A displacement analysis, evaluation, and compensation method for optimizing pipeline thermal expansion

Abstract

The present invention relates to the field of industrial piping systems, and in particular to a displacement analysis, evaluation, and compensation method for optimizing pipeline thermal expansion. The method comprises the following steps: collecting multi-temperature thermal snapshots to form a thermal change sequence; determining the thermal expansion constraint boundary based on the thermal change sequence to form boundary condition data; identifying the fixed points and free points of the pipeline system based on the boundary condition data, and constructing a degree of freedom distribution diagram; analyzing the displacement transfer relationship of each pipe section based on the degree of freedom distribution diagram to generate displacement transfer chain data; identifying the concentrated release area of ​​thermal expansion through the displacement transfer chain data and performing node resonance detection to form vibration risk assessment data; designing a thermal stress elimination path based on the vibration risk assessment data, and setting flexible constraints to form a balanced force network. The present invention tracks the thermal expansion displacement transfer path in real time through displacement transfer chain analysis, and synchronously identifies the resonance frequency in combination with vibration mode detection to achieve dynamic association between the thermal expansion process and the vibration mode.

Description

Technical Field

[0001] The present invention relates to the field of industrial piping systems, and in particular to a displacement analysis, evaluation and compensation method for optimizing pipeline thermal expansion. Background Art

[0002] Thermal expansion of pipes refers to the phenomenon in which, when heated, pipes increase in length, diameter, and other dimensions due to increased molecular motion and spacing. During this process, when thermal expansion is hindered, thermal stresses are generated within the pipe wall, potentially threatening the normal operation and structural safety of the pipe. Pipeline thermal expansion is primarily influenced by factors such as the linear expansion coefficient of the pipe material, the temperature range, the pipe length, and the pipe's constraints. For example, different materials have different linear expansion coefficients. A greater temperature range results in more significant thermal expansion, and longer pipes also experience greater thermal expansion. Constraints also affect the pipe's ability to expand and contract freely. To address thermal expansion and the resulting thermal stresses, various compensation measures can be implemented, including natural compensation, compensator compensation, expansion joint compensation, and pre-deformation compensation. Natural compensation utilizes the pipe's inherent shape, such as an L-shaped or Z-shaped shape, to absorb thermal expansion. Compensator compensation involves installing specialized compensators, such as square compensators, in the piping system, whose elastic deformation offsets thermal expansion. Expansion joint compensation adjusts the length of the expansion joint to accommodate thermal expansion. Pre-deformation compensation involves pre-stretching or compressing the pipe during installation to offset some of the thermal expansion.

[0003] However, in complex pipeline networks, there are the following technical bottlenecks: existing technologies mostly analyze thermal expansion based on the assumption of steady-state temperature, while in actual operation, frequent temperature fluctuations cause thermal expansion to exhibit dynamic nonlinear characteristics. Traditional methods have difficulty capturing displacement-temperature hysteresis effects and sudden changes in dynamic stress, resulting in large deviations in the triggering timing of the compensation device. Conventional solutions ignore the structural vibration amplification effect caused by the transfer of thermal expansion displacement. For example, when the thermal displacement of the free end of the pipeline is transferred to the fixed end, low-frequency resonance (2-15Hz) is easily triggered due to differences in node constraint stiffness, accelerating weld cracking. Existing vibration detection mostly relies on offline spectrum analysis, which cannot correlate the dynamic process of thermal expansion with vibration modes in real time. Summary of the Invention

[0004] Based on this, it is necessary for the present invention to provide a displacement analysis, evaluation and compensation method for optimizing pipeline thermal expansion to solve at least one of the above technical problems.

[0005] To achieve the above objectives, a displacement analysis, evaluation, and compensation method for optimizing pipeline thermal expansion is provided, comprising the following steps:

[0006] Step S1: Collecting multiple temperature thermal snapshots to form a thermal state change sequence; determining the thermal expansion constraint boundary according to the thermal state change sequence to form boundary condition data;

[0007] Step S2: Identify fixed points and free points of the piping system based on the boundary condition data and construct a degree of freedom distribution diagram; analyze the displacement transfer relationship of each pipe segment based on the degree of freedom distribution diagram to generate displacement transfer chain data; identify the concentrated release area of ​​thermal expansion through the displacement transfer chain data and perform node resonance detection to generate vibration risk assessment data;

[0008] Step S3: Design a thermal stress relief path based on the vibration risk assessment data, set flexible constraints to form a balanced force network; design a guided compensation scheme based on the thermal stress relief path and the balanced force network, calculate the thermal expansion energy distribution, and generate thermal energy distribution optimization data;

[0009] Step S4: Modeling a thermal expansion dynamic response curve based on the thermal energy distribution optimization data; generating an advance compensation parameter based on the thermal expansion dynamic response curve; and generating a temperature buffer configuration scheme based on the advance compensation parameter and the thermal energy distribution optimization data.

