Machine body frame assembly positioning and supporting layout optimization method

Abstract

The invention provides a fuselage frame assembly positioning and support layout optimization method, and belongs to the field of mechanical engineering / aircraft assembly. The optimization method comprises the following steps: firstly, parameterizing a model according to size parameters and material parameters of a fuselage frame; then, position vectors are adopted to represent positioning and supporting layout, and a variable range is determined; then, a random sampling and finite element calculation method is adopted for calculation and solution, and an SVR model of fuselage frame positioning and the number, position and maximum deformation of supporting points is established; on the basis, a random sampling and finite element calculation method is adopted to test and verify the SVR model; and finally, a constraint condition is established according to the discrete design domain space and the number of positioning supporting points, an optimization target is established with minimum deformation, and an optimal solution is searched by adopting a particle swarm optimization algorithm. The method can determine the positions of the positioning points and the supporting points, and has a wide application prospect in the field of aircraft assembly.

Description

Technical Field

[0001] The present invention belongs to the field of mechanical engineering / aircraft assembly, and relates to a method for optimizing fuselage frame assembly positioning and support layout, and in particular to a method suitable for optimizing fuselage frame assembly positioning and support layout. Background Art

[0002] Improved aircraft performance places high demands on the integrated, high-precision manufacturing of aircraft skeleton components, such as frames, beams, and ribs. These components are large in size, complex in structure, require high precision, and require complex assembly coordination. Flexible process equipment is an effective method for the rapid, high-precision assembly of large skeleton components, such as frames, beams, and ribs. A manufacturing system based on digital product coordination, combined with modular, standardized, and automated assembly technologies, can effectively reduce the number of tooling units used in the aircraft assembly process, improving assembly quality and efficiency. Flexible tooling transforms traditional rigid tooling, enabling digital control and reconfiguration of tooling structures, rapidly completing part clamping and component assembly, and making tooling the most efficient and cost-effective manufacturing unit. Because flexible tooling is simpler than traditional rigid tooling positioners, there can be a certain amount of error between the actual and theoretical positions of key points on large parts. Optimizing the assembly positioning of large parts and the layout of support points to suppress deformation is an effective method for improving aircraft manufacturing precision.

[0003] Finite element methods are widely used to address the deformation of frame components during assembly due to their own gravity. However, their accuracy is heavily dependent on mesh quality, resulting in low computational efficiency. In recent years, researchers at home and abroad have begun using genetic algorithms to optimize the clamping positions of large, thin-walled components or panel assemblies. This approach improves computational efficiency while maintaining accuracy, becoming a new approach to addressing deformation during frame assembly.

[0004] Currently, optimization of positioning and support location layouts based on genetic algorithms is mostly targeted at fuselage panel structures with a certain distribution pattern. With the goal of minimizing structural deformation or stress, optimization analysis is performed on the clamping point layout, and the optimization design domain is generally continuous space. However, the fuselage frame is an irregular reinforced structure with features such as staggered ribs, irregular edges, and grooves that restrict positioning and support point placement. Therefore, the optimal clamping point search region can only be a discrete space. Due to these process characteristics, the design domain constraints must be considered. Constrained optimization processing techniques have attracted extensive attention from researchers both domestically and internationally in constrained optimization problems. However, currently used constraint processing techniques often produce a large number of infeasible solutions, leading to algorithmic instability or low efficiency in the presence of complex or multiple constraints. Furthermore, the number of tooling positioning and support points is a key factor that requires important consideration. In engineering applications, the greater the number of positioning and support points, the smaller the deformation of the fuselage frame under its own weight. However, as a component of the entire fuselage, an increase in the number of positioning and support points can also affect the assembly of other fuselage structural components. Therefore, the existing optimization layout methods cannot well handle the optimization problem of minimizing deformation under the simultaneous constraints of discrete design domain and positioning support points. Summary of the Invention

[0005] In response to the above-mentioned technical problems existing in the prior art, the present invention provides a method for optimizing the assembly positioning and support layout of a fuselage frame. The method is a constrained optimization method that simultaneously considers the discrete design domain, the number of positioning and support points, and the deformation of the fuselage frame. The method can determine the position of the positioning and support points.

