preset threshold, including the final Kriging surrogate model and the predicted failure probability value of the multi-section beam structure.

[0010] On the other hand, the present invention provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the steps of the above-described reliability assessment method for multi-section beam structures.

[0011] On the other hand, the present invention provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the steps of the above-described reliability assessment method for multi-section beam structures.

[0012] On the other hand, the present invention provides a computer program product stored on a computer-readable storage medium and including computer instructions that, when executed by a processor, cause an electronic device to implement the steps of the above-described reliability assessment method for multi-section beam structures.

[0013] Compared with the prior art, the beneficial effects of the present invention are as follows: This invention provides a reliability assessment method for multi-section beam structures. Based on reliability test data of multi-section beam structures under a mixture of qualitative and quantitative factors, a high-quality training sample is gradually added through a UD learning function that integrates the uncertainty of structural performance prediction and the distance factor of the mixture of qualitative and quantitative factors. The Kriging model constructed based on the initial training set is iteratively updated until the set prediction relative error termination criterion is reached, and finally the prediction of the failure probability, a reliability index, is achieved.

[0014] This invention proposes an UD learning function that considers a mixture of qualitative and quantitative factors based on an active learning method. Using a relative error termination criterion based on the prediction results, it achieves accurate estimation of the failure probability of beam structures with a limited number of training samples. Furthermore, an example demonstrates that the method proposed in this invention can sequentially guide the selection of subsequent training points based on a QQ Kriging model constructed from the initial reliability test data of the beam structure, thereby supplementing the training data with high-quality data. This method exhibits significant advantages in terms of high solution efficiency and high prediction accuracy in estimating the failure probability of beam structures. Attached Figure Description

[0015] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0016] Figure 1 This is a flowchart of a reliability assessment method for multi-section beam structures provided in one embodiment; Figure 2 This is a schematic diagram of six cross-sectional shapes for the beam cross-sectional area in one embodiment, wherein... Figure 2 (a) is a diameter of A circular cross-section; Figure 2 (b) is the height of A square cross-section; Figure 2 (c) represents the height and width. The thickness is 0.1. The I-shaped cross-section; Figure 2 (d) is the outer side length. The thickness is 0.15. A hollow square cross-section; Figure 2 (e) represents the outer diameter. The thickness is 0.15. A hollow circular cross-section; Figure 2 (f) represents the height and width. The thickness is 0.1. H-shaped cross-section; Figure 3 This is a block diagram of an electronic device in one embodiment. Detailed Implementation

[0017] The technical solution of the present invention will now be clearly and completely described through specific embodiments. Obviously, the described embodiments are merely some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0018] One embodiment provides a reliability assessment method for multi-section beam structures, comprising the following steps: S1, determine the mixed factors affecting the performance of multi-section beam structures. The mixed factors include one or more quantitative factors and one or more qualitative factors, and determine the distribution characteristics of each factor. S2, based on the distribution characteristics of each factor, randomly generate a candidate sample pool containing candidate samples and a test sample dataset containing test samples and their actual performance responses. S3, Based on the Latin hypercube sampling method, an initial training sample containing a mixture of qualitative and quantitative factors is generated to construct a training set of the mixture of qualitative and quantitative factors; S4. Obtain the true performance response corresponding to the qualitative and quantitative mixed factor training set and construct the training set. S5, based on the training set, constructs a Kriging proxy model under a mixture of qualitative and quantitative factors; S6. Use the constructed Kriging surrogate model to predict the performance response of the test sample dataset, calculate the predicted failure probability of the multi-section beam structure, and determine whether the relative error between the predicted failure probability of the multi-section beam structure and the true failure probability of the multi-section beam structure calculated from the actual response value of the test sample dataset meets the preset termination criterion. If it meets the criterion, proceed to S9; otherwise, proceed to S7. S7, construct the UD learning function to select training samples to be supplemented from the candidate sample pool; S8: Add the selected training samples and their actual performance responses to the qualitative and quantitative mixed factor training set, update the qualitative and quantitative mixed factor training set, and return to S4. S9, calculate the coefficient of variation of the predicted failure probability of the multi-section beam structure based on the test sample dataset, and determine whether it is less than the preset threshold; if yes, proceed to S10; if no, return to S2 and expand the candidate sample pool. S10 outputs the final reliability assessment results, including the final Kriging surrogate model and the predicted failure probability of the multi-section beam structure.

