Submarine pipeline multi-dimensional response correlation optimization method under earthquake dynamic excitation

Abstract

The invention relates to the technical field of electric digital data processing, in particular to a submarine pipeline multi-dimensional response association optimization method under earthquake dynamic excitation, which comprises the following steps of: establishing a submarine pipeline model; setting constraint conditions for the submarine pipeline model, applying seismic displacement, and calculating modal frequency, Mises stress data and displacement deformation data of the submarine pipeline model; outputting the initial mass of the pipeline, and calculating the correlation degree between three optimization criteria, namely the maximum rice-ceas stress of the pipeline, the displacement difference between the end part and the middle part of the pipeline and the mass of the pipeline, and the sectional dimension; calculating weights of the three optimization criteria; and establishing an optimization function, and carrying out iterative optimization on the submarine pipeline model to obtain optimized pipeline inner and outer diameter parameters. According to the method provided by the invention, the anti-seismic property of the pipeline under the earthquake response can be more effectively improved, the strength, displacement control and quality optimization of the pipeline are considered, and the safety and reliability of the pipeline are improved.

Description

Technical Field

[0001] The invention relates to the technical field of electrical digital data processing, and in particular to a method for optimizing the multi-dimensional response correlation of a submarine pipeline under earthquake dynamic excitation. Background Art

[0002] With the continuous development of offshore oil and gas resources, submarine pipelines have become an important infrastructure connecting offshore oil and gas production facilities with land terminals. These pipelines are responsible for transporting oil and gas resources from the production site to onshore processing plants and storage facilities. However, submarine pipelines face a variety of complex environmental conditions and potential risks, especially under natural disaster conditions such as earthquakes, the safety and stability of the pipelines are easily threatened.

[0003] Earthquakes are one of the main natural disasters faced by submarine pipelines. During an earthquake, submarine pipelines may encounter complex stress states such as large surface deformation and strong vibration shocks, which in turn affect the structural stability and transportation safety of the pipelines. For submarine pipelines in deep sea areas, due to the complexity of their environment and the different distances from the epicenter, the stress and deformation of the pipelines under earthquakes may be more significant. Traditional pipeline design and optimization methods often find it difficult to fully consider earthquake responses, and therefore cannot effectively solve the safety issues of pipelines under earthquakes.

[0004] The existing optimization design of submarine pipelines usually focuses on a single objective, such as structural strength or economy, and fails to fully consider the multi-dimensional impact of seismic response. This makes it difficult for pipelines to balance safety, stability and economy under complex seismic conditions. Especially when faced with complex geological conditions and uncertain factors, it is difficult for traditional methods to provide a comprehensive optimization solution. Existing multi-objective methods still have some unresolved shortcomings. For example, the Pareto method provides a set of Pareto optimal solutions, but multiple objectives interfere with each other, and it is impossible to give the weight of each objective to obtain an accurate optimal solution; in addition, among the existing optimization methods that can handle the weight problem of each objective, most rely on expert scoring to determine the weight, and subjective factors account for the majority. Human scoring leads to uncertainty in the results. Therefore, there is an urgent need for a multi-dimensional corresponding correlation optimization method that can balance various engineering objectives while fully considering the seismic response and improve the safety and reliability of the pipeline. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a method for correlation optimization of multi-dimensional responses of submarine pipelines under earthquake dynamic excitation. By processing uncertain or incomplete input information in the optimization process and analyzing the weights of different optimization criteria, the seismic performance of the pipeline under earthquake response can be more effectively improved, while taking into account pipeline strength, displacement control and quality optimization, thereby improving the safety and reliability of the pipeline.