[0006] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0007] A method for optimizing the assembly positioning and support layout of a fuselage frame is a positioning and support layout constraint optimization method that combines the SVR and PSO methods. First, the model is parameterized according to the size parameters and material parameters of the fuselage frame. Then, the position vector is used to represent the positioning and support layout, and the variable range is determined. After that, random sampling and finite element calculation methods are used for calculation and solution to establish an SVR model for the positioning of the fuselage frame and the number, position and maximum deformation of the support points. On this basis, random sampling and finite element calculation methods are used to test and verify the SVR model. Finally, the constraints are established based on the discrete design domain space and the number of positioning support points, the optimization goal is established with the minimum deformation, and the particle swarm optimization algorithm is used to find the optimal solution. Specifically, the following steps are included:

[0008] Step 1: Parametrically model the fuselage frame structural parameters and material properties, control the shape through parameters, and define the relationship through constraints;

[0009] Step 2: Select areas on the fuselage frame other than those that restrict positioning and support point placement, such as staggered ribs, irregular edges, and grooves, as potential positioning and support points. Establish a Cartesian coordinate system with the specific location of the fuselage frame as the coordinate origin. Use the coordinates of the potential positioning and support points as the optimization variable X, which is defined as follows:

[0010] X=(x1,y1,x2,y2,…,x n ,y n ), there are n independent design variables, where x and y are the coordinates of the positioning and support points in the Cartesian coordinate system respectively;

[0011] Step 3: Based on the actual assembly requirements, variable X should meet the following constraints:

[0012] (1) The process characteristic constraints for optimizing the positioning and support positions and numbers are mainly that the selection of positions is constrained by the fuselage frame positioning and support process implementation conditions, that is, the positioning and support points should be within the feasible design domain, and the variable X should satisfy the constraints:

[0013] (x i ,y i )∈S,i=1,…,n, S is the feasible design domain;

[0014] (2) The process characteristics of the fuselage frame are structurally manifested as staggered reinforcement ribs, edges with varying curvatures, and grooves. When arranging the positioning and support positions, interference with the structural process characteristics should be avoided. At the same time, overlapping interference between positioning and support points should be avoided. The process characteristic constraints include inequality constraints and equality constraints in the generalized mathematical model. The variable X should satisfy the constraint conditions:

[0015] f k (X)≤0,k=1,…,p, there are k independent variables satisfying the inequality constraints;

[0016] g l (X)=0,l=1,…,q, there are l independent variables satisfying the equality constraint;

[0017] (3) In order to ensure the assembly accuracy of the fuselage frame, and considering that the increase in the number of positioning and support points will also affect the assembly of other fuselage structural parts, the number of positioning and support points should be within a certain range. The number of positioning and support points is set to not exceed M, and the number of constraint variables does not exceed the total number of design variables, that is,

[0018] 0 <n≤M,0<k≤n,0<l≤n;

[0019] Step 4: Establish a finite element analysis model. Create a three-dimensional model based on the size and geometric parameters of the fuselage frame. Establish the finite element model by meshing, assigning attributes, applying loads and constraints, and establishing analysis steps.

[0020] Step 5: Use random sampling and finite element analysis to form a training data set and establish an SVR model of the maximum deformation of the fuselage frame;

[0021] Step 6: Use random sampling and finite element analysis to form a test data set to test and verify the established SVR model;

[0022] Step 7: Comprehensively consider the deformation of the fuselage frame during assembly, positioning, and support, as well as the number and position of positioning and support points. Establish constraints using the discrete design domain space and the number of positioning support points. Establish the optimization goal with minimum deformation. Use the particle swarm optimization algorithm to find the optimal solution set for positioning and support position layout. This problem is a single-objective constrained optimization problem with high-dimensional deformation. Its mathematical model can be expressed as:

[0023] Find:X=(x1,y1,x2,y2,…,x n ,y n )

[0024] Minimize:maxδ j (X)

[0025] subject to:f k (X)≤0,k=1,…,p

[0026] g l (X)=0,l=1,…,q

[0027] (x i ,y i )∈S,i=1,…,n

[0028] 0 <n≤M,0<k≤n,0<l≤n

[0029] Where x and y are the coordinates of the positioning and support points in the Cartesian coordinate system respectively; δ j is the displacement of the jth finite element node after deformation, and its value comes from the SVR model;

[0030] Step 8: Convert the constrained optimization problem into a bi-objective unconstrained optimization problem by constructing a penalty function. The penalty function can be expressed as:

[0031]

[0032] Where, δ t (X) is the violation degree of variable X in the t-th constraint. Let the penalty function Indicates the degree to which variable X violates all constraints, and also indicates the distance from variable X to the feasible region;

[0033] Step 9: Convert the constrained optimization problem into a multi-objective optimization problem with two objective functions, which can be expressed as:

[0034] min{δ(X),p(X)};

[0035] Minimize the objective function δ(X) and find X * Make maxδ(X * ) reaches the minimum value; when the objective function p(X) is zero, find X * It satisfies all constraints; minimizing the objective functions δ(X) and p(X) simultaneously means finding a variable X that satisfies all constraints, that is, finding the optimal solution in step 7.

