Stiffened plate optimization design method integrating test design and optimization algorithm

Abstract

The invention relates to a stiffened plate optimization design method fusing experimental design and an optimization algorithm, which solves the problem that the calculation cost of optimization design of a complex stiffened plate structure is relatively high so as to improve the optimization design efficiency of the structure to the greatest extent, and the method can also be used for reference and is used for optimization design of other complex engineering structures. In order to achieve the target, the invention adopts the following design scheme, and a stiffened plate optimization design method fusing test design and an optimization algorithm is implemented. Therefore, the optimization design efficiency can be improved to the maximum extent, and a reliable way is provided for the design of the structure.

Description

Technical Field

[0001] The invention relates to the technical field of reinforced plate optimization design, and in particular to a reinforced plate optimization design method integrating experimental design and optimization algorithm. Background Art

[0002] Stiffened plate structures are widely used in aerospace, shipbuilding and other technological fields as the main load-bearing components in structures due to their high strength, stability, mature manufacturing process and light weight. However, the shape and position of the ribs in the stiffened plate structure and the combination of the ribs and the base plate will affect the overall mechanical properties of the structure, thereby affecting the quality and cost of the structure. Therefore, in engineering practice, optimizing the design of stiffened plates has become an important means to improve the mechanical properties of the structure and control the processing cost. However, the stiffened plate structures in aerospace and shipbuilding systems are generally complex in shape, resulting in many parameters in the optimization design and a large number of iterations to achieve convergence requirements. In particular, the calculation cost of the optimization design is high for multi-excitation situations. Summary of the invention

[0003] In response to the shortcomings in the above-mentioned existing production technology, the applicant provides a stiffened plate optimization design method that integrates experimental design and optimization algorithm, thereby effectively solving the problem of high computational cost of optimization design of complex stiffened plate structures and maximizing the optimization design efficiency of such structures. At the same time, this method can also be used as a reference for the optimization design of other complex engineering structures.

[0004] The technical solution adopted by the present invention is as follows:

[0005] A stiffened plate optimization design method integrating experimental design and optimization algorithm includes the following steps:

[0006] S1: Analyze the structural characteristics of the optimized stiffened plate and determine the structural parameters and boundaries that can be optimized;

[0007] S2: Establish a parametric model of the stiffened plate structure to characterize the structural parameters that can be optimized;

[0008] S3: Divide the interval of optimization parameters into N parts to form the block design interval of optimization parameters, and calculate each

[0009] From the center point of the interval;

[0010] S4: Calculate the target response of the stiffened plate at each center point, construct the optimization design objective function, and

[0011] Sort the objective functions at the center points of each interval;

[0012] S5: According to the sorting, taking the center point of the optimal value interval as the starting point, the sequential quadratic programming algorithm is used to optimize the design in the interval, and the optimal point in the interval and the optimal value of the objective function are calculated;

[0013] S6: Adopt the optimization design convergence criterion to judge the convergence of the optimization process and determine the optimal stiffened plate structural parameters;

[0014] S7: Round the optimized design parameter results to processable or standard values, and verify the structural model of the target layer.

[0015] S1 includes the following steps:

[0016] S1.1: The structure of the ribs in the stiffened plate includes L-type, C-type, T-type, I-type or hat-type. The parameters to be optimized are the length, thickness, various geometric parameters and the position of the ribs;

[0017] S1.2: The boundaries of the optimized parameters need to be defined according to the spatial layout design standards or specifications of the structure. S2 includes the following steps:

[0018] S2.1: The parametric model of the stiffened plate can be constructed based on a commercial finite element software platform. The target response for analysis can be the dynamic response of the key points such as velocity, acceleration, displacement, etc. under the natural frequency or load excitation.

[0019] S2.2: Based on the secondary development function of the software, the optimization parameters are characterized by variable design variables.

[0020] S3 includes the following steps:

[0021] S3.1: Divide the upper and lower limits of the optimization parameters Xi (i = 1, 2, 3 ..., N) into M equal parts, and the optimization parameter space is divided into M N space;

[0022] S3.2: Calculation of M N The centroid of the parameter interval

[0023] in:

[0024] Represents the optimization parameter x ij The central value or mean value of

[0025] Represents the optimization parameter x ij The lower limit of

[0026] Represents the optimization parameter x ij The upper limit value of .

[0027] 3.3: Calculate each center point according to the objective function construction requirements The target response of the stiffened plate at . In S4, the center point of each interval is Sort the objective function values ​​at and find the location of the optimal objective value.