[0006] The present invention is achieved through the following technical solutions: A method for optimizing the multi-dimensional response of a submarine pipeline under earthquake dynamic excitation, comprising the following steps: S1: Establish a submarine pipeline model in a finite element processor; S2: Set constraints on the submarine pipeline model, apply seismic displacement and create analysis steps to calculate the modal frequency of the submarine pipeline model. Under the premise that the modal frequency and the seismic excitation frequency do not resonate, calculate the Mises stress data and displacement deformation data at various locations of the submarine pipeline model. S3: Based on the Mises stress data and displacement deformation data of each part of the submarine pipeline model, the initial quality of the pipeline is output through the finite element processing software, and the inner and outer diameters of the pipeline are used as design variables to calculate the correlation between the maximum Mises stress of the pipeline, the displacement difference between the end and the middle of the pipeline, and the three optimization criteria of pipeline quality and the cross-sectional size; S4: According to the correlation between the three optimization criteria of maximum Mises stress of pipeline, the displacement difference between the end and the middle of pipeline, and pipeline quality and the cross-sectional size, the weights of the three optimization criteria of maximum Mises stress of pipeline, the displacement difference between the end and the middle of pipeline, and pipeline quality are calculated based on the multi-dimensional response sorting criterion; S5: An optimization function is established based on the weights of the three optimization criteria: maximum Mises stress of the pipeline, displacement difference between the end and middle of the pipeline, and pipeline quality. The submarine pipeline model is iteratively optimized to obtain the optimized inner and outer diameter parameters of the pipeline.

[0007] Optimized, establishing the submarine pipeline model in step S1 includes setting the pipeline length, pipeline cross-sectional shape, pipeline material parameters, initial pipeline inner diameter size and initial pipeline outer diameter size, and using beam units for meshing.

[0008] The optimized submarine pipeline model sets the pipeline length to 40 meters, the pipeline cross-section shape to be circular, the pipeline material to be steel, the elastic modulus to be 210 MPa, the Poisson's ratio to be 0.3, the density to be 7850 kg / m3, the initial pipeline inner diameter to be 0.31 meters, the initial pipeline outer diameter to be 0.32 meters, and the variation range of the pipeline inner diameter and pipeline outer diameter to be ±15%.

[0009] Optimized, the constraint conditions set for the submarine pipeline model in step S2 are: the nodes at both ends of the pipeline are subject to displacement constraints in the three directions of X, Y, and Z, and the remaining nodes remain free. When applying seismic displacement, a single-point displacement constraint command is used to apply the seismic displacement to the nodes at both ends of the pipeline to simulate the impact of the earthquake on the junction between the two ends of the pipeline and the soil.

[0010] Further, in step S2, the modal frequency of the submarine pipeline model is calculated according to formula (1): (1); in: represents the eigenvalue of the modal frequency, represents the model stiffness matrix, represents the modal frequency, Represents the model quality matrix.

[0011] Further, in step S2, the Mises stress data and displacement deformation data at each location of the submarine pipeline model are calculated according to formula (2): in: express The displacement of time, express The speed of time, express The acceleration of time, represents the damping matrix, represents transient excitation, represents the initial displacement, represents the initial velocity, express The node force at the moment, express The Mises stress at the time node, Represents the unit area.

[0012] Furthermore, in step S3, the correlation between the maximum Mises stress of the pipeline, the displacement difference between the end and the middle of the pipeline, and the pipeline quality and the cross-sectional size is calculated according to formula (3): (3); in: Indicates The correlation between the optimization criteria and the current cross-sectional dimensions, Indicates the current cross-section size corresponding to the The calculated value of the optimization criterion, Indicates The ideal target value of the optimization criterion is Indicates The maximum value of the optimization criteria, Indicates The minimum value of the optimization criteria.

[0013] Further, in step S4, the weights of the three optimization criteria of the maximum Mises stress of the pipeline, the displacement difference between the end and the middle of the pipeline, and the pipeline quality are calculated respectively according to the following method: S41: Calculate the differences between the correlations of the three optimization criteria of pipeline maximum Mises stress, displacement difference between the end and middle of the pipeline, and pipeline quality and the cross-sectional dimensions respectively, and compare the differences with the set scale value to obtain the importance degree and importance scale between the two optimization criteria; S42: Construct a judgment matrix based on the importance scale between the pairwise optimization criteria: S43: Normalize each column element in the judgment matrix to obtain a normalized judgment matrix, and add the normalized judgment matrix row by row to obtain the first The weights of the optimization criteria are: S44: Then The weights of the optimization criteria are normalized to obtain the normalized The weight of the optimization criterion.

[0014] Furthermore, the optimization function established in step S5 is formula (4): (4); in: represents the total objective function value, represents the weight of the normalized maximum Mises stress optimization criterion for the pipeline, represents the weight of the optimization criterion for the displacement difference between the end and the middle of the pipeline after normalization, represents the weight of the normalized pipeline quality optimization criterion, represents the maximum Mises stress of the pipeline after optimization, represents the maximum Mises stress of the pipeline before optimization, It indicates the maximum displacement difference between the end and the middle of the pipe after optimization. It indicates the maximum displacement difference between the end and the middle of the pipeline before optimization. represents the quality of the pipeline after optimization, Indicates the pipeline quality before optimization.

