A method for correlating and optimizing multi-dimensional response of submarine pipeline under seismic dynamic excitation

Abstract

The present application relates to the technical field of electric digital data processing, and especially relates to a kind of seabed pipeline multidimensional response correlation optimization method under seismic dynamic excitation, comprising the following steps: establishing seabed pipeline model;Seabed pipeline model is set constraint condition and is applied seismic displacement, the modal frequency of seabed pipeline model, mises stress data and displacement deformation data are calculated;Output pipeline initial mass, calculate pipeline maximum mises stress, pipeline end and central displacement difference, the correlation degree of three optimization criteria and cross section size;The weight of three optimization criteria is calculated;Establish optimization function, and seabed pipeline model is iteratively optimized, and the inner and outer diameter parameters of optimized pipeline are obtained.The method provided by the present application can more effectively improve the seismic performance of pipeline under seismic response, and takes into account pipeline strength, displacement control and quality optimization, improves the safety and reliability of pipeline.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of electric digital data processing, and in particular to a seabed pipeline multi-dimensional response correlation optimization method under seismic dynamic excitation. BACKGROUND

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

[0003] Seismic action is one of the main natural disasters faced by seabed pipelines. During an earthquake, seabed pipelines may encounter large-scale ground deformation, intense vibration impact, and other complex stress states, which can affect the structural stability and transportation safety of the pipelines. For seabed pipelines in deep sea areas, due to the complexity of their environment and the distance from the epicenter, the stress and deformation of the pipelines under seismic action may be more significant. Traditional pipeline design and optimization methods often fail to fully consider seismic response, so they cannot effectively address the safety of pipelines under seismic action.

[0004] Existing seabed pipeline optimization design usually focuses on a single objective, such as structural strength or economy, without fully considering the multi-dimensional influence in seismic response. This leads to difficulties in balancing safety, stability, and economy for pipelines under complex seismic conditions. Especially when facing complex geological conditions and uncertainty factors, traditional methods are difficult to provide a comprehensive optimization scheme. Existing multi-objective methods still have some unresolved shortcomings, such as the Pareto method, which provides a set of Pareto optimal solutions, but the multiple objectives interfere with each other, and the weights of each objective cannot be given to obtain an accurate optimal solution. In addition, most of the existing optimization methods that can handle the weight problem of each objective rely on expert scoring to determine the weight, with subjective factors dominating. Human scoring leads to uncertainty in the results. Therefore, there is an urgent need for a multi-dimensional response correlation optimization method that fully considers seismic response while balancing various engineering objectives to improve the safety and reliability of pipelines. SUMMARY

[0005] The technical problem to be solved by the present application is to provide a seabed pipeline multi-dimensional response correlation optimization method under seismic dynamic excitation. By processing uncertain or incomplete input information during optimization, the weights of different optimization criteria are analyzed, which can more effectively improve the seismic performance of the pipeline under seismic response, and also considers pipeline strength, displacement control, and quality optimization, improving the safety and reliability of the pipeline.

[0006] The application is implemented by the following technical solutions:

[0007] A method for correlating and optimizing multi-dimensional responses of a submarine pipeline under seismic dynamic excitation, comprising the following steps:

[0008] S1: establishing a submarine pipeline model in a finite element processor;

[0009] S2: setting constraint conditions for the submarine pipeline model, applying seismic displacement, creating an analysis step, calculating modal frequencies of the submarine pipeline model, and calculating Mises stress data and displacement deformation data at each location of the submarine pipeline model on the premise that no resonance occurs between the modal frequencies and the seismic excitation frequencies;

[0010] S3: outputting the initial mass of the pipeline according to the Mises stress data and displacement deformation data at each location of the submarine pipeline model through the finite element processing software, and calculating the correlation between the three optimization criteria of the maximum Mises stress of the pipeline, the displacement difference between the end and middle parts of the pipeline, and the mass of the pipeline and the cross-sectional size respectively with the inner and outer diameters of the pipeline as design variables;