[0036] The "SVR model" mentioned above refers to a support vector regression model, which is used to establish a nonlinear relationship between dependent variables and response values and is a neural network algorithm mathematical model.

[0037] The "PSO" mentioned above refers to the particle swarm optimization algorithm, which is an optimization algorithm based on swarm intelligence. It solves optimization problems by simulating the information sharing and collaboration mechanism in the foraging behavior of bird flocks. It has the advantages of simple calculation and good robustness.

[0038] The present invention is a constrained optimization method that simultaneously considers the discrete design domain, positioning and the number of support points, and the deformation of the fuselage frame. Its beneficial effects are:

[0039] (1) Compared with the prior art, the present invention not only considers the discrete design domain, but also analyzes the continuous optimization of design variables in the feasible domain space; uses a two-dimensional position vector to represent the positioning and support layout in the Cartesian coordinate system to determine the feasible domain range; uses random sampling and finite element calculation methods to establish an SVR model of fuselage frame positioning and the number, position and maximum gravity deformation of support points; uses random sampling and finite element calculation methods to verify the SVR model; establishes constraint conditions based on the discrete design domain space and the number of positioning support points, establishes the optimization goal based on the minimum gravity deformation, uses the particle swarm optimization algorithm to find the optimal solution, and transforms the constrained optimization problem into a multi-objective unconstrained optimization problem to achieve the optimization of the optimal layout of positioning and clamping points.

[0040] (2) During the optimization process, the present invention reduces the maximum gravity deformation of the fuselage frame while reducing the number of positioners, thereby achieving high efficiency, high precision and low cost in the assembly and positioning process of the fuselage frame. By optimizing the positioning and support point layout of fuselage frames with similar structures, it is beneficial to shorten the aircraft assembly cycle and has broad application prospects in the field of aircraft assembly. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 is a flow chart of the method of the present invention;

[0042] Figure 2 Schematic diagram of support vector regression. DETAILED DESCRIPTION

[0043] The present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0044] A method for optimizing fuselage frame assembly positioning and support layout is proposed. The method combines the SVR and PSO methods to optimize positioning and support layout constraints. The method specifically includes the following steps:

[0045] Step 1: Parametrically model the fuselage frame structural parameters and material properties, control the shape through parameters, and define the relationship through constraints;

[0046] Step 2: Select areas on the fuselage frame other than features such as staggered ribs, irregular edges, grooves, etc. that restrict the placement of positioning and support points as potential positioning and support points. Establish a Cartesian coordinate system with the specific position of the fuselage frame as the coordinate origin, and use the coordinates of the potential positioning and support points as optimization variables.

[0047] X=(x1,y1,x2,y2,…,x n ,y n ), there are n independent design variables, where x and y are the coordinates of the positioning and support points in the Cartesian coordinate system respectively;

[0048] Step 3: Based on the actual assembly requirements, variable X should meet the following constraints:

[0049] (1) The process characteristic constraints for optimizing the positioning and support positions and numbers are mainly that the selection of positions is constrained by the fuselage frame positioning and support process implementation conditions, that is, the positioning and support points should be within the feasible design domain, and the variable X should satisfy the constraints:

[0050] (x i ,y i )∈S,i=1,…,n, S is the feasible design domain;

[0051] (2) The process characteristics of the fuselage frame are structurally manifested as staggered reinforcement ribs, edges with varying curvatures, and grooves. When arranging the positioning and support positions, interference with the structural process characteristics should be avoided. At the same time, overlapping interference between positioning and support points should be avoided. The process characteristic constraints include inequality constraints and equality constraints in the generalized mathematical model. The variable X should satisfy the constraint conditions:

[0052] f k(X)≤0,k=1,…,p, there are k independent variables satisfying the inequality constraints;

[0053] g l (X)=0,l=1,…,q, there are l independent variables satisfying the equality constraint;

[0054] (3) In order to ensure the assembly accuracy of the fuselage frame, and considering that the increase in the number of positioning and support points will also affect the assembly of other fuselage structural parts, the number of positioning and support points should be within a certain range. The number of positioning and support points is set to no more than 8, and the number of constraint variables does not exceed the total number of design variables, that is,

[0055] 0 <n≤8,0<k≤n,0<l≤n;

[0056] Step 4: Establish a finite element analysis model. Create a three-dimensional model based on the size and geometric parameters of the fuselage frame. Establish the finite element model by meshing, assigning attributes, applying loads and constraints, and establishing analysis steps.