[0015] Furthermore, in step S5, based on the optimization function, the response surface is designed as a quadratic polynomial model as shown in formula (5), and the submarine pipeline model is iteratively optimized using the global response surface method to obtain the optimized inner and outer diameter parameters of the pipeline: (5); in: represents the parameter design target value, represents the basic target value when all design variables are zero, Indicates The linear effect of the design variables on the target, Indicates design variables, Indicates The square coefficients of the design variables, Indicates Design variables and The interaction effect coefficients between the design variables are Indicates design variables, Represents the total number of design variables.

[0016] Beneficial effects of the invention: The present invention provides a method for optimizing the multi-dimensional response of a submarine pipeline under earthquake dynamic excitation, which has the following advantages: 1. Multi-dimensional response correlation optimization can scientifically and reasonably handle complex multi-objective optimization problems, ensuring that the optimal pipeline section design solution is obtained when considering multiple optimization objectives, such as stress, displacement, quality, etc. 2. By introducing the multi-objective correlation calculation theory, the importance of each objective criterion is obtained, solving the problem that the weight calculation of each objective in the subsequent optimization process is greatly affected by human subjectivity, and providing a new method for comparing the importance.

[0017] 3. Through the multi-dimensional response sorting criteria, the stress, displacement, quality and other parameters of the pipeline are comprehensively considered, the weights of each optimization target criterion are calculated, and the multiple influencing factors under the seismic response are effectively transformed into optimization targets, which solves the problem of mutual interference among multiple targets and obtains the deterministic optimal solution under comprehensive evaluation.

[0018] 4. Through the iterative optimization process of the global response surface method, the key factors affecting pipeline performance can be accurately identified, and more targeted design parameters can be provided, which provides an important reference for the seismic design and optimization of submarine pipelines. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 It is a schematic diagram of the process of the present invention.

[0020] Figure 2 It is a schematic cross-sectional view of the optimized model of the present invention.

[0021] Figure 3 It is a curve diagram of the optimization iteration process of the present invention.

[0022] Figure 4 It is a schematic cross-sectional view of the optimized model of the present invention.

[0023] Figure 5 It is a schematic cross-sectional view of the optimized model of the present invention. DETAILED DESCRIPTION

[0024] A method for optimizing the multi-dimensional response of submarine pipelines under earthquake dynamic excitation, the flow diagram of which is shown in the figure Figure 1 As shown, the specific steps include: S1: Establish a submarine pipeline model in a finite element processor; Specifically, the submarine pipeline model established includes setting the pipeline length, pipeline cross-sectional shape, pipeline material parameters, initial pipeline inner diameter size and initial pipeline outer diameter size, and using beam units for meshing.

[0025] The optimized submarine pipeline model sets the pipeline length to 40 meters, the pipeline cross-section shape to be circular, the pipeline material to be steel, the elastic modulus to be 210 MPa, the Poisson's ratio to be 0.3, the density to be 7850 kg / m3, the initial pipeline inner diameter to be 0.31 meters, the initial pipeline outer diameter to be 0.32 meters, and the variation range of the pipeline inner diameter and pipeline outer diameter to be ±15%.

[0026] The length of the submarine pipeline model is set to 40 meters, which is in line with the common submarine pipeline length in actual projects; the initial size is set according to relevant engineering standards, taking into account the strength and weight requirements of the pipeline.

[0027] In the pipeline model, beam elements are used for meshing. Beam elements are suitable for simulating long and thin structures, especially structures like submarine pipelines. They can effectively capture the mechanical response of pipelines under various external forces (such as earthquakes). Specifically, they can be divided along the length of the pipeline with a step length of 0.08 meters, with a total of 500 elements.

[0028] The selection of pipeline material parameters can ensure that the submarine pipeline model can accurately simulate the mechanical behavior of steel during the calculation process. The material property assignment is performed through the material management module of the finite element processor to ensure that each beam unit of the pipeline has consistent mechanical properties.

