Aircraft structure reliability optimization method and device considering load uncertainty

Abstract

The invention belongs to the field of aircraft structure design, and particularly relates to an aircraft structure reliability optimization method and device considering load uncertainty. The method comprises the following steps: S1, establishing an uncertainty model between an uncertainty load P and a structure output response according to a structure model and a structure design variable d; s2, setting an optimization objective function, setting a structure constraint condition that a structure design variable d is located in an upper and lower bound range, and setting a reliability constraint condition that a structure failure probability is lower than a set value; s3, according to the dimension of the load variable, the failure probability of the structure is calculated through a quadrature formula point selection criterion of fifth algebraic precision; and S4, optimizing the structural design variable d according to the optimization objective function and the constraint condition. The efficiency of reliability analysis of the inner layer structure is greatly improved, and then the overall calculation efficiency of structural reliability optimization is effectively improved.

Description

Technical Field

[0001] This application belongs to the field of aircraft structural design, and specifically relates to a method and apparatus for optimizing the reliability of aircraft structures considering load uncertainties. Background Technology

[0002] In engineering practice, aircraft structures are often exposed to uncertainties due to various uncertainties. Among these uncertainties, the variability of external loads on the aircraft is the most significant, thus greatly impacting structural performance. To quantify the influence of load uncertainty on aircraft structural performance and incorporate this influence into the design process, a feasible approach is to perform reliability optimization design. This involves defining reliability constraints to design structural parameters that meet reliability requirements. However, structural reliability optimization requires embedding a structural reliability calculation process within deterministic optimization, significantly increasing the computational load and making the entire calculation process impractical for engineering applications. Summary of the Invention

[0003] To address the aforementioned issues, this application provides a method and apparatus for optimizing the reliability of aircraft structures considering load uncertainties. The use of a quadrature formula to calculate reliability indices will significantly reduce the number of calculations required for the finite element model of the aircraft structure.

[0004] The first aspect of this application provides a method for optimizing the reliability of aircraft structures considering load uncertainties, mainly including:

[0005] Step S1: Based on the structural model and structural design variable d, establish an uncertainty model between the uncertain load P and the structural output response;

[0006] Step S2: Set the optimization objective function, set the structural constraint condition that the structural design variable d is within the upper and lower bounds, and set the reliability constraint condition that the structural failure probability is lower than the set value.

[0007] Step S3: Calculate the failure probability of the structure based on the dimensions of the load variables and the point selection criterion using the quadrature formula with fifth-degree algebraic precision.

[0008] Step S4: Optimize the structural design variable d according to the optimization objective function and the constraints.

[0009] Preferably, step S2 further includes giving one or more inequality constraints.

[0010] Preferably, step S3 further includes:

[0011] Step S31: Determine the integration point function in the standard normal space based on the calculation results of the uncertainty model, and then determine the output mean and standard deviation by using the integration operator calculated by the selection criterion of the quadrature formula with fifth algebraic precision.

[0012] Step S32: Calculate the failure probability of the structure based on the output mean and standard deviation.

[0013] Preferably, in step S4, the structural design variable d is optimized using a sequential quadratic programming method or an activation set method.

[0014] The second aspect of this application provides an aircraft structural reliability optimization device that considers load uncertainty, mainly comprising:

[0015] The uncertainty model acquisition module is used to establish an uncertainty model between the uncertain load P and the structural output response based on the structural model and structural design variables d.

[0016] The optimization objective and constraint determination module is used to set the optimization objective function, set the structural constraint condition that the structural design variable d is within the upper and lower bounds, and set the reliability constraint condition that the structural failure probability is lower than the set value.

[0017] The failure probability calculation module is used to calculate the failure probability of the structure based on the dimension of the load variables and the point selection criterion of the quadrature formula with fifth algebraic precision.

[0018] The structural design variable optimization module is used to optimize the structural design variable d according to the optimization objective function and the constraints.

[0019] Preferably, the optimization objective and constraint determination module further includes an inequality constraint construction unit, used to provide one or more inequality constraints.

[0020] Preferably, the failure probability calculation module includes:

[0021] The mean and standard deviation calculation unit is used to determine the integration point function in the standard normal space based on the calculation results of the uncertainty model. The output mean and standard deviation are then determined by the integration operator calculated using the quadrature formula selection criterion of the fifth algebra precision.

[0022] The failure probability calculation unit is used to calculate the failure probability of the structure based on the output mean and standard deviation.

