Method and device for determining structural reliability based on a multi-fidelity model

Abstract

The application provides a structure reliability determination method and device based on a multi-fidelity model, relates to the technical field of structure reliability analysis, and generates a multi-fidelity active learning function with a sampling position and model fidelity as independent variables; the sampling position of multiple new sampling points and the model fidelity corresponding to the sampling position are determined at one time by optimizing the function; a sample set is updated and a multi-fidelity Gaussian process posterior is recalculated according to the sampling position and the model fidelity, and the posterior mean of the failure probability is output until a stop criterion is met. The application realizes joint optimization of the sampling position and the model fidelity, overcomes the limitation of traditional methods of optimizing only the sampling position, reduces inefficient calling of a high-fidelity model, and significantly reduces the calculation cost on the premise of ensuring the accuracy of failure probability estimation.

Description

Technical Field

[0001] This invention relates to the field of structural reliability analysis technology, and in particular to a method and apparatus for determining structural reliability based on a multi-fidelity model. Background Technology

[0002] Structural reliability analysis is a key technology for ensuring the safe operation of engineering structures under uncertain conditions. The core objective of structural reliability calculation is to solve for the failure probability. ,in For describing the uncertainties of random variables such as load, material properties, and geometric dimensions, For performance function ( (This indicates structural failure). Since the performance functions of actual engineering structures are usually implicit in high-precision numerical simulation models (such as finite element analysis), the computational cost of a single evaluation is high, making it difficult to afford to directly solve for the failure probability through methods such as Monte Carlo simulation that require a large number of samples in engineering practice.

[0003] To reduce computational costs, existing technologies have successively developed first-order reliability methods, second-order reliability methods, response surface methodology, Kriging surrogate models, and active learning reliability analysis methods. In recent years, to further utilize the commonly found low-cost, low-fidelity models in engineering (such as simplified physical models and coarse-grid models), multi-fidelity modeling methods have been introduced into the field of structural reliability analysis. Existing active learning reliability analysis methods based on multi-fidelity surrogate models reduce computational costs to some extent by fusing the global trend of the low-fidelity model with the local correction information of the high-fidelity model, and by combining active learning to select sample points near the failure boundary.

[0004] However, existing multi-fidelity reliability analysis methods can only optimize the sampling location when selecting new samples in each iteration, and cannot simultaneously decide which fidelity model should be used for that sample. Since the computational costs of low-fidelity models and high-fidelity models often differ by tens or even hundreds of times, the lack of a joint optimization mechanism for sampling location and model fidelity means that high-fidelity models may still be used inefficiently, making it difficult to achieve an effective balance between computational cost and estimation accuracy. This problem is particularly prominent in complex engineering structures (such as critical load-bearing components in aerospace) where the computational cost of high-fidelity models is extremely high.

[0005] Therefore, there is an urgent need for a structural reliability calculation method that can jointly optimize sampling location and model fidelity. Summary of the Invention

[0006] To address the problem in existing technologies where structural reliability calculations cannot jointly optimize sampling location and model fidelity, this invention provides a method and apparatus for determining structural reliability based on a multi-fidelity model. The technical solution is as follows: On the one hand, a method for determining structural reliability based on a multi-fidelity model is provided, including: S1. Determine the low-fidelity sample set and the high-fidelity sample set. Use the high-fidelity model to evaluate the high-fidelity sample set to obtain the first response output. Use the low-fidelity model to evaluate the low-fidelity sample set to obtain the second response output. Calculate the model difference between the high-fidelity samples and the low-fidelity samples based on the first response output and the second response output. Determine the initial observation dataset of the low-fidelity model and the initial observation dataset of the model difference. Determine the multi-fidelity Gaussian process posterior of the performance function based on the initial observation dataset of the low-fidelity model and the initial observation dataset of the model difference. S2. Based on the posterior of the multi-fidelity Gaussian process, calculate the posterior mean and posterior standard deviation of the failure probability; S3. When the posterior mean and posterior standard deviation of the failure probability do not meet the preset convergence condition, increase the importance sampling sample and recalculate the posterior mean and posterior standard deviation of the failure probability until the posterior mean and posterior standard deviation of the failure probability meet the preset convergence condition. S4. After the posterior mean of the failure probability and the posterior standard deviation of the failure probability satisfy the convergence condition, if the current multifidelity Gaussian process posterior does not satisfy the preset stopping criterion, a multifidelity active learning function is generated with sampling position and model fidelity as independent variables. By optimizing the multifidelity active learning function, the sampling positions of multiple new sampling points and the model fidelity corresponding to each new sampling point are determined. Then, the low-fidelity sample set and the high-fidelity sample set are updated according to the determined sampling positions and model fidelity, and the process returns to S1 to recalculate the multifidelity Gaussian process posterior. S5. When the posterior of the current multifidelity Gaussian process satisfies the stopping criterion, output the posterior mean of the failure probability as the calculated failure probability value.