[0029] S2: Set constraints on the submarine pipeline model, apply seismic displacement and create analysis steps to calculate the modal frequency of the submarine pipeline model. Under the premise that the modal frequency and the seismic excitation frequency do not resonate, calculate the Mises stress data and displacement deformation data at various locations of the submarine pipeline model. Specifically, the constraints set for the submarine pipeline model are as follows: the nodes at both ends of the pipeline are subject to displacement constraints in the X, Y, and Z directions, and the remaining nodes remain free. When applying seismic displacement, the single-point displacement constraint command is used to apply the seismic displacement to the nodes at both ends of the pipeline to simulate the impact of the earthquake on the junction between the two ends of the pipeline and the soil.

[0030] This constraint simulates the situation where both ends of the pipeline are fixed, that is, the pipeline cannot translate or rotate at its ends, thereby limiting the degrees of freedom and ensuring that the model can truly reflect the stress state under the action of an earthquake.

[0031] Specifically, the modal frequency of the submarine pipeline model can be calculated according to formula (1): (1); in: represents the eigenvalue of the modal frequency, represents the model stiffness matrix, represents the modal frequency, Represents the model quality matrix.

[0032] After calculating the modal frequency of the submarine pipeline model, make a difference between it and the seismic excitation frequency, so that the absolute value of the difference between the modal frequency of the submarine pipeline model and the seismic excitation frequency is greater than the set value, ensuring that the modal frequency and the seismic excitation frequency do not resonate. The setting value here can be preferably selected as 8% .

[0033] If the absolute value of the difference between the calculated modal frequency and the seismic excitation frequency is less than or equal to the set value, the modal frequency of the submarine pipeline model can be adjusted, damping can be increased, the support method can be changed, and other measures can be taken to avoid the coincidence of the natural frequency and the seismic excitation frequency and reduce the resonance response, thereby ensuring the safety of the pipeline under seismic conditions.

[0034] In order to simulate the displacement response of the pipeline under earthquake, the single-point displacement constraint SPCD command can be used to apply the displacement field caused by seismic waves in the model. According to the actual earthquake conditions, the main action direction is determined to be the Y-axis direction, and the corresponding displacement conditions are applied. Specifically, the SPCD constraint applies the seismic displacement to the nodes at both ends of the pipeline to simulate the impact of the earthquake on the connection between the two ends of the pipeline and the soil, so as to ensure that the model can truly simulate the nonlinear deformation caused by the earthquake.

[0035] Specifically, the seismic displacement load can be applied to the pipeline model through the load command TLOAD, which is used to define the dynamic load or displacement application process in the time domain. Specifically, when setting TLOAD, it is necessary to define the law of seismic displacement change over time and input the load curve in combination with the actual seismic working conditions. In order to accurately describe the change of seismic displacement over time, a curve can be created in the model, and the seismic load can be accurately defined through the curve to describe the displacement caused by the earthquake on the pipeline at different time points.

[0036] After the seismic displacement and load are applied, an analysis step can be created to perform the seismic response calculation. It is preferred to set the calculation time step to 0.01 and the total time to 25s in the analysis step to ensure that the seismic displacement is applied synchronously with the model response.

[0037] Specifically, the Mises stress data and displacement deformation data at each location of the submarine pipeline model can be calculated according to formula (2): in: express The displacement of time, express The speed of time, express The acceleration of time, represents the damping matrix, represents transient excitation, represents the initial displacement, represents the initial velocity, express The node force at the moment, express The Mises stress at the time node, Represents the unit area.

[0038] S3: Based on the Mises stress data and displacement deformation data of each part of the submarine pipeline model, the initial quality of the pipeline is output through the finite element processing software, and the inner and outer diameters of the pipeline are used as design variables to calculate the correlation between the maximum Mises stress of the pipeline, the displacement difference between the end and the middle of the pipeline, and the three optimization criteria of pipeline quality and the cross-sectional size; Mises stress is an indicator to measure the strength of a pipeline under complex stress conditions. Under earthquakes, various parts of the pipeline are subjected to stress in different directions. Through the results of finite element analysis, the Mises stress distribution of each unit is obtained, especially the maximum stress value of the pipeline. The finite element analysis software Hyperview can visualize the Mises stress results, identify the stress concentration area, and ensure that the key parts of the pipeline can meet the strength requirements.

