Shell stability prediction method and system based on combined proxy model sequence sampling

Abstract

The application belongs to the field of shell structure design, and particularly discloses a shell stability prediction method and system based on combined proxy model sequence sampling, which comprises the following steps: obtaining initial samples and corresponding shell critical pressures, and putting them into a database; obtaining training samples from the database, and establishing a temporary combined proxy model based on the training samples; randomly obtaining candidate samples, calculating the prediction uncertainty and sparsity degree of the candidate samples based on the temporary combined proxy model and the sample distribution in the database, and then selecting part of the samples in the candidate samples to add to the database; repeating the sampling until a preset termination condition is reached, and ending the sampling process; and using the samples in the database and the corresponding shell critical pressures to establish a final combined proxy model, so as to realize shell structure stability prediction. The application uses the information provided by the model and data to guide sample selection, can reduce the number of samples required for establishing a shell structure proxy model, and improves the design efficiency.

Description

Technical Field

[0001] This invention belongs to the field of shell structure design, and more specifically, relates to a shell stability prediction method and system based on sequence sampling of a combined surrogate model. Background Technology

[0002] In underwater environments, the shell structure serves to withstand external water pressure and protect internal equipment for normal operation. To accommodate more equipment within a limited internal space, the shell typically requires the largest possible volume and the lowest possible weight, making shell structure design crucial. Traditional shell structure design relies on empirical formulas, involving a cyclical process of checking and modifying the shell's strength and stability in underwater environments. This process is time-consuming, labor-intensive, and yields inaccurate results.

[0003] With the development of computer technology, using computer simulation to analyze product performance during industrial product design has become a trend. Finite Element Analysis (FEA) has become a widely adopted method for analyzing the stability of shell structures. Although computer computing power has significantly increased, performing a complete strength and stability analysis of a shell structure requires substantial time and computational resources, greatly increasing design costs. Furthermore, the relationship between shell structure performance and shell design parameters is often an unknown black box problem, making it difficult to obtain effective relevant information and further increasing design complexity.

[0004] A surrogate model is an approximate model that establishes a functional relationship between design variables and the objective function, thereby predicting the performance of unknown designs and improving design efficiency. The accuracy of the surrogate model significantly impacts prediction performance; model accuracy is directly related to the distribution of samples in the design space. Experimental design methods determine the distribution of samples in the design space, and are categorized into one-time sampling methods and sequential sampling methods. Sequential sampling methods first generate a small number of samples in the design space using one-time sampling. Then, combining the distribution information of existing samples with the established surrogate model, new samples are iteratively added to the design space according to sampling criteria, gradually improving the accuracy of the surrogate model. Summary of the Invention

[0005] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a shell stability prediction method and system based on combined surrogate model sequence sampling. Its purpose is to establish a more accurate shell structure stability prediction model using fewer samples.

[0006] To achieve the above objectives, according to one aspect of the present invention, a shell stability prediction method based on sequence sampling of a combined surrogate model is proposed, comprising the following steps:

[0007] S1. Using the shell thickness and the cross-sectional shape parameters of the ribs on the shell as design variables, the initial samples and the critical pressure of the shell corresponding to each sample are obtained and put into the database.

[0008] S2. Obtain training samples from the database and build a temporary combined agent model based on the training samples;

[0009] S3. Randomly obtain multiple candidate samples, and calculate the prediction uncertainty and sparsity of the candidate samples based on the temporary combined proxy model and the sample distribution in the database.

[0010] S4. Based on the prediction uncertainty and sparsity of the candidate samples, select a portion of the candidate samples and add them to the database.

[0011] S5. Repeat steps S2 to S4 until the preset termination condition is met, and the sampling process ends.

[0012] S6. Using the samples in the database at this time and their corresponding critical pressures of the shell, establish the final combined surrogate model to achieve the prediction of shell structure stability.

[0013] As a further preferred step, in step S4, a stratified sampling strategy is adopted to select a portion of the candidate samples to be added to the database, including: sorting the candidate samples in descending order of prediction uncertainty, and selecting a portion of the samples with higher uncertainty; sorting the selected samples in descending order of sparsity, and selecting the candidate sample with the highest sparsity, and adding it to the database as the final selected portion of the samples.

[0014] As a further preferred embodiment, in step S3, the method for calculating the prediction uncertainty of the candidate sample is as follows: the corresponding predicted value of the candidate sample is calculated using a temporary combined surrogate model, and then its prediction variance is calculated and normalized. The normalized value is used to represent the prediction uncertainty of the candidate sample.