[0007] This invention achieves joint optimization of sampling position and model fidelity by generating an active learning function that simultaneously uses sampling position and model fidelity as independent variables. This overcomes the limitation of traditional methods that only optimize sampling position and reduces inefficient calls to high-fidelity models.

[0008] Optionally, before step S1, the method further includes: Using the Hammersley sequence, in standard normal space, the radius is... Genesis within the supersphere We obtain an initial low-fidelity sample set by taking a few low-fidelity samples. A swapping algorithm is used to select from the initial low-fidelity sample set. One sample is used as a high-fidelity sample to generate the initial high-fidelity sample set.

[0009] The initial sample set was constructed using the Hammersley sequence and exchange algorithm, which ensured the spatial uniformity of the samples and provided high-quality initial data for subsequent modeling.

[0010] Optionally, the determination of the multifidelity Gaussian process posterior of the performance function based on the initial observation dataset of the low-fidelity model and the initial observation dataset of the model difference in S1 includes: Based on observation dataset and Hyperparameters in the prior of multifidelity Gaussian processes and The marginal likelihood is maximized for estimation, and the multifidelity Gaussian process posterior of the performance function is calculated, where... This represents the prior mean of a low-fidelity Gaussian process. This represents the standard deviation of the signal in a low-fidelity Gaussian process. Each element in the diagram represents the length scale of the low-fidelity Gaussian process in the corresponding dimension. This represents the scale factor in the prior of a multifidel Gaussian process. The standard deviation of the signal representing the Gaussian process of model bias, [ Each element in ] represents the length scale of the model bias Gaussian process in the corresponding dimension.

[0011] By maximizing the marginal likelihood estimation hyperparameter, adaptive fusion of information sources with different precision was achieved, thereby improving the accuracy of the surrogate model.

[0012] Optionally, the calculation of the posterior mean and posterior standard deviation of the failure probability in S2 includes: The posterior mean of the failure probability is calculated using a numerical integration method based on variance-amplified importance sampling. Posterior standard deviation.

[0013] By employing variance amplification importance sampling to calculate the posterior mean and posterior standard deviation of the failure probability, the computational cost is reduced while ensuring accuracy.

[0014] Optionally, the preset convergence condition in S3 includes: The variance of the posterior mean of the failure probability is less than a first preset threshold, and the variance of the posterior standard deviation of the failure probability is less than a second preset threshold.

[0015] By using the variance of the posterior mean and the variance of the posterior standard deviation of the failure probability as convergence criteria, the statistical stability of the estimation results is ensured.

[0016] Optionally, the multi-fidelity active learning function includes: a multi-fidelity variance posterior contribution function.

[0017] By employing a multi-fidelity variance posterior contribution function as the active learning function, the sampling decision can comprehensively balance information gain and computational cost.

[0018] Optionally, in step S4, determining the sampling positions of multiple newly added sampling points and the model fidelity corresponding to each of the newly added sampling points by optimizing the multi-fidelity active learning function includes: Using a genetic algorithm, the multi-fidelity active learning function is optimized in parallel based on the following formula: ; The sampling locations of multiple new sampling points and the model fidelity corresponding to each new sampling point are determined based on the following formula: .

[0019] By using a genetic algorithm to optimize in parallel and determine multiple sampling points and their fidelity at once, the iteration efficiency is improved and the short-sightedness of single-point decision-making is avoided.

[0020] On the other hand, embodiments of the present invention also provide a structural reliability determination device based on a multi-fidelity model. This device is used to implement the structural reliability determination method based on a multi-fidelity model provided in embodiments of the present invention. The device includes: The determination module is used to determine a low-fidelity sample set and a high-fidelity sample set, evaluate the high-fidelity sample set using a high-fidelity model to obtain a first response output, evaluate the low-fidelity sample set using a low-fidelity model to obtain a second response output, calculate the model difference between the high-fidelity samples and the low-fidelity samples based on the first response output and the second response output, determine the initial observation dataset of the low-fidelity model and the initial observation dataset of the model difference, and determine the multi-fidelity Gaussian process posterior of the performance function based on the initial observation dataset of the low-fidelity model and the initial observation dataset of the model difference. The calculation module is used to calculate the posterior mean and posterior standard deviation of the failure probability based on the posterior of the multi-fidelity Gaussian process. The sample addition module is used to add importance sampling samples and recalculate the posterior mean and posterior standard deviation of the failure probability when the posterior mean and posterior standard deviation of the failure probability do not meet the preset convergence condition, until the posterior mean and posterior standard deviation of the failure probability meet the preset convergence condition. The optimization module is used to generate a multi-fidelity active learning function with sampling position and model fidelity as independent variables after the posterior mean and posterior standard deviation of the failure probability satisfy the convergence condition. If the current multi-fidelity Gaussian process posterior does not satisfy the preset stopping criterion, the module optimizes the multi-fidelity active learning function to determine the sampling position of multiple new sampling points and the model fidelity corresponding to each new sampling point. Then, the module updates the low-fidelity sample set and the high-fidelity sample set according to the determined sampling position and the model fidelity, and returns to S1 to recalculate the multi-fidelity Gaussian process posterior. The output module is used to output the posterior mean of the failure probability as the calculated failure probability value when the posterior of the current multifidelity Gaussian process satisfies the stopping criterion.

