A genetic algorithm-based initial alignment optimization method for submarine cable laying simulation

Abstract

The present invention discloses a method for optimizing the initial alignment of submarine cable laying simulations based on a genetic algorithm. By constructing a genetic algorithm population to generate cubic spline curves with different control points as the initial alignment of the submarine cable, a numerical iteration method is used to calculate the static equilibrium of each initial alignment of the submarine cable using finite element analysis software. The fitness function of the genetic algorithm is used to calculate the fitness value based on the tension at the bottom point of each submarine cable alignment that meets the convergence conditions and the deformation of the submarine cable end. The initial alignment of the submarine cable corresponding to the minimum fitness value is determined as the optimal initial alignment of the submarine cable. The present invention solves the problem that the iterative solution process of the submarine cable simulation calculation diverges when the catenary equation is used to determine the initial alignment of the submarine cable, and also solves the problem that the trial-and-error rate of determining the initial alignment of the submarine cable based on empirical parameters is high.

Description

Technical Field

[0001] The present invention relates to the field of submarine cable laying modeling, and in particular to a method for optimizing the initial linear shape of submarine cable laying simulation based on a genetic algorithm. Background Art

[0002] In order to obtain the changes in cable tension under different working conditions, these tensions are applied during the actual cable laying process to control cable tension and other parameters, ensuring cable laying safety, preventing cable damage, and improving cable laying quality. Before the actual laying of the cable, a simulated cable laying process is required. In the cable laying simulation calculation, its convergence depends on the assumption of the initial line shape. Traditional methods use the catenary equation or empirical parameters to determine the initial line shape of the cable. When the bending stiffness and boundary conditions of the cable are complex, the initial line shape of the cable deviates from the true solution, causing the iterative solution process of the cable laying simulation calculation to diverge and fail to obtain correct calculation results. In addition, when the stiffness and boundary conditions of the cable change, the initial line shape of the cable will also change, and the initial line shape of the cable needs to be adjusted to ensure the convergence of the calculation. Currently, manual adjustment of the initial line shape of the cable relies on experience to solve the problem of iterative divergence. This manual adjustment of the initial line shape of the cable requires repeated trial and error, which reduces the efficiency of the cable laying simulation. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for optimizing the initial line shape of a submarine cable laying simulation based on a genetic algorithm, so as to solve the problem that the use of a catenary equation to determine the initial line shape of the submarine cable leads to the divergence of the iterative solution process of the submarine cable simulation calculation and the high trial and error rate of determining the initial line shape of the submarine cable based on empirical parameters.

[0004] In order to solve the above technical problems, the present invention provides a method for optimizing the initial line shape of submarine cable laying simulation based on a genetic algorithm, comprising:

[0005] Step S1, construct n A genetic algorithm population of individuals:

[0006] (1);

[0007] In formula (1), O n For the n There are genetic algorithm populations, P1 is the first control point, P2 is the second control point, P i =( x i , y i , z i ) is the i The three-dimensional coordinates of the control points;

[0008] Step S2: Generate multiple cubic spline curves with different control points as the initial linear shapes of multiple submarine cables according to the genetic algorithm population:

[0009] (5);

[0010] In formula (5), C( u ) is a cubic spline curve, P i =( x i , y i , z i ) is the i The three-dimensional coordinates of the control points, B i,3 ( u ) is the cubic basis function of the spline curve, u are the configuration parameters of the cubic spline curve, m is the number of control points;

[0011] Step S3, using a numerical iteration method to calculate the static balance of the initial linear shape of each submarine cable through finite element analysis software. The initial static balance equation for each initial linear shape of the submarine cable input into the finite element analysis software is:

[0012] (6);

[0013] In formula (6), F is the node residual force vector, O n,0 is the initial line shape of the submarine cable;

[0014] The computational convergence condition of the numerical iterative method is:

[0015] (7);

[0016] In formula (7), O n,k For the k The cable line shape after iterations, J is the Jacobian matrix, is the convergence tolerance, and are the upper and lower limits of the condition number;

[0017] Step S4: When the static equilibrium iterative calculation of the initial cable line shape satisfies the convergence condition, the tension of the bottom point of the corresponding cable and the deformation of the cable end are extracted:

[0018] Step S5, calculating the fitness value of the initial linear shape of each submarine cable that meets the convergence condition according to the fitness function (8) of the genetic algorithm;

[0019] (8);

[0020] In formula (8), f is the fitness value of the initial linear shape of the submarine cable, T is the tension at the point where the cable touches the bottom, =| - |Deformation of the submarine cable end Allowable deformation of the end The absolute difference, Pt is the penalty term of the fitness function;

[0021] Step S6: Compare the fitness values ​​of the initial line shapes that meet the convergence condition, and determine that the submarine cable initial line shape corresponding to the minimum fitness value is the optimal submarine cable initial line shape.