[0011] S4: calculating the weights of the three optimization criteria of the maximum Mises stress of the pipeline, the displacement difference between the end and middle parts of the pipeline, and the mass of the pipeline based on the correlation between the cross-sectional size and the three optimization criteria according to the correlation between the three optimization criteria of the maximum Mises stress of the pipeline, the displacement difference between the end and middle parts of the pipeline, and the mass of the pipeline and the cross-sectional size;

[0012] S5: establishing an optimization function according to the weights of the three optimization criteria of the maximum Mises stress of the pipeline, the displacement difference between the end and middle parts of the pipeline, and the mass of the pipeline, and iteratively optimizing the submarine pipeline model to obtain the inner and outer diameter parameters of the optimized pipeline.

[0013] In the optimization, the establishment of the submarine pipeline model in step S1 includes setting the pipeline length, the pipeline cross-sectional shape, the pipeline material parameters, the initial pipeline inner diameter size, and the initial pipeline outer diameter size, and performing grid division using beam elements.

[0014] In the optimization, the submarine pipeline model is set to have a pipeline length of 40 meters, a circular pipeline cross-sectional shape, a pipeline material of steel, an elastic modulus of 210 MPa in the pipeline material parameters, a Poisson's ratio of 0.3, a density of 7850 kg / m3, an initial pipeline inner diameter size of 0.31 meters, and an initial pipeline outer diameter size of 0.32 meters, and the variation ranges of the pipeline inner diameter size and the pipeline outer diameter size are both ±15%.

[0015] In the optimization, the constraint conditions set for the submarine pipeline model in step S2 are that the two end nodes of the pipeline are subjected to displacement constraints in X, Y, and Z directions, and the remaining nodes remain free, and when the seismic displacement is applied, a single-point displacement constraint command is used to apply the seismic displacement to the two end nodes of the pipeline to simulate the influence of the earthquake on the parts where the two ends of the pipeline are combined with the soil.

[0016] Furthermore, in step S2, the modal frequencies of the subsea pipeline model are calculated according to equation (1):

[0017] (1);

[0018] in: Eigenvalues ​​representing modal frequencies Represents the model stiffness matrix. Indicates modal frequency, This represents the model quality matrix.

[0019] Furthermore, in step S2, the Mises stress data and displacement deformation data at various points on the subsea pipeline model are calculated according to equation (2):

[0020]

[0021] in: express Displacement at any moment express The speed of time, express acceleration at any moment Represents the damping matrix. Indicates transient excitation, Indicates the initial displacement. Indicates the initial velocity. express The force at the moment, express Mises stress at time node Represents the area of ​​a unit.

[0022] Furthermore, in step S3, the correlation between the three optimization criteria—maximum Mises stress of the pipeline, displacement difference between the pipeline end and middle, and pipeline mass—and the cross-sectional dimensions is calculated according to equation (3):

[0023] (3);

[0024] in: Indicates the first The correlation between each optimization criterion and the current cross-sectional dimensions. Indicates the first dimension corresponding to the current cross-section. The calculated values ​​of each optimization criterion Indicates the first The ideal target value of an optimization criterion Indicates the first The maximum value of each optimization criterion. Indicates the first The minimum value of each optimization criterion.

[0025] Further, 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 mass of the pipeline are calculated respectively in step S4 by the following method:

[0026] S41: the difference between the correlation degree 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 mass of the pipeline and the cross-sectional size is calculated respectively, and the difference is compared with the set scale value, so as to obtain the importance degree between the two optimization criteria and the importance scale;

[0027] S42: a judgment matrix is constructed according to the importance scale between the two optimization criteria:

[0028] S43: each column element in the judgment matrix is normalized to obtain the normalized judgment matrix, and the sum of the rows of the normalized judgment matrix is obtained to obtain the weight of the first optimization criterion:

[0029] S44: the weight of the first optimization criterion is normalized to obtain the weight of the second optimization criterion after normalization.