[0039] Earthquakes can cause overall displacement and local deformation of the pipeline. By calculation, the displacement changes of each node of the pipeline under the action of earthquake loads can be obtained. Focus on the displacement difference between the middle and end of the pipeline, because this difference reflects the bending deformation of the pipeline during the earthquake. Too large displacement difference may cause local instability or damage to the pipeline.

[0040] The quality of the pipeline is an important indicator in structural optimization. The quality of the pipeline itself has a certain degree of influence on the stress and displacement of the pipeline under dynamic load. By rationalizing the quality of the pipeline, on the one hand, the displacement fluctuation caused by the quality of the pipeline under the earthquake amplitude can be reduced, and on the other hand, the construction cost and energy consumption can be reduced. Therefore, in the calculation process, the present invention can directly output the quality of the entire pipeline through finite element software and use it as one of the optimization targets.

[0041] The present invention adopts the inner diameter and outer diameter of the pipeline cross section as optimization design variables. By adjusting the cross-sectional dimensions, the mechanical properties and quality of the pipeline are optimized to meet the requirements of multi-objective optimization. The selection range of the inner diameter and outer diameter parameters is set according to actual engineering requirements and standard specifications to ensure that the design variables vary within a feasible range, thereby avoiding over-optimization or infeasible designs. The initial value of the outer diameter is 0.32 meters and the inner diameter is 0.31 meters. During the optimization process, the outer diameter and the inner diameter can be allowed to vary within the range of ±15%, respectively. Through this adjustment, the optimal balance between stress, displacement and quality is sought to achieve multi-objective optimization of the pipeline cross section.

[0042] The maximum Mises stress is a key indicator to measure whether the pipeline can maintain structural integrity under earthquakes. In order to ensure that the pipeline will not yield or fail under earthquake loads, the constraint condition of the maximum Mises stress is set. According to the yield strength of the pipeline material, the present invention limits the maximum stress value to no more than 235 MPa, ensuring that the pipeline still has sufficient safety margin under extreme working conditions.

[0043] A large displacement difference between the end and the middle of the pipeline may cause excessive bending or local damage to the pipeline, so this displacement difference is used as a constraint. The displacement difference between the middle and the end of the pipeline is calculated and limited to be smaller than the displacement difference before optimization to ensure that the pipeline deformation is within a controllable range.

[0044] Specifically, the correlation between the maximum Mises stress of the pipeline, the displacement difference between the end and the middle of the pipeline, and the pipeline quality and the cross-sectional size can be calculated according to formula (3): (3); in: Indicates The correlation between the optimization criteria and the current cross-sectional dimensions, Indicates the current cross-section size corresponding to the The calculated value of the optimization criterion, Indicates The ideal target value of the optimization criterion is Indicates The maximum value of the optimization criteria, Indicates The minimum value of the optimization criteria.

[0045] The value range of the correlation degree is between 0 and 1. The average value is calculated by taking multiple groups of data. The larger the value, the higher the correlation between the optimization criterion and the calculation result, and the greater the impact on the dynamic response result of the pipeline under this example condition.

[0046] The specific calculated correlation values ​​are shown in Table 1: Table 1

[0047] S4: According to the correlation between the three optimization criteria of maximum Mises stress of pipeline, the displacement difference between the end and the middle of pipeline, and pipeline quality and the cross-sectional size, the weights of the three optimization criteria of maximum Mises stress of pipeline, the displacement difference between the end and the middle of pipeline, and pipeline quality are calculated based on the multi-dimensional response sorting criterion; Specifically, the weights of the three optimization criteria, namely, the maximum Mises stress of the pipeline, the displacement difference between the end and the middle of the pipeline, and the pipeline quality, can be calculated respectively according to the following method: S41: Calculate the differences between the correlations of the three optimization criteria of pipeline maximum Mises stress, displacement difference between the end and middle of the pipeline, and pipeline quality and the cross-sectional dimensions respectively, and compare the differences with the set scale value to obtain the importance degree and importance scale between the two optimization criteria; S42: Construct a judgment matrix based on the importance scale between the pairwise optimization criteria: Calculate the weights of the three criteria in multi-objective optimization, make a one-to-one comparison between every two criteria, and quantify the relative importance of each objective according to Table 2. Set three optimization criteria: displacement difference, stress and quality. The judgment matrix is ​​as follows. According to Table 2, we have: in: represents the judgment matrix, Indicates the importance of displacement difference relative to stress; Indicates the importance of displacement difference relative to mass; Indicates the importance of stress relative to mass.