[0019] The above embodiments combine the qualitative and quantitative mixed factor UD learning function, sequentially supplement the training set to update the Kriging surrogate model under the qualitative and quantitative mixed factor, and based on the set prediction relative error termination criterion, can achieve efficient and accurate reliability assessment of beam structures with as few training samples as possible.

[0020] This invention primarily considers the qualitative factors of different cross-sections of multi-section beam structures and the quantitative factors of the beam structure's own dimensions. In practice, this invention is also applicable to other qualitative and quantitative factors of beam structures. (Quantitative factors) Engineering parameters related to the material properties, geometric dimensions, and external loads of the multi-section beam, including but not limited to Young's modulus, length, width, and the magnitude of the applied external force; qualitative factors. The classification variable describes the cross-sectional shape type of the multi-section beam, including but not limited to circular, square, or I-shaped cross-sections. The actual performance response... The structural mechanical response of the multi-section beam under a given combination of factors is used to evaluate its reliability, including but not limited to deformation, displacement or stress at critical locations.

[0021] This invention first determines the mixing factor that affects the performance of multi-section beam structures. and its distribution characteristics, including Quantitative factors and Qualitative factors For example, the Young's modulus of a certain beam follows a normal distribution. The length of the beam follows a uniform distribution. .

[0022] Based on the distribution characteristics of each factor, randomly generate... Candidate pool of candidate samples For example, for a factor that follows a normal distribution ,according to A certain number of normally distributed random numbers are generated by taking values.

[0023] Based on the distribution characteristics of each factor, randomly generate... Test sample set of 1 test sample and obtain its real response. This yields a test sample dataset containing test samples and their actual performance responses. .

[0024] To ensure good uniformity and space-filling properties in the initial training set, the classic Latin hypercube sampling (LHS) method is used to generate training samples with qualitative and quantitative mixing factors. And obtain its corresponding actual performance response. Obtain the initial training set The empirical value for the initial training set size is... When using LHS, the range of values ​​for the factor must be predetermined. For example, the upper and lower limits of a uniformly distributed factor can be used as the range. For a factor that follows a normal distribution... When the range of values ​​is not explicitly given, an empirical range can be used. .

[0025] In one embodiment, constructing a Kriging proxy model with qualitative and quantitative mixed factors based on the current training set includes the following steps: For the first training set Sample data In the Kriging proxy model with a mixture of qualitative and quantitative factors, the following conditions are met: (8) in , The size of the training set; For the first Qualitative and quantitative confluence factors for individual sample data For the first A set of basis functions corresponding to each sample data point, including first-order... Second order Step basis functions; For regression coefficients, First order Second order Step The regression coefficients corresponding to the basis functions; , They are respectively , The error terms at each point have a mean of 0 and a variance of . The normal distribution; For the first Qualitative and quantitative mixing factors for individual sample data; covariance of the error term , , , Gaussian correlation function: (9) For inclusion Qualitative factor combination consisting of quantitative factors as well as A combination of qualitative factors consisting of several qualitative factors. , , For indicator functions, They represent The One quantitative factor, They represent The One quantitative factor, for The One quantitative factor, for The One quantitative factor, , For the first The true performance response of a sample data set For hyperparameters, including the first Hyperparameters of a quantitative factor and the Hyperparameters of a qualitative factor , , The first The first sample data, the first The first sample data A qualitative factor, .

[0026] Regression coefficients of a Kriging proxy model with mixed qualitative and quantitative factors Hyperparameters and variance Estimate using the following steps: The true performance response of the training set Modeled as follows: follows the mean The variance is The Gaussian correlation matrix is Multivariate normal distribution: (10) Its likelihood function is: (11) Trend function matrix Gaussian correlation matrix ,have: (12) (13) Log-likelihood function using maximum likelihood estimation: (14) Regression coefficient and variance The estimated value , They are respectively: (15) (16) Hyperparameters The estimated value The following equation is obtained by optimizing the solution: (17) After constructing the current Kriging proxy model with mixed qualitative and quantitative factors, the candidate sample pool is directly... Sample data in As input, sample data can be obtained. The corresponding predicted performance response values ​​and prediction variances are as follows: (18) (19) in and It is an intermediate variable.