[0028] S5 includes the following steps:

[0029] S5.1: The sequential quadratic programming method is used to optimize the design of the stiffened plate structure in the corresponding interval; S5.2: The steps of the sequential quadratic programming method are:

[0030] Given an optimization problem with nonlinear constraints:

[0031] minf(x)

[0032] stgu(x)≤0(u=1,2,…,p)

[0033] h v (x) = 0 (υ = 1, 2, ..., m)

[0034] f(x): The result of the dynamic response of the key point such as velocity, acceleration, displacement, etc. under the natural frequency or load excitation;

[0035] in:

[0036] x : Parameters such as the length, thickness, geometric parameters and position of the ribs;

[0037] g u (x): inequality constraint function;

[0038] h v (x): equality constraint function;

[0039] Taylor expansion converts the objective function of the nonlinear constraint problem in the above equation into the iteration point x k Simplifying into a quadratic function, simplifying the nonlinear constraint function into a linear function, we get the following quadratic programming problem:

[0040]

[0041] in:

[0042] X k : The optimization variable value of the current iteration point;

[0043] The gradient vector of the objective function at the current iteration point represents the partial derivatives of the objective function with respect to each variable;

[0044] The Hessian matrix of the target function at the current iteration point represents the second-order derivative matrix of the target function;

[0045] g u (X k ): inequality constraint function;

[0046] h v (X k ): equality constraint function;

[0047] The gradient vector of the inequality constraint function at the current iteration point;

[0048] The gradient vector of the equality constraint function at the current iteration point;

[0049] Let S = XX k , solve this quadratic programming problem and take its optimal solution S * As the next search direction S of the original problem k , and perform a one-dimensional search of the objective function of the original constraint problem in this direction, so that an approximate solution X of the original constraint problem can be obtained k+1 , repeating this process, we can get the optimal solution to the original problem.

[0050] S6 includes the following steps:

[0051] S6.1: Set the convergence tolerance δ of the objective function, which is equal to one thousandth of the objective function corresponding to the center point of the first iteration interval;

[0052] S6.2: Compare the current iteration interval with the previous optimization design results, and use the optimal design point

[0053] The gradient of the objective function is used as the convergence criterion, namely:

[0054]

[0055] in:

[0056] Δ: represents the convergence index of the current iteration;

[0057] fj: represents the objective function value of the jth iteration;

[0058] fj-1: represents the objective function value of the j-1th iteration;

[0059] X *j : represents the design variable value of the jth iteration;

[0060] X *j-1 : represents the design variable value of the j-1th iteration;

[0061] Δ: represents a preset threshold used to judge convergence;

[0062] S6.3: If the above convergence criteria are met, the iteration is stopped; if not, return and iterate further.

[0063] S7 includes the following steps:

[0064] S7.1: Check the design specifications or manufacturing standards and round off the optimized design results;

[0065] S7.2: Bring the rounded design variables into the parametric model, determine the structure of the optimized stiffened plate, perform dynamic response calculations, and measure the comprehensive performance of the optimized structure from the perspectives of mechanical properties, computational cost, and processing technology.

[0066] The beneficial effects of the present invention are as follows:

[0067] The present invention combines the experimental design method with the sequential quadratic programming method to propose an efficient optimization design method for the stiffened plate structure. The method is used to optimize the stiffened plate structure, which can avoid the problem of obtaining local optimal solutions by traditional optimization methods, and also avoid the huge computational cost problem of using intelligent optimization methods, thereby maximizing the optimization design efficiency and providing a reliable approach for the design of such structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 It is a front view of a typical stiffened plate of the present invention.

[0069] Figure 2 for Figure 1 Side view of.

[0070] Figure 3 It is a flow chart of the present invention.

[0071] Figure 4 This is the finite element model diagram of the stiffened plate of the present invention. DETAILED DESCRIPTION

[0072] The specific implementation of the present invention will be described below in conjunction with the accompanying drawings.