[0030] Further, the optimization function established in step S5 is formula (4):

[0031] (4);

[0032] wherein: represents the total objective function value, represents the weight of the normalized pipeline maximum Mises stress optimization criterion, represents the weight of the normalized displacement difference between the end and the middle of the pipeline optimization criterion, represents the weight of the normalized pipeline mass optimization criterion, represents the optimized maximum Mises stress of the pipeline, represents the maximum Mises stress of the pipeline before optimization, represents the maximum displacement difference between the end and the middle of the optimized pipeline, represents the maximum displacement difference between the end and the middle of the pipeline before optimization, represents the optimized mass of the pipeline, represents the mass of the pipeline before optimization.

[0033] Further, based on the optimization function, the response surface is designed as a quadratic polynomial model shown in formula (5), 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:

[0034] (5);​​​

[0035] wherein: represents a parameter design target value, represents a basic target value when all design variables are zero, represents the linear influence of the design variable on the target, represents the design variable, represents the square term coefficient of the design variable, represents the interaction effect coefficient between the design variable and the design variable, represents the design variable, represents the total number of design variables.

[0036] Advantages of the application:

[0037] The application provides a seabed pipeline multi-dimensional response correlation optimization method under seismic dynamic excitation, which has the following advantages:

[0038] 1. The multi-dimensional response correlation optimization can scientifically and reasonably process complex multi-objective optimization problems, and ensure that the optimal pipeline cross-section design scheme is obtained under the consideration of multiple optimization objectives, such as stress, displacement, mass, etc. 2. By introducing the multi-objective correlation degree calculation theory, the importance degree of each objective is obtained, solving the problem that the calculation of the weight of each objective in the subsequent optimization process is greatly affected by human subjective influence, and providing a new method for comparing the importance degree.

[0039] 3. By comprehensively considering the stress, displacement and mass parameters of the pipeline through the multi-dimensional response ranking criterion, the weight of each optimization objective is calculated, the multiple influence factors under the seismic response are effectively converted into optimization objectives, the problem of mutual interference of multiple objectives is solved, and the deterministic optimal solution under comprehensive evaluation is obtained.

[0040] 4. Through the global response surface method iterative optimization process, the key factors affecting the performance of the pipeline can be accurately identified, more targeted design parameters are provided, and important reference basis is provided for the seismic design and optimization of the seabed pipeline. BRIEF DESCRIPTION OF DRAWINGS

[0041] Figure 1 is the flowchart of the application.

[0042] Figure 2 is the schematic diagram of the optimized model cross-section of the application.

[0043] Figure 3 is the optimization iteration process curve diagram of the application.

[0044] Figure 4 is a schematic diagram of an optimized model cross section of the present application.

[0045] Figure 5 is a schematic diagram of an optimized model cross section of the present application. DETAILED DESCRIPTION

[0046] A method for correlating optimization of multi-dimensional response of a submarine pipeline under seismic dynamic excitation, a flowchart of which is shown in Figure 1 and specifically comprises the following steps:

[0047] S1: establishing a submarine pipeline model in a finite element processor;

[0048] Specifically, the established submarine pipeline model includes setting the pipeline length, the pipeline cross-sectional shape, the pipeline material parameters, the initial pipeline inner diameter size and the initial pipeline outer diameter size, and using beam elements for meshing.

[0049] Optimally, the submarine pipeline model is set to have a pipeline length of 40 meters, a pipeline cross-sectional shape of a circle, a pipeline material of steel, a pipeline material parameter of an elastic modulus of 210 MPa, a Poisson's ratio of 0.3, a density of 7850 kg / m3, an initial pipeline inner diameter size of 0.31 meters, an initial pipeline outer diameter size of 0.32 meters, and a variation range of the pipeline inner diameter size and the pipeline outer diameter size of ±15%.

