A pipeline route design method based on single-pipe mathematical model

Abstract

The present invention provides a pipeline route design method based on a single-pipe mathematical model, comprising the following steps: determining a three-dimensional longitudinal section and a UCS coordinate system based on a real-life three-dimensional model of the target pipeline installation area; establishing a single-pipe mathematical model based on the three-dimensional longitudinal section and the UCS coordinate system; performing micro-piping of the pipeline installation according to the single-pipe mathematical model; during the micro-piping process, calculating a directional similarity index based on the similarity between the pipeline shape and the trench shape; calculating a stress accumulation index based on the elastic modulus and moment of inertia; constructing a total cost calculation model based on the pipeline installation, and performing cost optimization based on the directional similarity index and the stress accumulation index to optimize the micro-piping of the pipeline installation. A technical effect of the present invention is that it significantly improves the accuracy and efficiency of pipeline installation design, reduces costs, and enhances system safety.

Description

Technical Field

[0001] The present invention belongs to the technical field of pipeline line design, and in particular relates to a pipeline line design method based on a single-pipe mathematical model. Background Art

[0002] As an important mode of transportation, pipeline line projects usually account for more than 90% of the total project investment. The scientific nature of its design, technological advancement and economic rationality are important indicators for evaluating project quality.

[0003] Currently, common dimensional software used for pipeline design includes AutoCAD and ArcGIS. These existing software can only provide construction drawings at the corner pile level, failing to refine them down to the weld level. Furthermore, at pipe bends, existing designs only provide parameters such as angle and radius, resulting in a lack of intuitive, three-dimensional feedback on design results throughout the design process. Furthermore, during on-site construction, construction companies cut materials and adjust trenches based on a limited number of design parameters, a process that requires multiple iterations. This is especially true for large-diameter pipelines, where piping cannot fit through them, leading construction companies to request additional elbows, bends, or design changes.

[0004] Therefore, existing pipeline design methods are unable to achieve weld-level precision, resulting in extensive manual alignment and bending operations on-site. This extensive manual work cannot guarantee the accuracy of trench excavation and pipeline laying, ultimately leading to widespread problems such as pipe-to-trench mismatch and stress concentration. Furthermore, during construction, the earthmoving and welding teams often had different understandings of the pipeline route design, resulting in overlapping and repetitive work, resulting in low overall efficiency. Summary of the Invention

[0005] The present invention aims to solve at least one of the technical problems existing in the prior art and provide a new technical solution for a pipeline line design method based on a single-pipe mathematical model.

[0006] According to one aspect of the present invention, a pipeline route design method based on a single-pipe mathematical model is provided, comprising the following steps:

[0007] Step S100, determining a 3D longitudinal section and a UCS coordinate system based on a real-scene 3D model of the target area for pipeline laying;

[0008] Step S200, establishing a single-tube mathematical model according to the three-dimensional longitudinal section and the UCS coordinate system;

[0009] Step S300, performing micro-piping of pipelines according to the single-pipe mathematical model;

[0010] Step S400, during the process of laying micro-piping in the pipeline, calculating a direction similarity index based on the similarity between the pipeline shape and the trench shape; and calculating a stress accumulation index based on the elastic modulus and the moment of inertia;

[0011] Step S500: constructing a total cost calculation model based on pipeline laying, and performing cost optimization based on the direction similarity index and the stress accumulation index to optimize pipeline laying micro-piping.

[0012] Optionally, the calculation formula of the total cost calculation model is as follows:

[0013] ;

[0014] In the above formula, TC is the total cost;

[0015] C m is the material cost per unit length of pipe;

[0016] C l is the construction cost per unit length of pipeline;

[0017] C b is the pipe bending cost per unit angle;

[0018] C s is the stress accumulation cost per unit length;

[0019] L is the total length of the pipeline;

[0020] n is the number of pipeline segments;

[0021] A di is the angle of the i-th pipe section on the xy plane;

[0022] A gi is the angle of the i-th trench on the xy plane;

[0023] B di is the angle of the i-th pipe section on the yz plane;

[0024] B gi is the angle of the i-th trench on the yz plane;

[0025] SAI is the stress accumulation index.

[0026] Optionally, performing cost optimization based on the direction similarity index and the stress accumulation index includes:

[0027] In the first stage, the direction similarity index is calculated using the stochastic gradient descent method and the pipeline laying plan is iteratively adjusted to determine whether the direction similarity index reaches a first preset value;

[0028] In the second stage, based on the direction similarity index reaching the first preset value, the stress accumulation index is optimized and the pipeline laying plan is iteratively adjusted to determine whether the stress accumulation index reaches the second preset value;

[0029] In the third stage, on the basis that the stress accumulation index reaches the second preset value, cost optimization is carried out to minimize the total cost of pipeline laying.