[0021] On the other hand, embodiments of the present invention also provide a structural reliability determination device based on a multi-fidelity model, the structural reliability determination device based on a multi-fidelity model comprising: processor; A memory storing computer-readable instructions, which, when executed by the processor, implement the method provided in the embodiments of the present invention.

[0022] On the other hand, embodiments of the present invention also provide a computer-readable storage medium storing program code, which can be invoked by a processor to execute the method provided in the embodiments of the present invention.

[0023] The beneficial effects of the technical solutions provided in the embodiments of the present invention include at least the following: This invention achieves joint optimization of sampling position and model fidelity by generating an active learning function that simultaneously uses sampling position and model fidelity as independent variables. This overcomes the limitation of traditional methods that only optimize sampling position and reduces inefficient calls to high-fidelity models. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying 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.

[0025] Figure 1 This is a flowchart of a structural reliability determination method based on a multi-fidelity model provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of a multimodal function at different fidelities provided in the embodiments of the present invention; Figure 3 This is a schematic diagram of initial sampling and multi-fidelity proxy modeling provided in an embodiment of the present invention; Figure 4 This is a schematic diagram of posterior statistical calculation of failure probability under multi-fidelity conditions provided in the embodiments of the present invention; Figure 5 This is a schematic diagram of the optimization iteration process provided in an embodiment of the present invention; Figure 6 This is a schematic diagram of the optimization iteration results provided in the embodiments of the present invention; Figure 7 This is a schematic diagram of a structural reliability determination device based on a multi-fidelity model provided in an embodiment of the present invention; Figure 8 This is a schematic diagram of a structural reliability determination device based on a multi-fidelity model provided in an embodiment of the present invention. Detailed Implementation

[0026] The technical solution of the present invention will now be described with reference to the accompanying drawings.

[0027] In embodiments of the present invention, words such as "exemplarily," "for example," etc., are used to indicate that something is an example, illustration, or description. Any embodiment or design described as "exemplary" in the present invention should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of the word "exemplary" is intended to present the concept in a concrete manner. Furthermore, in embodiments of the present invention, the meaning expressed by "and / or" can be both, or either one.

[0028] In the embodiments of this invention, the terms "image" and "picture" may sometimes be used interchangeably. It should be noted that, without emphasizing the distinction between them, they convey the same meaning. Similarly, the terms "of," "corresponding (relevant)," and "corresponding" may sometimes be used interchangeably. It should be noted that, without emphasizing the distinction between them, they convey the same meaning.

[0029] In this embodiment of the invention, sometimes a subscript such as W1 may be mistakenly written as a non-subscript form such as W1. When the difference is not emphasized, the meaning they express is the same.

[0030] To make the technical problems, technical solutions and advantages of the present invention clearer, a detailed description will be given below in conjunction with the accompanying drawings and specific embodiments.

[0031] To address the issue that existing material retrieval methods cannot simultaneously handle semantic and data retrieval, this invention provides a method and apparatus for determining structural reliability based on a multi-fidelity model. The technical solution is as follows: like Figure 1 As shown, this embodiment of the invention provides a method for determining structural reliability based on a multi-fidelity model, the method comprising: S1. Determine the low-fidelity sample set and the high-fidelity sample set. Use the high-fidelity model to evaluate the high-fidelity sample set to obtain the first response output. Use the low-fidelity model to evaluate the low-fidelity sample set to obtain the second response output. Calculate the model difference between the high-fidelity samples and the low-fidelity samples based on the first response output and the second response output. Determine the initial observation dataset of the low-fidelity model and the initial observation dataset of the model difference. Determine the multi-fidelity Gaussian process posterior of the performance function based on the initial observation dataset of the low-fidelity model and the initial observation dataset of the model difference. S2. Based on the posterior of the multi-fidelity Gaussian process, calculate the posterior mean and posterior standard deviation of the failure probability; S3. When the posterior mean and posterior standard deviation of the failure probability do not meet the preset convergence condition, increase the importance sampling sample and recalculate the posterior mean and posterior standard deviation of the failure probability until the posterior mean and posterior standard deviation of the failure probability meet the preset convergence condition. S4. After the posterior mean of the failure probability and the posterior standard deviation of the failure probability satisfy the convergence condition, if the current multifidelity Gaussian process posterior does not satisfy the preset stopping criterion, a multifidelity active learning function is generated with sampling position and model fidelity as independent variables. By optimizing the multifidelity active learning function, the sampling positions of multiple new sampling points and the model fidelity corresponding to each new sampling point are determined. Then, the low-fidelity sample set and the high-fidelity sample set are updated according to the determined sampling positions and model fidelity, and the process returns to S1 to recalculate the multifidelity Gaussian process posterior. S5. When the posterior of the current multifidelity Gaussian process satisfies the stopping criterion, output the posterior mean of the failure probability as the calculated failure probability value.