[0050] The length of the submarine pipeline model is set to 40 meters, which conforms to the common submarine pipeline length in actual engineering; the initial size is set in accordance with relevant engineering standards, taking into account the strength and weight requirements of the pipeline.

[0051] Beam elements are used for meshing in the pipeline model, which are suitable for simulating slender structures, especially structures like submarine pipelines, and can effectively capture the mechanical response of the pipeline under various external forces (such as seismic action). Specifically, the pipeline can be divided along the length direction with a step size of 0.08 meters, totaling 500 elements.

[0052] The selection of pipeline material parameters can ensure that the submarine pipeline model can accurately simulate the mechanical behavior of steel during calculation. Material property assignment is performed through the material management module of the finite element processor, ensuring that each beam element of the pipeline has consistent mechanical properties.

[0053] S2: setting constraint conditions for the submarine pipeline model and applying seismic displacement and creating an analysis step, calculating the modal frequency of the submarine pipeline model, and calculating the Mises stress data and displacement deformation data at each place of the submarine pipeline model under the premise that the modal frequency does not resonate with the seismic excitation frequency;

[0054] Specifically, the constraint conditions set for the submarine pipeline model are that the two end nodes of the pipeline are subjected to displacement constraints in X, Y and Z directions, and the remaining nodes are kept free. When the seismic displacement is applied, the single-point displacement constraint command is used to apply the seismic displacement to the two end nodes of the pipeline to simulate the influence of the earthquake on the parts of the two ends of the pipeline combined with the soil.

[0055] The constraint simulates the case where the two ends of the pipeline are fixed, i.e., the pipeline cannot translate and rotate at its two ends, thereby limiting the degrees of freedom and ensuring that the model can truly reflect the stress state under the action of the earthquake.

[0056] Specifically, the modal frequency of the submarine pipeline model can be calculated according to formula (1):

[0057] (1);

[0058] wherein: ω represents the eigenvalue of the modal frequency, K represents the stiffness matrix of the model, ω represents the modal frequency, M represents the mass matrix of the model.

[0059] After the modal frequency of the submarine pipeline model is calculated, the difference between the modal frequency and the seismic excitation frequency is calculated, so that the absolute value of the difference between the modal frequency and the seismic excitation frequency is greater than a set value, to ensure that the modal frequency and the seismic excitation frequency do not resonate. The set value can be preferably selected as 8% .

[0060] 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, the damping can be increased, and the support mode can be changed to avoid the coincidence of the natural frequency and the seismic excitation frequency, reduce the resonance response, and thus ensure the safety of the pipeline under the seismic working condition.

[0061] To simulate the displacement response of the pipeline under the action of the earthquake, the single-point displacement constraint SPCD command can be used to apply the displacement field caused by the seismic wave in the model. According to the actual seismic working condition, the main action direction is determined to be the Y-axis direction, and the corresponding displacement condition is applied. Specifically, the SPCD constraint applies the seismic displacement to the two end nodes of the pipeline to simulate the influence of the earthquake on the parts of the two ends of the pipeline combined with the soil, to ensure that the model can truly simulate the nonlinear deformation generated under the action of the earthquake.

[0062] Specifically, seismic displacement loads can be applied to the pipeline model using the TLOAD load command. TLOAD is used to define the dynamic load or displacement application process within the time domain. Specifically, when setting up TLOAD, it is necessary to define the law of seismic displacement change over time and input the load curve based on actual seismic conditions. To accurately describe the change of seismic displacement over time, a curve can be created in the model, and this curve can be used to precisely define the seismic load, describing the displacement of the pipeline caused by the earthquake at different time points.

[0063] After applying seismic displacement and load, an analysis step can be created to perform seismic response calculations. It is preferable to set the calculation time step in the analysis step to 0.01 seconds and the total time to 25 seconds to ensure that the application of seismic displacement is synchronized with the model response.