[0022] Furthermore, in the method for optimizing the initial linear shape of submarine cable laying simulation based on genetic algorithm provided by the present invention, in step S1, the boundary conditions of the three-dimensional coordinates of each control point are determined according to formulas (2), (3), and (4):

[0023] (2);

[0024] (3);

[0025] (4);

[0026] In formula (2), (3), and (4), x i , y i , z i For the i The three-dimensional coordinates of the control points, x min , x max , y min , y max , z min , z max They are x, y and z The minimum and maximum values ​​of the control point coordinates corresponding to the direction.

[0027] Furthermore, in the genetic algorithm-based initial line shape optimization method for submarine cable laying simulation provided by the present invention, in step S3, the Newton-Raphson method is used as the numerical iteration method.

[0028] Furthermore, the genetic algorithm-based initial line shape optimization method for submarine cable laying simulation provided by the present invention further includes:

[0029] Step S7, repeating steps S1 to S6 to determine the optimal initial cable shape, and determining the initial cable shape corresponding to the minimum fitness value as the optimal initial cable shape.

[0030] Furthermore, the genetic algorithm-based initial linear optimization method for submarine cable laying simulation provided by the present invention stops iteration when the minimum fitness value of the iterative calculation does not change for 10 consecutive generations or reaches the maximum number of iterations.

[0031] Compared with the prior art, the present invention has the following beneficial effects:

[0032] The present invention provides a method for optimizing the initial linear shape of a submarine cable laying simulation based on a genetic algorithm. The method generates cubic spline curves with different control points as the initial linear shape of the submarine cable by constructing a genetic algorithm population, calculates the static equilibrium of the initial linear shape of each submarine cable through finite element analysis software using a numerical iteration method, calculates the fitness value based on the tension of the submarine cable bottoming point and the deformation of the submarine cable end of each submarine cable initial linear shape that meets the convergence condition through the fitness function of the genetic algorithm, and determines the initial linear shape of the submarine cable corresponding to the minimum fitness value as the optimal initial linear shape of the submarine cable. This solves the problem of divergence of the iterative solution process of the submarine cable simulation calculation caused by using the catenary equation to determine the initial linear shape of the submarine cable, and solves the problem of high trial and error rate of determining the initial line of the submarine cable based on empirical parameters, thereby improving the efficiency of the submarine cable laying simulation.

[0033] The present invention provides a method for optimizing the initial linear shape of a submarine cable laying simulation based on a genetic algorithm. The method uses a numerical iteration method to calculate the convergence conditions of a spline curve generated by the genetic algorithm as the control point coordinates of the initial linear shape, and combines the fitness function of the genetic algorithm to calculate the fitness value of the initial linear shape of each submarine cable that meets the convergence conditions. The initial linear shape of the submarine cable corresponding to the minimum fitness value is determined as the optimal initial linear shape of the submarine cable. This solves the problem that when the initial linear shape of the submarine cable is determined by using a catenary equation, the initial linear shape of the submarine cable deviates from the true solution when the bending stiffness and boundary conditions of the submarine cable are complex. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 This is a flow chart of the initial line shape optimization method for submarine cable laying simulation based on genetic algorithm;

[0035] Figures 2 to 3 It is a schematic diagram of submarine cable simulation laying with different initial cable shapes and iterative cable shapes under the control of different control points;

[0036] Figure 4 It is a schematic diagram of the cable line shape that satisfies the convergence condition of static equilibrium after the iteration of the optimal initial line shape, as well as its bottoming point, cable end, and allowable deformation of the end;

[0037] Figure 5 yes Figure 4 Enlarged view of point A in the middle;

[0038] Figure 6 yes Figure 4 Enlarged view of point B in the middle;

[0039] Figures 7 and 8 It is a schematic diagram of the cable line shape that does not meet the convergence condition of static equilibrium after the initial line shape iteration;

[0040] Figure 9 Schematic diagram of the cable line shape that satisfies the convergence condition of static equilibrium after the optimal initial line shape iteration;

[0041] Figure 10 It is a schematic diagram of the calculation results of the tension at the bottoming point;

[0042] Figure 11 It is a schematic diagram of the deformation result of the submarine cable end;

[0043] As shown in the figure:

[0044] 1. Sea surface, 2. Seabed, 3. Cable-laying vessel, 4. Cable drum, 5. Initial cable shape, 6. Iterated cable shape. DETAILED DESCRIPTION

[0045] The present invention will be described in detail below with reference to the accompanying drawings. The advantages and features of the present invention will become more apparent from the following description. It should be noted that the drawings are all in a very simplified form and are not accurately scaled, and are only used to facilitate and clearly illustrate the embodiments of the present invention.

