Aircraft structure design parameter global sensitivity analysis method based on variance

Abstract

The invention provides a variance-based aircraft structure design parameter global sensitivity analysis method, and aims to solve the problems of high calculation cost, difficulty in quantizing parameter interaction effect and coupling propagation influence and the like in the application of existing Sobol and other methods, the method comprises the following steps: firstly, identifying key structure parameters and establishing a probability model of the key structure parameters; then, a Sobol sequence is adopted to generate a sample matrix, and output response is calculated through an aircraft structure system model; constructing a mixed sample matrix to perform variance decomposition, and respectively calculating a first-order sensitivity index and a total sensitivity index of each parameter to quantify main effect and interaction effect contribution; and finally identifying performance key parameters and interaction sensitive parameters according to the index sequence. According to the method, global analysis of a high-dimensional nonlinear structure system is realized under acceptable calculation cost, the result can provide a quantitative decision basis for lightweight design, tolerance allocation and multidisciplinary collaborative optimization of an aircraft structure, and the design efficiency and reliability are remarkably improved.

Description

Technical Field

[0001] This invention relates to the field of aircraft parameter sensitivity analysis technology, specifically a variance-based global sensitivity analysis method for aircraft structural design parameters. Background Technology

[0002] In the field of aircraft design and multidisciplinary optimization, sensitivity analysis of structural design parameters is a crucial step in identifying key design variables, optimizing system performance, and improving design reliability. Sensitivity analysis quantifies the impact of changes in various design parameters on the system's output response (such as structural weight, stress, and deformation), thereby guiding designers to focus on optimizing key parameters.

[0003] Existing sensitivity analysis methods can be broadly categorized into two types: local sensitivity analysis methods and global sensitivity analysis methods. Local sensitivity analysis methods, such as differential methods or finite difference methods, assess the impact of parameters by calculating the partial derivatives of parameters near a specific design point. These methods are computationally efficient, but their analysis results heavily depend on the selected design baseline and cannot reflect the global impact of parameter variations across the entire design space on the system output. Therefore, their applicability is limited in nonlinear, strongly coupled aircraft structural design.

[0004] To overcome the limitations of local methods, global sensitivity analysis methods have emerged. These methods consider the variation of parameters across their entire probability distribution, enabling a more comprehensive assessment of parameter impact. Among them, the Sobol method based on variance decomposition, due to its solid mathematical foundation and ability to clearly quantify the main effects and interaction effects of parameters, has become one of the most widely used global sensitivity analysis methods. Other methods include the Morris method based on screening and the moment independence method based on the cumulative distribution function.

[0005] However, despite significant advancements in existing technologies, several technical challenges remain to be addressed when applied to the complex engineering problem of aircraft structural design:

[0006] First, the high computational cost is a particularly prominent issue. Methods such as Sobol require extensive model sampling to accurately estimate variance components. However, for high-dimensional, high-fidelity finite element models or fluid-structure interaction models of aircraft structures, a single simulation is extremely time-consuming, making the total computational resource requirements for global sensitivity analysis unbearable and severely restricting its application in practical engineering.

[0007] Secondly, the ability to handle mixed uncertainties is insufficient. Most existing global sensitivity analysis methods are based on the assumption that the input parameters are purely random uncertainties. However, in the early stages of aircraft development, many structural design parameters often exhibit cognitive uncertainty rather than probabilistic models due to sparse experimental data or incomplete understanding. Existing methods lack effective sensitivity analysis tools within a unified framework of mixed random and cognitive uncertainties.

[0008] Therefore, there is an urgent need for a sensitivity analysis method for aircraft structural design parameters that can significantly reduce computational costs, adapt to the mixed uncertainties in engineering, and incorporate prior knowledge. Summary of the Invention

[0009] This invention aims to provide a variance-based global sensitivity analysis method for aircraft structural design parameters, addressing the problems of high computational costs, difficulty in handling multidisciplinary coupling effects, and failure to effectively integrate prior engineering knowledge in existing technologies. This method can efficiently and accurately identify design parameters that have a critical impact on structural performance in the early stages of aircraft design, providing precise evidence for optimized design, reliability analysis, and risk control.