[0064] Specifically, the Mises stress and displacement deformation data at various points on the subsea pipeline model can be calculated according to equation (2):

[0065]

[0066] in: express Displacement at any moment express The speed of time, express acceleration at any moment Represents the damping matrix. Indicates transient excitation, Indicates the initial displacement. Indicates the initial velocity. express The force at a given moment express Mises stress at time node Represents the area of ​​a unit.

[0067] S3: Based on the Mises stress data and displacement deformation data at various points in the subsea pipeline model, the initial mass of the pipeline is output through finite element processing software. The correlation between the maximum Mises stress of the pipeline, the displacement difference between the pipeline end and the middle, and the pipeline mass, three optimization criteria and the cross-sectional dimensions are calculated using the inner and outer diameters of the pipeline as design variables.

[0068] Mises stress is a measure of the strength of pipelines under complex stress states. Under seismic loading, different parts of the pipeline are subjected to stresses in different directions. Finite element analysis (FEM) is used to obtain the Mises stress distribution of each element, with particular attention paid to the maximum stress value of the pipeline. The Mises stress results can be visualized using the finite element analysis software Hyperview, clearly identifying stress concentration areas and ensuring that critical components of the pipeline meet strength requirements.

[0069] The earthquake action can cause the overall displacement and local deformation of the pipeline, and through calculation, the displacement change of each node of the pipeline under the earthquake load can be obtained. The displacement difference between the middle and end of the pipeline is focused on, because the displacement difference reflects the bending deformation of the pipeline during the earthquake process, and excessive displacement difference can cause local instability or damage of the pipeline.

[0070] The mass of the pipeline is an important index in structure optimization, and the mass of the pipeline itself has a certain degree of influence on the stress and displacement of the pipeline under dynamic load. By rationalizing the mass of the pipeline, on the one hand, the displacement fluctuation of the pipeline under the earthquake amplitude due to the mass itself can be reduced, and on the other hand, the construction cost and energy consumption can be reduced. Therefore, in the calculation process, the mass of the entire pipeline can be directly output by the finite element software, and it is taken as one of the optimization objectives.

[0071] The present application adopts the inner diameter and outer diameter of the pipeline section as the optimization design variables. By adjusting the section size, the mechanical properties and mass 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 the actual engineering requirements and standard specifications to ensure that the design variables change within a feasible range, thereby avoiding excessive optimization or unfeasible design. The initial value of the outer diameter is 0.32 meters, and the inner diameter is 0.31 meters. In the optimization process, the outer diameter and the inner diameter can be allowed to change within ±15% respectively. Through this adjustment, the best balance between stress, displacement and mass is sought to realize the multi-objective optimization of the pipeline section.

[0072] The maximum Mises stress is a key index to measure whether the pipeline can maintain structural integrity under the action of the earthquake. In order to ensure that the pipeline does not yield or fail under the action of the earthquake load, the constraint condition of the maximum Mises stress is set. According to the yield strength of the pipeline material, the present application limits the maximum stress value to be less than 235 MPa, ensuring that the pipeline still has sufficient safety margin under extreme working conditions.

[0073] A larger displacement difference between the end and the middle of the pipeline can cause excessive bending or local damage of the pipeline, so the displacement difference is taken as a constraint condition. The displacement difference between the middle and the end of the pipeline is calculated, and it is limited to be less than the displacement difference before optimization, to ensure that the deformation of the pipeline is within a controllable range.

[0074] Specifically, the correlation between 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 mass of the pipeline and the section size can be calculated according to formula (3) respectively:

[0075] (3);

[0076] Wherein: represents the correlation between the i-th optimization criterion and the section size. a correlation degree of the current cross-sectional size, a calculated value of the first optimization criterion corresponding to the current cross-sectional size, a calculated value of the first optimization criterion corresponding to the current cross-sectional size, an ideal target value of the first optimization criterion, an ideal target value of the first optimization criterion, a maximum value of the first optimization criterion, a maximum value of the first optimization criterion, a minimum value of the first optimization criterion.