[0015] As a further preferred option, in step S3, the sparsity of the candidate samples is calculated as follows: the minimum Euclidean distance between each candidate sample and the existing samples in the database is calculated and normalized, and the normalized value is used to represent the sparsity of the candidate samples.

[0016] As a further preferred embodiment, step S2, obtaining training samples from the database specifically includes:

[0017] The database contains m samples. Using the sampling with replacement method, m samples are selected from the database. After removing duplicate samples, a training sample of size m′ is formed.

[0018] Repeat the above sampling method M times to obtain M sets of training samples.

[0019] As a further preferred option, in step S2, corresponding Kriging base models are established based on the M groups of training samples, and then temporary combined proxy models are established.

[0020] As a further preferred option, the temporary combined proxy model is as follows:

[0021]

[0022] In the formula, x is the design variable. For the i-th Kriging base model, This is the predicted value of the shell critical pressure by the combined surrogate model.

[0023] As a further preferred option, in step S1, the two variables, shell thickness and cross-sectional shape parameters of the ribs on the shell, are merged into a single vector, corresponding to a shell structure design; the design space is determined based on the upper and lower limits of the design variables; and an initial sample is generated in the design space using the Latin hypercube sampling method, where each sample is a vector.

[0024] As a further preferred option, in step S1, the critical pressure of the shell corresponding to each sample is calculated using a simulation framework.

[0025] According to another aspect of the present invention, a shell stability prediction system based on combined surrogate model sequence sampling is provided, which includes a processor for executing the above-described shell stability prediction method based on combined surrogate model sequence sampling.

[0026] In summary, compared with the prior art, the above-described technical solutions conceived by this invention mainly possess the following technical advantages:

[0027] 1. This invention proposes a shell structure stability prediction method based on a combined surrogate model and sequential sampling for ribbed cylindrical shell structures. It establishes a surrogate model of the structural parameters and instability critical pressure of the ribbed cylindrical shell using a small amount of simulation data, providing a prediction model for shell structure design. During the sequential sampling process, new shell structure samples are selected based on the information provided by the temporary combined model and the spatial distribution information of the samples, thereby improving the accuracy of the shell structure stability model.

[0028] 2. This invention proposes a hierarchical sampling strategy to perform two rounds of screening for candidate shell parameters, reflecting the trade-off between local search and global exploration in the sample selection strategy. This hierarchical sampling method synergistically considers the relationship between the prediction variance of the combined model and the minimum distance between samples, and can selectively increase the number of samples in the nonlinear and sparse regions of the shell structure design variable space, effectively improving the accuracy of the shell structure stability model, saving simulation costs, and improving design efficiency. Attached Figure Description

[0029] Figure 1 This is a flowchart of the shell stability prediction method based on sequence sampling of a combined surrogate model according to an embodiment of the present invention;

[0030] Figure 2 This is a schematic diagram of a ribbed cylindrical shell according to an embodiment of the present invention;

[0031] Figure 3 (a) and (b) are schematic diagrams of the design variables of the cylindrical shell in the embodiments of the present invention.

[0032] In all the accompanying drawings, the same reference numerals are used to denote the same elements or structures, wherein: 1-shell plate, 2-rib. Detailed Implementation

[0033] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0034] This invention provides a shell stability prediction method based on sequence sampling using a combined surrogate model, such as... Figure 1 As shown, it includes the following steps:

[0035] S1. For a ribbed cylindrical shell structure, determine the shell's working conditions, material parameters, and fixed geometric parameters; determine the shell's design parameters (variables) and their ranges, generate initial data for the design variables, and calculate the critical pressure of the shell structure using simulation methods. This includes the following steps:

[0036] S11. Determine the working depth of the shell to obtain the external pressure value; after determining the shell material, the material's density, yield strength, elastic modulus, Poisson's ratio, and other parameters can be obtained; determine the fixed geometric parameters of the shell, including the shell length, shell outer diameter, number of ribs, and distribution pattern, etc.

[0037] Specifically, by determining the underwater working depth of the ribbed cylindrical shell, the external pressure it withstands can be known; taking aluminum alloy as an example, the density (ρ) and yield strength (σ) of the aluminum alloy can be obtained. s Parameters such as elastic modulus (E) and Poisson's ratio (μ) are considered. For a sealed shell, the cylindrical side is the location with the greatest pressure, and only the critical pressure of this part needs to be considered; such as Figure 2 As shown, the ribbed cylindrical shell includes a shell plate 1 and ribs 2. Figure 3The relevant parameters in the shell structure design are given. The shell length (L), shell diameter (D), and number of ribs (N) are fixed parameters. The ribs are evenly distributed along the axial direction of the shell, and are half a spacing from each side.

