A GA-GLM-based automatic hierarchical layout optimization algorithm for umbilical cable cross-section

Abstract

This invention provides an automatic layered layout optimization algorithm for umbilical cable cross-sections based on GA-GLM, belonging to the field of marine umbilical cable structural optimization design. This invention establishes an optimization design model considering cross-sectional compactness, balance, and frictional losses. First, a genetic algorithm is used to solve the optimal solution for the layout problem within the global solution space, determining feasible solutions for the center coordinates of each component in the optimal layout. Then, using the feasible solutions obtained by the GA algorithm as initial values, the GLM algorithm is used for fast and accurate solution. After obtaining the overall optimal cross-sectional layout, a layered strategy is introduced, and the GLM algorithm is continued for optimization to obtain the optimal layered cross-sectional layout of the umbilical cable. This invention fully utilizes the strong global search capability of GA and the fast convergence speed of the GLM algorithm to automatically design the umbilical cable cross-sectional layout, replacing manual operation and providing a useful reference for umbilical cable cross-sectional layout design.

Description

Technical Field

[0001] This invention belongs to the field of umbilical cable cross-section optimization, and relates to an optimization algorithm that combines genetic algorithm (GA) and generalized multiplier method (GLM) to improve the solution speed and accuracy. Background Technology

[0002] As the water depth and scale of oil and gas development continue to expand, the number of functional components in umbilical cables is constantly increasing, exhibiting highly integrated structural characteristics. The arrangement of the core components in the cross-section directly affects the structural mechanical properties of the umbilical cable. How to rationally design the cross-sectional layout is an important issue in the umbilical cable design process. Due to the complexity of the component cross-sectional layout and the diversity of optimization objectives, an optimization algorithm with global optimization capabilities is needed to solve the above optimization problems. Genetic algorithms, based on biological genetics and natural selection theory, iteratively search from a randomly generated initial population. Through a series of operations such as encoding, evolution, selection, crossover, and mutation, a new generation of individuals is generated, and through continuous iterative updates, it gradually converges to the optimal solution. Since genetic algorithms can search the entire solution space simultaneously without requiring initial values, they are more likely to find the global optimum. However, due to their large computational cost and slow convergence speed, they are not suitable for fast solutions. In contrast, traditional optimization algorithms can quickly approximate the optimal solution by using function gradient information as the search direction, and have strong local search capabilities for optimization problems with constraints. However, the calculation results of this method are highly sensitive to the selection of initial values; different initial values ​​often yield different calculation results, making it difficult to solve the problem accurately on a global scale. This paper proposes an optimization algorithm based on a combination of genetic algorithm and generalized multiplier method to solve the problem of umbilical cable cross-section layout design. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings of existing algorithms and propose an optimization algorithm based on the combination of genetic algorithm and generalized multiplier method. The method of this invention first uses genetic algorithm for coarse solution and then uses generalized multiplier method for fast solution, which can improve the solution speed and accuracy of multi-objective constrained optimization problems and obtain the desired optimal solution in a short time.

[0004] The objective of this invention is achieved as follows: The steps are as follows:

[0005] (1) Simplify the umbilical cable cross-section components by simplifying them into disks with different properties in the same plane;

[0006] (2) Considering that the cross-sectional diameters of various functional components in the actual umbilical cable are not much different, it is assumed that the cross-sectional diameters of each functional component are the same;

[0007] (3) Extract design variables. Establish a rectangular coordinate system with any point in the plane of the umbilical cable as the center. Assume that the umbilical cable contains m cables with a radius of R. S The steel pipe and n rods with radius R Q The cable; based on the established coordinate system, the center positions of the steel pipe and cable cross-sections are respectively described as... and The problem of optimizing the cross-sectional layout of umbilical cables can be transformed into an optimization problem with the coordinates of the center position of the components as continuous design variables.