[0077] The correlation degree has a value range of 0 to 1, and the average value is calculated by taking multiple groups of data. The greater the value, the higher the correlation degree of the optimization criterion and the calculation result, and the greater the influence on the dynamic response result of the pipeline under the example working condition.

[0078] The specific correlation degree values are shown in Table 1:

[0079] Table 1

[0080]

[0081] S4: According to the correlation degrees 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 mass of the pipeline and the cross-sectional size, 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 mass of the pipeline are calculated based on the multi-dimensional response ranking criterion.

[0082] Specifically, 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 mass of the pipeline can be calculated according to the following method:

[0083] S41: The differences between the correlation degrees 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 mass of the pipeline and the cross-sectional size are calculated respectively, and the differences are compared with the set scale value, so as to obtain the importance degrees and importance scales between the two optimization criteria.

[0084] S42: According to the importance scales between the two optimization criteria, a judgment matrix is constructed:

[0085] The weight values of the three criteria in multi-objective optimization are calculated, each two criteria are compared one by one, and the relative importance of each target is quantified according to Table 2. The three optimization criteria are set as displacement difference, stress and mass, and the judgment matrix is as follows. According to Table 2, we have:

[0086]

[0087] Wherein: represents the judgment matrix, ​importance of displacement difference value relative to stress; importance of displacement difference value relative to mass; importance of stress relative to mass.

[0088] According to the comparison of the correlation degree difference, the importance of displacement difference value relative to stress is set to 3, indicating that displacement difference value is more important than stress; the importance of stress relative to mass is 5, indicating that stress is obviously more important than mass; and the importance of stress relative to mass is 2, indicating that stress is slightly more important than mass. Therefore, the matrix A is:

[0089] ;

[0090] Table 2

[0091]

[0092] S43: Normalize each column element in the judgment matrix to obtain a normalized judgment matrix, and add the normalized judgment matrix by row to obtain the weight of the first optimization criterion:

[0093] Specifically, the normalized judgment matrix is processed according to the following formula:

[0094]

[0095] wherein: represents the weight of the first optimization criterion before normalization, represents the element in the first row and the first column of the judgment matrix, represents the element in the first row and the first column of the normalized judgment matrix, represents the weight vector, represents the weight of the stress optimization criterion before normalization, represents the weight of the displacement difference value optimization criterion before normalization, represents the weight of the mass optimization criterion before normalization, represents the matrix transpose.

[0096] Specifically, the final calculated .

[0097] S44: The weight of the first optimization criterion is normalized to obtain the weight of the first optimization criterion after normalization.

[0098] Further, the optimization function established in step S5 is formula (4):

[0099] (4);

[0100] Wherein: represents the total objective function value, represents the weight of the normalized maximum Mises stress optimization criterion of the pipeline, represents the weight of the normalized displacement difference optimization criterion between the end and the middle of the pipeline, represents the weight of the normalized pipeline quality optimization criterion, represents the maximum Mises stress of the optimized pipeline, represents the maximum Mises stress of the pipeline before optimization, represents the maximum displacement difference between the end and the middle of the optimized pipeline, represents the maximum displacement difference between the end and the middle of the pipeline before optimization, represents the quality of the optimized pipeline, represents the quality of the pipeline before optimization.

[0101] Through the above optimization process, the importance of each target in the optimization process can be reasonably considered.

[0102] S5: An optimization function is established according to 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 quality of the pipeline, and the submarine pipeline model is iteratively optimized to obtain the inner and outer diameter parameters of the optimized pipeline.

[0103] The model can be iteratively optimized by the global response surface method. In the implementation process of the present application, optimization iteration is the core of the entire multi-objective optimization. By establishing a reasonable optimization model, setting weight coefficients and constraint conditions, and using optimization algorithms for iterative solution, the optimized cross-sectional parameters of the pipeline are finally obtained.

