Method for evaluating buckling load deviation probability of rocket reinforced shell structure

Abstract

According to the method for evaluating the buckling load deviation probability characteristics of the rocket reinforced shell structure, in view of the fact that a traditional deterministic method cannot effectively cope with uncertainty influences such as external environments and material attributes, the uncertainty of variables is modeled by utilizing a Copula mixed model, and the buckling load deviation probability characteristics of the rocket reinforced shell structure are evaluated by combining an improved probability weight point collocation method through a division and treatment strategy. Performing independent uncertainty propagation analysis on each parameter cluster; according to the method, high-dimensional parameter space response probability distribution is efficiently obtained, and the buckling load deviation probability is evaluated by integrating cluster results; the method provides a basis for the evaluation of the buckling load deviation probability distribution characteristics of the reinforced shell structure considering the multi-parameter random deviation, and assists the reliability analysis and optimization design.

Description

Technical Field

[0001] The present invention relates to the field of structural performance uncertainty analysis, and in particular to a method for evaluating the probability of buckling load deviation of a rocket stiffened shell structure. Background Art

[0002] The structural integrity and reliability of a rocket body are key factors in ensuring the success of a space mission. The stiffened shell structure significantly improves the local and overall stability of the structure by arranging stiffeners or ribs on a thin shell, making it more resistant to harsh environments such as aerodynamic heating, vibration, and pressure fluctuations. Therefore, it is widely used in the lightweight design of key parts such as rocket bodies and fuel tanks. However, buckling, as a potential failure mode of the stiffened shell structure, may cause catastrophic damage to the structure before the material strength limit is reached. Therefore, the importance of buckling analysis in rocket structural design is self-evident, and it is a key step to ensure the stability and safety of the rocket structure.

[0003] Traditional buckling analysis methods are based on a deterministic framework and cannot fully quantify the impact of uncertainty factors such as external environmental fluctuations, material property deviations, design errors, and their correlations on structural buckling performance, which is particularly limited in modern rocket structural design. In order to overcome these limitations, advanced analysis techniques that can quantify the impact of uncertainty must be used. Through in-depth analysis and understanding of buckling risks under uncertain environments, potential risk points can be identified efficiently and accurately during the design phase, thereby ensuring that the rocket structure maintains integrity and functionality in the face of a complex and changing space environment, providing a solid guarantee for the smooth progress of space missions.

[0004] However, in the field of probabilistic assessment of buckling load deviation of rocket stiffened shell structures, the application of these methods is still in its infancy, and a systematic assessment process and technical system has not yet been formed. The present invention aims to model and propagate the uncertainty deviation of rocket stiffened shell structure parameters through the Copula hybrid model and the probability weighted point matching method, so as to obtain the probabilistic characteristics of the structural buckling load deviation, thereby laying the foundation for subsequent optimization design. Summary of the invention

[0005] In view of the above problems, the purpose of the present invention is to model and propagate the uncertainty deviation of the rocket stiffened shell structure parameters through the Copula hybrid model and the probability weighted point matching method, so as to obtain the probabilistic characteristics of the structural buckling load deviation and lay the foundation for subsequent optimization design.

[0006] The technical solution adopted by the present invention is a method for evaluating the probability characteristics of buckling load deviation of a rocket stiffened shell structure, and the evaluation method comprises the following steps:

[0007] S1 determines the uncertainty parameters of the stiffened shell structure, obtains sample data corresponding to the variables, and uses the K-means clustering method to perform initial clustering on the sample data;

[0008] S2 builds a Copula mixed model based on the clustering results of step 1, measures the marginal probability density function of each cluster sample after clustering and the correlation between parameters, and then completes the uncertainty modeling of the rocket stiffened shell structure parameters;

[0009] S3, based on the uncertainty modeling results and the idea of ​​"divide and conquer", adopts a representative point selection method based on generalized F deviation for each cluster of samples that completes the modeling and obtains representative points and probability weights;

[0010] S4 brings the data corresponding to the representative point into the finite element analysis software, solves the critical buckling load of the stiffened shell structure under the corresponding data, and obtains the response value of the representative point;

[0011] S5 directly calculates the corresponding probability density functions of the two cluster variables using the improved probability weight point matching equation based on the obtained representative point response values;

[0012] S6 combines the two clusters of probability density functions according to the weights, and finally obtains the probability distribution characteristics of the buckling load deviation of the rocket stiffened shell structure.