[0032] In practical applications, before S1, there is also a step of constructing the initial sample set: using Hammersley sequences, generating a sample set within a hypersphere of radius R in standard normal space. We obtain an initial low-fidelity sample set by generating a set of low-fidelity samples; then, we use a swapping algorithm to select samples from this initial low-fidelity sample set. One sample is used as a high-fidelity sample to generate the initial high-fidelity sample set.

[0033] The initial high-fidelity sample set is evaluated using a high-fidelity model to obtain a first response output. The initial low-fidelity sample set is then evaluated using a low-fidelity model to obtain a second response output. Based on the first and second response outputs, the model difference between the high-fidelity and low-fidelity samples is calculated, thus constructing an initial observation dataset for the low-fidelity model and an initial observation dataset for the model difference. ,in, This is the initial observation dataset for the low-fidelity model. The initial observation dataset for model discrepancies, This represents a low-fidelity input in the standard normal space. Indicates low-fidelity output. This represents the model bias input in standard normal space. This indicates the output of the model bias.

[0034] Based on the initial observation dataset of the low-fidelity model and the initial observation dataset of model differences, hyperparameters in the prior of the multifidelity Gaussian process are analyzed. and We use the maximum marginal likelihood estimation method to calculate the multifidelity Gaussian process posterior of the performance function.

[0035] , ,in, Scale factor; It is the mean function of a low-fidelity Gaussian process; yes The size of the covariance matrix; yes The size of the covariance matrix, This represents a high-fidelity input in the standard normal space. This indicates high-fidelity output in the standard normal space. This indicates the number of low-fidelity samples. This indicates the number of high-fidelity samples.

[0036] In practical applications, a numerical integration method based on variance-amplified importance sampling can be used to calculate the posterior mean of the failure probability. and the posterior standard deviation of the failure probability .

[0037] Check the preset convergence conditions and If the conditions are not met, then the sampling density will be considered. Add to For each sample, the convergence condition is re-evaluated until the posterior mean and posterior standard deviation of the failure probability satisfy the preset convergence condition, wherein... .

[0038] After the posterior mean and posterior standard deviation of the failure probability satisfy the convergence condition, if the current multifidelity Gaussian process posterior does not satisfy the preset stopping criterion, a multifidelity active learning function is generated with sampling position and model fidelity as independent variables. By optimizing the multifidelity active learning function, the sampling positions of multiple new sampling points and the model fidelity corresponding to each new sampling point are determined. Then, the low-fidelity sample set and high-fidelity sample set are updated according to the determined sampling positions and model fidelity, and the process returns to S1 to recalculate the multifidelity Gaussian process posterior.

[0039] In practical applications, check the preset stopping criteria. If the conditions are not met, a multi-fidelity active learning function is generated, with both sampling location and model fidelity as independent variables. This multi-fidelity active learning function can be a multi-fidelity variance posterior contribution function. The formula is shown below: ,in This represents the proposed learning function. This represents the input in the standard normal space. This represents the model fidelity derived from the input in the standard normal space. Indicates the penalty factor. This represents the posterior contribution function of the variance. Represents the model correlation function. Represents the sample density function, This represents the model cost function.

[0040] By optimizing the multi-fidelity active learning function, the sampling positions of multiple newly added sampling points and the model fidelity corresponding to each newly added sampling point are determined, as shown in the following formula: , This represents the number of new samples added during an active learning process. Indicates high fidelity. Indicates low fidelity. Indicates the penalty factor The way to obtain the value.

[0041] Update the low-fidelity sample set and high-fidelity sample set according to the sampling location of the newly added sampling points and the model fidelity corresponding to each newly added sampling point, and return to S1 to recalculate the posterior of the multi-fidelity Gaussian process.

[0042] When the posterior of the current multifidelity Gaussian process satisfies the stopping criterion, the posterior mean of the failure probability is output as the calculated failure probability value.

[0043] The following is combined with Figure 2 The multimodal function shown provides a further detailed description of the embodiments of the present invention.

