A method for evaluating the buckling load deviation probability of a rocket stiffened shell structure

Abstract

This invention proposes a method for evaluating the probabilistic characteristics of buckling load deviation in rocket stiffened shell structures. Given that traditional deterministic methods cannot effectively address the uncertainties caused by external environment and material properties, this invention utilizes a Copula hybrid model to model variable uncertainties and employs a divide-and-conquer strategy combined with an improved probability weighting method to perform independent uncertainty propagation analysis on each parameter cluster. This method efficiently obtains the high-dimensional parameter space response probability distribution and comprehensively evaluates the buckling load deviation probability by integrating the results from each cluster. This invention provides a foundation for evaluating the probabilistic distribution characteristics of buckling load deviation in stiffened shell structures considering multi-parameter random deviations, thus aiding in reliability analysis and optimization design.

Description

Technical Field

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

[0002] The structural integrity and reliability of a rocket body are critical factors in ensuring the success of space missions. Stiffened shell structures, by incorporating stiffeners or ribs into a thin shell, significantly improve the local and overall stability of the structure, making it more resistant to the effects of harsh environments such as aerodynamic heating, vibration, and pressure fluctuations. Therefore, they are widely used in lightweight design for critical components such as rocket bodies and fuel tanks. However, buckling, as a potential failure mode of stiffened shell structures, can lead to catastrophic failure before the material's strength limit is reached. Therefore, the importance of buckling analysis in rocket structural design is self-evident; it is a crucial step in ensuring the stability and safety of rocket structures.

[0003] Traditional buckling analysis methods, based on a deterministic framework, cannot fully quantify the impact of uncertainties such as external environmental fluctuations, material property deviations, and design errors, as well as their correlations, on the buckling performance of structures. This is particularly limiting in modern rocket structural design. To overcome these limitations, advanced analytical techniques capable of quantifying the effects of uncertainties must be employed. Through in-depth analysis and understanding of buckling risks under uncertain environments, potential risk points can be efficiently and accurately identified during the design phase. This ensures that rocket structures maintain integrity and functionality in the face of complex and ever-changing space environments, providing a solid guarantee for the successful execution of space missions.

[0004] However, in the field of probabilistic assessment of buckling load deviation in rocket stiffened shell structures, the application of these methods is still in its early stages, and a systematic assessment process and technical system have not yet been formed. This invention aims to model and propagate the uncertainty deviation of rocket stiffened shell structure parameters through the Copula hybrid model and the probabilistic weighted collocation method, so as to obtain the probabilistic characteristics of structural buckling load deviation and lay the foundation for subsequent optimization design. Summary of the Invention

[0005] In view of the above problems, the purpose of this invention is to model and propagate the uncertainty deviation of rocket stiffened shell structure parameters by using the Copula hybrid model and the probabilistic weighted collocation method, thereby obtaining the probabilistic characteristics of the structural buckling load deviation, and laying the foundation for subsequent optimization design.

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

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

[0008] S2 constructs a Copula mixture model based on the clustering results of step 1, and measures the marginal probability density function and the correlation between parameters of each cluster sample after clustering, thereby completing the uncertainty modeling of rocket stiffening shell structure parameters;

[0009] Based on the uncertainty modeling results, S3 uses the "divide and conquer" approach to select representative points and probability weights for each cluster of samples that have completed modeling, and adopts a representative point selection method based on generalized F-bias.

[0010] S4 inputs the data corresponding to the representative point into the finite element analysis software to solve the critical buckling load of the stiffened shell structure under the corresponding data and obtain the response value of the representative point.

[0011] Based on the representative point response values, S5 uses an improved probability weighted collocation equation to directly calculate the corresponding probability density functions of these two clusters of variables.

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

[0013] S2 further includes: for the rocket stiffened shell structure, obtaining through sampling... s Using the structural parameters of the reinforced shell as sample data, the formula for calculating its log-likelihood function when performing uncertainty modeling based on the Copula mixture model is as follows:

[0014]

[0015] In the formula, The first result obtained from the Copula mixture model j The weight of each cluster sample data, , Indicates the first j The Copula function corresponding to the cluster sample, For the first j Marginal distribution parameters and correlation parameters of clustering Indicates the measurement obtained s Structural parameters of reinforced shells.

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

[0017]

[0018]

[0019]

[0020] in n Indicates the number of representative points required. , and These represent the CDF values ​​corresponding to each representative point after the three inverse transforms, where It is generated based on the SOBO random sequence. , and Let each of the three inverse transformations represent the coordinates of the representative points in each dimension, where That is, the final representative point coordinates. Indicates the first m 1 sample point. Indicates the first i Uncertainty parameters of a dimensional random variable.