[0046] Please refer to Figure 1 The embodiment of the present invention provides a method for optimizing the initial line shape of submarine cable laying simulation based on a genetic algorithm, which may include:

[0047] Step S1, genetic algorithm population.

[0048] Build with n A genetic algorithm population of individuals:

[0049] (1);

[0050] In formula (1), O n For the n There are genetic algorithm populations, P1 is the first control point, P2 is the second control point, P i =( x i , y i , z i ) is the iThe three-dimensional coordinates of the control points.

[0051] In order to ensure that each control point meets the boundary conditions, the boundary conditions of the three-dimensional coordinates of each control point in formula (1) can be determined according to formulas (2), (3), and (4):

[0052] (2);

[0053] (3);

[0054] (4);

[0055] In formula (2), (3), and (4), x i , y i , z i For the i The three-dimensional coordinates of the control points, x min , x max , y min , y max , z min , z max They are x, y and z The minimum and maximum values ​​of the control point coordinates corresponding to the direction. The minimum and maximum values ​​of the boundary conditions of the three-dimensional coordinates of each control point need to be determined according to the actual laying conditions of the construction site.

[0056] Step S2, generate the initial line shape of the submarine cable, such as Figures 2 to 3 shown.

[0057] Generate multiple cubic spline curves with different control points as the initial line shapes of multiple submarine cables based on the genetic algorithm population:

[0058] (2);

[0059] In formula (2), C( u ) is a cubic spline curve, which is equal to the initial linear shape of the submarine cable 5, P i =( x i , y i , z i ) is the i The three-dimensional coordinates of the control points, B i,3 (u ) is the cubic basis function of the spline curve, u are the configuration parameters of the cubic spline curve, m is the number of control points.

[0060] Please refer to Figures 2 to 3 , use the marine engineering calculation software orcaflex to model the laying of submarine cables. Figures 2 to 3 In the example, two control points P1 and P2 at different coordinate positions are used to generate different initial cable shapes 5. Due to the different control point positions, the initial cable shape 5 based on the cubic spline curve also exhibits different shapes. The subsequent calculation iteration based on the initial cable shape 5 also has different cable shapes 6.

[0061] Step S3: Perform static balance calculation on the initial line shape of the submarine cable.

[0062] The static equilibrium of the initial line shape of each submarine cable is calculated using a numerical iteration method (e.g., the Newton-Raphson method) through finite element analysis software. The initial static equilibrium equation for each initial line shape of the submarine cable input into the finite element analysis software is:

[0063] (6);

[0064] In formula (6), F is the node residual force vector, O n,0 is the initial line shape of the submarine cable;

[0065] The computational convergence condition of the numerical iterative method is:

[0066] (7);

[0067] In formula (7), O n,k For the k The cable line shape after iterations, J is the Jacobian matrix, is the convergence tolerance, and are the upper and lower limits of the condition number.

[0068] The iterative process of static balance calculation using formula (7) is the process of adjusting the control points of the initial line shape of each submarine cable.

[0069] Step S4: extract calculation data.

[0070] When the static equilibrium iterative calculation of the initial cable line shape meets the convergence condition, the tension of the cable bottom point and the deformation of the cable end of the corresponding initial cable line shape are extracted, such as Figures 4 to 6 、 Figures 9 to 11 shown.

[0071] Step S5, calculating fitness.

[0072] According to the fitness function (8) of the genetic algorithm, the fitness value of the initial linear shape of each submarine cable that meets the convergence condition is calculated;

[0073] (8);

[0074] In formula (8), f is the fitness value of the initial linear shape of the submarine cable, T is the tension at the point where the cable touches the bottom, =| - |Deformation of the submarine cable end Allowable deformation of the end The absolute difference, Pt is the penalty term of the fitness function;

[0075] Step S6, determine the optimal initial cable line shape, such as Figure 4 and Figure 9 shown.

[0076] The fitness values ​​of the initial line shapes that meet the convergence conditions are compared, and the initial line shape of the submarine cable corresponding to the minimum fitness value is determined as the optimal initial line shape of the submarine cable. After the optimal initial line shape of the submarine cable is determined, the three-dimensional coordinate positions of the control points on it can be determined.