[0010] To achieve the above objectives, the present invention adopts the following technical solution:

[0011] A variance-based global sensitivity analysis method for aircraft structural design parameters includes the following steps:

[0012] Step 1: Identification of key structural parameters and uncertainty modeling:

[0013] Identify key design parameters in the aircraft's structural system, such as wing area. bullet length-to-slenderness ratio Material density Wall thickness Based on historical test data, manufacturing tolerances, or expert experience, determine the probability distribution type and distribution parameters for each parameter, thereby completing the processing of the input random vector. Uncertainty modeling, where This represents the total number of parameters.

[0014] Step 2: Sample matrix generation based on efficient sampling strategy:

[0015] Using Latin hypercube sampling or Sobol sequence methods, generate in the parameter probability distribution space determined in step 1 The input samples form a sample matrix. ; The value of should take into account both calculation accuracy and efficiency.

[0016] Step 3: Calculation of aircraft structural system response:

[0017] The sample matrix generated in step 2 Each sample is input into the aircraft structural system model to calculate the corresponding system output response. The system model is a structural finite element model, a fluid-structure interaction simulation model, or a validated surrogate model; the output response... For example, the total structural weight Maximum equivalent stress or maximum deformation of key parts One or more of them.

[0018] Step 4: Calculation of sensitivity index based on variance decomposition:

[0019] Based on the system input and output data obtained in step 3, the first-order sensitivity index of each structural parameter is calculated using the Sobol variance decomposition method. and total sensitivity index The specific process is as follows:

[0020] Step 4.1: Calculate the total variance of the system output. :

[0021] Total variance of system output response The system performance was characterized under the common fluctuation of all structural parameters. The total uncertainty (such as structural weight). Its estimation formula is:

[0022]

[0023] in, It is the first The system output response value corresponding to each sample; It is the sample mean of the system output response.

[0024] Step 4.2: Calculate the variance of the main effects of the parameters :

[0025] parameter Main effects variance This characterizes the effect of individual changes in this parameter on the system output variance. The contribution of [the entity / entity]. Its estimation formula is:

[0026]

[0027] in, Indicates the first In each sample, except All other parameter values ​​except those specified. and It is a parameter Two independent random sample values. This represents the structural system model of the aircraft.

[0028] Step 4.3: Calculate the first-order and total sensitivity indices:

[0029] parameter The first-order sensitivity index (main effect index) The calculation is as follows:

[0030]

[0031] The larger the value, the higher the parameter. The greater the change in itself, the greater the impact on the performance fluctuations of the structural system.

[0032] parameter Total sensitivity index The calculation is as follows:

[0033]

[0034] in It is all that does not include The sum of the variance terms. Quantified parameters The combined contribution of the system output variance to the system and its interaction with all other parameters.

[0035] Step 5: Identify key parameters and provide design guidance:

[0036] Comparative analysis of the first-order sensitivity index of all parameters and total sensitivity index Sort the parameters by exponent value from largest to smallest. and Parameters with consistently high values ​​are identified as key performance parameters; Lower but The parameters with higher values ​​were identified as interaction-sensitive parameters. Based on the identification results, the design team was guided to prioritize tolerance control and optimization design for key performance parameters, and to focus on the analysis and verification of the coupling links where the interaction-sensitive parameters are located.