[0013] The S2 further includes: for the rocket reinforced shell structure, obtaining n groups of structural parameters of the reinforced shell as sample data by sampling, and when performing uncertain modeling based on the Copula hybrid model, the calculation formula of the log-likelihood function is:

[0014]

[0015] In the formula, Ω j Represents the weight of each sample data of the jth cluster obtained by the Copula mixed model, h j represents the Copula function corresponding to the j-th cluster sample, ξ j is the marginal distribution parameter and correlation parameter of the jth cluster, x i (i=1,2,3,…,n) represents the structural parameters of n groups of stiffened shells obtained by measurement.

[0016] The S3 further includes selecting the representative point based on the following formula:

[0017] x” m,i =F i -1 (u” m,i |θ i )

[0018]

[0019] Where n represents the number of required representative points, u" m,i 、u' m,i and u m,i Respectively represent the CDF values ​​corresponding to each representative point after three inverse transformations, where u" m,i It is generated based on the sobol random sequence, x" m,i 、x' m,i and x m,i Respectively represent the coordinates of each dimension of each representative point after three inverse transformations, where x m,i That is the final representative point coordinates, m = (1, 2, 3, L, n) represents the mth sample point. θ i represents the uncertainty parameter of the i-th dimension random variable.

[0020] To solve the probability weight p corresponding to the representative point m First, we use the Monte Carlo method to generate N according to the constructed metric model. MC Then, take the representative point as the cluster center and cluster N MC For cluster analysis of samples, the probability weight p corresponding to the representative point m It can be obtained by the following formula

[0021]

[0022] Λ(x m ) indicates that after cluster analysis, N MC The samples are classified into x m The number of samples in the cluster.

[0023] The S5 further includes that the improved probability weighted point matching method adopts the following formula to obtain the probability distribution characteristics of the response:

[0024]

[0025] Among them, n is the number of selected representative points, x m is the mth representative point, g(x m ) The calculated response value of the finite element simulation is Θ X,m For its representative area, P t is the probability value corresponding to the representative area. This formula makes the probability density function of the response continuous and smooth based on the Gaussian function, which is a good replacement for the Dirac function.

[0026] The method for evaluating the probability of buckling load deviation of a rocket stiffened shell structure also includes a pre-step 0: data preprocessing, which includes removing outliers and missing values ​​in the sample data and normalizing the remaining samples to eliminate the influence of different dimensions on subsequent analysis.

[0027] When solving the critical buckling load, the finite element analysis software in S4 considers the nonlinear characteristics of structural mechanics under uncertainty conditions to improve the accuracy of the solution results.

[0028] The beneficial effects of the present invention are that by combining finite element simulation, Copula hybrid model and improved probability weighted point collocation method, the probabilistic characteristic analysis of the buckling load deviation of the rocket stiffened shell structure is realized, which has the significant advantages of quantification, high accuracy and high efficiency, which are specifically embodied as follows:

[0029] 1. Quantitative analysis of parameter deviation and correlation effects: The present invention combines finite element simulation to perform propagation analysis on the uncertainty deviation and correlation existing in the rocket stiffened shell structure. It can quantitatively analyze the effect of parameter deviation and correlation on the buckling load, thereby obtaining the probability distribution characteristics of the buckling load deviation of the stiffened shell structure. This characteristic is of great significance for evaluating the stability and safety of the rocket structure.

[0030] 2. Accurate measurement of high-dimensional parameter deviation characteristics: The present invention realizes the uncertainty modeling of rocket reinforced shell model parameters based on the Copula hybrid model, which can accurately measure the high-dimensional parameter deviation characteristics and their correlations, and has high universality. This modeling method not only improves the accuracy of the analysis, but also effectively broadens the application scope of the present invention to different types of correlations by combining multiple Copula functions.