[0021] To solve for the probability weights corresponding to the representative points First, the Monte Carlo method is used to sample and produce data based on the constructed metric model. N MC One sample. Then, using the representative point as the cluster center, the clusters were... If a cluster analysis is performed on a sample, then the probability weight corresponding to the point is... It can be obtained through the following formula

[0022]

[0023] This indicates that after cluster analysis, In each sample, Number of samples in a cluster.

[0024] S5 further includes that the improved probability weighting method for point allocation uses the following formula to obtain the probability distribution characteristics of the response:

[0025]

[0026] in, n The number of representative points required. For the first m One representative point, The calculated response value from the finite element simulation is For its representative region, Let represent the probability value corresponding to the region. This formula, based on the Gaussian function, makes the probability density function of the response continuous and smooth, thus effectively replacing the Dirac function.

[0027] The method for evaluating the buckling load deviation probability of a rocket stiffened shell structure further includes a preliminary step 0: data preprocessing. This step includes removing outliers and missing values ​​from the sample data and normalizing the remaining samples to eliminate the influence of different dimensions on subsequent analysis.

[0028] The finite element analysis software in S4 considers the nonlinear characteristics of structural mechanics under uncertainty conditions when solving for critical buckling loads, in order to improve the accuracy of the solution results.

[0029] The beneficial effects of this invention are that by combining finite element simulation, Copula hybrid model, and improved probabilistic weighted collocation method, it achieves probabilistic characteristic analysis of buckling load deviation of rocket stiffened shell structure, which has significant advantages of quantification, high accuracy, and high efficiency, as specifically reflected as follows:

[0030] 1. Quantitative analysis of the effects of parameter deviation and correlation: This invention combines finite element simulation to conduct propagation analysis of the uncertainties and correlations existing in the stiffened shell structure of rockets. It can quantitatively analyze the influence of parameter deviation and correlation on buckling load, thereby obtaining the probability distribution characteristics of buckling load deviation of stiffened shell structure. This characteristic is of great significance for evaluating the stability and safety of rocket structure.

[0031] 2. Accurate Measurement of High-Dimensional Parameter Bias Characteristics: This invention, based on a Copula hybrid model, achieves uncertainty modeling of rocket stiffening shell model parameters, accurately measuring high-dimensional parameter bias characteristics and their correlations, and possesses high universality. This modeling method not only improves the accuracy of the analysis but also effectively broadens the application scope of this invention to different types of correlations by combining various Copula functions.

[0032] 3. Improved Evaluation Efficiency and Optimized Analysis Process: This invention employs an improved probability weighted point allocation method. Leveraging the advantages of integrated algorithms, it reduces the number of representative points required, effectively solving the computational efficiency bottleneck in deviation propagation analysis. The evaluation method in this 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 flow, and shorten the solution time. Based on this, it can significantly improve the evaluation efficiency of buckling load deviation probability characteristics and reduce analysis costs and time consumption. Attached Figure Description

[0033] The accompanying 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 parts throughout the drawings.

[0034] Figure 1 This is a schematic diagram of the stiffened shell model structure in the launch vehicle of this invention.

[0035] Figure 2 This is a schematic diagram of the stiffened cross section of the stiffened shell model in the launch vehicle of this invention.

[0036] Figure 3 This is a schematic diagram of the initial sample data of the reinforced shell structure of the present invention.

[0037] Figure 4 This is a schematic diagram of the uncertainty measurement results of the reinforced shell structure of the present invention.

[0038] Figure 5 This is a schematic diagram of the critical buckling load deviation probability assessment results of the reinforced shell structure of the present invention. Detailed Implementation

[0039] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and, together with the embodiments of the present invention, serve to illustrate the principles of the present invention.

[0040] The method of this invention can be used to assess the probability of buckling load deviation in rocket stiffened shell structures. With the development of my country's aerospace industry, the size and complexity of stiffened shell structures have increased, and uncertainties in the manufacturing process have a significantly greater impact on their performance. Stiffened shell structures are used in rocket fuel tanks and load-bearing tubes, and their failure mode is buckling instability. The magnitude of the buckling load on the stiffened shell structure directly affects the service safety of the equipment. Analyzing the uncertainties in stiffened shell structures and obtaining the probability density function of the structural buckling load response can lay the foundation for subsequent optimization design.