[0037] Beneficial effects

[0038] Compared with the prior art, the present invention has the following beneficial effects:

[0039] This invention employs the Sobol method based on variance decomposition, which can comprehensively evaluate the impact of structural parameters and their interactions on system performance across the entire distribution range, resulting in more accurate and reliable identification results. By distinguishing between first-order effects and total effects, this invention can not only identify the main influencing parameters but also reveal the complex coupling relationships between parameters, providing a clear direction for multidisciplinary collaborative optimization. Furthermore, this invention combines efficient sampling techniques and can be used in conjunction with structural surrogate models (such as neural network order reduction models), enabling sensitivity analysis of complex aircraft structural systems at an acceptable computational cost, resulting in high computational efficiency. Moreover, the sensitivity index output by this invention has clear physical meaning and mathematical interpretation, making it easy for designers to understand and apply, and can be directly integrated into existing multidisciplinary aircraft design optimization processes.

[0040] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Detailed Implementation

[0041] The embodiments of the present invention are described in detail below. These embodiments are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0042] This embodiment elaborates on a variance-based global sensitivity analysis method for aircraft structural design parameters, based on a typical aircraft wing structure design scenario. Those skilled in the art can apply this method to the structural design analysis of other aircraft components or the entire aircraft based on the description herein.

[0043] This embodiment focuses on the wing structure of a certain type of aircraft. The wing is the primary load-bearing and lift-generating component of the aircraft, and uncertainties in its structural design parameters (such as dimensions and material properties) significantly affect the overall structural weight, stiffness, and strength. This embodiment aims to quantify the contribution of each design parameter to the uncertainty of the wing structure's weight—a key performance indicator—thereby guiding lightweight design and tolerance allocation.

[0044] Specifically, the following steps are included:

[0045] Step 1: Identification of key structural parameters and uncertainty modeling:

[0046] Based on experience in missile wing design, four parameters that significantly affect weight and are subject to uncertainty are selected to form a random vector. Each parameter and its uncertainty are characterized as follows:

[0047] : Reference area of ​​missile wings The uncertainty stems from manufacturing tolerances and aerodynamic shape fine-tuning, which are modeled as a uniform distribution: ;

[0048] : average relative thickness of airfoil This is the ratio of the airfoil's maximum thickness to its chord length, affecting the structural height and material usage. It can be modeled as a normal distribution: ;

[0049] : Density of skin material Aluminum alloy is used, and batch fluctuations in material composition are considered. It is modeled as a normal distribution: ;

[0050] Skin design thickness The initial determination was based on strength and stiffness requirements, but there are issues with processing thinning or manufacturing errors. Therefore, it is modeled as a uniform distribution. ;

[0051] Therefore, the input random vector is , dimension .

[0052] Step 2: Sample matrix generation based on efficient sampling strategy:

[0053] To ensure the stability of variance estimation, the sample size is set. The Sobol sequence method is used to generate [the sequence] in a 4-dimensional parameter space (where each parameter is transformed according to its respective probability distribution). There are 10 samples. The first sample matrix generated is denoted as . Its form is as follows:

[0054] A = [ S A ( 1 ) t ¯ A ( 1 ) r A ( 1 ) t s , A ( 1 ) S A ( 2 ) t ¯ A ( 2 ) r A ( 2 ) t s , A ( 2 ) ⋮ ⋮ ⋮ ⋮ S A ( N ) t ¯ A ( N ) r A ( N ) t s , A ( N ) ]

[0055] Simultaneously, another set of independent sample matrices is generated using the same Sobol sequence but with different random offsets. For subsequent calculations:

[0056] B = [ S B ( 1 ) t ¯ B ( 1 ) r B ( 1 ) t s , B ( 1 ) S B ( 2 ) t ¯ B ( 2 ) r B ( 2 ) t s , B ( 2 ) ⋮ ⋮ ⋮ ⋮ S B ( N ) t ¯ B ( N ) r B ( N ) t s , B ( N ) ]

[0057] Step 3: Calculation of aircraft structural system response:

[0058] This embodiment focuses primarily on sensitivity analysis; therefore, a simplified aircraft wing structure weight estimation model is used as the system model. This model reflects the influence of the main parameters.