[0073] like Figure 1-Figure 4 As shown, a stiffened plate optimization design method integrating experimental design and optimization algorithm in this embodiment includes the following steps:

[0074] S1: Analyze the structural characteristics of the optimized stiffened plate and determine the structural parameters and boundaries that can be optimized;

[0075] S2: Establish a parametric model of the stiffened plate structure to characterize the structural parameters that can be optimized;

[0076] S3: Divide the interval of the optimization parameter into N parts to form a block design interval of the optimization parameter, and calculate the center point of each interval;

[0077] S4: Calculate the target response of the stiffened plate at each center point respectively, construct the optimization design objective function, and sort the objective functions at the center point of each interval;

[0078] S5: According to the sorting, taking the center point of the optimal value interval as the starting point, the sequential quadratic programming algorithm is used to optimize the design in the interval, and the optimal point in the interval and the optimal value of the objective function are calculated;

[0079] S6: Adopt the optimization design convergence criterion to judge the convergence of the optimization process and determine the optimal stiffened plate structural parameters;

[0080] S7: Round the optimized design parameter results to processable or standard values, and verify the structural model of the target layer.

[0081] S1 includes the following steps:

[0082] S1.1: The structure of the ribs in the stiffened plate includes L-type, C-type, T-type, I-type or hat-type. The parameters to be optimized are the length, thickness, various geometric parameters and the position of the ribs;

[0083] S1.2: The boundaries of the optimized parameters must be defined based on the spatial layout design standards or specifications of the structure.

[0084] S2 includes the following steps:

[0085] S2.1: The parametric model of the stiffened plate can be constructed based on a commercial finite element software platform. The target response for analysis can be the dynamic response of the key points such as velocity, acceleration, displacement, etc. under the natural frequency or load excitation.

[0086] S2.2: Based on the secondary development function of the software, the optimization parameters are characterized by variable design variables.

[0087] S3 includes the following steps:

[0088] S3.1: Divide the upper and lower limits of the optimization parameters Xi (i = 1, 2, 3 ..., N) into M equal parts, and the optimization parameter space is divided into M N space;

[0089] S3.2: Calculation of M N The centroid of the parameter interval

[0090] in:

[0091] Represents the optimization parameter x ij The central value or mean value of

[0092] Represents the optimization parameter x ij The lower limit of

[0093] Represents the optimization parameter x ij The upper limit value of .

[0094] 3.3: Calculate each center point according to the objective function construction requirements The target response of the stiffened plate at . In S4, the center point of each interval is Sort the objective function values ​​at and find the location of the optimal objective value.

[0095] S5 includes the following steps:

[0096] S5.1: The sequential quadratic programming method is used to optimize the design of the stiffened plate structure in the corresponding interval; S5.2: The steps of the sequential quadratic programming method are:

[0097] Given an optimization problem with nonlinear constraints:

[0098] minf(x)

[0099] stgu(x)≤0(u=1,2,…,p)

[0100] h v (x) = 0 (υ = 1, 2, ..., m)

[0101] f(x): The result of the dynamic response of the key point such as velocity, acceleration, displacement, etc. under the natural frequency or load excitation;

[0102] in:

[0103] x: Parameters such as the length, thickness, geometric parameters and position of the ribs;

[0104] g u (x): inequality constraint function;

[0105] h v (x): equality constraint function;

[0106] Taylor expansion converts the objective function of the nonlinear constraint problem in the above equation into the iteration point x k Simplifying into a quadratic function, simplifying the nonlinear constraint function into a linear function, we get the following quadratic programming problem:

[0107]

[0108] in:

[0109] X k: The optimization variable value of the current iteration point;

[0110] The gradient vector of the objective function at the current iteration point represents the partial derivatives of the objective function with respect to each variable;

[0111] The Hessian matrix of the target function at the current iteration point represents the second-order derivative matrix of the target function;

[0112] g u (X k ): inequality constraint function;

[0113] h v (X k ): equality constraint function;

[0114] The gradient vector of the inequality constraint function at the current iteration point;

[0115] The gradient vector of the equality constraint function at the current iteration point;

[0116] Let S = X - Xk ， Solve this quadratic programming problem and find its optimal solution S * As the next search direction S of the original problem k , and perform a one-dimensional search of the objective function of the original constraint problem in this direction, so that an approximate solution X of the original constraint problem can be obtained k+1 , repeating this process, we can get the optimal solution to the original problem.