[0023] Preferably, in the structural design variable optimization module, the structural design variable d is optimized using a sequential quadratic programming method or an activation set method.

[0024] This application significantly improves the efficiency of internal structure reliability analysis, thereby effectively improving the overall computational efficiency of structural reliability optimization. Attached Figure Description

[0025] Figure 1 This is a flowchart of a preferred embodiment of the aircraft structural reliability optimization method considering load uncertainty in this application.

[0026] Figure 2 This application Figure 1 A schematic cross-sectional view of the wing structure in the embodiment shown.

[0027] Figure 3 This application Figure 1 A simplified schematic diagram of an aircraft wing structure in the embodiment shown. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions in the embodiments of this application will be described in more detail below with reference to the accompanying drawings. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are only some, not all, of the embodiments of this application. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain this application, and should not be construed as limiting this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application. The embodiments of this application will be described in detail below with reference to the accompanying drawings.

[0029] The first aspect of this application provides a method for optimizing the reliability of aircraft structures considering load uncertainties, such as... Figure 1 As shown, it mainly includes:

[0030] Step S1: Based on the structural model and structural design variable d, establish an uncertainty model between the uncertain load P and the structural output response;

[0031] Step S2: Set the optimization objective function, set the structural constraint condition that the structural design variable d is within the upper and lower bounds, and set the reliability constraint condition that the structural failure probability is lower than the set value.

[0032] Step S3: Calculate the failure probability of the structure based on the dimensions of the load variables and the point selection criterion using the quadrature formula with fifth-degree algebraic precision.

[0033] Step S4: Optimize the structural design variable d according to the optimization objective function and the constraints.

[0034] In the reliability analysis of structural systems, the first step is to determine the uncertainty model of the structure, where the input-output variable relationship of the structural model can be derived from... This indicates that X is the input variable and Y is the corresponding structure output variable. For the function of the structural model, in step S1, the input variable is the uncertain load P, thus forming the uncertainty model. Different structural design variables d will cause changes in the parameters within g. The purpose of this application is to optimize the structural design variable d. During the optimization process, for a specified structural design variable d, a specified output parameter Y will be generated.

[0035] Step S2 is used to define a given optimization model. For structural reliability design problems, the essence is an inverse problem of uncertainty analysis. Typically, structural reliability indices are pre-assigned based on actual engineering needs. Therefore, structural reliability optimization design can be regarded as adding an extra constraint on structural reliability on the basis of deterministic optimization design. The commonly used reliability optimization model is as follows.

[0036] ;

[0037] In the above formula, Variables for structural design. and These are the lower and upper bounds of the design variable, respectively. In some alternative implementations, For structural reliability constraints, This is the failure probability calculated in subsequent step S3. As mentioned earlier, this is a given value. Step S2 further includes giving one or more inequality constraints, i.e., in the above equation... For other inequality constraints.

[0038] To address the aforementioned optimization model, this application designs two frameworks: an inner and an outer layer. The outer computational framework for reliability optimization employs a suitable optimization algorithm to continuously obtain structural design variable parameters that may satisfy the optimization conditions. The inner-layer computational framework for reliability optimization calculates the given structural parameters based on the integration points and integration weights of the quadrature formula in step S3. Structural failure probability .

[0039] Specifically, step S3 further includes:

[0040] Step S31: Determine the integration point function in the standard normal space based on the calculation results of the uncertainty model, and then determine the output mean and standard deviation by using the integration operator calculated by the selection criterion of the quadrature formula with fifth algebraic precision.

[0041] Step S32: Calculate the failure probability of the structure based on the output mean and standard deviation.

[0042] Based on the structural function, if defined If the structure fails, the probability of structural failure can be expressed as follows:

[0043] ;

[0044] in, Let be the probability density function of the input variable, and the integral expressed by equation (1) can also be transformed into the following formula for calculating the mathematical expectation of the failure domain indicator function:

[0045] ;

[0046] in For failure domain indicator functions, For mathematical expectation operators.

[0047] The most commonly used method for calculating failure probability is the Monte Carlo numerical simulation method. However, this method generally requires a large number of model calculations, making the computational workload of reliability analysis unacceptable for practical engineering applications. Besides numerical simulation, another feasible method for calculating failure probability is the moment method. This method first calculates the reliability index by estimating the first two or fourth moments output by the structural model, and then approximates the structural failure probability by using the relationship between the reliability index and the failure probability.