[0059]

[0060] in, It is an empirical constant that combines wingspan, aspect ratio, and structural form; in this example, we take... However, in practical applications, Use a high-precision finite element model or a verified proxy model.

[0061] sample matrix and Substitute each row (i.e., each set of parameter combinations) into the above model. The output response vectors are calculated respectively. and Each vector contains Estimated weight of each warhead :

[0062] Y A = [ W w , A ( 1 ) W w , A ( 2 ) ⋮ W w , A ( N ) ] , Y B = [ W w , B ( 1 ) W w , B ( 2 ) ⋮ W w , B ( N ) ]

[0063] in , .

[0064] Step 4: Calculation of sensitivity index based on variance decomposition:

[0065] Based on the system input and output data obtained in step 3, the first-order sensitivity index of each structural parameter is calculated using the Sobol variance decomposition method. and total sensitivity index The specific process is as follows:

[0066] Step 4.1: Construct the mixed sample matrix:

[0067] For each parameter , Construct two mixing matrices: and ,in To make the matrix The Column replacement with matrix The Column 1 remains unchanged, while the rest remain the same; To make the matrix The Column replacement with matrix The Column 1 remains unchanged, while the rest remain the same;

[0068] by For example:

[0069] A B ( 1 ) = [ S B ( 1 ) t ¯ A ( 1 ) r A ( 1 ) t s , A ( 1 ) S B ( 2 ) t ¯ A ( 2 ) r A ( 2 ) t s , A ( 2 ) ⋮ ⋮ ⋮ ⋮ S B ( N ) t ¯ A ( N ) r A ( N ) t s , A ( N ) ] , B A ( 1 ) = [ S A ( 1 ) t ¯ B ( 1 ) r B ( 1 ) t s , B ( 1 ) S A ( 2 ) t ¯ B ( 2 ) r B ( 2 ) t s , B ( 2 ) ⋮ ⋮ ⋮ ⋮ S A ( N ) t ¯ B ( N ) r B ( N ) t s , B ( N ) ]

[0070] Step 4.2: Calculate the output response of the mixing matrix:

[0071] For each parameter, calculate , ;

[0072] Step 4.3: Calculate variance estimation and sensitivity index:

[0073] (1) Calculate the total variance of the system output. :

[0074] Total variance of system output response The system performance was characterized under the common fluctuation of all structural parameters. The total uncertainty. Its estimation formula is:

[0075]

[0076] Calculate the variance of main effects parameters :

[0077] parameter Main effects variance This characterizes the effect of individual changes in this parameter on the system output variance. The contribution of [the entity / entity]. Its estimation formula is:

[0078]

[0079] in, express The Each element. This formula uses parameters... The value ranges from Change to , while fixing others To estimate the parameters The individual impact.

[0080] parameter First-order sensitivity index :

[0081]

[0082] This value indicates that if the parameter is... The uncertainty was completely eliminated, and the weight of the missile wings was reduced. The expected reduction in variance. The larger the value, the higher the parameter. Changes in the weight of the warhead The greater the impact of fluctuations.

[0083] parameter Total sensitivity index :

[0084]

[0085] in It is all that does not include The sum of the variance terms. Quantified parameters The joint contribution of the system output variance to the system and its interaction with all other parameters, i.e., if the parameters are fixed. Given a fixed value, while allowing all other parameters to vary freely within their uncertainty range, the weight of the missile wing... The expected decrease in variance is the proportion that will occur.

[0086] Based on the above calculations, the following sensitivity index table is obtained in this embodiment:

[0087]

[0088] Comparative analysis of the first-order sensitivity index of all parameters and total sensitivity index Sort the parameters in descending order of their exponent values. It can be observed that: wing area... First exponent The highest value indicates that it is the most significant independent factor affecting the weight variation of the missile wing. Strict control of its manufacturing tolerances should be prioritized in the design, and it should be treated as a primary design variable in lightweight optimization. Relative thickness Total sensitivity index Significantly higher than its first exponent This indicates It exhibits significant interactions with other parameters. This means that optimizing it individually... The effect may be limited, requiring coordinated optimization design with other parameters. Material density Both indices are at their lowest, indicating that under current design and technological conditions, batch fluctuations have a relatively small impact on weight variation. Therefore, in cost control, the inspection specifications for this material parameter can be appropriately relaxed.