[0044] The high-fidelity expression for a multimodal function is: , The low-fidelity expression for a multimodal function is: .

[0045] in, X 1 follows a normal distribution with a mean of 1.5 and a standard deviation of 1. X 2 follows a normal distribution with a mean of 2.5 and a standard deviation of 1.

[0046] Using the Hammersley sequence, in standard normal space, the radius is... Ten low-fidelity samples were generated within the hypersphere, of which the radius... Set as , Using a swapping algorithm, six samples are selected from the low-fidelity samples as high-fidelity samples to construct the initial observation dataset for the low-fidelity model and the initial observation dataset for model differences. ,like Figure 3 As shown.

[0047] Based on observation dataset and Hyperparameters in the prior of multifidelity Gaussian processes and The marginal likelihood is maximized for estimation, and the multifidelity Gaussian process posterior of the performance function is calculated, where... This represents the prior mean of a low-fidelity Gaussian process. This represents the standard deviation of the signal in a low-fidelity Gaussian process. Each element in the diagram represents the length scale of the low-fidelity Gaussian process in the corresponding dimension. This represents the scale factor in the prior of a multifidel Gaussian process. The standard deviation of the signal representing the Gaussian process of model bias, [ Each element in ] represents the length scale of the model bias Gaussian process in the corresponding dimension.

[0048] Next, a numerical integration method based on variance-amplified importance sampling is used to sample from a density with a mean of 0 and a standard deviation of 2. In the middle, generate For each sample, evaluate the following four statistics: , , , .

[0049] in, Represents the multifidelity posterior mean of the performance function. This represents the posterior standard deviation of the multifidelity of the performance function. The probability density function of a standard normal variable, and the equivalent correlation coefficient. Set as .

[0050] The posterior mean of the failure probability, the posterior standard deviation of the failure probability, and the variances of the posterior mean and standard deviation of the failure probability are determined using the following formulas: Posterior mean of failure probability: , Posterior standard deviation of failure probability: , Variance of the posterior mean of the failure probability: , Variance of the posterior standard deviation of the failure probability: .

[0051] Check the preset convergence conditions and Does it meet the requirements? If not, consider the sampling density. Add to For each sample, the posterior statistics of the failure probability are recalculated. .

[0052] If the preset convergence condition is met, check whether the stopping criterion of the Bayesian active learning process is met. If not, optimize the multi-fidelity active learning function to determine the sampling positions of multiple new sampling points and the model fidelity corresponding to each new sampling point. Then, update the low-fidelity sample set and the high-fidelity sample set according to the determined sampling positions and model fidelity, and return to S1 to recalculate the posterior of the multi-fidelity Gaussian process. The side length of the rectangular optimization region is set to... , The number of new samples added in each iteration is set to , ,like Figure 5 , Figure 6 As shown.

[0053] Step 6: Output the posterior mean of the failure probability. Used as a value for calculating the probability of failure.

[0054] On the other hand, such as Figure 7 As shown, this embodiment of the invention also provides a structural reliability determination device based on a multi-fidelity model. The device is used to implement the structural reliability determination method based on a multi-fidelity model provided in this embodiment of the invention. The device includes: The determination module 701 is used to determine a low-fidelity sample set and a high-fidelity sample set, evaluate the high-fidelity sample set using a high-fidelity model to obtain a first response output, evaluate the low-fidelity sample set using a low-fidelity model to obtain a second response output, calculate the model difference between the high-fidelity samples and the low-fidelity samples based on the first response output and the second response output, determine the initial observation dataset of the low-fidelity model and the initial observation dataset of the model difference, and determine the multifidelity Gaussian process posterior of the performance function based on the initial observation dataset of the low-fidelity model and the initial observation dataset of the model difference. Calculation module 702 is used to calculate the posterior mean and posterior standard deviation of the failure probability based on the posterior of the multi-fidelity Gaussian process. The sample addition module 703 is used to add importance sampling samples and recalculate the posterior mean and posterior standard deviation of the failure probability when the posterior mean and posterior standard deviation of the failure probability do not meet the preset convergence condition, until the posterior mean and posterior standard deviation of the failure probability meet the preset convergence condition. The optimization module 704 is used to generate a multi-fidelity active learning function with sampling position and model fidelity as independent variables after the posterior mean of the failure probability and the posterior standard deviation of the failure probability satisfy the convergence condition. If the current multi-fidelity Gaussian process posterior does not satisfy the preset stopping criterion, the module optimizes the multi-fidelity active learning function to determine the sampling position of multiple new sampling points and the model fidelity corresponding to each new sampling point. Then, the module updates the low-fidelity sample set and the high-fidelity sample set according to the determined sampling position and the model fidelity, and returns to S1 to recalculate the multi-fidelity Gaussian process posterior. The output module 705 is used to output the posterior mean of the failure probability as the calculated failure probability value when the posterior of the current multifidelity Gaussian process satisfies the stopping criterion.