[0048] According to the comparison of the correlation difference, the importance of displacement difference relative to stress is set to 3, indicating that displacement difference is more important than stress; the importance of stress relative to mass is 5, indicating that stress is obviously more important than mass; the importance of stress relative to mass is 2, indicating that stress is slightly more important than mass. Therefore, the matrix A is: ; Table 2

[0049] S43: Normalize each column element in the judgment matrix to obtain a normalized judgment matrix, and add the normalized judgment matrix row by row to obtain the first The weights of the optimization criteria are: Specifically, the normalized judgment matrix is ​​processed according to the following formula: in: Indicates that the first The weight of the optimization criterion, Indicates the judgment matrix Line The elements of the column, Represents the first Line The elements of the column, A vector representing weights, represents the weight of the stress optimization criterion before normalization, represents the weight of the displacement difference optimization criterion before normalization, represents the weight of the quality optimization criterion before normalization, Represents matrix transpose.

[0050] Specifically, the final calculated .

[0051] S44: Then The weights of the optimization criteria are normalized to obtain the normalized The weight of the optimization criterion.

[0052] Furthermore, the optimization function established in step S5 is formula (4): (4); in: represents the total objective function value, represents the weight of the normalized maximum Mises stress optimization criterion for the pipeline, represents the weight of the optimization criterion for the displacement difference between the end and the middle of the pipeline after normalization, represents the weight of the normalized pipeline quality optimization criterion, represents the maximum Mises stress of the pipeline after optimization, represents the maximum Mises stress of the pipeline before optimization, It indicates the maximum displacement difference between the end and the middle of the pipe after optimization. It indicates the maximum displacement difference between the end and the middle of the pipeline before optimization. represents the quality of the pipeline after optimization, Indicates the pipeline quality before optimization.

[0053] Through the above optimization processing, it can be ensured that the importance of each objective in the optimization process is reasonably considered.

[0054] S5: An optimization function is established based on the weights of the three optimization criteria: maximum Mises stress of the pipeline, displacement difference between the end and middle of the pipeline, and pipeline quality. The submarine pipeline model is iteratively optimized to obtain the optimized inner and outer diameter parameters of the pipeline.

[0055] The model can be optimized and iterated by the global response surface method. In the implementation process of the present invention, optimization iteration is the core of the entire multi-objective optimization. By establishing a reasonable optimization model, setting weight coefficients and constraints, and using the optimization algorithm to iteratively solve, the optimized cross-sectional parameters of the pipeline are finally obtained.

[0056] The response surface refers to the relatively accurate approximation of the functional relationship in a local range through experiments and expressing it with a simple algebraic expression.

[0057] Specifically, the response surface can be designed as a quadratic polynomial model as shown in formula (5) based on the optimization function, and the global response surface method is used to iteratively optimize the submarine pipeline model to obtain the optimized inner and outer diameter parameters of the pipeline: (5); in: represents the parameter design target value, represents the basic target value when all design variables are zero, Indicates The linear effect of the design variables on the target, Indicates design variables, Indicates The square coefficients of the design variables, Indicates Design variables and The interaction effect coefficients between the design variables are Indicates design variables, Represents the total number of design variables.

[0058] After multiple rounds of iterations, the optimized pipe section parameters are obtained, with an outer diameter R of 0.352 meters and an inner diameter r of 0.343 meters. This result reduces the mass of the pipe and improves its stability under earthquake dynamic excitation, improves the utilization rate of pipe materials, and the optimization achieves the expected effect.

[0059] The schematic diagram of the optimized model cross section is as follows: Figure 2 As shown in the figure, the optimization iteration process curve is as follows Figure 3 As shown in the figure, the midpoint and end point displacement curves before and after optimization are as follows Figure 4 As shown, the stress curves of the middle part of the pipeline before and after optimization are shown in Figure 5. Figure 4 , Figure 5 The upper middle curve is the curve before optimization, and the lower curve is the curve after optimization.