[0041] like Figure 1-5 As shown, according to a specific embodiment of the present invention, a method for evaluating the buckling load deviation probability of a rocket stiffened shell structure is disclosed, which specifically includes the following steps:

[0042] S1 determines the uncertainty parameters of the stiffened shell structure, obtains the corresponding sample data, and uses the K-means clustering method to perform initial clustering of the sample data; a typical launch vehicle stiffened shell and its stiffened section are shown below. Figure 1 As shown. The structure is made of aluminum alloy, and the diameter of the stiffened shell is... D It is 3m high. L The shell is 2m long, with 90 axial stiffeners and 25 circumferential stiffeners. For the rocket's stiffened shell structure parameters, three random variables are mainly considered in the uncertainty propagation analysis: skin thickness, etc. t s Reinforcement thickness t r and reinforcement height h .

[0043] S2 constructs a Copula mixture model based on the clustering results of S1, measuring the marginal probability density functions and the correlation between parameters of the two clusters after clustering, thereby completing the uncertainty modeling of the rocket stiffening shell structure parameters; measurements are obtained. s The structural parameters of the reinforced shell were used as sample data, with a sample size of 280. The scatter plot and marginal probability density distribution results are as follows: Figure 2 As shown, X 1. X 2 and X 3 corresponds to the skin thickness, stiffening thickness, and stiffening height of the stiffened shell, respectively. The diagonal part of the figure represents the statistical results of the marginal probability density of the random variable. An uncertainty measurement method based on the Copula mixture model was used to measure the uncertainty of this sample, with the number of clusters set to 2. The measurement results are as follows: Figure 3 As shown in the figure, 'o' represents sample data that is clustered into cluster 1, and '*' represents sample data that is clustered into cluster 2.

[0044] First, the marginal probability density function of the random variable is obtained, and the correlation of the random variable is modeled using the basis Copula function. For the stiffened shell structure, its joint probability density function is... It can be represented as:

[0045]

[0046] in , and Let be the marginal probability density function of the random variables, and the other parts represent the pairwise correlations between the random variables. When modeling uncertainty based on the Copula mixture model, the formula for calculating its log-likelihood function is:

[0047]

[0048] In the formula, and Based on the weights of the two clusters of sample data obtained from the Copula mixture model, , and This represents the Copula function corresponding to these two clusters of samples. and These include the marginal distribution parameters and correlation parameters of the two clusters, respectively. Indicates the measurement obtained s Structural parameters of reinforced shells.

[0049] Based on the uncertainty modeling results, S3, using the "divide and conquer" approach, selects representative points and probability weights for each cluster of samples after modeling, employing a representative point selection method based on generalized F-bias. When using the probability weighted point allocation method for uncertainty propagation, the primary task is to select representative points. This invention uses a generalized F-bias method to select representative points, and then performs an inverse transformation on the CDF value based on the inverse of the b-marginal distribution. The specific method is as follows:

[0050]

[0051]

[0052]

[0053] in n Indicates the number of representative points required. , and These represent the CDF values ​​corresponding to each representative point after the three inverse transforms, where It is generated based on the SOBO random sequence. , and Let each of the three inverse transformations represent the coordinates of the representative points in each dimension, where That is, the final representative point coordinates. Indicates the first m 1 sample point. Indicates the first i Uncertainty parameters of a dimensional random variable.

[0054] To solve for the probability weights corresponding to the representative points First, the Monte Carlo method is used to sample and produce data based on the constructed metric model. N MC One sample. Then, using the representative point as the cluster center, the clusters were... If a cluster analysis is performed on a sample, then the probability weight corresponding to the point is... It can be obtained through the following formula

[0055]

[0056] This indicates that after cluster analysis, In each sample, Number of samples in a cluster.

[0057] S4 inputs the data corresponding to the representative point into the finite element analysis software to solve for the critical buckling load of the stiffened shell structure under the corresponding data, obtaining the response value of the representative point; during the finite element analysis, all degrees of freedom at the bottom of the structure and all degrees of freedom at the top except for axial displacement are constrained, and the data corresponding to the representative point is input into the finite element analysis software to obtain the critical buckling load of the structure under the corresponding values. t s =4mm t r =9mm h The buckling modal analysis of the stiffened shell structure with a thickness of 15mm is shown in the figure. The critical buckling load corresponding to the structure is 15704kN.

[0058] Based on the representative point response values, S5 uses an improved probability weighting point allocation method to directly calculate the corresponding probability density functions of these two clusters of variables.