[0057] Step 5: Use random sampling and finite element analysis to form a training data set and establish an SVR model with maximum deformation of the fuselage frame. The principle diagram of the SVR model is as follows: Figure 2 shown.

[0058] Step 6: Use random sampling and finite element analysis to form a test data set to test and verify the established SVR model;

[0059] Step 7: Comprehensively consider the deformation of the fuselage frame during assembly, positioning, and support, as well as the number and position of positioning and support points. Establish constraints using the discrete design domain space and the number of positioning support points. Establish the optimization goal with minimum deformation. Use the particle swarm optimization algorithm to find the optimal solution set for positioning and support position layout. This problem is a single-objective constrained optimization problem with high-dimensional deformation. Its mathematical model can be expressed as:

[0060] Find:X=(x1,y1,x2,y2,…,x n ,y n )

[0061] Minimize:maxδ j (X)

[0062] subject to:f k (X)≤0,k=1,…,p

[0063] g l (X)=0,l=1,…,q

[0064] (x i ,y i)∈S,i=1,…,n

[0065] 0 <n≤8,0<k≤n,0<l≤n

[0066] Where x and y are the coordinates of the positioning and support points in the Cartesian coordinate system respectively; δ j is the displacement of the jth finite element node after deformation, and its value comes from the SVR model;

[0067] Step 8: Convert the constrained optimization problem into a bi-objective unconstrained optimization problem by constructing a penalty function. The penalty function can be expressed as:

[0068]

[0069] Where, δ t (X) is the violation degree of variable X in the t-th constraint. Let the penalty function Indicates the degree to which variable X violates all constraints, and also indicates the distance from variable X to the feasible region;

[0070] Step 9: Convert the constrained optimization problem into a multi-objective optimization problem with two objective functions, expressed as:

[0071] min{δ(X),p(X)};

[0072] Minimize the objective function δ(X) and find X * Make maxδ(X * ) reaches the minimum value; when the objective function p(X) is zero, find X * It satisfies all constraints; minimizing the objective functions δ(X) and p(X) simultaneously means finding a variable X that satisfies all constraints, that is, finding the optimal solution in step 7.

[0073] The above-described embodiments merely express the implementation methods of the present invention, but should not be understood as limiting the scope of the patent of the present invention. It should be pointed out that for those skilled in the art, several variations and improvements can be made without departing from the concept of the present invention, and these all fall within the scope of protection of the present invention.

Claims

1. A method for optimizing fuselage frame assembly positioning and support layout, characterized in that: The optimization method first parameterizes the model based on the dimensional parameters and material parameters of the fuselage frame; then, position vectors are used to represent the positioning and support layout to determine the variable range; then, random sampling and finite element calculation methods are used to calculate and solve, and an SVR model of the fuselage frame positioning and the number, position and maximum deformation of the support points is established; on this basis, random sampling and finite element calculation methods are used to test and verify the SVR model; finally, constraints are established based on the discrete design domain space and the number of positioning support points, and the optimization goal is established with minimum deformation, and a particle swarm optimization algorithm is used to find the optimal solution.