[0008] (4) Establish the objective function

[0009] The objective function f1 is optimized as follows:

[0010] f1 = minR

[0011] A virtual gravity index is introduced based on the axial tensile stiffness of the cross-sectional members to describe the equilibrium of the cross-sectional layout:

[0012] G = EA

[0013] Where: E is the elastic modulus; A is the cross-sectional area;

[0014] The balance symmetry of the umbilical cable cross-section bearing capacity depends on the distance Δ from the center of the parallel force system to the geometric center of the cross-section. The relationship between the resultant center of the virtual gravity of each component and the offset distance from the center of the cross-section is as follows:

[0015]

[0016] Assume there is a relationship between the mechanical properties (MB) of the umbilical cable and the deviation distance:

[0017] M B =ξ B / Δ,

[0018] Where: ξ B The correlation coefficient for mechanical properties; Let be the virtual gravity vector of the i-th steel pipe; Let f be the virtual gravity vector of the j-th cable; the optimization objective function f2 is:

[0019] f2=minΔ

[0020] The mechanical damage D caused by the contact between steel pipes f The description is a functional expression for the distance between any two steel pipes:

[0021]

[0022] in: ψ f The correlation coefficient of mechanical properties; the optimization objective function f3 is:

[0023] f3 = minD f

[0024] The multi-objective optimization problem of umbilical cable cross-section layout is transformed into a single-objective optimization problem by weighting coefficients: min: f=C1·f1+C2·f2+C3·f3, where C1+C2+C3=1;

[0025] (5) Establish constraints

[0026] The constraints on the center coordinate variables of each functional component are expressed as follows:

[0027]

[0028] Let R s =R Q =r, C1=C2=C3=1 / 3, the optimized formula can be expressed as:

[0029] to find: X = [(x i x i ), (x j x j )] (i=1, 2,...m; j=1, 2,...n),

[0030]

[0031]

[0032] (6) Layered strategy for cross-section components: The cross-section of the functional components of the umbilical cable is a circle on a plane. The layered cross-section layout of the umbilical cable can be obtained by solving the problem.

[0033] (7) After establishing the above multi-objective optimization model, the required solution is obtained according to the corresponding solution process.

[0034] The present invention also includes the following structural features:

[0035] 1. The solution method in step (6) is as follows: Solve the linear equation of the line connecting the two centers and the equation of the common chord of the two circles to obtain the intersection of the two lines. The intersection is the contact point of the two circles and is marked as *. After obtaining all the contact points, use the farthest point priority asymptotic algorithm to construct the smallest enclosing circle containing all the contact points, which is called the quasi-layered circle.

[0036] To determine the number of circles arranged within the quasi-layered circle, a scaling factor C is introduced to control the setting; the scaling factor is based on the distance d between the center of all circles within the quasi-layered circle and the center of the quasi-layered circle. i Set the values ​​in ascending order as Dis = [d1, d2, ... d... i](i=1,2,...n);If the number of circles in the first layer is 3, then the proportionality coefficient C=Dis(3);After determining the components of the first layer, construct the layered circles, and then arrange the remaining components in the second layer. Finally, the layered cross-sectional layout of the umbilical cable can be obtained.

[0037] 2. The corresponding solution process in step (7) is as follows: First, the optimal solution of the problem is solved in the global solution space using a genetic algorithm to determine the feasible solution of the center coordinates of each component in the optimal layout; then, the feasible solution obtained by GA is used as the initial value, and the overall cross-sectional layout is obtained by using GLM for fast and accurate solution; after obtaining the overall optimal layout of the cross-section, a layering strategy is introduced, and the GLM algorithm is used to continue to optimize in order to obtain the layered layout form of the umbilical cable cross-section.

[0038] Compared with existing technologies, the advantages of this invention are as follows: This invention establishes an optimized design model considering cross-sectional compactness, balance, and frictional loss. First, it uses a genetic algorithm to solve the optimal solution for the layout problem within the global solution space, determining feasible solutions for the center coordinates of each component in the optimal layout. Then, using the feasible solutions obtained by the GA algorithm as initial values, it uses the GLM algorithm for fast and accurate solution. After obtaining the overall optimal cross-sectional layout, a layered strategy is introduced, and the GLM algorithm is used for further optimization to obtain the optimal layered cross-sectional layout of the umbilical cable. This invention fully utilizes the strong global search capability of GA and the fast convergence speed of the GLM algorithm to automatically design the cross-sectional layout of the umbilical cable, replacing manual operation and providing a useful reference for umbilical cable cross-sectional layout design.