[0030] Optionally, if the optimization requirement of the stress accumulation index is not met under the first stage conditions, the constraint condition of the directional similarity index is relaxed, and the range of the optimal solution is expanded to ±2% of the minimum value.

[0031] Optionally, the optimization algorithm for the stress accumulation index includes a gradient descent algorithm and a simulated annealing algorithm.

[0032] Optionally, the calculation formula of the moment of inertia is as follows:

[0033] ;

[0034] In the above formula, I is the moment of inertia; D o is the outer diameter of the pipe; D i is the inside diameter of the pipe.

[0035] Optionally, the calculation formula of the direction similarity index DSI is as follows:

[0036] ;

[0037] In the above formula, n is the number of pipeline sections;

[0038] A di is the angle of the i-th pipe section on the xy plane;

[0039] A gi is the angle of the i-th trench on the xy plane;

[0040] B di is the angle of the i-th pipe section on the yz plane;

[0041] B gi is the angle of the i-th trench on the yz plane.

[0042] Optionally, the three-dimensional longitudinal section is composed of several two-dimensional longitudinal sections connected end to end.

[0043] Optionally, any point on the three-dimensional longitudinal section has the attributes of mileage, elevation, and three-dimensional spatial coordinates.

[0044] Optionally, the single tube mathematical model includes size data and posture data.

[0045] A technical effect of the present invention is:

[0046] In the embodiment of the present application, the pipeline route design method based on the single-pipe mathematical model is based on obtaining an accurate three-dimensional longitudinal section by cutting the real-life three-dimensional model; by applying the single-pipe mathematical model, the pipeline laying and piping design at the weld level is realized; the design scheme is optimized and evaluated using the optimization algorithm of the direction similarity index, stress accumulation index, and total pipeline laying cost, thereby achieving the purpose of improving the laying design accuracy and efficiency, reducing costs, and enhancing the safety of the system.

[0047] Compared with existing technologies, this pipeline route design method based on a single-pipe mathematical model improves the level of design detail from corner piles to weld joints; enhances the interactive form from two-dimensional to dynamic three-dimensional, providing engineers with dynamic feedback of "what you think is what you see, what you get"; and upgrades the evaluation method from intuitive qualitative evaluation to multi-index quantitative evaluation. This method can achieve a qualitative improvement for the pipeline design industry. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 This is a flow chart of a pipeline route design method based on a single-pipe mathematical model according to an embodiment of the present invention;

[0049] Figure 2 Schematic diagram of a micro-piping process of a pipeline route design method based on a single-pipe mathematical model according to an embodiment of the present invention. DETAILED DESCRIPTION

[0050] Various exemplary embodiments of the present application will now be described in detail with reference to the accompanying drawings. It should be noted that unless otherwise specifically stated, the relative arrangements of components and steps, numerical expressions and numerical values ​​set forth in these embodiments do not limit the scope of the present application.

[0051] The embodiments of the present application will be described in detail below. Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present application and are not to be construed as limiting the present application. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0052] The terms "first" and "second" in the specification and claims of this application may explicitly or implicitly refer to one or more of the features. Throughout the description of this application, unless otherwise specified, "plurality" means two or more. Furthermore, "and / or" in the specification and claims refers to at least one of the connected entities, and the character " / " generally indicates an "or" relationship between the connected entities.

[0053] According to one aspect of the present invention, see Figures 1 to 2 , provides a pipeline route design method based on a single-pipe mathematical model, including the following steps:

[0054] Step S100: determining a three-dimensional longitudinal section and a UCS coordinate system based on a real-scene three-dimensional model of a target area for pipeline laying.

[0055] Step S200: establishing a single-tube mathematical model according to the three-dimensional longitudinal section and the UCS coordinate system.

[0056] Step S300: performing micro-piping of pipelines according to the single-pipe mathematical model.

[0057] Step S400 , during the process of laying micro-piping in the pipeline, calculating a direction similarity index according to the similarity between the pipeline shape and the trench shape; and calculating a stress accumulation index according to the elastic modulus and the moment of inertia.