[0027] In step S6 of this invention, it is determined whether the relative error termination criterion is met. Specifically, the relative error between the predicted failure probability value of the multi-section beam structure and the true failure probability value of the multi-section beam structure calculated from the actual response values ​​of the test sample dataset is determined. Is it less than the set relative error threshold? If the value is less than the preset termination criterion, then proceed to S9; otherwise, proceed to S7. The preset termination criterion is: (20) In the formula, and These are the true failure probability values ​​of the multi-section beam structure calculated from the actual response values ​​of the test sample dataset obtained by the MCS method, and the predicted failure probability values ​​of the multi-section beam structure obtained by the Kriging surrogate model based on the current qualitative and quantitative mixed factor. In this invention, these are defined as... .

[0028] In S7 of one embodiment, the UD learning function is constructed to select training samples to be supplemented from the candidate sample pool, including: S7.1 Calculate the comprehensive distance between each candidate sample in the candidate sample pool and each training sample in the current training set; For any candidate sample in the candidate sample pool It is related to any training sample in the current training set. The combined distance between Calculate using the following formula: (twenty one) in, , The number of candidate samples in the candidate sample pool is given. The comprehensive distance between the two samples is obtained by calculating the distance between the quantitative part and the qualitative part of the mixed factor of the two samples. The quantitative part uses Euclidean distance and the qualitative part uses Hamming distance. Candidate samples in the candidate sample pool The A quantitative factor, the training samples in the current training set. No. One quantitative factor, , These are the weighting coefficients. Candidate samples in the candidate sample pool The One qualitative factor, the training samples in the current training set. No. A qualitative factor, , , This represents the number of training samples in the current training set.

[0029] S7.2, based on the candidate sample pool ( Each candidate sample in the candidate sample set and the current training set ( ) The distance matrix between the current training set and the candidate sample pool is constructed by combining the comprehensive distances between each training sample in the training set. (twenty two) S7.3 For each candidate sample in the candidate sample pool, take the minimum value of the comprehensive distance between the candidate sample and all training samples in the current training set as the distance index of the candidate sample. ; (twenty three) in .

[0030] S7.4, combine the U function, which reflects the uncertainty of prediction, with the distance index of candidate samples to construct the UD learning function for each candidate sample in the candidate sample pool; For the first in the candidate sample pool candidate samples Its UD learning function for: (twenty four) In the formula, and The current Kriging surrogate model in candidate samples The predicted mean and variance of the performance response at the location, , This represents the number of samples in the candidate sample pool.

[0031] At this point, the UD function encompasses both the symbolic prediction uncertainty and the distance metric measured by the U function. The latter ensures that the newly added point is far from the current training set, resulting in better overall spatial filling of the training set.

[0032] S7.5, select the candidate sample with the smallest UD learning function value as the next training sample to be supplemented. ; (25) S8, Add to the current training set, i.e., the updated current training set. , Return to S4.

[0033] S9, use formula (3) to calculate the coefficient of variation of the predicted failure probability of the multi-section beam structure based on the test sample dataset. The coefficient of variation Compare with a preset threshold, such as 5%. If the sample size of the MCS is sufficient, proceed to step S10; otherwise, increase the sample size of the candidate sample pool and return to S2.

[0034] S10 outputs the final reliability assessment results, including the final Kriging surrogate model and the predicted failure probability of the multi-section beam structure.