[0055] On the other hand, embodiments of the present invention also provide a structural reliability determination device based on a multi-fidelity model, the structural reliability determination device based on a multi-fidelity model comprising: processor; A memory storing computer-readable instructions, which, when executed by the processor, implement the method provided in the embodiments of the present invention.

[0056] On the other hand, embodiments of the present invention also provide a computer-readable storage medium storing program code, which can be invoked by a processor to execute the method provided in the embodiments of the present invention.

[0057] The beneficial effects of the technical solutions provided in the embodiments of the present invention include at least the following: Reduced computational cost: This invention introduces a multi-fidelity modeling method within the Bayesian active learning framework. By constructing a multi-fidelity Gaussian process model and fusing information sources of different accuracies, it achieves efficient approximation of the performance function. While ensuring prediction accuracy, it significantly reduces the number of calls to the high-fidelity model, thereby greatly reducing the computational cost of structural reliability.

[0058] Achieving joint optimization of sampling location and model fidelity: This invention proposes an active learning strategy that jointly optimizes sampling location and model fidelity. By comprehensively considering model correlation, sample distribution and computational cost through multi-fidelity learning functions, it achieves global parallel optimization of sampling decisions, overcomes the limitation of traditional methods that only optimize sampling location, and improves sample utilization efficiency and algorithm convergence speed.

[0059] Quantifying the uncertainty of failure probability: This invention models and updates the failure probability based on Bayesian inference, which not only obtains the reliability estimate, but also simultaneously quantifies its uncertainty, thereby improving the reliability of the calculation results and the rigor of the theory.

[0060] Applicable to complex engineering problems: This invention combines efficient numerical integration methods to achieve stable solutions for complex posterior statistics, which is applicable to reliability analysis problems of complex structures with high dimensions and strong nonlinearity. It can be extended to high-computational-cost engineering systems such as key load-bearing components in aerospace, precision mechanical structures and large-scale engineering equipment.

[0061] Figure 8 This is a structural schematic diagram of a structural reliability determination device based on a multi-fidelity model provided in an embodiment of the present invention, as shown below. Figure 8 As shown, optionally, the structural reliability determination device 810 based on the multi-fidelity model may include a first processor 2001.

[0062] Optionally, the structural reliability determination device 810 based on the multi-fidelity model may also include a memory 8002 and a transceiver 8003.

[0063] The first processor 8001, memory 8002, and transceiver 8003 can be connected via a communication bus.

[0064] The following is combined with Figure 8 A detailed description of each component of the structural reliability determination device 810 based on a multi-fidelity model is provided below: The first processor 8001 is the control center of the structure reliability determination device 810 based on a multi-fidelity model. It can be a single processor or a collective term for multiple processing elements. For example, the first processor 8001 can be one or more central processing units (CPUs), application-specific integrated circuits (ASICs), or one or more integrated circuits configured to implement embodiments of the present invention, such as one or more digital signal processors (DSPs), or one or more field-programmable gate arrays (FPGAs).

[0065] Optionally, the first processor 8001 can perform various functions of the structure reliability determination device 810 based on the multifidelity model by running or executing software programs stored in the memory 8002 and calling data stored in the memory 8002.

[0066] In a specific implementation, as one example, the first processor 8001 may include one or more CPUs, for example... Figure 8 CPU0 and CPU1 are shown in the diagram.

[0067] In a specific implementation, as one example, the structural reliability determination device 810 based on a multi-fidelity model may also include multiple processors, for example... Figure 8 The first processor 8001 and the second processor 8004 are shown. Each of these processors can be a single-core processor or a multi-core processor. Here, a processor can refer to one or more devices, circuits, and / or processing cores used to process data (such as computer program instructions).

[0068] The memory 8002 is used to store the software program that executes the present invention, and is controlled by the first processor 8001 to execute it. The specific implementation method can be referred to the above method embodiment, and will not be repeated here.

[0069] Optionally, the memory 8002 may be a read-only memory (ROM) or other type of static storage device capable of storing static information and instructions, random access memory (RAM) or other type of dynamic storage device capable of storing information and instructions, or electrically erasable programmable read-only memory (EEPROM), compact disc read-only memory (CD-ROM) or other optical disc storage, optical disc storage (including compressed optical discs, laser discs, optical discs, digital universal optical discs, Blu-ray discs, etc.), magnetic disk storage media or other magnetic storage devices, or any other medium capable of carrying or storing desired program code in the form of instructions or data structures and accessible by a computer, but not limited thereto. The memory 8002 may be integrated with the first processor 8001 or may exist independently, and the interface circuit of the device 810 is determined by the structural reliability based on a multi-fidelity model. Figure 8 (Not shown in the figure) is coupled to the first processor 8001, and the embodiments of the present invention do not specifically limit this.