[0038] S12. Determine the design variables and range of the shell structure. Generally, when the outer diameter of the shell is determined, the pressure-bearing performance of the shell is changed by changing the shell thickness. Therefore, the shell thickness (t) is a design variable. When the distribution of the ribs is determined, the pressure-bearing performance of the shell is changed by changing the geometric parameters (b1, h1, b2, h2) of the ribs. Therefore, the cross-sectional shape parameters of the ribs are used as design variables. Combine the two types of variables into a vector, which corresponds to a shell structure design. The length of the vector is the number (n) of the shell structure design variables.

[0039] S13. Determine the upper and lower limits of each variable based on the degree of change of the variables; this constitutes the design space (x∈R). n The objective function is the critical pressure representing the shell stability index. A small number of initial samples are generated in the design space using the Latin hypercube sampling (LHS) method. Each sample is a vector, corresponding to a shell structure design.

[0040] S14. Calculate the objective function value for each sample using a high-precision simulation framework, i.e., the critical pressure value for each type of shell structure; use the secondary development module of CAD software to generate a geometric model from the design variables, import the geometric model into CAE software, and use the static analysis and stability module in ANSYS Workbench to perform stability analysis of the shell structure. This process includes steps such as importing the geometric model, setting material properties, meshing, applying loads, and solving to obtain the critical pressure of the shell; put the initial samples and their function values ​​into the database.

[0041] S2. Using the Kriging model as the surrogate model, a temporary combined surrogate model for shell stability is established using ensemble learning methods, specifically including the following steps:

[0042] S21. The number of samples in the database is m. Using the sampling with replacement method, m samples are selected from the database. After removing duplicate samples, a training sample of size m′ is formed. The sampling method is repeated M times to obtain M training samples.

[0043] S22. Using M sets of training samples, establish the corresponding Kriging model. Employ the ensemble learning method Bagging to establish a temporary combined surrogate model for the shell critical pressure. The combined surrogate model takes the following form:

[0044]

[0045] In the formula, x is the design variable. For the i-th Kriging base model, This represents the predicted critical pressure of the shell using the combined surrogate model.

[0046] Temporary surrogate models can be used to predict the critical pressure of unknown shell structures, and combined surrogate models can also be used to assess the uncertainty of critical pressure prediction.

[0047] S3. Based on the established shell structure proxy model and the sample distribution in the database, determine the prediction uncertainty and sparsity of the candidate samples, specifically including the following steps:

[0048] S31. Prediction Uncertainty: A large number of random candidate sample points are generated in the design space. The prediction variance of the candidate sample points is calculated using a temporary combined surrogate model and then normalized. It can be summarized as follows:

[0049]

[0050]

[0051] In the formula, The predicted variance of candidate sample x is given by the predicted values ​​of each basic Kriging model in the combined surrogate model; This represents the normalized prediction variance, i.e., the prediction uncertainty.

[0052] The larger the prediction variance of a candidate sample, the higher the degree of difference between the predictions of the basic surrogate models at that sample, which further indicates a higher degree of nonlinearity at that point. Adding new samples in regions with high nonlinearity can quickly reduce model error and improve the prediction accuracy of the surrogate model for the critical pressure of the shell.

[0053] S32. Sparsity: Calculate the minimum distance between each candidate sample point and existing samples in the database and normalize it. This can be summarized in the following form:

[0054]

[0055] i = 1, 2, ..., m, k = 1, 2, ..., n

[0056]

[0057] In the formula, d(x) is the minimum Euclidean distance between the candidate sample point and the sample in the database; The minimum distance after normalization, i.e. the degree of sparsity;

[0058] The greater the minimum spatial distance between a candidate sample point and existing samples, the more likely it is to be located in a sparsely distributed region of the design space. Adding new samples in sparsely distributed regions can improve the spatial filling characteristics of the samples and help improve the prediction accuracy of the shell structure in that region.

[0059] S4. Combining the assessment of the prediction uncertainty and distribution of a large number of candidate samples in step S3, a stratified sampling strategy is adopted to select new shell parameter samples and add them to the database, including:

[0060] S41. Sort the candidate samples in descending order of normalized prediction variance, and select the samples with the largest p% uncertainty. Then, sort these selected p% samples in descending order of normalized minimum distance, and select the candidate sample with the largest minimum distance. This is the newly added shell structure parameter sample in this iteration. The stratified sampling strategy is based on the following idea: the selected candidate samples with larger prediction variances indicate areas with greater design space uncertainty. In these areas, further select the candidate sample with the largest distance from existing samples, considering space-filling characteristics. The stratified samples can provide more shell parameter information, thereby improving modeling efficiency.