[0104] The response surface refers to the function relationship that is accurately approximated in a local range through experiments and expressed by a simple algebraic expression.

[0105] Specifically, the response surface can be designed as a quadratic polynomial model 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 inner and outer diameter parameters of the optimized pipeline.

[0106] (5);

[0107] Wherein: represents the parameter design target value, represents the basic target value when all design variables are zero, represents the first linear influence of the design variable on the target, represents the design variable, represents the square term coefficient of the design variable, represents the interaction effect coefficient between the design variable and the design variable, represents the total number of design variables.

[0108] After multiple rounds of iteration, the optimized pipe section parameters are: outer diameter R is 0.352 meters, and inner diameter r is 0.343 meters. This result reduces the mass of the pipe and improves the stability of the pipe under seismic dynamic excitation, improves the utilization rate of pipe material, and the optimization achieves the expected effect.

[0109] The schematic diagram of the optimized model section is shown in Figure 2 , the optimization iteration process curve diagram is shown in Figure 3 , the midpoint and endpoint displacement curve diagrams before and after optimization are shown in Figure 4 , and the pipe middle stress curve diagrams before and after optimization are shown in Figure 4 , Figure 5 The upper curve is the curve before optimization, and the lower curve is the curve after optimization.

[0110] According to Figure 3 , Figure 4 , Figure 5, after calculation, the optimized pipeline response result has the following characteristics: the pipeline quality is reduced by about 1%; the peak value of the displacement difference between the end and the middle of the pipeline is reduced by 96%; the maximum Mises stress is increased by 20% compared with before optimization, which is lower than the safety value 235MPa, and reaches 55% of the yield stress, compared with the maximum stress of about 46% of the yield stress before optimization, under the premise of ensuring that the pipeline will not occur plastic deformation or failure under the action of earthquake load, the utilization rate of pipeline material is improved. 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%, which shows that the deformation of the optimized pipeline under the action of earthquake displacement is more uniform, and the stability of the overall structure is obviously improved. By analyzing the node displacement curve of the pipeline under the action of earthquake, the coincidence degree of the displacement peak value curve 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 working conditions, help to improve the service life of the pipeline in extreme environment, and the pipeline quality is slightly reduced, the maximum Mises stress after optimization is controlled within the allowable range of material, compared with before optimization, the economic consumption is reduced, and the engineering economy is improved.

[0111] In summary, the present application provides a kind of seabed pipeline multi-dimensional response correlation optimization method under seismic dynamic excitation, good balance is reached between stress, displacement and quality, the expected effect of multi-objective optimization is realized, and the optimization scheme successfully realizes the balance and performance improvement of multi-objective.The optimization method of the present application has good universality and practicality, and can be widely applied to the optimization design of other similar structures, and provides an efficient multi-objective optimization solution.