[0058] It should be noted that during micro-piping, it is crucial to prioritize the directional differences between the pipe and trench at each section. Therefore, a "Direction Similarity Index" (DSI) is defined. The DSI is used to evaluate the similarity between the pipe and trench shapes. The smaller the DSI value, the more closely the pipe conforms to the trench shape. Controlling the DSI helps reduce construction difficulty and material waste, while also improving the stability and safety of the piping system.

[0059] Step S500: constructing a total cost calculation model based on pipeline laying, and performing cost optimization based on the direction similarity index and the stress accumulation index to optimize pipeline laying micro-piping.

[0060] In the embodiment of the present application, the pipeline route design method based on the single-pipe mathematical model is based on obtaining an accurate three-dimensional longitudinal section by cutting the real-life three-dimensional model; by applying the single-pipe mathematical model, the pipeline laying and piping design at the weld level is realized; the design scheme is optimized and evaluated using the optimization algorithm of the direction similarity index, stress accumulation index, and total pipeline laying cost, thereby achieving the purpose of improving the laying design accuracy and efficiency, reducing costs, and enhancing the safety of the system.

[0061] Compared with existing technologies, this pipeline route design method based on a single-pipe mathematical model improves the level of design detail from corner piles to weld joints; enhances the interactive form from two-dimensional to dynamic three-dimensional, providing engineers with dynamic feedback of "what you think is what you see, what you get"; and upgrades the evaluation method from intuitive qualitative evaluation to multi-index quantitative evaluation. This method can achieve a qualitative improvement for the pipeline design industry.

[0062] It should be noted that the Stress Accumulation Index (SAI) measures the accumulation of pipeline stress. It is used to assess the potential stress concentration and cumulative effects of repeated loading on pipelines. The SAI helps prevent pipeline fatigue failure. By optimizing pipeline design using the SAI, it allows for the rational planning of construction piping layouts to reduce stress accumulation caused by terrain variations.

[0063] Elastic modulus and moment of inertia are two important physical parameters related to the properties and shape of materials.

[0064] Elastic modulus (E) is a material property that describes how much a material deforms when subjected to stress. A higher elastic modulus indicates a lower deformation for the same stress. For steel, the elastic modulus is typically around 200 GPa (gigaPascals). This value is typically determined experimentally and can be considered a constant for the same material.

[0065] Optionally, the calculation formula of the total cost calculation model is as follows:

[0066] ;

[0067] In the above formula, TC is the total cost;

[0068] C m is the material cost per unit length of pipe;

[0069] C l is the construction cost per unit length of pipeline;

[0070] C b is the pipe bending cost per unit angle;

[0071] C s is the stress accumulation cost per unit length;

[0072] L is the total length of the pipeline;

[0073] n is the number of pipeline segments;

[0074] Adi is the angle of the i-th pipe section on the xy plane;

[0075] A gi is the angle of the i-th trench on the xy plane;

[0076] B di is the angle of the i-th pipe section on the yz plane;

[0077] B gi is the angle of the i-th trench on the yz plane;

[0078] SAI is the stress accumulation index.

[0079] Optionally, performing cost optimization based on the direction similarity index and the stress accumulation index includes:

[0080] In the first stage, the stochastic gradient descent method is used to calculate the directional similarity index and iteratively adjust the pipeline laying plan to achieve the best match between the pipeline and the trench shape. It is then determined whether the directional similarity index reaches a first preset value;

[0081] In the second stage, based on the directional similarity index reaching the first preset value, the stress accumulation index is optimized and the pipeline laying plan is iteratively adjusted to determine whether the stress accumulation index has reached the second preset value; that is, on the basis of ensuring that the directional similarity index meets the predetermined standard, the stress accumulation index (SAI) is further optimized to reduce the stress concentration and cumulative effects of the pipeline in long-term operation.

[0082] In the third phase, once the stress accumulation index reaches the second preset value, cost optimization is performed to minimize the total cost of pipeline installation. This optimization is performed while maintaining both shape similarity and the stress accumulation index. If the cost target is not achieved, the stress accumulation index conditions of the second phase are gradually adjusted, and the optimization process continues iteratively.

[0083] In the above embodiment, the optimization process of micro-piping is a phased strategy aimed at achieving a high degree of similarity between the pipe shape and the trench shape, minimizing stress accumulation, and ultimately reducing the total cost of pipeline laying.

[0084] It should be noted that the optimization strategy follows the principles of stepwise optimization and iterative adjustment. At each stage, if the current solution fails to meet all conditions, the conditions are relaxed and the process is repeated until the optimal solution that meets all technical requirements is found. Furthermore, multiple optimization algorithms, including but not limited to gradient descent and simulated annealing, are employed to increase the likelihood of finding a globally optimal solution. Through stepwise optimization and iterative adjustment, a pipeline routing solution is achieved that maximizes cost-effectiveness while ensuring pipeline installation safety and reliability.