[0060] according to Figure 3 , Figure 4 , Figure 5, after calculation, it can be concluded that the optimized pipeline response results have the following characteristics: the pipeline mass is reduced by about 1%; the peak displacement difference between the end and the middle of the pipeline is reduced by 96%; the maximum Mises stress is 20% higher than before optimization, which is lower than the safety value of 235MPa, and reaches 55% of the yield stress. Compared with the maximum stress before optimization, which accounts for about 46% of the yield stress, the pipeline material utilization rate is improved while ensuring that the pipeline will not undergo plastic deformation or failure under the action of seismic load. Therefore, this slight increase in stress is considered to be a reasonable price for structural optimization under the premise of maintaining pipeline safety. The maximum displacement difference between the middle and the end of the optimized pipeline is reduced by 96%. This result shows that the deformation of the optimized pipeline under the action of seismic displacement is more uniform, and the stability of the overall structure is significantly improved. By analyzing the node displacement curves of the pipeline under seismic action, the coincidence of the peak displacement period curves of the optimized pipeline is significantly improved. This improvement can effectively improve the seismic performance of the pipeline, effectively reduce the risk of excessive deformation of the pipeline under complex seismic conditions, help to increase the service life of the pipeline in extreme environments, and slightly reduce the quality of the pipeline. The optimized maximum Mises stress is controlled within the allowable range of the material. Compared with before optimization, it reduces economic consumption and improves the economic efficiency of the project.

[0061] In summary, the present invention provides a method for optimizing the multi-dimensional response of submarine pipelines under earthquake dynamic excitation, which achieves a good balance between stress, displacement and mass, realizes the expected effect of multi-objective optimization, and the optimization scheme successfully achieves the balance of multiple objectives and performance improvement. The optimization method of the present invention has good versatility and practicality, can be widely used in the optimization design of other similar structures, and provides an efficient multi-objective optimization solution.

[0062] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for correlation optimization of multi-dimensional responses of submarine pipelines under earthquake dynamic excitation, characterized in that: The steps include: S1: Establish a submarine pipeline model in a finite element processor; S2: Set constraints on the submarine pipeline model, apply seismic displacement and create analysis steps to calculate the modal frequency of the submarine pipeline model. Under the premise that the modal frequency and the seismic excitation frequency do not resonate, calculate the Mises stress data and displacement deformation data at various locations of the submarine pipeline model. S3: Based on the Mises stress data and displacement deformation data of each part of the submarine pipeline model, the initial quality of the pipeline is output through the finite element processing software, and the inner and outer diameters of the pipeline are used as design variables to calculate the correlation between the maximum Mises stress of the pipeline, the displacement difference between the end and the middle of the pipeline, and the three optimization criteria of pipeline quality and the cross-sectional size; S4: According to the correlation between the three optimization criteria of maximum Mises stress of pipeline, the displacement difference between the end and the middle of pipeline, and pipeline quality and the cross-sectional size, the weights of the three optimization criteria of maximum Mises stress of pipeline, the displacement difference between the end and the middle of pipeline, and pipeline quality are calculated based on the multi-dimensional response sorting criterion; S5: An optimization function is established based on the weights of the three optimization criteria: maximum Mises stress of the pipeline, displacement difference between the end and middle of the pipeline, and pipeline quality. The submarine pipeline model is iteratively optimized to obtain the optimized inner and outer diameter parameters of the pipeline.

2. The method for optimizing the multi-dimensional response of a submarine pipeline under earthquake dynamic excitation according to claim 1, characterized in that: Establishing the submarine pipeline model in step S1 includes setting the pipeline length, pipeline cross-sectional shape, pipeline material parameters, initial pipeline inner diameter size and initial pipeline outer diameter size, and using beam units for meshing.

3. The method for correlation optimization of multi-dimensional responses of submarine pipelines under earthquake dynamic excitation according to claim 2 is characterized in that: The submarine pipeline model is set with a pipeline length of 40 meters, a circular cross-sectional shape, and a pipeline material of steel. The elastic modulus of the pipeline material parameters is 210 MPa, the Poisson's ratio is 0.3, the density is 7850 kg / m3, the initial pipeline inner diameter is 0.31 meters, and the initial pipeline outer diameter is 0.32 meters. The variation range of the pipeline inner diameter and the pipeline outer diameter is ±15%.