[0059] The probability density integral equation of the response PDF is solved using an improved probability weighted collocation method, as shown in the following equation.

[0060]

[0061] in, n The number of selected table points. For the first m One representative point, The calculated response value from the finite element simulation is For its representative region, This represents the probability value corresponding to the region. Based on this, the response values ​​of the two clusters of random variables are obtained as follows: Figure 4 As shown by the dashed line and dotted line.

[0062] S6 merges the two clusters of probability density functions according to their weights to finally obtain the probability distribution characteristics of the buckling load deviation of the rocket stiffened shell structure.

[0063] The two cluster response results obtained in S4 are merged, as follows: Figure 4 As shown by the solid black line in the figure, this result represents the probability distribution of the critical buckling load deviation of the stiffened shell structure. This completes the probability assessment of the critical buckling load deviation of the stiffened shell structure, taking into account deviations in the stiffened shell skin thickness, stiffening thickness, and stiffening height.

[0064] To improve the verification and validation process and optimize the multi-objective optimization strategy, a preliminary step 0 can be designed in a specific embodiment: data preprocessing. This step includes removing outliers and missing values ​​from the sample data and normalizing the remaining samples to eliminate the influence of different units on subsequent analysis.

[0065] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for evaluating the buckling load deviation probability characteristics of a rocket stiffened shell structure, characterized in that, The evaluation method includes the following steps: S1 determines the uncertainty parameters of the stiffened shell structure, obtains the sample data corresponding to the variables, and uses the K-means clustering method to perform initial clustering of the sample data; S2 constructs a Copula mixture model based on the clustering results of step 1, and measures the marginal probability density function and the correlation between parameters of each cluster sample after clustering, thereby completing the uncertainty modeling of rocket stiffening shell structure parameters; Based on the uncertainty modeling results, S3 uses the "divide and conquer" approach to select representative points and probability weights for each cluster of samples that have completed modeling, and adopts a representative point selection method based on generalized F-bias. S4 inputs the data corresponding to the representative point into the finite element analysis software to solve the critical buckling load of the stiffened shell structure under the corresponding data and obtain the response value of the representative point. Based on the representative point response values, S5 uses an improved probability weighted collocation equation to directly calculate the corresponding probability density functions of these two clusters of variables. S6 combines the two clusters of probability density functions according to their weights to finally obtain the probability distribution characteristics of the buckling load deviation of the rocket stiffened shell structure.

2. The method for evaluating the buckling load deviation probability characteristics of a rocket stiffened shell structure according to claim 1, characterized in that... S2 further includes: For the stiffened shell structure of a rocket, the structural parameters of the stiffened shell are obtained through sampling as sample data in group s. When performing uncertainty modeling based on the Copula mixture model, the formula for calculating its log-likelihood function is: In the formula, The first result obtained from the Copula mixture model j The weight of each cluster sample data, , Indicates the first j The Copula function corresponding to the cluster sample, For the first j Marginal distribution parameters and correlation parameters of clustering Indicates the measurement obtained s Structural parameters of reinforced shells.

3. The method for evaluating the buckling load deviation probability characteristics of a rocket stiffened shell structure according to claim 1, characterized in that, S3 further includes selecting representative points based on the following formula: in n Indicates the number of representative points required. , and These represent the CDF values ​​corresponding to each representative point after the three inverse transforms, where It is generated based on the SOBO random sequence. , and Let each of the three inverse transformations represent the coordinates of the representative points in each dimension, where That is, the final representative point coordinates. Indicates the first m One sample point; Indicates the first i Uncertainty parameters of a dimensional random variable; To solve for the probability weights corresponding to the representative points First, the Monte Carlo method is used to sample and produce data based on the constructed metric model. N MC One sample; then, using the representative point as the cluster center, for If a cluster analysis is performed on a sample, then the probability weight corresponding to the point is... It can be obtained through the following formula This indicates that after cluster analysis, In each sample, Number of samples in a cluster.

4. The method for evaluating the buckling load deviation probability characteristics of a rocket stiffened shell structure according to claim 1, characterized in that, S5 further includes that the improved probability weighting method for point allocation uses the following formula to obtain the probability distribution characteristics of the response: in, n The number of points to be represented. For the first m One representative point, The calculated response value from the finite element simulation is For its representative region, The probability value represents the region; this formula, based on the Gaussian function, makes the probability density function of the response continuous and smooth, thus effectively replacing the Dirac function.

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

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

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