[0048] This application uses the first two moments of the output to calculate the reliability index. Specifically, in step S31, to calculate the mean and standard deviation of the structural model output, this invention employs the quadrature formula method for efficient calculation. The quadrature formula is an efficient numerical integration method for estimating the central moments of a sample. It selects appropriate integration points in the standard normal distribution space and calculates the corresponding integration weights, thereby weightedly calculating the moments of the output samples. The selection criteria for the fifth-algebraic precision quadrature formula used in this invention are as follows:

[0049] ;

[0050] in, Let be the integral operator, and n be the dimension of the input variable. The above is the standard formula, which can efficiently calculate the mean and variance of the structural model output using the integral points and corresponding weights determined under different input dimensions. The relationship between the number of integral points required (i.e., the final number of model operations) and the dimension of the input variable is as follows: Specifically, in this application, parameter substitution is required, specifically for the integration points in the standard normal space. When calculating the output mean, The integral operator calculated from this is the output mean, while when calculating the output variance, we have... The integral operator calculated from this is the variance, and the standard deviation can then be obtained.

[0051] Then, in step S32, the reliability index is calculated as follows:

[0052] ;

[0053] in, and These output the mean and standard deviation of the structural model, respectively. Based on the reliability index, the probability of structural failure can be obtained. for:

[0054] ;

[0055] in, is the cumulative distribution function of a normal distribution.

[0056] Finally, in step S4, parameter optimization is performed when the structural parameters... When all constraints are satisfied and the objective function is minimized, This is the final result of structural reliability optimization.

[0057] In some alternative implementations, in step S4, the structural design variable d is optimized using a sequential quadratic programming method or an activation set method.

[0058] This application will use an aircraft wing structure to illustrate the calculation process and application effect of the proposed structural reliability optimization method. First, the cross-section and overall schematic diagram of the wing model are shown below. Figure 2 and Figure 3 As shown, one of the box segments has a length of L = 3m. The finite element model of the entire wing structure can be considered as being composed entirely of rod-plate elements, where the cross-sectional area of ​​all rod elements is A = 100mm². 2 The thickness of the plate units used for the ribs and wing walls is... The thickness of the plate unit used for the skin is All the rod and plate units are made of 7050 aluminum alloy, with an elastic modulus of 70,000 MPa and a Poisson's ratio of 0.33. Assuming the wing structure is subjected to a concentrated load P with a mean of 1700 N and a standard deviation of 170 N, we can focus on whether the maximum stress value of the entire structure exceeds the tensile strength of the aluminum alloy. Therefore, we can construct the limit state function of the wing structure and perform reliability analysis and optimization design.

[0059] .

[0060] For this wing structure, the currently expected structural failure probability is: The structural parameter to be optimized is the skin thickness. And the thickness of the wing ribs and wing walls is The optimization interval is , The optimization objective of this problem is to minimize the structural weight, i.e., minimize the thickness. and Therefore, this optimization problem has two optimization objectives, namely... and These two optimization objectives can be combined into a weighted objective function. The weights of the two optimization objectives are both 1.

[0061] To address this optimization problem, this invention employs two optimization algorithms: Sequential Quadratic Programming (SQP) and the Active Set method, to optimize the outer structural parameters. and The inner layer calculates the reliability constraints using a quadrature formula to estimate the structural reliability index, and then calculates the probability of structural failure. Since the load variables in this problem are only one-dimensional, only three finite element model operations are required each time a reliability calculation is performed in the inner layer. Finally, the results of this reliability optimization problem are shown in Table 1:

[0062] Table 1 Reliability optimization results of aircraft wing structure

[0063]

[0064] As can be seen from the calculation results in Table 1, the optimal structural parameters obtained by the two optimization methods are consistent, and the calculated structural failure probability under the optimized structural parameters almost satisfies the pre-defined reliability constraints. The active set method shows higher optimization accuracy. In terms of computational complexity, both methods require 10 finite element model operations. 2 The SQP method requires far fewer model computations than the method of this invention. Compared to the method of this invention, the basic Monte Carlo numerical simulation method estimates 10 for each structural parameter. -5 The failure probability needs to be at least 10 on the order of magnitude. 7 The multiple model calculations are sufficient to demonstrate the computational efficiency and effectiveness of the method of the present invention. Therefore, the method of the present invention can provide a powerful tool for the effective quantification of aircraft structural safety and further refined design.