[0085] Alternatively, if the stress accumulation index optimization requirements are not met under the first-stage conditions, the constraints on the directional similarity index are relaxed, and the range of the optimal solution is expanded to ±2% of the minimum value. This allows the stress accumulation index to have a certain range of deviations, and the solution can be re-iterated, which helps to obtain the optimal solution.

[0086] Optionally, the optimization algorithm for the stress accumulation index includes a gradient descent algorithm and a simulated annealing algorithm, which helps to increase the possibility of finding a global optimal solution.

[0087] Optionally, the calculation formula of the moment of inertia is as follows:

[0088] ;

[0089] In the above formula, I is the moment of inertia; D o is the outer diameter of the pipe; D i is the inside diameter of the pipe.

[0090] In the above embodiment, the moment of inertia (I) is a parameter related to the shape of an object, which describes the rotation of the object when subjected to torque and helps to accurately calculate the stress accumulation index.

[0091] Optionally, the calculation formula of the direction similarity index DSI is as follows:

[0092] ;

[0093] A di is the angle of the i-th pipe section on the xy plane;

[0094] A gi is the angle of the i-th trench on the xy plane;

[0095] B di is the angle of the i-th pipe section on the yz plane;

[0096] B gi is the angle of the i-th trench on the yz plane.

[0097] In the above embodiment, for each section of pipeline, first, the difference between its axial direction vector and the corresponding trench axial direction vector is calculated; then, the above difference is squared to eliminate the sign effect that may be brought about by the direction difference and emphasize the impact of large deviations; then, the square differences of all pipeline sections are accumulated to obtain the total sum of square differences; finally, the sum of square differences is added by 1 to ensure that the denominator is not zero, and then the reciprocal of this value is taken, thereby achieving normalization of the sum of square differences, so that the DSI value range is between 0 and 1.

[0098] In this embodiment, the DSI value ranges from 0 to 1. The closer the DSI is to 1, the more similar the pipeline's orientation is to the trench's, the closer the pipeline is to the ground, the less stress accumulation there is, and the safer the installation is. Conversely, the closer the DSI is to 0, the greater the difference between the pipeline's orientation and the trench's orientation, which may lead to stress accumulation and increase the difficulty of operation, maintenance, and disaster prevention.

[0099] Exemplarily, SAI is calculated using the following mathematical formula:

[0100] First, for the cold bent straight section (CBS):

[0101] .

[0102] For Cold Bend Section (CB):

[0103] .

[0104] For Hot Bend Straight Section (HBS):

[0105] .

[0106] For the Hot Bend Section (HB):

[0107] .

[0108] In the above formula:

[0109] n is the number of pipeline segments;

[0110] E i is the elastic modulus of the i-th section of the pipeline;

[0111] I i is the moment of inertia of the i-th pipe section;

[0112] A di is the angle of the i-th pipe section on the xy plane;

[0113] A gi is the angle of the i-th trench on the xy plane;

[0114] B di is the angle of the i-th pipe section on the yz plane;

[0115] B giis the angle of the i-th trench on the yz plane. Where WCBS, WCBF, WCBR, WHBS, WHBF, and WHBR represent the weights of the cold-bend straight pipe section, the minimum cold-bend angle, the cold-bend radius, the hot-bend straight pipe section, the minimum hot-bend angle, and the hot-bend radius, respectively.

[0116] The total stress accumulation index is obtained by weighted summation of the stress accumulation indices of these four parts:

[0117] ;

[0118] Optionally, the three-dimensional longitudinal section is formed by connecting a plurality of two-dimensional longitudinal sections end to end, which helps to realize the three-dimensional continuous visualization design of the pipeline.

[0119] Optionally, any point on the three-dimensional longitudinal section has the attributes of mileage, elevation, and three-dimensional spatial coordinates.

[0120] In the above implementation, each 2D longitudinal section constitutes a "file," and several linked files form a "segment." Within a file, the "UCS User Coordinate System" achieves the same application effects as the original 2D longitudinal section. Any point on a 3D longitudinal section possesses attributes such as mileage, elevation, and 3D spatial coordinates. The establishment of 3D longitudinal sections and the UCS User Coordinate System enables cross-file routing and piping design, achieving continuous 3D spatial visualization.