[0039] This invention belongs to the field of marine umbilical cable structure optimization design, and relates to an algorithm GA-GLM that combines a genetic algorithm (GA) and a generalized lagrange multiplier (GLM) to optimize the layered layout of umbilical cable cross sections. Attached Figure Description

[0040] Figure 1 This is a schematic diagram showing the coordinates of the center positions of each component in the umbilical cable cross-section.

[0041] Figure 2 This is a schematic diagram of the virtual gravity of each component in the cross-section of the umbilical cable.

[0042] Figure 3 This is a schematic diagram of the layering strategy for each component of the umbilical cable cross-section.

[0043] Figure 4 (a)-(d) represent four cross-sectional layout forms.

[0044] Figure 5 This is an overall flowchart of the method of the present invention. Detailed Implementation

[0045] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0046] This invention includes the following steps:

[0047] (1) Simplification of umbilical cable cross-section components

[0048] The umbilical cable cross-section component is simplified into a disk with different properties in the same plane;

[0049] (2) Propose a hypothesis

[0050] Considering that the cross-sectional diameters of various functional components in the actual umbilical cable are not significantly different, it is assumed that the cross-sectional diameters of each functional component are the same.

[0051] When the umbilical cable cross-section is subjected to external forces, the internal functional components deform due to their interactions. However, this deformation has a negligible impact on the layout design of the umbilical cable cross-section; therefore, this factor is not considered in the optimization model.

[0052] To facilitate verification of the effectiveness of the proposed optimization design method, the influence of circular or irregular filling on the cross-sectional layout design of the umbilical cable is ignored. The cross-sectional layout design optimization algorithm only considers hydraulic pipes (steel pipes or hoses) and cables. Moreover, considering that optical cables and electrical cables have similar characteristics in structural mechanical properties, optical cables can be simulated as electrical cables.

[0053] (3) Extracting design variables

[0054] First, establish a rectangular coordinate system centered at any point within the plane of the umbilical cable. Then, the umbilical cable cross-section layout optimization problem can be transformed into an optimization problem with the coordinates of the component's center position as continuous design variables. Assume the umbilical cable contains m cables with a radius of R. S The steel pipe and n rods with radius R Q cables, such as Figure 1 As shown, based on the established coordinate system, the center positions of the steel pipe and cable cross-sections can be described as follows: and Therefore, the umbilical cable cross-section layout optimization problem can be transformed into an optimization problem with the coordinates of the center position of the components as continuous design variables. At the same time, all functional components are enclosed in an envelope circle with a radius of R. During the cross-section layout optimization design process, the center position of the internal functional components changes continuously until the position that best corresponds to the geometric and mechanical properties of the umbilical cable cross-section is found.

[0055] (4) Establish the objective function

[0056] Umbilical cable design specifications require that the cross-sectional layout be as compact as possible, which necessitates minimizing the radius of the cross-section. The optimization objective function f1 is:

[0057] f1=minR (1)

[0058] When the umbilical cable cross-section is subjected to load, all components should maintain a uniform load-bearing capacity, exhibiting an overall state of force equilibrium. A virtual gravity index is introduced based on the axial tensile stiffness of the cross-sectional components to describe the balance of the cross-sectional layout.

[0059] G = EA

[0060] Where: E is the elastic modulus; A is the cross-sectional area;

[0061] Given the cross-sectional layout of a certain umbilical cable, the virtual gravity of each component will form a parallel force system at the cross-section. The balance symmetry of the umbilical cable's cross-sectional load-bearing capacity depends on the distance Δ from the center of the parallel force system to the geometric center of the cross-section, such as... Figure 2 As shown, the relationship between the offset distance of the resultant center of the virtual gravity of each component and the center of the cross section is as follows:

[0062]

[0063] Assuming the mechanical properties M of the umbilical cable B The relationship between deviation distance

[0064] M B =ξ B / Δ,

[0065] Where: ξ B The correlation coefficient for mechanical properties; Let be the virtual gravity vector of the i-th steel pipe; Let f be the virtual gravity vector of the j-th cable; the optimization objective function f2 is:

[0066] f2=minΔ (2)

[0067] The rigid components of the umbilical cable come into contact, leading to wear and reducing its service life. Assume the mechanical damage D caused by the contact between the steel pipes. f The description is a functional expression for the distance between any two steel pipes:

[0068]

[0069] in: ψ f The correlation coefficient of mechanical properties; the optimization objective function f3 is:

[0070] f3 = minD f (4)

[0071] The multi-objective optimization problem of umbilical cable cross-section layout is transformed into a single-objective optimization problem by using weighted coefficients: min: f=C1·f1+C2·f2+C3·f3, where C1+C2+C3=1;

[0072] (5) Establish constraints

[0073] The constraints on the center coordinate variables of each functional component can be expressed as:

[0074]

[0075] Let R s =R Q =r, C1=C2=C3=1 / 3, the optimized formula can be expressed as:

[0076] to find: X = [(x i x i ), (x j x j )] (i=1, 2,...m; j=1, 2,...n),

[0077]

[0078]

[0079] (6) Layering strategy for cross-section members

[0080] The umbilical cable cross-section is assembled from various components, involving multiple processes in actual manufacturing. First, several components are bundled together and placed at the center, followed by the bundling of other components. An automated layering process helps reduce manufacturing costs and processing risks in the production of umbilical cables; therefore, the layered arrangement of the umbilical cable cross-section components is of great significance. The cross-section of the functional components of the umbilical cable can be considered as a circle on a plane. The layered cross-sectional layout of the umbilical cable can be obtained through calculation.

[0081] The cross-section of the functional components of the umbilical cord can be considered as a circle on a plane. By solving the linear equation of the line connecting the centers of the two circles and the equation of the common chord of the two circles, the intersection point of the two lines can be obtained. This intersection point, which is the contact point of the two circles, is marked as *.

[0082] After obtaining all contact points, the farthest point first asymptotic algorithm (DFAA) is used to construct the minimum enclosing circle containing all contact points, which is called the quasi-layered circle;

[0083] To determine the number of circles arranged within the quasi-layered circle, a scaling factor C is introduced to control the setting. The scaling factor is based on the distance d between the centers of all circles within the quasi-layered circle and the center of the quasi-layered circle. i Set the values ​​in ascending order as Dis = [d1, d2, ... d...i (i = 1, 2, ..., n). If the number of circles in the first layer is 3, then the scaling factor C = Dis(3). After determining the components of the first layer, the layered circles are constructed, and then the remaining components are arranged in the second layer. Finally, the layered cross-sectional layout of the umbilical cable can be obtained.

[0084] (7) After establishing the above multi-objective optimization model, the required solution is obtained according to the corresponding solution process;

[0085] After establishing the above multi-objective optimization model, the optimal solution of the problem is first solved in the global solution space using a genetic algorithm to determine the feasible solution of the center coordinates of each component in the optimal layout. Then, using the feasible solution obtained by GA as the initial value, the overall cross-sectional layout is obtained by using GLM for fast and accurate solution. After obtaining the overall optimal cross-sectional layout, a layered strategy is introduced, and the GLM algorithm is used to continue optimization to obtain the layered layout form of the umbilical cable cross-section.

[0086] This example uses an umbilical cable containing 7 cables and 6 steel pipes as an example to design the cross-sectional layout. The basic dimensions and parameters of each component are shown in Table 1. The cross-sectional layout optimization design algorithm of the umbilical cable is substituted into the algorithm for iterative calculation.

[0087] Table 1 Basic parameters of the components

[0088] Component types D(mm) G(N) steel pipe 40 <![CDATA[132×10 5 ]]> cable 40 <![CDATA[26×10 5 <!-- 5 -->]]> filling 40 18840

[0089] By inputting the basic parameters and initial coordinates of each component into the corresponding arrays, four hierarchical layout forms considering the three objectives mentioned above can be obtained through iterative calculation, such as... Figure 4 As shown in (a)-(d), the minimum envelope circle radius, virtual centroid offset distance, and number of steel pipe contact points are extracted from them, as shown in Table 2.