[0035] like Figure 1 As shown, the flowchart of a reliability assessment method for a multi-section beam structure according to the above embodiment is briefly described as follows: (1) First, determine the mixing factors that affect the performance of multi-section beam structures. and sample generation methods; (2) Generate candidate sample pool Test sample dataset ; (3) Generate a qualitative and quantitative mixed factor training set ; (4) Obtain the training set of qualitative and quantitative mixed factors. The corresponding actual performance response is obtained ; (5) Based on Construct the QQ Kriging model (i.e., the Kriging proxy model under a mixture of qualitative and quantitative factors). (6) Determine whether the termination criterion is met. If it is met, proceed to (9); otherwise, proceed to (7). (7) Calculate The UD learning function is used to select training samples to be supplemented; (8) Select the training samples Add qualitative and quantitative mixed factor training set, update qualitative and quantitative mixed factor training set. Then return (4); (9) Calculate the coefficient of variation Determine whether it satisfies If satisfied, proceed to (10); otherwise expand. , return (2); (10) Output the QQ Kriging model and calculate the predicted failure probability of the multi-section beam structure. ,Finish.

[0036] On the other hand, a reliability assessment device for multi-section beam structures is provided, which is used to implement a reliability assessment method for multi-section beam structures, including: The factor configuration module is used to determine the mixed factors that affect the performance of multi-section beam structures. The mixed factors include one or more quantitative factors and one or more qualitative factors, and determine the distribution characteristics of each factor. The sample generation module is used to randomly generate a candidate sample pool containing candidate samples and a test sample dataset containing test samples and their actual performance responses, based on the distribution characteristics of each factor. The initial training sample generation module is used to generate initial training samples containing qualitative and quantitative mixed factors based on the Latin hypercube sampling method, and to construct a qualitative and quantitative mixed factor training set. The training set construction module is used to obtain the true performance response corresponding to the qualitative and quantitative mixed factor training set and construct the training set. The proxy model construction and update module is used to construct a Kriging proxy model with qualitative and quantitative mixed factors based on the training set. The reliability calculation and error judgment module is used to predict the performance response of the test sample dataset using the constructed Kriging surrogate model, calculate the predicted failure probability value of the multi-section beam structure, and judge whether the relative error between the predicted failure probability value of the multi-section beam structure and the true failure probability value of the multi-section beam structure calculated from the actual response value of the test sample dataset meets the preset termination criteria. The active learning and sample selection module is used to select training samples to be supplemented from the candidate sample pool based on the constructed UD learning function when the termination criteria are not met. The training set update module is used to add the selected training samples and their true performance responses to the training set, and trigger the surrogate model construction and update module to rebuild the Kriging surrogate model under the qualitative and quantitative mixed factors. The convergence judgment and result output module is used to further calculate the coefficient of variation of the predicted failure probability value of the multi-section beam structure based on the test sample dataset when the termination criterion is met, and output the final reliability assessment result when the coefficient of variation is less than a preset threshold, including the final Kriging surrogate model and the predicted failure probability value of the multi-section beam structure.

[0037] To demonstrate the effectiveness of this invention, a specific example is provided below to analyze the proposed solution: In this example, we consider the classic problem of beam bending resistance, taking into account factors affecting beam bending, including beam length. , beam width and beam cross-sectional shape Three factors. Among them, the beam length , beam width These are two quantitative factors: the cross-sectional shape of the beam. It is a six-level qualitative factor. (Refer to...) Figure 2 This is a schematic diagram of six cross-sectional shapes for beam cross-sectional area, among which... Figure 2 (a) is a diameter of A circular cross-section; Figure 2 (b) is the height of A square cross-section; Figure 2 (c) represents the height and width. The thickness is 0.1. The I-shaped cross-section; Figure 2 (d) is the outer side length. The thickness is 0.15. A hollow square cross-section; Figure 2 (e) represents the outer diameter. The thickness is 0.15. A hollow circular cross-section; Figure 2 (f) represents the height and width. The thickness is 0.1. The H-shaped cross section.

[0038] Elastic modulus of the beam It operates within its elastic range. Table 1 provides the reliability test factor information for this example. Assume the beam length... and beam width Such a continuous quantitative factor can take any value within its range, and the beam length... The value range is 10 meters to 20 meters, and the beam width is... The value range is 1~2 meters. For the qualitative factor of the beam cross-sectional shape, six different shape levels are sequentially labeled as 1, 2, ..., 6, and there is no magnitude relationship between the values. In the example, the shape of the beam cross-sectional area... The disordered qualitative factor at level 6 only serves as a classification marker in the experiment.