[0010] Step S5: According to the guided compensation scheme and the temperature buffer configuration scheme, the pipeline system is modified, and a thermal snapshot is collected to form thermal data after the modification; the compensation efficiency is verified based on the thermal data after the modification to form a seasonal compensation parameter set.

[0011] This invention achieves precise control of thermal expansion effects by analyzing and optimizing the response of a piping system under thermal changes in a phased manner. First, by collecting multi-temperature thermal snapshots to construct a thermal change sequence, the system can understand thermal stress trends in a dynamic thermal environment, providing a comprehensive data foundation for subsequent analysis. Determining thermal expansion constraint boundaries based on the thermal change sequence effectively restores the stress boundaries under actual operating conditions, enhancing the accuracy of the model. Furthermore, by combining boundary conditions to identify fixed and free points, constructing a degree-of-freedom distribution diagram, and analyzing the displacement transfer relationship of each pipe segment, the thermal stress conduction path in the piping system is precisely revealed, key stress locations are identified, and areas of concentrated thermal expansion release are identified. Nodal resonance detection is then performed in these areas, helping to warn of potential vibration risks and enhance structural safety assurance. Furthermore, based on the vibration analysis results, a thermal stress mitigation path is designed, flexible constraints are set, and a balanced force network is formed. This balances the system's deformation behavior during heating, thereby reducing local stress concentrations. This path is then used to design a guided compensation scheme, which, combined with thermal expansion energy distribution calculations, optimizes the system's thermal energy conduction structure, ensuring the directional and efficient thermal compensation scheme. Subsequently, a dynamic response curve for thermal expansion is constructed and lead compensation parameters are generated, so that the system has forward-looking response capabilities under different temperature conditions and avoids structural damage caused by lag. At the same time, a temperature buffer configuration scheme is designed in combination with the thermal energy distribution to provide the system with a multi-level thermal stability buffer, effectively extending the life of the pipeline. Finally, through the actual transformation of the pipeline system and the collection of thermal snapshots, a thermal data model after the transformation is constructed, and a seasonal compensation parameter set is formed through verification and analysis, so that the compensation strategy is more in line with the periodic operation law and improves the adaptability and reliability of long-term operation. The overall approach realizes closed-loop optimization from thermal perception, mechanical analysis, compensation design to transformation verification, comprehensively improving the operational stability, structural safety and energy utilization efficiency of the pipeline system in a thermal environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] Other features, objects and advantages of the present invention will become more apparent upon reading the detailed description of non-limiting embodiments thereof made with reference to the following drawings:

[0013] Figure 1 A schematic flow chart of the steps of the displacement analysis, evaluation and compensation method for optimizing pipeline thermal expansion according to the present invention;

[0014] Figure 2 for Figure 1 Detailed step flow diagram of step S1;

[0015] Figure 3 for Figure 1 Detailed step flow chart of step S3 in FIG. DETAILED DESCRIPTION

[0016] The following is a clear and complete description of the technical method of the present invention in conjunction with the accompanying drawings. It is obvious that the embodiments described are part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without making any creative efforts are within the scope of protection of the present invention.

[0017] In addition, the accompanying drawings are merely schematic illustrations of the present invention and are not necessarily drawn to scale. Identical reference numerals in the figures denote identical or similar parts, and thus repetitive descriptions thereof will be omitted. Some of the block diagrams shown in the accompanying drawings are functional entities that do not necessarily correspond to physically or logically separate entities. These functional entities may be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor and / or microcontroller approaches.

[0018] It should be understood that although the terms "first," "second," and the like may be used herein to describe various elements, these elements should not be limited by these terms. These terms are used solely to distinguish one element from another. For example, a first element may be referred to as a second element, and similarly, a second element may be referred to as a first element, without departing from the scope of the exemplary embodiments. The term "and / or" as used herein includes any and all combinations of one or more of the listed associated items.