[0090] Table 2 Evaluation Parameters

[0091]

[0092] This invention proposes an automatic layered layout optimization algorithm for umbilical cable cross-sections based on GA-GLM. The overall process is as follows: Figure 5 As shown.

Claims

1. A GA-GLM-based umbilical cable cross-section automatic hierarchical layout optimization algorithm, characterized in that, The steps are as follows: (1) Simplify the umbilical cable cross-section components by simplifying them into disks with different properties in the same plane; (2) Considering that the cross-sectional diameters of various functional components in the actual umbilical cable are not much different, it is assumed that the cross-sectional diameters of each functional component are the same; (3) Extract design variables, and establish a rectangular coordinate system with any point in the plane of the umbilical cable as the center. Assume that the umbilical cable contains Root radius is steel pipes and Root radius is The cable; based on the established coordinate system, the center positions of the steel pipe and cable cross-sections are respectively described as... and , , The optimization problem of umbilical cable cross-section layout can be transformed into an optimization problem with the coordinates of the center position of the component as continuous design variables; (4) Establish the objective function Optimization objective function is: A virtual gravity index is introduced based on the axial tensile stiffness of the cross-sectional members to describe the equilibrium of the cross-sectional layout: wherein E is the modulus of elasticity; A is the cross-sectional area; The balance symmetry of umbilical cable cross-section carrying capacity depends on the distance from the center of parallel force system to the geometric center of cross-section The offset distance relationship between the center of gravity of each component and the cross-section center is: Assuming the mechanical properties of the umbilical There is a relationship between the distance of deviation: M B = ξ B / Δ in, The correlation coefficient for mechanical properties; For the first The virtual gravity vector of the steel pipe; For the first Virtual gravity vector of the root cable; optimization objective function for: Mechanical damage caused by the contact between steel pipes The description is a functional expression for the distance between any two steel pipes: wherein ; is the correlation coefficient for the mechanical properties; the optimization objective function is: The multi-objective optimization problem of umbilical cable cross-section layout is transformed into a single-objective optimization problem by using weighted coefficients: ,in ; (5) Establish constraints The constraints on the center coordinate variables of each functional component are expressed as follows: set up , The optimized formula is expressed as: (6) Layered strategy for cross-section components: The cross-section of the functional components of the umbilical cable is a circle on a plane. The layered cross-section layout of the umbilical cable can be obtained by solving the problem. (7) After establishing the above multi-objective optimization model, the required solution is obtained according to the corresponding solution process.

2. The GA-GLM-based umbilical cross-section automatic hierarchical layout optimization algorithm according to claim 1, characterized in that, The solution method in step (6) is as follows: Solve the linear equation of the line connecting the two centers and the equation of the common chord of the two circles to obtain the intersection of the two lines. The intersection is the contact point of the two circles and is marked as *. After obtaining all the contact points, use the farthest point priority asymptotic algorithm to construct the smallest enclosing circle containing all the contact points, which is called the quasi-layered circle. To determine the number of circles arranged within the layered circles, a scaling factor is introduced. To control the settings; the scaling factor is based on the distance between the center of all circles within the quasi-layered circle and the center of the quasi-layered circle. The settings are arranged in ascending order. , If the number of circles in the first layer is 3, then the scaling factor is... After determining the components of the first layer, a layered circle is constructed, and then the remaining components are arranged in the second layer. Finally, the layered cross-sectional layout of the umbilical cable can be obtained.

3. The GA-GLM-based umbilical cross-section automatic hierarchical layout optimization algorithm according to claim 1, characterized in that, The corresponding solution process in step (7) is as follows: First, the optimal solution of the problem is solved in the global solution space using a genetic algorithm to determine the feasible solution of the center coordinates of each component in the optimal layout; then, the feasible solution obtained by GA is used as the initial value, and the overall cross-sectional layout is obtained by using GLM for fast and accurate solution; after obtaining the overall optimal layout of the cross-section, a layering strategy is introduced, and the GLM algorithm is used to continue to optimize in order to obtain the layered layout form of the umbilical cable cross-section.

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