[0031] 3. Improve evaluation efficiency and optimize analysis process: The present invention adopts an improved probability weighted point matching method, which reduces the number of required representative points through the advantages of integrated algorithms, and effectively solves the bottleneck problem of computational efficiency in deviation propagation analysis. The evaluation method in the present invention can utilize parallel computing platforms and acceleration technologies (such as GPU acceleration and multi-core CPU parallel processing) to accelerate the finite element analysis process, optimize the analysis process, and shorten the solution time. Based on this, the evaluation efficiency of the buckling load deviation probability characteristics can be significantly improved, and the analysis cost and time consumption can be reduced. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] The drawings are only for the purpose of illustrating particular embodiments and are not to be considered limiting of the present invention. Like reference symbols denote like components throughout the drawings.

[0033] Figure 1 It is a schematic diagram of the structure of the reinforced shell model in the launch vehicle of the present invention.

[0034] Figure 2 It is a schematic diagram of the reinforced cross section of the reinforced shell model in the launch vehicle of the present invention.

[0035] Figure 3 It is a schematic diagram of initial sample data of the reinforced shell structure of the present invention.

[0036] Figure 4 It is a schematic diagram of the uncertainty measurement results of the stiffened shell structure of the present invention.

[0037] Figure 5 It is a schematic diagram of the probability assessment result of the critical buckling load deviation of the stiffened shell structure of the present invention. DETAILED DESCRIPTION

[0038] The preferred embodiments of the present invention will be described in detail below in conjunction with the accompanying drawings, wherein the accompanying drawings constitute a part of this application and are used to illustrate the principles of the present invention together with the embodiments of the present invention.

[0039] The method of the present invention can be used to realize the probability assessment of the buckling load deviation of the rocket reinforced shell structure. With the development of my country's aerospace industry, the size of the reinforced shell structure has increased, the details have become more complex, and the influence of the uncertainty in the manufacturing process on the performance of the reinforced shell structure has increased significantly. The reinforced shell structure is used for the fuel tank and load-bearing cylinder of the rocket. Its failure mode is buckling instability. The buckling load of the reinforced shell structure directly affects the service safety of the equipment. How to analyze the uncertainty in the reinforced shell structure and then obtain the response probability density function of the structural buckling load can lay the foundation for the subsequent optimization design.

[0040] like Figure 1-5 As shown, according to a specific embodiment of the present invention, a method for evaluating the probability of buckling load deviation of a rocket stiffened shell structure is disclosed, which specifically includes the following steps:

[0041] S1 determines the uncertainty parameters of the reinforced shell structure, obtains the sample data corresponding to the variables, and uses the K-means clustering method to perform initial clustering on the sample data; a typical launch vehicle reinforced shell and its reinforced cross section are shown in Figure 1 As shown. The material used for the structure is aluminum alloy, the diameter D of the reinforced shell is 3m, the height L is 2m, the number of axial reinforcements is 90, and the number of circumferential reinforcements is 25. For the structural parameters of the rocket reinforced shell, three random variables are mainly considered in the uncertainty propagation analysis, namely, the skin thickness t s , reinforcement thickness t r And reinforcement height h.

[0042] S2 builds a Copula mixed model based on the clustering results of S1, and measures the marginal probability density function of the two clusters of samples after clustering and the correlation between the parameters, thereby completing the uncertainty modeling of the rocket reinforced shell structural parameters; n groups of reinforced shell structural parameters are measured as sample data, with a sample capacity of 280. The sample correlation scatter plot and marginal probability density distribution results are shown in Figure 2As shown in the figure, X1, X2 and X3 correspond to the skin thickness, reinforcement thickness and reinforcement height of the stiffened shell respectively. The diagonal part of the figure is the statistical result of the marginal probability density of the random variable. The uncertainty measurement method based on the Copula mixed model is used to measure the uncertainty of the sample. The number of clusters is set to 2. The measurement results are shown in Figure 3 As shown in the figure, 'o' represents the sample data whose clustering result is cluster 1, and '*' represents the sample data whose clustering result is cluster 2.