[0039] Table 1 Reliability Test Factors for Beam Structures

[0040] In the reliability test of this example, one end of the beam was fixed, and a pressure was applied in the vertical direction of the free end. The force, and the deformation at the free end of the beam, are denoted as the performance value. Its theoretical expression is: (26) in, ; Set threshold Then the performance function The expression is: (27) Based on the method proposed in this invention, an analysis was conducted on an example. Furthermore, to avoid the influence of random factors, the process was repeated 10 times, and the average result was taken to obtain the final result.

[0041] Taking a single random run as an example, the process is explained in detail. In this example, there are 2 quantitative factors and 1 qualitative factor, with the qualitative factor having a level of 6. Therefore, the initial number of training samples is 10. Table 2 shows an example of the initial training samples based on LHS sampling, which shows that the levels of the three factors are relatively evenly distributed.

[0042] Table 2 Examples of Initial Training Samples for Reliability Tests of Beam Structures

[0043] According to the technical solution proposed in this invention, a reliability assessment of the beam structure was conducted. The solution was implemented through programming, and the results of 10 random runs are shown in Table 3. Finally, with an average increase of 64.1 training samples, an estimated failure probability was obtained. The "true" value of the beam structure failure probability obtained by MCS The relative error between the two is .

[0044] Table 3. Results of 10 reliability tests on the beam structure

[0045] Figure 3 A block diagram of an embodiment of an electronic device is shown, such as Figure 3 As shown, the electronic device includes one or more processors and a memory. The memory stores a computer program, and when the processor executes the computer program, it implements the steps of the reliability assessment method for multi-section beam structures provided in any of the above embodiments. The processor may be a central processing unit (CPU) or other processing unit with data processing capabilities and / or instruction execution capabilities, and can control other components in the electronic device to perform desired functions. The memory may include one or more computer program products, which may include various forms of computer-readable storage media, such as volatile memory and / or non-volatile memory. Volatile memory may include, for example, random access memory (RAM) and / or cache memory. Non-volatile memory may include, for example, read-only memory (ROM), hard disk, flash memory, etc.

[0046] In one example, the electronic device may also include input devices and output devices, which are interconnected via a bus system and / or other forms of connection mechanism (not shown).

[0047] Of course, for the sake of simplicity, Figure 3 Only some of the components of the electronic device relevant to this application are shown in this illustration; components such as buses, input / output interfaces, etc., are omitted. In addition, the electronic device may include any other suitable components depending on the specific application.

[0048] Embodiments of the present invention may also be computer-readable storage media storing a computer program thereon, which, when executed by a processor, implements the steps of the reliability assessment method for multi-section beam structures provided in any of the above embodiments. The computer-readable storage medium may be any combination of one or more readable media. The readable medium may be a readable signal medium or a readable storage medium. The readable storage medium may include, for example, but not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, or any combination thereof. More specific examples of readable storage media (a non-exhaustive list) include: electrical connections having one or more wires, portable disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0049] The basic principles of this application have been described above with reference to specific embodiments. However, it should be noted that the advantages, benefits, and effects mentioned in this application are merely examples and not limitations, and should not be considered as essential features of each embodiment of this application. Furthermore, the specific details disclosed above are for illustrative and facilitative purposes only, and are not limitations. These details do not restrict the application from being implemented using the specific details described above.

[0050] The block diagrams of devices, apparatuses, devices, and systems involved in this application are merely illustrative examples and are not intended to require or imply that they must be connected, arranged, or configured in the manner shown in the block diagrams. As those skilled in the art will recognize, these devices, apparatuses, devices, and systems can be connected, arranged, and configured in any manner. Words such as “comprising,” “including,” “having,” etc., are open-ended terms meaning “including but not limited to,” and are used interchangeably with them. The terms “or” and “and” as used herein refer to the terms “and / or,” and are used interchangeably with them unless the context clearly indicates otherwise. The term “such as” as used herein refers to the phrase “such as but not limited to,” and is used interchangeably with it.