[0061] S42. Calculate the critical pressure value of the shell using the high-precision simulation framework in step S14, and put the obtained new sample data into the database; as the number of simulation sample data increases, the accuracy of the shell stability prediction model gradually improves.

[0062] S5. Repeat steps S2 to S4 to continue sampling until the preset termination condition is met, and the sampling process ends.

[0063] S6. Using the samples and function values ​​in the database at this time, establish the final combined proxy model of the shell stability prediction model to realize the stability prediction of the shell structure and assist in the design of the shell structure.

[0064] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A shell stability prediction method based on sequential sampling of combined proxy models, characterized by, The method comprises the following steps: S1, taking the shell thickness and the cross-sectional shape parameters of the ribs on the shell as design variables, then obtaining initial samples and the corresponding critical pressure of the shell of each sample, and putting them into a database; S2, obtaining training samples from the database, and establishing a temporary combined proxy model based on the training samples; S3, randomly obtaining a plurality of candidate samples, calculating the prediction uncertainty and the sparsity degree of each candidate sample based on the temporary combined proxy model and the sample distribution in the database; S4, selecting part of the candidate samples according to the prediction uncertainty and the sparsity degree of the candidate samples, and adding them to the database; S5, repeating steps S2-S4 until a preset termination condition is reached, and the sampling process ends; S6, using the samples in the database and the corresponding critical pressure of the shell to establish a final combined proxy model, and realizing the stability prediction of the shell structure. 2.The shell stability prediction method based on the sequence sampling of the combined proxy model according to claim 1, wherein, In step S4, a hierarchical sampling strategy is adopted to select part of the candidate samples and add them to the database, including: arranging the candidate samples in descending order of prediction uncertainty, and selecting part of the samples with larger uncertainty; arranging the selected samples in descending order of sparsity degree, and selecting the candidate sample with the largest sparsity degree as the final selected part of the samples and adding it to the database. 3.The shell stability prediction method based on the sequence sampling of the combined proxy model according to claim 1, wherein, In step S3, the calculation method of the prediction uncertainty of the candidate sample is: using the temporary combined proxy model to calculate the corresponding prediction value of the candidate sample, then calculating the prediction variance and normalizing it, and using the normalized value to represent the prediction uncertainty of the candidate sample. 4.The shell stability prediction method based on the sequence sampling of the combined proxy model according to claim 1, wherein, In step S3, the calculation method of the sparsity degree of the candidate sample is: calculating the minimum Euclidean distance between each candidate sample and the existing samples in the database and normalizing it, and using the normalized value to represent the sparsity degree of the candidate sample. 5.The shell stability prediction method based on the sequence sampling of the combined proxy model according to claim 1, wherein, In step S2, the training samples are obtained from the database, specifically including: The number of samples in the database is m, and m samples are selected from the database by using a replaceable sampling method, and after removing the repeated samples, a set of m' training samples is formed; Repeat the above sampling method M times to obtain M sets of training samples. 6.The shell stability prediction method based on the sequence sampling of the combined proxy model according to claim 5, wherein, In step S2, Kriging base models corresponding to the M sets of training samples are established, and then a temporary combined proxy model is established.

7. The shell stability prediction method based on the sequence sampling of the combined proxy model according to claim 6, wherein, The temporary combined proxy model is specifically: In the formula, x is a design variable, is the ith Kriging base model, is the predicted value of the combined surrogate model for the critical pressure of the shell.

8. The shell stability prediction method based on sequential sampling of ensemble surrogate models according to any one of claims 1 to 7, characterized in that, In step S1, the two variables of the shell thickness and the cross-sectional shape parameters of the ribs on the shell are combined into a vector, corresponding to a shell structure design; the design space is determined according to the upper and lower limits of the design variables; the Latin hypercube sampling method is used to generate initial samples in the design space, wherein each sample is a vector. 9.The shell stability prediction method based on the sequence sampling of the combined proxy model according to claim 8, wherein, In step S1, the simulation framework is used to calculate the critical pressure of the shell corresponding to each sample.

10. A shell stability prediction system based on sequential sampling of combined proxy models, characterized in that, The processor is configured to execute the shell stability prediction method based on the combined proxy model sequence sampling according to any one of claims 1-9.

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