[0043] Firstly, the marginal probability density function of random variables is obtained, and the correlation modeling of random variables is completed based on the Copula function. For the reinforced shell structure, its joint probability density function f(X1,X2,X3) can be expressed as:

[0044] f(X1,X2,X3)=f1(X1)·f 2|1 (X2|X1)·f 3|12 (X3|X1,X2)

[0045] =f1(X1)·f2(X2)·c 12 (F1(X1),F2(X2))

[0046] ·f3(X3)·c 13|2 (F 1|2 (X1|X2),F 3|2 (X3|X2))·c 23 (F2(X2), F3(X3)) where f1(X1), f2(X2) and f3(X3) are the marginal probability density functions of random variables, and the other parts are the correlations between random variables. When performing uncertain modeling based on the Copula mixture model, the calculation formula for its log-likelihood function is:

[0047]

[0048] Where Ω1 and Ω2 are based on the weights of the two clusters of sample data obtained by the Copula mixture model, Ω1+Ω2=1, h1 and h2 represent the Copula functions corresponding to the two clusters of samples, ξ1 and ξ2 include the marginal distribution parameters and correlation parameters of the two clusters, respectively, and x i (i=1,2,3,…,n) represents the structural parameters of n groups of stiffened shells obtained by measurement.

[0049] S3, based on the uncertainty modeling results and the idea of ​​"divide and conquer", adopts a representative point selection method based on generalized F deviation for each cluster of samples that have completed modeling and obtains representative points and probability weights; when the probability weight point matching method is used for uncertainty propagation, the primary task is to select representative points. The present invention selects representative points based on the generalized F deviation method, and performs an inverse transformation on the CDF value according to the inverse of the b marginal distribution when selecting representative points. The specific method is as follows:

[0050] x” m,i =F i -1 (u” m,i |θ i )

[0051]

[0052] Where n represents the number of required representative points, u" m,i 、u' m,i and u m,i Respectively represent the CDF values ​​corresponding to each representative point after three inverse transformations, where u" m,i It is generated based on the sobol random sequence, x" m,i 、x' m,i and x m,i Respectively represent the coordinates of each dimension of each representative point after three inverse transformations, where x m,i That is the final representative point coordinates, m = (1, 2, 3, L, n) represents the mth sample point. θ i represents the uncertainty parameter of the i-th dimension random variable.

[0053] To solve the probability weight p corresponding to the representative point m First, we use the Monte Carlo method to generate N according to the constructed metric model. MC Then, take the representative point as the cluster center and cluster N MC For cluster analysis of samples, the probability weight p corresponding to the representative point m It can be obtained by the following formula

[0054]

[0055] Λ(x m ) indicates that after cluster analysis, N MC The samples are classified into x m The number of samples in the cluster.

[0056] S4 brings the data corresponding to the representative point into the finite element analysis software, solves the critical buckling load of the stiffened shell structure under the corresponding data, and obtains the response value of the representative point; when performing finite element analysis, constrains all degrees of freedom at the bottom of the structure and all degrees of freedom at the top except axial displacement, inputs the data corresponding to the representative point into the finite element analysis software, and obtains the critical buckling load of the structure under the corresponding value. s =4mm, t r The buckling modal analysis structure of the stiffened shell structure when =9mm and h=15mm is shown in the figure. The critical buckling load corresponding to the structure is 15704kN.

[0057] S5, based on the obtained representative point response values, uses the improved probability weight point matching method to directly calculate the corresponding probability density functions of the two cluster variables;

[0058] The probability density integral equation of the response PDF is solved by using the improved probability weighted point matching method as follows:

[0059]

[0060] Among them, n is the number of selected representative points, x m is the mth representative point, g(x m ) The calculated response value of the finite element simulation is Θ X,m For its representative area, P t is the probability value corresponding to the representative area. Based on this, the response values ​​of the two clusters of random variables are obtained as follows: Figure 4 Shown in dashed and dotted lines.

[0061] S6 combines the obtained two clusters of probability density functions according to the weights, and finally obtains the probability distribution characteristics of the buckling load deviation of the rocket stiffened shell structure;

[0062] The two cluster response results obtained in S4 are merged, as Figure 4 As shown by the black solid line in the figure, this result is the probability distribution result of the critical buckling load deviation of the stiffened shell structure. So far, the probability evaluation of the critical buckling load deviation of the stiffened shell structure has been completed. The deviation in the stiffened shell skin thickness, stiffening thickness and stiffening height has been taken into account in this deviation evaluation result.

[0063] In order to improve the verification and calibration process and optimize the multi-objective optimization strategy, in a specific embodiment, a pre-step 0 can also be designed: data preprocessing, which includes removing outliers and missing values ​​in the sample data and normalizing the remaining samples to eliminate the impact of different dimensions on subsequent analysis.