[0070] The transceiver 8003 is used to communicate with network devices or with terminal devices.

[0071] Optionally, transceiver 8003 may include a receiver and a transmitter. Figure 8 (Not shown separately). The receiver is used to implement the receiving function, and the transmitter is used to implement the transmitting function.

[0072] Optionally, the transceiver 8003 can be integrated with the first processor 8001 or exist independently, and the interface circuit of the device 810 is determined by the structural reliability based on the multi-fidelity model. Figure 8 (Not shown in the figure) is coupled to the first processor 8001, and the embodiments of the present invention do not specifically limit this.

[0073] It should be noted that, Figure 8 The structure of the multi-fidelity model-based structural reliability determination device 810 shown does not constitute a limitation on the multi-fidelity model-based structural reliability determination device. The actual multi-fidelity model-based structural reliability determination device may include more or fewer components than shown, or combine certain components, or have different component arrangements.

[0074] Furthermore, the technical effect of the structure reliability determination device 810 based on the multi-fidelity model can be referred to the technical effect of the structure reliability determination method based on the multi-fidelity model described in the above method embodiments, and will not be repeated here.

[0075] It should be understood that the first processor 8001 in this embodiment of the invention may be a central processing unit (CPU), or it may be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or any conventional processor.

[0076] It should also be understood that the memory in the embodiments of the present invention can be volatile memory or non-volatile memory, or may include both volatile and non-volatile memory. The non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), or flash memory. The volatile memory can be random access memory (RAM), which is used as an external cache. By way of example, but not limitation, many forms of random access memory (RAM) are available, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate synchronous DRAM (DDR SDRAM), enhanced synchronous DRAM (ESDRAM), synchronous linked DRAM (SLDRAM), and direct rambus RAM (DR RAM).

[0077] The above embodiments can be implemented, in whole or in part, by software, hardware (such as circuits), firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, as a computer program product. The computer program product includes one or more computer instructions or computer programs. When the computer instructions or computer programs are loaded or executed on a computer, all or part of the processes or functions described in the embodiments of the present invention are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, motor drive, or data center to another website, computer, motor drive, or data center via infrared, microwave, or other means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a motor drive or data center that includes one or more sets of available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium. A semiconductor medium can be a solid-state drive.

[0078] It should be understood that the term "and / or" in this article is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. A and B can be singular or plural. Additionally, the character " / " in this article generally indicates an "or" relationship between the preceding and following related objects, but it can also represent an "and / or" relationship. Please refer to the context for a more accurate understanding.

[0079] In this invention, "at least one" means one or more, and "more than one" means two or more. "At least one of the following" or similar expressions refer to any combination of these items, including any combination of a single item or a plurality of items. For example, at least one of a, b, or c can represent: a, b, c, ab, ac, bc, or abc, where a, b, and c can be a single item or multiple items.

[0080] It should be understood that, in various embodiments of the present invention, the order of the above-mentioned process numbers does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0081] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0082] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the devices, apparatuses, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0083] In the several embodiments provided by this invention, it should be understood that the disclosed devices, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another device, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0084] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0085] In addition, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0086] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, essentially, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, a motor driver, or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0087] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for determining structural reliability based on a multi-fidelity model, characterized in that, include: S1. Determine the low-fidelity sample set and the high-fidelity sample set. Use the high-fidelity model to evaluate the high-fidelity sample set to obtain the first response output. Use the low-fidelity model to evaluate the low-fidelity sample set to obtain the second response output. Calculate the model difference between the high-fidelity samples and the low-fidelity samples based on the first response output and the second response output. Determine the initial observation dataset of the low-fidelity model and the initial observation dataset of the model difference. Determine the multi-fidelity Gaussian process posterior of the performance function based on the initial observation dataset of the low-fidelity model and the initial observation dataset of the model difference. S2. Based on the posterior of the multi-fidelity Gaussian process, calculate the posterior mean and posterior standard deviation of the failure probability; S3. When the posterior mean and posterior standard deviation of the failure probability do not meet the preset convergence condition, increase the importance sampling sample and recalculate the posterior mean and posterior standard deviation of the failure probability until the posterior mean and posterior standard deviation of the failure probability meet the preset convergence condition. S4. After the posterior mean of the failure probability and the posterior standard deviation of the failure probability satisfy the convergence condition, if the current multifidelity Gaussian process posterior does not satisfy the preset stopping criterion, a multifidelity active learning function is generated with sampling position and model fidelity as independent variables. By optimizing the multifidelity active learning function, the sampling positions of multiple new sampling points and the model fidelity corresponding to each new sampling point are determined. Then, the low-fidelity sample set and the high-fidelity sample set are updated according to the determined sampling positions and model fidelity, and the process returns to S1 to recalculate the multifidelity Gaussian process posterior. S5. When the posterior of the current multifidelity Gaussian process satisfies the stopping criterion, output the posterior mean of the failure probability as the calculated failure probability value.