[0117] S6 includes the following steps:

[0118] S6.1: Set the convergence tolerance δ of the objective function, which is equal to one thousandth of the objective function corresponding to the center point of the first iteration interval;

[0119] S6.2: Compare the current iteration interval with the previous optimization design results, and use the gradient of the objective function at the optimization design point as the convergence criterion, that is:

[0120]

[0121] in:

[0122] Δ: represents the convergence index of the current iteration;

[0123] f j : represents the objective function value of the jth iteration;

[0124] f j-1 : represents the objective function value of the j-1th iteration;

[0125] X *j : represents the design variable value of the jth iteration;

[0126] X *j-1 : represents the design variable value of the j-1th iteration;

[0127] Δ: represents a preset threshold used to judge convergence;

[0128] S6.3: If the above convergence criteria are met, the iteration is stopped; if not, return and iterate further.

[0129] S7 includes the following steps:

[0130] S7.1: Check the design specifications or manufacturing standards and round off the optimized design results;

[0131] S7.2: Bring the rounded design variables into the parametric model, determine the structure of the optimized stiffened plate, perform dynamic response calculations, and measure the comprehensive performance of the optimized structure from the perspectives of mechanical properties, computational cost, and processing technology.

[0132] Specifically, Figure 1 and Figure 2 As shown, the optimization design method is completed through the following steps:

[0133] Step 1: Analyze the structural characteristics of the optimized stiffened plate, such as Figure 1 As shown, the length and width of the reinforced plate are 500m, the plate thickness is 6mm, a rectangular groove is opened in the middle of the plate, the side length of the groove is 100mm, and there are two horizontal and vertical ribs distributed. The structure of the ribs is I-type ribs, the rib height is 10mm, and the rib thickness is 5mm. Optimize the positions of the four ribs x1, x2, x3, and x4 to find the parameter combination with the highest natural frequency F.

[0134]

[0135] Step 2: Establish a parametric simulation model of the stiffened plate structure, build it based on the commercial finite element software abaqus platform, and analyze the natural frequency of the target response. Write a python program to realize automatic modeling, parameterize the position of the ribs, and extract the first-order natural frequency of the model.

[0136] Step 3: Divide the intervals of the four optimization parameters x1, x2, x3, and x4 into 4 parts each, forming the block design intervals of the optimization parameters. The optimization parameter space is 4×4×4×4=256 spaces. Calculate the centroid of each interval And according to the objective function construction requirements, calculate each center point Target response F of the stiffened plate at .

[0137] Step 4: Set the center points of each interval Sort the objective function values ​​F at and find the midpoint x0 of the interval with the highest frequency F.

[0138] Step 5: Taking the center point x0 of the interval with the highest frequency value as the starting point, the sequential quadratic programming optimization algorithm is used to convert the complex nonlinear optimization problem into a simpler quadratic programming problem for solution. The optimization design is performed in the interval with x0 as the midpoint and 75 as the radius, and the optimal point in the interval and the optimal value of the objective function are calculated.

[0139] Step 6: Round the optimized design parameter results to machinable or standard values, verify the structural model of the target layer, bring the rounded design variables into the parametric model, determine the structure of the optimized stiffened plate, perform dynamic response calculations, and measure the comprehensive performance of the optimized structure from the perspectives of mechanical properties, computational costs, and processing technology.

[0140] The above description is an explanation of the present invention, not a limitation of the present invention. The scope of the present invention is defined in the claims. Any form of modification may be made within the scope of protection of the present invention.

Claims

1. A stiffened plate optimization design method integrating experimental design and optimization algorithm, characterized in that: The steps are as follows: S1: Analyze the structural characteristics of the optimized stiffened plate and determine the structural parameters and boundaries that can be optimized; S2: Establish a parametric model of the stiffened plate structure to characterize the structural parameters that can be optimized; S3: Divide the interval of the optimization parameter into N parts to form a block design interval of the optimization parameter, and calculate the center point of each interval; S4: Calculate the target response of the stiffened plate at each center point respectively, construct the optimization design objective function, and sort the objective functions at the center point of each interval; S5: According to the sorting, taking the center point of the optimal value interval as the starting point, the sequential quadratic programming algorithm is used to optimize the design in the interval, and the optimal point in the interval and the optimal value of the objective function are calculated; S6: Adopt the optimization design convergence criterion to judge the convergence of the optimization process and determine the optimal stiffened plate structural parameters; S7: Round the optimized design parameter results to processable or standard values, and verify the structural model of the target layer.

2. The method for optimizing the design of stiffened panels by integrating experimental design and optimization algorithm as claimed in claim 1, characterized in that: S1 includes the following steps: S1.1: The structure of the ribs in the stiffened plate includes L-type, C-type, T-type, I-type or hat-type. The parameters to be optimized are the length, thickness, various geometric parameters and the position of the ribs; S1.2: The boundaries of the optimized parameters must be defined based on the spatial layout design standards or specifications of the structure.