2. A method for optimizing fuselage frame assembly positioning and support layout according to claim 1, characterized in that: The optimization method comprises the following steps: Step 1: Parametrically model the fuselage frame structural parameters and material properties, control the shape through parameters, and define the relationship through constraints; Step 2: Select potential positioning and support points on the fuselage frame, establish a Cartesian coordinate system with the specific position of the fuselage frame as the coordinate origin, and use the coordinates of the potential positioning and support points as the optimization variable X; Step 3: Based on the actual assembly requirements, determine the constraints that the optimization variable X needs to meet; Step 4: Establish a finite element analysis model and create a three-dimensional model based on the size parameters and geometric parameters of the fuselage frame; Step 5: Use random sampling and finite element analysis to form a training data set and establish an SVR model of the maximum deformation of the fuselage frame; Step 6: Use random sampling and finite element analysis to form a test data set to test and verify the established SVR model; Step 7: Comprehensively consider the deformation of the fuselage frame during assembly, positioning, and support, as well as the number and location of positioning and support points. Constraints are established using the discrete design domain space and the number of positioning support points. Minimizing deformation is the optimization goal. A particle swarm optimization algorithm is used to find the optimal solution set for positioning and support position layout. Step 8: Convert the constrained optimization problem of the optimization objective in step 7 into a bi-objective unconstrained optimization problem by constructing a penalty function; Step 9: Convert the constrained optimization problem into a multi-objective optimization problem with two objective functions.

3. The method for optimizing fuselage frame assembly positioning and support layout according to claim 2, characterized in that: In step 2, areas on the fuselage frame other than the staggered reinforcement ribs, irregular edges, and grooves that restrict positioning and support point arrangement are selected as potential positioning and support points.

4. The method for optimizing fuselage frame assembly positioning and support layout according to claim 2, wherein: In step 2, the optimized variable X is as follows: X=(x1,y1,x2,y2,…,x n ,y n ), there are n independent design variables, where x and y are the coordinates of the positioning and support points in the Cartesian coordinate system, respectively.

5. The method for optimizing fuselage frame assembly positioning and support layout according to claim 2, characterized in that: The step 3 is specifically as follows: (1) The process characteristic constraints for optimizing the positioning and support positions and numbers are mainly that the selection of positions is constrained by the fuselage frame positioning and support process implementation conditions, that is, the positioning and support points should be within the feasible design domain and meet the constraints: (x i ,y i )∈S,i=1,…,n, S is the feasible design domain; (2) The process characteristics of the fuselage frame are structurally manifested as staggered reinforcement ribs, edges with varying curvatures, and grooves. When arranging the positioning and support positions, interference with the structural process characteristics should be avoided. At the same time, overlapping interference between positioning and support points should be avoided. The process characteristic constraints include inequality constraints and equality constraints in the generalized mathematical model. The variable X satisfies the constraint conditions: f k (X)≤0,k=1,…,p, there are k independent variables satisfying the inequality constraints; g l (X)=0,l=1,…,q, there are l independent variables satisfying the equality constraint; (3) In order to ensure the assembly accuracy of the fuselage frame, and considering that the increase in the number of positioning and support points will also affect the assembly of other fuselage structural parts, the number of positioning and support points should be within a certain range. The number of positioning and support points is set to not exceed M, and the number of constraint variables does not exceed the total number of design variables, that is: 0 <n≤M,0<k≤n,0<l≤n。 6. The method for optimizing fuselage frame assembly positioning and support layout according to claim 2, characterized in that: In step 4, a finite element model is established according to meshing, attribute assignment, load and constraint application, and analysis step establishment.

7. The method for optimizing fuselage frame assembly positioning and support layout according to claim 2, characterized in that: The model of the optimization objective in step 7 is expressed as: Find:X=(x1,y1,x2,y2,…,x n ,y n ) Minimize:maxδ j (X) subject to:f k (X)≤0,k=1,…,p g l (X)=0,l=1,…,q (x i ,y i )∈S,i=1,…,n 0 <n≤M,0<k≤n,0<l≤n Where x and y are the coordinates of the positioning and support points in the Cartesian coordinate system respectively; δ j is the displacement of the jth finite element node after deformation, and its value comes from the SVR model.

8. The method for optimizing fuselage frame assembly positioning and support layout according to claim 2, characterized in that: The penalty function in step 8 is expressed as: Where, δ t (X) is the violation degree of the optimization variable X in the tth constraint; let the penalty function It indicates the degree to which variable X violates all constraints, and also indicates the distance from the optimized variable X to the feasible region.

9. The method for optimizing fuselage frame assembly positioning and support layout according to claim 2, characterized in that: In step 9, the multi-objective optimization problem is expressed as: min{δ(X),p(X)}; Minimize the objective function δ(X) and find X * Make maxδ(X * ) reaches the minimum value; when the objective function p(X) is zero, find X * It satisfies all constraints; minimizing the objective functions δ(X) and p(X) simultaneously means finding a variable X that satisfies all constraints, that is, finding the optimal solution in step 7.

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