[0121] Optionally, the single-pipe mathematical model includes dimension data and position data, which helps the single-pipe mathematical model accurately perform micro-piping of pipelines. A single pipe is the smallest unit of micro-piping.

[0122] For example, the mathematical model of a single tube is shown in Table 1.

[0123] Table 1

[0124]

[0125] In the examples of this application, first, a 3D longitudinal section was developed, enabling better utilization of modern spatial data to provide robust spatial data support for subsequent micro-piping. Second, a single-pipe data model was designed, enabling weld-level design precision and achieving a WYSIWYG design environment. Furthermore, multi-objective evaluation metrics were employed to replace the traditional "do-it-yourself" approach. Therefore, the method presented here is intuitive, efficient, and scientific, representing a significant evolution of traditional methods.

[0126] In a specific implementation, a 3D longitudinal section and a UCS coordinate system are established. Since the 3D longitudinal section is the basis of micro-piping, it is cut and mapped based on the real-life model of modern measurement technology. The system also supports generation based on the import of ground GNSS measurement data. Each file in the 3D longitudinal section is named after its own serial number and establishes its own UCS coordinate system. Compared with the traditional 2D section, the coordinates of any point on the 3D longitudinal section are real coordinates, such as Figure 2 This is an example of a 3D longitudinal section with 4 levels and 4 USC coordinate systems.

[0127] In the micro-piping of pipeline laying, automatic piping and manual piping can be performed. Among them, automatic piping design can realize fully automatic piping design according to the input parameters and multi-objective evaluation parameters. Manual piping can be optimized and adjusted based on the results of automatic piping, or it can be piping from scratch. Manual piping supports mouse dragging design and parametric configuration down to a single pipe. It includes "vertical piping" and "plane piping". Among them, plane piping can be divided into "ordinary superimposed angle piping" with consistent front and back slopes and "special superimposed angle piping" with inconsistent front and back slopes. Furthermore, all manual piping starts with vertical piping, because in this environment, it is easier to determine the starting posture; during the piping process, the "Tab" key can be used to freely switch between "vertical piping" and "plane piping", and automatic bending can also be completed to achieve continuous piping within the entire section.

[0128] In addition, manual piping can also be done according to the direction of the piping, including forward (forward mileage) and reverse (reverse mileage).

[0129] It should be noted that automatic bending is a challenging part of the micro-piping process, as it achieves continuous design between adjacent steps. Automatic bending is performed in the "Planar Piping" state. Activate the automatic bending design process by pressing "P" on the keyboard. Enter the bending parameters on the parameter screen, and the program will automatically complete the bending operation, including the overlap angle.

[0130] In the automatic bending superposition angle form, the various parameters will be automatically filled in when the form is initialized. If the front and rear slopes are the same, the normal superposition angle bending is performed at this time. The user can modify the rear slope according to the actual situation. If the front and rear slopes are inconsistent, the special superposition angle bending is performed at this time. The program can automatically calculate the new superposition angle and update the allowed equal divisions, and the corresponding equal division angle will also be automatically adjusted. In terms of determining the equal division number, the program executes the logic that the equal division number "1" represents a single tube. The maximum equal division number does not exceed "6", that is, a maximum of 6 tubes are used for cold bending instead of hot bending. The option value in the equal division number is related to the equal division angle and the maximum angle of cold bending.

[0131] For example, in any piping mode, the user can press the "R" key to activate the "Single Pipe Parameter Edit" window, where they can edit four parameters: L1, R, Alpha, and L2. To adjust these parameters, manually adjust the alpha angle first. The program will automatically calculate the remaining pipe parameters, which can then be adjusted according to specifications. The program verifies the validity of the parameter entries, and invalid entries will be automatically identified and prompted.

[0132] This method significantly improves the accuracy and quality of pipeline layout design by establishing precise single-pipe mathematical models and three-dimensional longitudinal sections. Compared to traditional empirical methods, this method utilizes advanced optimization algorithms, such as stochastic gradient descent, to effectively plan pipeline paths, reduce the number of elbows and material usage, directly reducing construction costs and improving efficiency.

[0133] In terms of safety, this invention significantly reduces stress concentration and accumulation in pipelines under complex terrain by optimizing the directional similarity index and stress accumulation index, thereby enhancing the stability and reliability of the pipeline system. This is crucial for preventing pipeline fatigue damage and extending its service life.

[0134] Therefore, the pipeline line design method based on the single-pipe mathematical model of the present invention can improve pipeline laying accuracy, reduce construction costs, enhance safety, improve construction efficiency, and enhance environmental adaptability.