2. The method according to claim 1, characterized in that, Before S1, it also includes: Using the Hammersley sequence, in standard normal space, the radius is... Genesis within the supersphere We obtain an initial low-fidelity sample set by taking a few low-fidelity samples. A swapping algorithm is used to select from the initial low-fidelity sample set. One sample is used as a high-fidelity sample to generate the initial high-fidelity sample set.

3. The method according to claim 1, characterized in that, The multi-fidelity Gaussian process posterior in S1, which determines the performance function based on the initial observation dataset of the low-fidelity model and the initial observation dataset of the model difference, includes: Based on observation dataset and Hyperparameters in the prior of multifidelity Gaussian processes and The marginal likelihood is maximized for estimation, and the multifidelity Gaussian process posterior of the performance function is calculated, where... This represents the prior mean of a low-fidelity Gaussian process. This represents the standard deviation of the signal in a low-fidelity Gaussian process. Each element in the diagram represents the length scale of the low-fidelity Gaussian process in the corresponding dimension. This represents the scale factor in the prior of a multifidel Gaussian process. The standard deviation of the signal representing the Gaussian process of model bias, [ Each element in ] represents the length scale of the model bias Gaussian process in the corresponding dimension.

4. The method according to claim 1, characterized in that, The calculation of the posterior mean and posterior standard deviation of the failure probability in S2 includes: The posterior mean of the failure probability is calculated using a numerical integration method based on variance-amplified importance sampling. Posterior standard deviation.

5. The method according to claim 1, characterized in that, The preset convergence conditions in S3 include: The variance of the posterior mean of the failure probability is less than a first preset threshold, and the variance of the posterior standard deviation of the failure probability is less than a second preset threshold.

6. The method according to claim 1, characterized in that, The multi-fidelity active learning function includes: a multi-fidelity variance posterior contribution function.

7. The method according to claim 1, characterized in that, In step S4, the sampling positions of multiple newly added sampling points and the model fidelity corresponding to each newly added sampling point are determined by optimizing the multi-fidelity active learning function, including: Using a genetic algorithm, the multi-fidelity active learning function is optimized in parallel based on the following formula: ； The sampling locations of multiple new sampling points and the model fidelity corresponding to each new sampling point are determined based on the following formula: 。 8. A structural reliability determination device based on a multi-fidelity model, characterized in that, The structural reliability determination device based on the multi-fidelity model is used to implement the structural reliability determination method based on the multi-fidelity model as described in any one of claims 1-7, and the device includes: The determination module is used to determine a low-fidelity sample set and a high-fidelity sample set, evaluate the high-fidelity sample set using a high-fidelity model to obtain a first response output, evaluate the low-fidelity sample set using a low-fidelity model to obtain a second response output, calculate the model difference between the high-fidelity samples and the low-fidelity samples based on the first response output and the second response output, determine the initial observation dataset of the low-fidelity model and the initial observation dataset of the model difference, and determine the multi-fidelity Gaussian process posterior of the performance function based on the initial observation dataset of the low-fidelity model and the initial observation dataset of the model difference. The calculation module is used to calculate the posterior mean and posterior standard deviation of the failure probability based on the posterior of the multi-fidelity Gaussian process. The sample addition module is used to add importance sampling samples and recalculate the posterior mean and posterior standard deviation of the failure probability when the posterior mean and posterior standard deviation of the failure probability do not meet the preset convergence condition, until the posterior mean and posterior standard deviation of the failure probability meet the preset convergence condition. The optimization module is used to generate a multi-fidelity active learning function with sampling position and model fidelity as independent variables after the posterior mean and posterior standard deviation of the failure probability satisfy the convergence condition. If the current multi-fidelity Gaussian process posterior does not satisfy the preset stopping criterion, the module optimizes the multi-fidelity active learning function to determine the sampling position of multiple new sampling points and the model fidelity corresponding to each new sampling point. Then, the module updates the low-fidelity sample set and the high-fidelity sample set according to the determined sampling position and the model fidelity, and returns to S1 to recalculate the multi-fidelity Gaussian process posterior. The output module is used to output the posterior mean of the failure probability as the calculated failure probability value when the posterior of the current multifidelity Gaussian process satisfies the stopping criterion.

9. A structural reliability determination device based on a multi-fidelity model, characterized in that, The structural reliability determination device based on the multi-fidelity model includes: processor; A memory storing computer-readable instructions that, when executed by the processor, implement the method as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium contains program code that can be invoked by a processor to execute the method as described in any one of claims 1 to 7.

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