[0019] To achieve this, please refer to Figures 1 to 3 The present invention provides a displacement analysis, evaluation and compensation method for optimizing pipeline thermal expansion, the method comprising the following steps:

[0020] Step S1: Collecting multiple temperature thermal snapshots to form a thermal state change sequence; determining the thermal expansion constraint boundary according to the thermal state change sequence to form boundary condition data;

[0021] In a thermal pipeline monitoring project of a certain city's heating backbone network, an embodiment of the present invention selects three temperature nodes at the initial, middle and final stages of winter operation, and uses an infrared thermal imager to periodically photograph the pipeline, obtaining a high-precision thermal snapshot image sequence at 60°C, 90°C and 120°C, respectively. The thermal imaging images collected at each moment are subjected to image denoising and temperature stratification processing to form a temperature-time two-dimensional thermal change sequence. In this sequence, the temperature gradient evolution of the pixel points in the thermal image of each pipe section is combined with the external anchoring structure of the pipeline to identify whether there is a phenomenon of thermal expansion restriction. These restricted areas are divided into "thermal expansion constraint boundaries", and the boundary coordinates and constraint type data (such as rigid anchors, sliding supports, etc.) are output in GIS format to form boundary condition data for subsequent analysis.

[0022] Step S2: Identify fixed points and free points of the piping system based on the boundary condition data and construct a degree of freedom distribution diagram; analyze the displacement transfer relationship of each pipe segment based on the degree of freedom distribution diagram to generate displacement transfer chain data; identify the concentrated release area of ​​thermal expansion through the displacement transfer chain data and perform node resonance detection to generate vibration risk assessment data;

[0023] Based on the boundary condition data generated in step S1, the embodiment of the present invention marks the stress points of the pipeline in the three-dimensional CAD model, identifies points with high constraint strength as fixed points (such as anchor devices set on a concrete foundation), and identifies points with low constraint strength or allowed sliding as free points (such as sliding supports with Teflon gaskets), thereby establishing a "degree of freedom distribution diagram" for the entire system. In this diagram, color and arrows are used to indicate the force release direction and constraint degree of each node. Further analysis is performed on the stress links between adjacent pipe sections, and "displacement transfer chain data" is established based on the nodes to indicate how thermal expansion propagates in space along the pipeline structure. Dynamic response simulation is performed on the relay nodes in the transfer chain, and the transient displacement value under the action of the maximum temperature difference is calculated using the finite element method to identify the area where thermal expansion transfer is concentrated. Node resonance detection is performed on this area, that is, a periodic thermal load is applied (simulating day and night temperature changes) and the amplitude response of the node is recorded. Fourier analysis is used to determine whether there is a resonance phenomenon near the natural frequency, and ultimately vibration risk assessment data including the coordinates of high-risk nodes, displacement amplitude, and frequency response is generated.

[0024] Step S3: Design a thermal stress relief path based on the vibration risk assessment data, set flexible constraints to form a balanced force network; design a guided compensation scheme based on the thermal stress relief path and the balanced force network, calculate the thermal expansion energy distribution, and generate thermal energy distribution optimization data;

[0025] The embodiment of the present invention designs a "thermal stress relief path" based on the principle of the shortest path and minimum stress concentration for the high-risk vibration area identified in step S2, that is, a force transmission buffer path is constructed between free points, and flexible compensation devices are introduced into the path, such as metal corrugated compensators, sliding guide brackets, etc. According to this path, a flexible constraint boundary is set in the three-dimensional pipeline model, and a "balanced force network" is constructed, that is, distributed flexible points are introduced in the thermal stress transmission chain, so that the internal force of the system is reasonably dispersed along the path and no concentration points are formed. Subsequently, based on the thermal stress relief path and the balanced network structure, a guided compensation scheme is designed, multi-directional guided sliding supports are set at key turns or vertical sections, and some anchoring positions are adjusted to control the direction of thermal expansion. The thermal expansion energy distribution under unit temperature difference is calculated using the principles of energy conservation and node work balance, and thermal energy distribution optimization data containing thermal energy storage, transfer and release parameters for each section is generated.

[0026] Step S4: Modeling a thermal expansion dynamic response curve based on the thermal energy distribution optimization data; generating an advance compensation parameter based on the thermal expansion dynamic response curve; and generating a temperature buffer configuration scheme based on the advance compensation parameter and the thermal energy distribution optimization data.

[0027] Based on the optimized thermal energy distribution data obtained in step S3, this embodiment of the present invention employs thermal-structural coupling analysis to model the pipeline's dynamic thermal expansion response curve. Specifically, using a 90°C temperature rise process as the initial boundary condition, the thermal stress change and displacement response of the pipeline are calculated every 30 seconds, forming a dynamic curve of thermal expansion over time. This curve extracts dynamic characteristics of the expansion response, such as the rise delay time, steady-state response time, and retraction inertia time. This curve then generates a "lead compensation parameter," which specifies that to prevent hysteresis caused by thermal inertia, the compensator should be activated xx minutes before the temperature rise begins. Combining the optimized thermal energy distribution and the lead parameter, a "temperature buffer configuration" is established. Phase change material packs or flow-limiting steam bypass devices are placed in the concentrated expansion zone to absorb and slowly release thermal energy, suppressing sharp temperature rises. The buffer configuration adheres to the principles of a forward-facing center of gravity for thermal energy distribution and high capacity matching accuracy, ensuring a linear and controllable expansion response.