[0051] It should also be noted that in the apparatus, equipment, and methods of this application, the components or steps can be disassembled and / or recombined. These disassemblies and / or recombinations should be considered as equivalent solutions of this application.

[0052] The above description of the disclosed aspects is provided to enable any person skilled in the art to make or use this application. Various modifications to these aspects will be readily apparent to those skilled in the art, and the general principles defined herein can be applied to other aspects without departing from the scope of this application. Therefore, this application should not be limited to the aspects shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

[0053] The above description has been given for purposes of illustration and description. Furthermore, this description is not intended to limit the embodiments of this application to the forms disclosed herein. Although numerous exemplary aspects and embodiments have been discussed above, those skilled in the art will recognize certain variations, modifications, alterations, additions, and sub-combinations thereof.

Claims

1. A reliability assessment method for multi-section beam structures, characterized in that, Includes the following steps: S1, determine the mixed factors affecting the performance of multi-section beam structures. The mixed factors include one or more quantitative factors and one or more qualitative factors, and determine the distribution characteristics of each factor. S2, based on the distribution characteristics of each factor, randomly generate a candidate sample pool containing candidate samples and a test sample dataset containing test samples and their actual performance responses. S3, Based on the Latin hypercube sampling method, an initial training sample containing a mixture of qualitative and quantitative factors is generated to construct a training set of the mixture of qualitative and quantitative factors; S4. Obtain the true performance response corresponding to the qualitative and quantitative mixed factor training set and construct the training set. S5, based on the training set, constructs a Kriging proxy model with qualitative and quantitative mixed factors, including: For the first in the training set Sample data In the Kriging proxy model with a mixture of qualitative and quantitative factors, the following conditions are met: in , The size of the training set; For the first Qualitative and quantitative confluence factors for individual sample data For the first A set of basis functions corresponding to each sample data point, including first-order... Second order Step basis functions; For regression coefficients, First order Second order Step The regression coefficients corresponding to the basis functions; , They are respectively , The error terms at each point have a mean of 0 and a variance of . The normal distribution; For the first Qualitative and quantitative mixing factors for individual sample data; covariance of the error term , , , Gaussian correlation function: For inclusion Qualitative factor combination consisting of quantitative factors as well as A combination of qualitative factors, consisting of qualitative factors , , For indicator functions, They represent The One quantitative factor, They represent The One quantitative factor, for The One quantitative factor, for The One quantitative factor, , For the first The true performance response of a sample data set For hyperparameters, including the first Hyperparameters of a quantitative factor and the Hyperparameters of a qualitative factor , , The first The first sample data, the first The first sample data A qualitative factor, ; S6. Use the constructed Kriging surrogate model to predict the performance response of the test sample dataset, calculate the predicted failure probability of the multi-section beam structure, and determine whether the relative error between the predicted failure probability of the multi-section beam structure and the true failure probability of the multi-section beam structure calculated from the actual response value of the test sample dataset meets the preset termination criterion. If it meets the criterion, proceed to S9; otherwise, proceed to S7. S7, Construct the UD learning function to select training samples to be supplemented from the candidate sample pool, including: S7.1 Calculate the comprehensive distance between each candidate sample in the candidate sample pool and each training sample in the current training set; S7.2 Construct a distance matrix between the current training set and the candidate sample pool based on the comprehensive distance between each candidate sample in the candidate sample pool and each training sample in the current training set; S7.3 For each candidate sample in the candidate sample pool, take the minimum value of the comprehensive distance between the candidate sample and each training sample in the current training set as the distance index of the candidate sample. S7.4, combining the U function reflecting prediction uncertainty with the distance index of candidate samples, constructs an UD learning function for each candidate sample in the candidate sample pool. For the th candidate sample in the candidate sample pool... candidate samples Its UD learning function for: In the formula, and The current Kriging surrogate model in candidate samples The predicted mean and variance of the performance response at the location, , This represents the number of samples in the candidate sample pool. This is a distance metric for candidate samples; S7.5 Select the candidate sample with the smallest UD learning function value as the next training sample to be supplemented; S8: Add the selected training samples and their actual performance responses to the qualitative and quantitative mixed factor training set, update the qualitative and quantitative mixed factor training set, and return to S4. S9, calculate the coefficient of variation of the predicted failure probability of the multi-section beam structure based on the test sample dataset, and determine whether it is less than the preset threshold; if yes, proceed to S10; otherwise, return to S2 and expand the candidate sample pool. S10 outputs the final reliability assessment results, including the final Kriging surrogate model and the predicted failure probability of the multi-section beam structure.