[0077] in Figures 4 to 6 、 Figures 9 to 11 The example shows the optimal initial cable shape 5 and its iterative cable shape 6, as well as the cable bottoming point, cable end and allowable deformation position of the end. Here, the tension of the cable bottoming point and the deformation of the cable end need to be extracted to calculate the fitness of the genetic algorithm. Figure 9 An example of an optimal initial cable shape 5 at the end of the evolution and a cable shape 6 after iteration is shown. Figure 10 The calculation results of the submarine cable tension in the diagram show that the submarine cable has been laid smoothly to the seabed. At this time, the submarine cable is only balanced by its weight and the seabed support, and the tension at the bottom of the cable is close to 0. At the same time, Figure 11 The end of the submarine cable in the figure is completely in line with the allowable deformation position of the end, which shows that the iterative calculation using the optimal initial linear shape has reached convergence.

[0078] in Figures 7 and 8 Example 2: Non-convergent calculation results. Figure 7 The first type of non-convergence is shown as the result of the overall non-convergence of the submarine cable. Figure 8 The second type of non-convergence result is that the end of the submarine cable exceeds the allowable deformation of the end. When similar non-convergence calculation results appear, the penalty term of the fitness function can be used. Pt To reduce the occurrence of non-convergence results.

[0079] To improve the quality of determining the optimal initial submarine cable shape, the genetic algorithm-based initial cable shape optimization method for submarine cable installation simulation provided by an embodiment of the present invention may include step S7, repeating steps S1 to S6 to determine the optimal initial submarine cable shape, and determining the initial submarine cable shape corresponding to the minimum fitness value as the optimal initial submarine cable shape. A crossover mutation operation may be performed on the individuals in the current genetic algorithm population corresponding to the optimal submarine cable shape, generating a new generation population according to step S1, and then repeating steps S2 to S6.

[0080] To improve computational efficiency and avoid resource waste caused by infinite iterations while ensuring the optimal submarine cable alignment, the genetic algorithm-based initial alignment optimization method for submarine cable installation simulations provided by the present invention stops iterations when the minimum fitness value remains unchanged for 10 consecutive iterations or when the maximum number of iterations is reached. At this point, the submarine cable initial alignment corresponding to the minimum fitness value is determined to be the optimal submarine cable alignment.

[0081] The embodiment of the present invention provides a method for optimizing the initial linear shape of a submarine cable laying simulation based on a genetic algorithm. A genetic algorithm population is constructed to generate a cubic spline curve with different control points as the initial linear shape of the submarine cable. A numerical iteration method is used to calculate the static equilibrium of the initial linear shape of each submarine cable using finite element analysis software. The fitness function of the genetic algorithm is used to calculate the fitness value based on the tension of the submarine cable bottoming point and the deformation of the submarine cable end of each submarine cable initial linear shape that meets the convergence condition. The initial linear shape of the submarine cable corresponding to the minimum fitness value is determined as the optimal initial linear shape of the submarine cable. This solves the problem of divergence of the iterative solution process of the submarine cable simulation calculation caused by using the catenary equation to determine the initial linear shape of the submarine cable, and solves the problem of high trial and error rate in determining the initial line of the submarine cable based on empirical parameters, thereby improving the efficiency of the submarine cable laying simulation.

[0082] The embodiment of the present invention provides a method for optimizing the initial linear shape of a submarine cable laying simulation based on a genetic algorithm. The coordinates of the control points of the initial linear shape, which are used as a spline curve generated by the genetic algorithm, are iteratively adjusted through the calculation convergence conditions of a numerical iteration method. The fitness value of the initial linear shape of each submarine cable that meets the convergence conditions is calculated in combination with the fitness function of the genetic algorithm. The initial linear shape of the submarine cable corresponding to the minimum fitness value is determined as the optimal initial linear shape of the submarine cable. This solves the problem that when the initial linear shape of the submarine cable is determined by using the catenary equation, the initial linear shape of the submarine cable deviates from the true solution when the bending stiffness and boundary conditions of the submarine cable are complex.

[0083] The embodiment of the present invention provides a method for optimizing the initial linear shape of a submarine cable laying simulation based on a genetic algorithm. The initial linear shape of the submarine cable is automatically adjusted based on the spline curve control points generated by the genetic algorithm. The obtained optimal initial linear shape of the submarine cable can ensure the convergence of the finite element calculation. Since the process of adjusting the control points is automatically controlled by the genetic algorithm, the precise control of the iteration of the initial linear shape of the submarine cable can be achieved by adjusting the coordinates of the control points of the spline curve. Therefore, the adjustment and optimization efficiency of the initial linear shape of the submarine cable can be greatly improved, and the efficiency of the submarine cable laying simulation is further improved.