[0064] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for evaluating the probabilistic characteristics of buckling load deviation of rocket stiffened shell structure, characterized in that: The evaluation method comprises the following steps: S1 determines the uncertainty parameters of the stiffened shell structure, obtains sample data corresponding to the variables, and uses the K-means clustering method to perform initial clustering on the sample data; S2 builds a Copula mixed model based on the clustering results of step 1, measures the marginal probability density function of each cluster sample after clustering and the correlation between parameters, and then completes the uncertainty modeling of the rocket stiffened shell structure parameters; S3, based on the uncertainty modeling results and the idea of ​​"divide and conquer", adopts the representative point selection method based on generalized F deviation for each cluster of samples that completes the modeling and obtains the representative point and probability weight; S4 brings the data corresponding to the representative point into the finite element analysis software, solves the critical buckling load of the stiffened shell structure under the corresponding data, and obtains the response value of the representative point; S5 directly calculates the corresponding probability density functions of the two cluster variables using the improved probability weight point matching equation based on the obtained representative point response values; S6 combines the two clusters of probability density functions according to the weights, and finally obtains the probability distribution characteristics of the buckling load deviation of the rocket stiffened shell structure.

2. According to the method for evaluating the probability of buckling load deviation of rocket stiffened shell structure described in claim 1, it is characterized in that , the S2 further comprises: For the rocket reinforced shell structure, n groups of reinforced shell structural parameters are obtained by sampling as sample data. When uncertain modeling is performed based on the Copula mixed model, the calculation formula of its log-likelihood function is: In the formula, Ω j Represents the weight of each sample data of the jth cluster obtained by the Copula mixed model, h j represents the Copula function corresponding to the j-th cluster sample, ξ j is the marginal distribution parameter and correlation parameter of the jth cluster, x i (i=1,2,3,…,n) represents the structural parameters of n groups of stiffened shells obtained by measurement.

3. According to the method for evaluating the probability of buckling load deviation of a rocket stiffened shell structure as described in claim 1, it is characterized in that: The S3 further includes selecting the representative point based on the following formula: x” m,i =F i -1 (u” m,i |θ i ) Where n represents the number of required representative points, u" m,i 、u' m,i and u m,i Respectively represent the CDF values ​​corresponding to each representative point after three inverse transformations, where u" m,i It is generated based on the sobol random sequence, x" m,i 、x' m,i and x m,i Respectively represent the coordinates of each dimension of each representative point after three inverse transformations, where x m,i That is the final representative point coordinates, m = (1, 2, 3, L, n) represents the mth sample point. θ i represents the uncertainty parameter of the i-th dimension random variable. To solve the probability weight p corresponding to the representative point m First, we use the Monte Carlo method to generate N according to the constructed metric model. MC Then, take the representative point as the cluster center and cluster N MC For cluster analysis of samples, the probability weight p corresponding to the representative point m It can be obtained by the following formula Λ(x m ) indicates that after cluster analysis, N MC The samples are classified into x m The number of samples in the cluster.

4. According to the method for evaluating the probability of buckling load deviation of a rocket stiffened shell structure as described in claim 1, it is characterized in that: The S5 further includes that the improved probability weighted point matching method adopts the following formula to obtain the probability distribution characteristics of the response: Among them, n is the number of selected representative points, x m is the mth representative point, g(x m ) The calculated response value of the finite element simulation is Θ X,m For its representative area, P t is the probability value corresponding to the representative area. This formula makes the probability density function of the response continuous and smooth based on the Gaussian function, which is a good replacement for the Dirac function.

5. The method for evaluating the probability of buckling load deviation of a rocket stiffened shell structure according to claim 1, characterized in that: It also includes the pre-step 0: data preprocessing, which includes removing outliers and missing values ​​in the sample data and normalizing the remaining samples to eliminate the influence of different dimensions on subsequent analysis.

6. The method for evaluating the probability of buckling load deviation of a rocket stiffened shell structure according to claim 1, characterized in that: In S4, when solving the critical buckling load, the finite element analysis software considers the nonlinear characteristics of structural mechanics under uncertainty conditions to improve the accuracy of the solution results.

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