[0112] The above only describes the preferred embodiments of the present application and is not intended to limit the present application. For those skilled in the art, the present application can have various modifications and changes. Any modification, equivalent replacement, improvement, etc. within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A method for correlating optimization of multi-dimensional response of a submarine pipeline under seismic dynamic excitation, characterized in that: Comprising the following steps: S1: establishing a submarine pipeline model in a finite element processor; S2: setting constraint conditions for the submarine pipeline model and applying seismic displacement and creating an analysis step, calculating the modal frequency of the submarine pipeline model, and calculating the Mises stress data and displacement deformation data of the submarine pipeline model under the premise that the modal frequency does not resonate with the seismic excitation frequency; S3: according to the Mises stress data and displacement deformation data of the submarine pipeline model, outputting the initial mass of the pipeline through the finite element processing software, and calculating the correlation between 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 mass of the pipeline and the cross-sectional size respectively with the inner and outer diameters of the pipeline as design variables; S4: according to the correlation between 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 mass of the pipeline and the cross-sectional size, calculating 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 mass of the pipeline respectively based on the multi-dimensional response ranking criteria; S5: according to 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 mass of the pipeline, establishing an optimization function as formula (4), and based on the optimization function, designing the response surface into a quadratic polynomial model shown in formula (5), and using the global response surface method to iteratively optimize the submarine pipeline model to obtain the optimized inner and outer diameter parameters of the pipeline: （4）； wherein: represents the total objective function value, represents the weight of the normalized maximum Mises stress optimization criterion of the pipe, represents the weight of the normalized displacement difference between the end and middle of the pipe optimization criterion, represents the weight of the normalized mass of the pipe optimization criterion, represents the maximum Mises stress of the optimized pipe, represents the maximum Mises stress of the unoptimized pipe, represents the maximum displacement difference between the end and middle of the optimized pipe, represents the maximum displacement difference between the end and middle of the unoptimized pipe, represents the mass of the optimized pipe, represents the mass of the unoptimized pipe; （5）； wherein: represents a parameter design target value, represents a base target value when all design variables are zero, represents a linear effect of the design variable on the target, represents the design variable, represents a squared term coefficient of the design variable, represents an interaction effect coefficient between the design variable and the design variable, represents the design variable, represents the total number of design variables.

2. The method of claim 1, wherein: The establishment of 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 elements for meshing.

3. The method of claim 2, wherein: The pipeline length set in the submarine pipeline model is 40 meters, the pipeline cross-sectional shape is circular, the pipeline material is steel, the elastic modulus in 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 size is 0.31 meters, the initial pipeline outer diameter size is 0.32 meters, and the variation range of the pipeline inner diameter size and the pipeline outer diameter size is ±15%.

4. The method of claim 1, wherein: The constraint conditions set for the submarine pipeline model in step S2 are: the nodes at both ends of the pipeline are subjected to displacement constraints in X, Y, and Z directions, and the remaining nodes are free. When applying seismic displacement, single-point displacement constraint command is used to apply seismic displacement to the nodes at both ends of the pipeline to simulate the influence of the soil on the pipeline at both ends.

5. The method of claim 1, wherein: The modal frequency of the submarine pipeline model is calculated according to formula (1) in step S2: （1）； wherein: characteristic value representing a modal frequency, model stiffness matrix, modal frequency, model mass matrix.

6. The method of claim 5, wherein: The Mises stress data and displacement deformation data of the submarine pipeline model are calculated according to formula (2) in step S2: wherein: represents the displacement at time t, represents the velocity at time t, represents the acceleration at time t, represents the damping matrix, represents the transient excitation, represents the initial displacement, represents the initial velocity, represents the nodal force at time t, represents the Mises stress at the node at time t, represents the element area.

7. The method of claim 6, wherein: The correlation between 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 mass of the pipeline and the cross-sectional size is calculated according to formula (3) in step S3: （3）； in: Indicates the first The correlation between each optimization criterion and the current cross-sectional dimensions. Indicates the first dimension corresponding to the current cross-section. The calculated values ​​of each optimization criterion Indicates the first The ideal target value of an optimization criterion Indicates the first The maximum value of each optimization criterion. Indicates the first The minimum value of each optimization criterion.

8. The method of claim 7, wherein: 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 mass of the pipeline are calculated according to the following method in step S4: S41: respectively calculate the difference between the correlation degree of the pipeline maximum Mises stress, the displacement difference between the end and the middle of the pipeline, the pipeline quality and the cross-sectional size, and compare the difference with the set scale value, to obtain the importance degree between the two optimization criteria and the importance scale; S42: construct a judgment matrix according to the importance scale between the two optimization criteria: S43: normalizing each column element in the judgment matrix to obtain a normalized judgment matrix, and adding the normalized judgment matrix by row to obtain the weight of the first optimization criterion: S44: normalize the weight of the first optimization criterion to obtain the normalized weight of the first optimization criterion. the second optimization criterion.​

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