[0084] The genetic algorithm-based initial alignment optimization method for submarine cable laying simulations provided in an embodiment of the present invention integrates intelligent optimization algorithms with structural mechanics calculations to provide an efficient numerical iterative convergence solution for marine engineering cable laying (i.e., submarine cables). This method is suitable for deep-sea cable laying simulation engineering scenarios where the initial alignment is highly sensitive. A general static equilibrium equation for submarine cables is constructed to realistically reflect the nonlinear mechanical behavior of submarine cables in marine environments. A cubic spline curve is used as a parameterized expression of the initial alignment. A genetic algorithm is used to construct a population of individuals containing multidimensional control points. Under preset engineering constraints, the optimal initial alignment that meets both mechanical performance requirements and exhibits numerical stability is automatically generated and selected, addressing the inefficiency of traditional trial-and-error methods.

[0085] The present invention is not limited to the specific embodiments described above. Obviously, the embodiments described above are only some embodiments of the embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention described, all other embodiments obtained by ordinary technicians in this field fall within the scope of protection of the present invention. Those skilled in the art can make other levels of modifications and changes to the present invention. In this way, if these modifications and changes of the present invention fall within the scope of the claims of the present invention, the present invention is also intended to include these changes and changes.

Claims

1. A method for optimizing the initial linear shape of submarine cable laying simulation based on genetic algorithm, characterized in that: include: Step S1, construct n A genetic algorithm population of individuals: （1）； In formula (1), O n For the n There are genetic algorithm populations, P1 is the first control point, P2 is the second control point, P i =( x i , y i , z i ) is the i The three-dimensional coordinates of the control points; Step S2: Generate multiple cubic spline curves with different control points as the initial linear shapes of multiple submarine cables according to the genetic algorithm population: （5）； In formula (5), C( u ) is a cubic spline curve, P i =( x i , y i , z i ) is the i The three-dimensional coordinates of the control points, B i,3 ( u ) is the cubic basis function of the spline curve, u are the configuration parameters of the cubic spline curve, m is the number of control points; Step S3, using a numerical iteration method to calculate the static balance of the initial linear shape of each submarine cable through finite element analysis software. The initial static balance equation for each initial linear shape of the submarine cable input into the finite element analysis software is: （6）； In formula (6), F is the node residual force vector, O n,0 is the initial line shape of the submarine cable; The computational convergence condition of the numerical iterative method is: （7）； In formula (7), O n,k For the k The cable line shape after iterations, J is the Jacobian matrix, is the convergence tolerance, and are the upper and lower limits of the condition number; Step S4: When the static equilibrium iterative calculation of the initial cable line shape satisfies the convergence condition, the tension of the bottom point of the corresponding cable and the deformation of the cable end are extracted: Step S5, calculating the fitness value of the initial linear shape of each submarine cable that meets the convergence condition according to the fitness function (8) of the genetic algorithm; （8）； In formula (8), f is the fitness value of the initial linear shape of the submarine cable, T is the tension at the point where the cable touches the bottom, =| - |Deformation of the submarine cable end Allowable deformation of the end The absolute difference, Pt is the penalty term of the fitness function; Step S6: comparing the fitness values ​​of the initial line shapes that meet the convergence condition, and determining the submarine cable initial line shape corresponding to the minimum fitness value as the optimal submarine cable initial line shape.

2. The method for optimizing the initial linear shape of submarine cable laying simulation based on genetic algorithm according to claim 1, characterized in that: In step S1, the boundary conditions of the three-dimensional coordinates of each control point are determined according to formulas (2), (3), and (4): （2）； （3）； （4）； In formula (2), (3), and (4), x i , y i , z i For the i The three-dimensional coordinates of the control points, x min , x max , y min , y max , z min , z max They are x, y and z The minimum and maximum values ​​of the control point coordinates corresponding to the direction.

3. The method for optimizing the initial linear shape of submarine cable laying simulation based on genetic algorithm according to claim 1, characterized in that: In step S3 , the Newton-Raphson method is used as the numerical iteration method.

4. The method for optimizing the initial linear shape of submarine cable laying simulation based on genetic algorithm according to claim 1, characterized in that: Also includes: Step S7, repeating steps S1 to S6 to determine the optimal initial cable shape, and determining the initial cable shape corresponding to the minimum fitness value as the optimal initial cable shape.

5. The method for optimizing the initial linear shape of submarine cable laying simulation based on genetic algorithm according to claim 4, characterized in that: When the minimum fitness value calculated iteratively does not change for 10 consecutive generations or reaches the maximum number of iterations, the iteration is stopped.

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