[0089] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A variance-based global sensitivity analysis method for design parameters of an aircraft structure, characterized in that: Comprising the following steps: Step 1: Select parameters that have influence on the design objectives of the aircraft structure and exist uncertainty as key design parameters, to form a random vector ; Step 2: Generate sample matrix by sampling strategy according to the uncertainty model of the random vector selected in step 1; Step 3: Establishing the aircraft structure system model, inputting each sample generated in step 2 into the aircraft structure system model to calculate the corresponding system output response ; Step 4: Calculate the first order sensitivity index of each structural parameter based on the input and output data of step 3 and the total sensitivity index ; Step 5: First order sensitivity indices of all parameters are compared and total sensitivity indices to determine performance critical and interaction sensitive parameters.

2. The method of claim 1, wherein: In Step 1, after selecting the key design parameters, the type of probability distribution and distribution parameters of each parameter are determined according to historical test data, manufacturing tolerances or expert experience, to realize the uncertainty modeling of the input random vector .

3. The method of claim 2, wherein: In step 2, input samples are generated in the random vector probability distribution space determined in step 1 using Latin hypercube sampling or Sobol sequence method, constituting a sample matrix .​ 4. The method of claim 3, wherein: In step 4, Sobol variance decomposition method is used to calculate the first order sensitivity index of each structural parameter and the total sensitivity index , the specific process is as follows: Computing system outputs total variance : wherein, is the system output response value corresponding to the first sample; is the system output response value corresponding to the first sample; is the sample mean of the system output response; computing the main effect variance of the parameters : wherein, represents the first sample of all other parameters values except ; and are two independent random sample values of the parameter ; represents the aircraft structure system model; Calculate the first-order and total sensitivity indices: Parameters first order sensitivity index are calculated as follows: Parameters Total Sensitivity Index is calculated as follows: wherein is the sum of all variance terms not containing the term 5. The method of claim 1, wherein: In step 5, the parameters that are both high and are identified as performance critical parameters; the parameters that are low but high are identified as interaction sensitive parameters.

6. The method of claim 1, wherein: The aircraft structure is an aircraft wing structure, the selected key design parameters and uncertainty characterizations are: : wing reference area , uncertainty modeled as uniform distribution; : mean airfoil relative thickness , uncertainty modeled as normal distribution; : skin material density , uncertainty modeled as normal distribution; : skin design thickness , uncertainty modeled as uniform distribution; the input random vector is , with dimension .

7. The method of claim 6, wherein: In step 3, the system model is: wherein is the wing structure weight, is an empirical constant.

8. The method of claim 7, wherein: In step 2, Sobol sequence method is used to generate samples in 4-dimensional parameter space, and the first set of sample matrix is denoted as : Another set of independent sample matrices is generated using the same Sobol sequence but different random offsets : In step 3, the sample matrix is... and Substituting each line into the system model, the output response vector is calculated. and Each vector contains Estimated weight of each warhead : ， wherein , .

9. The method of claim 8, wherein: In step 4, for each parameter , , construct two mixing matrices: and where is the matrix obtained by replacing the column of the matrix with the column of the matrix , leaving the remaining columns unchanged; is the matrix obtained by replacing the column of the matrix with the column of the matrix , leaving the remaining columns unchanged; and compute the output response of the mixing matrix for each parameter: , ; Computing system outputs total variance : computing the main effect variance of the parameters : wherein represents the first element of the array Parameters first order sensitivity index : Parameters Total Sensitivity Index : 。

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