3. The method for optimizing the design of stiffened panels by integrating experimental design and optimization algorithm as claimed in claim 1, characterized in that: S2 includes the following steps: S2.1: The parametric model of the stiffened plate can be constructed based on a commercial finite element software platform. The target response for analysis can be the dynamic response of the key points such as velocity, acceleration, displacement, etc. under the natural frequency or load excitation. S2.2: Based on the secondary development function of the software, the optimization parameters are characterized by variable design variables.

4. The method for optimizing the design of stiffened panels by integrating experimental design and optimization algorithm as claimed in claim 1, characterized in that: S3 includes the following steps: S3.1: Divide the upper and lower limits of the optimization parameters Xi (i = 1, 2, 3 ..., N) into M equal parts, then the optimization parameter space is divided into M N space; S3.2: Calculation of M N The centroid of the parameter interval in: Represents the optimization parameter x ij The central value or mean value of Represents the optimization parameter x ij The lower limit of Represents the optimization parameter x ij The upper limit value of 3.3: Calculate each center point according to the objective function construction requirements Target response of the stiffened plate at .

5. The method for optimizing the design of stiffened panels by integrating experimental design and optimization algorithm as claimed in claim 4, characterized in that: In S4, the center point of each interval Sort the objective function values ​​at and find the location of the optimal objective value.

6. The method for optimizing the design of stiffened panels by integrating experimental design and optimization algorithm as claimed in claim 1, characterized in that: S5 includes the following steps: S5.1: The sequential quadratic programming method is used to optimize the design of the stiffened plate structure in the corresponding interval; S5.2: The steps of the sequential quadratic programming method are: Given an optimization problem with nonlinear constraints: min f(x) s.t.g u (x)≤0(u=1,2,…,p) h υ (x)=0(υ=1,2,…,m) f(x): The result of the dynamic response of the key point such as velocity, acceleration, displacement, etc. under the natural frequency or load excitation; in: x: Parameters such as the length, thickness, geometric parameters and position of the ribs; g u (x): inequality constraint function; h v (x): equality constraint function; Taylor expansion converts the objective function of the nonlinear constraint problem in the above equation into the iteration point x k Simplifying into a quadratic function, simplifying the nonlinear constraint function into a linear function, we get the following quadratic programming problem: in: X k : The optimization variable value of the current iteration point; The gradient vector of the objective function at the current iteration point represents the partial derivatives of the objective function with respect to each variable; The Hessian matrix of the target function at the current iteration point represents the second-order derivative matrix of the target function; g u (X k ): inequality constraint function; h v (X k ): equality constraint function; The gradient vector of the inequality constraint function at the current iteration point; The gradient vector of the equality constraint function at the current iteration point; Let S = XX k , solve this quadratic programming problem and take its optimal solution S * As the next search direction S of the original problem k , and perform a one-dimensional search of the objective function of the original constraint problem in this direction, so that an approximate solution X of the original constraint problem can be obtained k+1 , repeating this process, we can get the optimal solution to the original problem.

7. The method for optimizing the design of stiffened panels by integrating experimental design and optimization algorithm as claimed in claim 1, characterized in that: S6 includes the following steps: S6.1: Set the convergence tolerance δ of the objective function, which is equal to one thousandth of the objective function corresponding to the center point of the first iteration interval; S6.2: Compare the current iteration interval with the previous optimization design results, and use the gradient of the objective function at the optimization design point as the convergence criterion, that is: in: Δ: represents the convergence index of the current iteration; f j : represents the objective function value of the jth iteration; f j-1 : represents the objective function value of the j-1th iteration; X *j : represents the design variable value of the jth iteration; X *j-1 : represents the design variable value of the j-1th iteration; Δ: represents a preset threshold used to judge convergence; S6.3: If the above convergence criteria are met, the iteration is stopped; if not, return and iterate further.

8. The method for optimizing the design of stiffened panels by integrating experimental design and optimization algorithm as claimed in claim 1, characterized in that: S7 includes the following steps: S7.1: Check the design specifications or manufacturing standards and round off the optimized design results; S7.2: Bring the rounded design variables into the parametric model, determine the structure of the optimized stiffened plate, perform dynamic response calculations, and measure the comprehensive performance of the optimized structure from the perspectives of mechanical properties, computational cost, and processing technology.

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