[0135] In summary, the pipeline route design method based on a single-pipe mathematical model presented in this paper provides an efficient, economical, safe, and environmentally friendly solution for the pipeline design industry. Through its precise mathematical model and optimization algorithm, this method not only improves the accuracy and efficiency of pipeline laying but also ensures the long-term stability and safety of the pipeline system, bringing positive impact to the field of pipeline engineering construction.

[0136] It will be understood that the above embodiments are merely exemplary embodiments for illustrating the principles of the present invention, and the present invention is not limited thereto. Those skilled in the art will appreciate that various modifications and improvements can be made without departing from the spirit and substance of the present invention, and such modifications and improvements are also considered to be within the scope of protection of the present invention.

Claims

1. A pipeline route design method based on a single-pipe mathematical model, characterized in that: The steps include: Step S100, determining a 3D longitudinal section and a UCS coordinate system based on a real-scene 3D model of the target area for pipeline laying; Step S200, establishing a single-tube mathematical model according to the three-dimensional longitudinal section and the UCS coordinate system; Step S300, performing micro-piping of pipelines according to the single-pipe mathematical model; Step S400, during the process of laying micro-piping in the pipeline, calculating a direction similarity index based on the similarity between the pipeline shape and the trench shape; and calculating a stress accumulation index based on the elastic modulus and the moment of inertia; Step S500, constructing a total cost calculation model based on pipeline laying, and performing cost optimization based on the direction similarity index and the stress accumulation index to optimize pipeline laying micro-piping; The calculation formula of the total cost calculation model is as follows: ； In the above formula, TC is the total cost; C m is the material cost per unit length of pipe; C l is the construction cost per unit length of pipeline; C b is the pipe bending cost per unit angle; C s is the stress accumulation cost per unit length; L is the total length of the pipeline; n is the number of pipeline segments; A di is the angle of the i-th pipe section on the xy plane; A gi is the angle of the i-th trench on the xy plane; B di is the angle of the i-th pipe section on the yz plane; B gi is the angle of the i-th trench on the yz plane; SAI is the stress accumulation index.

2. The pipeline route design method based on a single-pipe mathematical model according to claim 1 is characterized in that: Cost optimization is performed based on the directional similarity index and the stress accumulation index, including: In the first stage, the direction similarity index is calculated using the stochastic gradient descent method and the pipeline laying plan is iteratively adjusted to determine whether the direction similarity index reaches a first preset value; In the second stage, based on the direction similarity index reaching the first preset value, the stress accumulation index is optimized and the pipeline laying plan is iteratively adjusted to determine whether the stress accumulation index reaches the second preset value; In the third stage, on the basis that the stress accumulation index reaches the second preset value, cost optimization is carried out to minimize the total cost of pipeline laying.

3. The pipeline route design method based on a single-pipe mathematical model according to claim 2 is characterized in that: If the optimization requirements of the stress accumulation index are not met under the first stage conditions, the constraints of the directional similarity index are relaxed and the range of the optimal solution is expanded to ±2% of the minimum value.

4. The pipeline route design method based on a single-pipe mathematical model according to claim 3 is characterized in that: The optimization algorithm of the stress accumulation index includes a gradient descent algorithm and a simulated annealing algorithm.

5. The pipeline route design method based on a single-pipe mathematical model according to claim 4 is characterized in that: The calculation formula of the moment of inertia is as follows: ； In the above formula, I is the moment of inertia; D o is the outer diameter of the pipe; D i is the inside diameter of the pipe.

6. The pipeline route design method based on a single-pipe mathematical model according to claim 5 is characterized in that: The calculation formula of the directional similarity index DSI is as follows: ； In the above formula, n is the number of pipeline sections; A di is the angle of the i-th pipe section on the xy plane; A gi is the angle of the i-th trench on the xy plane; B di is the angle of the i-th pipe section on the yz plane; B gi is the angle of the i-th trench on the yz plane.

7. The pipeline route design method based on a single-pipe mathematical model according to claim 6 is characterized in that: The three-dimensional longitudinal section is composed of a plurality of two-dimensional longitudinal sections connected end to end.

8. The pipeline route design method based on a single-pipe mathematical model according to claim 7 is characterized in that: Any point on the three-dimensional longitudinal section has the attributes of mileage, elevation, and three-dimensional spatial coordinates.

9. The pipeline route design method based on a single-pipe mathematical model according to claim 8, characterized in that: The single tube mathematical model includes size data and posture data.

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