4. The method for optimizing the multi-dimensional response of a submarine pipeline under earthquake dynamic excitation according to claim 1, characterized in that: The constraint conditions set for the submarine pipeline model in step S2 are as follows: displacement constraints in the three directions of X, Y, and Z are imposed on the nodes at both ends of the pipeline, and the remaining nodes remain free. When applying seismic displacement, a single-point displacement constraint command is used to apply the seismic displacement to the nodes at both ends of the pipeline to simulate the impact of the earthquake on the junction between the two ends of the pipeline and the soil.

5. The method for correlation optimization of multi-dimensional responses of submarine pipelines under earthquake dynamic excitation according to claim 1, characterized in that: In step S2, the modal frequency of the submarine pipeline model is calculated according to formula (1): （1）； in: represents the eigenvalue of the modal frequency, represents the model stiffness matrix, represents the modal frequency, Represents the model quality matrix.

6. The method for correlation optimization of multi-dimensional responses of submarine pipelines under earthquake dynamic excitation according to claim 5, characterized in that: In step S2, the Mises stress data and displacement deformation data at each location of the submarine pipeline model are calculated according to formula (2): in: express The displacement of time, express The speed of time, express The acceleration of time, represents the damping matrix, represents transient excitation, represents the initial displacement, represents the initial velocity, express The node force at the moment, express The Mises stress at the time node, Represents the unit area.

7. The method for correlation optimization of multi-dimensional responses of submarine pipelines under earthquake dynamic excitation according to claim 6 is characterized in that: In step S3, the correlation between the maximum Mises stress of the pipeline, the displacement difference between the end and the middle of the pipeline, and the pipeline quality and the cross-sectional size is calculated according to formula (3): （3）； in: Indicates The correlation between the optimization criteria and the current cross-sectional dimensions, Indicates the current cross-section size corresponding to the The calculated value of the optimization criterion, Indicates The ideal target value of the optimization criterion is Indicates The maximum value of the optimization criteria, Indicates The minimum value of the optimization criteria.

8. The method for correlation optimization of multi-dimensional responses of submarine pipelines under earthquake dynamic excitation according to claim 7 is characterized in that: In step S4, the weights of the three optimization criteria of the maximum Mises stress of the pipeline, the displacement difference between the end and the middle of the pipeline, and the pipeline quality are calculated respectively according to the following method: S41: Calculate the differences between the correlations of the three optimization criteria of pipeline maximum Mises stress, displacement difference between the end and middle of the pipeline, and pipeline quality and the cross-sectional dimensions respectively, and compare the differences with the set scale value to obtain the importance degree and importance scale between the two optimization criteria; S42: Construct a judgment matrix based on the importance scale between the pairwise optimization criteria: S43: Normalize each column element in the judgment matrix to obtain a normalized judgment matrix, and add the normalized judgment matrix row by row to obtain the first The weights of the optimization criteria are: S44: Then The weights of the optimization criteria are normalized to obtain the normalized The weight of the optimization criterion.

9. The method for correlation optimization of multi-dimensional responses of submarine pipelines under earthquake dynamic excitation according to claim 8, characterized in that: The optimization function established in step S5 is formula (4): （4）； in: represents the total objective function value, represents the weight of the normalized maximum Mises stress optimization criterion for the pipeline, represents the weight of the optimization criterion for the displacement difference between the end and the middle of the pipeline after normalization, represents the weight of the normalized pipeline quality optimization criterion, represents the maximum Mises stress of the pipeline after optimization, represents the maximum Mises stress of the pipeline before optimization, It indicates the maximum displacement difference between the end and the middle of the pipe after optimization. It indicates the maximum displacement difference between the end and the middle of the pipeline before optimization. represents the quality of the pipeline after optimization, Indicates the pipeline quality before optimization.

10. The method for correlation optimization of multi-dimensional responses of submarine pipelines under earthquake dynamic excitation according to claim 9, characterized in that: In step S5, based on the optimization function, the response surface is designed as a quadratic polynomial model as shown in formula (5). The global response surface method is used to iteratively optimize the submarine pipeline model and obtain the optimized inner and outer diameter parameters of the pipeline: （5）； in: represents the parameter design target value, represents the basic target value when all design variables are zero, Indicates The linear effect of the design variables on the target, Indicates design variables, Indicates The square coefficients of the design variables, Indicates Design variables and The interaction effect coefficients between the design variables are Indicates design variables, Represents the total number of design variables.

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