2. The reliability assessment method for multi-section beam structures according to claim 1, characterized in that, The quantitative factors are engineering parameters related to the material properties, geometric dimensions, and external loads of the multi-section beam, including Young's modulus, length, width, and the magnitude of the applied external force; the qualitative factors are categorical variables describing the cross-sectional shape type of the multi-section beam; and the performance response is the structural mechanical response of the multi-section beam under a given qualitative-quantitative hybrid factor, used to evaluate its reliability.

3. The reliability assessment method for multi-section beam structures according to claim 1, characterized in that, The regression coefficients of the Kriging proxy model under the qualitative and quantitative mixed factors in S5 Hyperparameters and variance Estimate using the following steps: The true performance response of the training set Modeled as follows: follows the mean The variance is The Gaussian correlation matrix is multivariate normal distribution Gaussian correlation matrix The elements in the corresponding ,have: Regression coefficient and variance The estimated value , They are respectively: Hyperparameters The estimated value The following equation is obtained by optimizing the solution: 。 4. The reliability assessment method for multi-section beam structures according to claim 1, 2, or 3, characterized in that, In S6, the relative error between the predicted failure probability of the multi-section beam structure and the true failure probability of the multi-section beam structure calculated from the actual response values ​​of the test sample dataset is determined. Is it less than the set relative error threshold? If the value is less than the preset termination criterion, then proceed to S9; otherwise, proceed to S7.

5. A reliability assessment device for multi-section beam structures, used to implement the reliability assessment method for multi-section beam structures as described in claim 1, characterized in that, include: The factor configuration module is used to determine the mixed factors that affect the performance of multi-section beam structures. The mixed factors include one or more quantitative factors and one or more qualitative factors, and determine the distribution characteristics of each factor. The sample generation module is used to randomly generate a candidate sample pool containing candidate samples and a test sample dataset containing test samples and their actual performance responses, based on the distribution characteristics of each factor. The initial training sample generation module is used to generate initial training samples containing qualitative and quantitative mixed factors based on the Latin hypercube sampling method, and to construct a qualitative and quantitative mixed factor training set. The training set construction module is used to obtain the true performance response corresponding to the qualitative and quantitative mixed factor training set and construct the training set. The proxy model construction and update module is used to construct a Kriging proxy model with qualitative and quantitative mixed factors based on the training set. The reliability calculation and error judgment module is used to predict the performance response of the test sample dataset using the constructed Kriging surrogate model, calculate the predicted failure probability value of the multi-section beam structure, and judge whether the relative error between the predicted failure probability value of the multi-section beam structure and the true failure probability value of the multi-section beam structure calculated from the actual response value of the test sample dataset meets the preset termination criteria. The active learning and sample selection module is used to select training samples to be added from the candidate sample pool based on the constructed UD learning function when the termination criteria are not met. The training set update module is used to add the selected training samples and their true performance responses to the training set, and trigger the surrogate model construction and update module to rebuild the Kriging surrogate model under the qualitative and quantitative mixed factors. The convergence judgment and result output module is used to further calculate the coefficient of variation of the predicted failure probability value of the multi-section beam structure based on the test sample dataset when the termination criterion is met, and output the final reliability assessment result when the coefficient of variation is less than a preset threshold, including the final Kriging surrogate model and the predicted failure probability value of the multi-section beam structure.

6. An electronic device comprising a memory and a processor, characterized in that: The memory stores a computer program, and when the processor executes the computer program, it implements the steps of the reliability assessment method for multi-section beam structures as described in claim 1.

7. A computer storage medium storing a computer program thereon, characterized in that: When the computer program is executed by the processor, it implements the steps of the reliability assessment method for multi-section beam structures as described in claim 1.

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