[0065] A second aspect of this application provides an aircraft structural reliability optimization device considering load uncertainty, corresponding to the above method, mainly comprising:

[0066] The uncertainty model acquisition module is used to establish an uncertainty model between the uncertain load P and the structural output response based on the structural model and structural design variables d.

[0067] The optimization objective and constraint determination module is used to set the optimization objective function, set the structural constraint condition that the structural design variable d is within the upper and lower bounds, and set the reliability constraint condition that the structural failure probability is lower than the set value.

[0068] The failure probability calculation module is used to calculate the failure probability of the structure based on the dimension of the load variables and the point selection criterion of the quadrature formula with fifth algebraic precision.

[0069] The structural design variable optimization module is used to optimize the structural design variable d according to the optimization objective function and the constraints.

[0070] In some optional implementations, the optimization objective and constraint determination module further includes an inequality constraint construction unit for providing one or more inequality constraints.

[0071] In some optional implementations, the failure probability calculation module includes:

[0072] The mean and standard deviation calculation unit is used to determine the integration point function in the standard normal space based on the calculation results of the uncertainty model. The output mean and standard deviation are then determined by the integration operator calculated using the quadrature formula selection criterion of the fifth algebra precision.

[0073] The failure probability calculation unit is used to calculate the failure probability of the structure based on the output mean and standard deviation.

[0074] In some optional implementations, the structural design variable optimization module uses a sequential quadratic programming method or an activation set method to optimize the structural design variable d.

[0075] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. An aircraft structure reliability optimization method considering load uncertainty, characterized in that, include: Step S1: Based on the structural model and structural design variable d, establish an uncertainty model between the uncertain load P and the structural output response; Step S2: Set the optimization objective function, set the structural constraint condition that the structural design variable d is within the upper and lower bounds, and set the reliability constraint condition that the structural failure probability is lower than the set value. Step S3: Calculate the failure probability of the structure based on the dimensions of the load variables and the point selection criterion using the quadrature formula with fifth-degree algebraic precision. Step S4: Optimize the structural design variable d according to the optimization objective function and the constraints.

2. The aircraft structure reliability optimization method considering load uncertainty of claim 1, wherein, Step S2 further includes giving one or more inequality constraints.

3. The method for aircraft structure reliability optimization considering load uncertainty according to claim 1, wherein, Step S3 further includes: Step S31: Determine the integration point function in the standard normal space based on the calculation results of the uncertainty model, and then determine the output mean and standard deviation by using the integration operator calculated by the selection criterion of the quadrature formula with fifth algebraic precision. Step S32: Calculate the failure probability of the structure based on the output mean and standard deviation.

4. The method for aircraft structure reliability optimization considering load uncertainty according to claim 1, characterized in that, In step S4, the structural design variable d is optimized using either sequential quadratic programming or activation set method.

5. An aircraft structure reliability optimization device considering load uncertainty, characterized by, include: The uncertainty model acquisition module is used to establish an uncertainty model between the uncertain load P and the structural output response based on the structural model and structural design variables d. The optimization objective and constraint determination module is used to set the optimization objective function, set the structural constraint condition that the structural design variable d is within the upper and lower bounds, and set the reliability constraint condition that the structural failure probability is lower than the set value. The failure probability calculation module is used to calculate the failure probability of the structure based on the dimension of the load variables and the point selection criterion of the quadrature formula with fifth algebraic precision. The structural design variable optimization module is used to optimize the structural design variable d according to the optimization objective function and the constraints.

6. The apparatus for optimizing the reliability of an aircraft structure taking into account load uncertainty according to claim 5, characterized in that, The optimization objective and constraint determination module also includes an inequality constraint construction unit, which is used to provide one or more inequality constraints.

7. The apparatus for optimizing the reliability of an aircraft structure taking into account load uncertainty according to claim 5, characterized in that, The failure probability calculation module includes: The mean and standard deviation calculation unit is used to determine the integration point function in the standard normal space based on the calculation results of the uncertainty model. The output mean and standard deviation are then determined by the integration operator calculated using the quadrature formula selection criterion of the fifth algebra precision. The failure probability calculation unit is used to calculate the failure probability of the structure based on the output mean and standard deviation.

8. The apparatus for optimizing the reliability of an aircraft structure taking into account load uncertainty according to claim 5, characterized in that, In the structural design variable optimization module, the structural design variable d is optimized using a sequential quadratic programming method or an activation set method.

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