[0028] Step S5: According to the guided compensation scheme and the temperature buffer configuration scheme, the pipeline system is modified, and a thermal snapshot is collected to form thermal data after the modification; the compensation efficiency is verified based on the thermal data after the modification to form a seasonal compensation parameter set.

[0029] In the embodiment of the present invention, the pipeline system is modified on site according to the guided compensation scheme and temperature buffer configuration scheme formulated in step S4: a guided compensator is installed on the thermal expansion path, the original fixed point is replaced with a flexible anchoring device with micro-displacement tolerance, and a paraffin-based phase change buffer module is arranged in the concentrated heat source area. After the system modification is completed, the thermal snapshot is re-collected during the temperature rise process (from room temperature to 110°C), the thermal imaging images of each period after the modification are recorded, and the pixel temperature is matched and dynamically compared with the original thermal data. The displacement change trend line and the vibration amplitude change curve are extracted using the comparison results to verify the compensation effectiveness. If the vibration drops by more than 40% and the maximum displacement is reduced by more than 30%, the compensation scheme is deemed effective. The advance response time, maximum displacement, and compensation onset time recorded in different seasons (such as slow temperature rise in spring and autumn, and fast temperature rise in winter) are sorted into a "seasonal compensation parameter set" to provide a periodic dynamic adjustment basis for subsequent thermal operation and maintenance.

[0030] Preferably, step S1 includes the following steps:

[0031] Step S11: measuring the diameter, wall thickness, length and angle of the pipeline system at room temperature to form reference dimension data;

[0032] In an oil pipeline thermal expansion compensation project in a large chemical park, an embodiment of the present invention first performs a baseline measurement of the pipeline system in a completely cooled state. A laser caliper is used to measure the outer diameter of the pipeline with an accuracy of 0.01 mm. Measurement points are set every 2 meters, for a total of 30 measurement points. An ultrasonic thickness gauge is used to measure the wall thickness of the pipeline. Three points at both ends and the middle of each pipe section are measured and the average value is recorded. The thickness data is used for subsequent thermal stress calculations. The length of the pipe section is measured at a fixed point using a total station. The horizontal projection error is corrected with a rangefinder to obtain the center length of each pipe section. The measurement accuracy is controlled within the range of ±2 mm. An electronic goniometer is used at each connection node to record the angle information between the pipe joints, with particular attention paid to the three-dimensional connection angle data in the T-type, L-type and elbow areas. Finally, a data set containing the "diameter-wall thickness-length-angle" four-tuple information is formed, which serves as the benchmark dimension data for subsequent thermal comparison and expansion calculations.

[0033] Step S12: Install temperature sensors and displacement measurement equipment on the pipeline system and establish a data acquisition network;

[0034] The embodiment of the present invention arranges temperature and displacement sensing equipment on the basis of the geometric measuring points provided in step S11 to construct a thermal monitoring data acquisition network. In a specific implementation, two groups of temperature sensors are set up on each section of the pipeline, located at the top and bottom respectively, to monitor the influence of thermal convection on the temperature distribution. A platinum resistance temperature sensor (accuracy ±0.15°C) is selected and connected to the main controller via RS485 serial communication. A unique address number is set for each node. In order to monitor the deformation caused by thermal expansion, a combination of laser displacement sensors and fiber grating sensors is adopted. The laser displacement sensor is used to capture the axial displacement, and the fiber grating is used to track the angular deformation changes in real time. Both types of sensors are centrally managed through a distributed data acquisition module and equipped with a time synchronization system to ensure that the data timing is unified under the condition of simultaneous response of multiple measuring points. The network supports full synchronous acquisition of 30 points within 1 second, ensuring that dynamic response can still be accurately obtained during the rapid heating stage.

[0035] Step S13: The pipeline system is tested and operated under different operating temperature conditions. The temperature changes of various parts of the pipeline system are recorded through a data acquisition network. The deformation state of the pipeline system under different temperature conditions is also collected to generate thermal measurement data, where the deformation state includes linear expansion, angular deformation, and spatial displacement.

[0036] In an embodiment of the present invention, a pipeline system with sensors installed is subjected to a temperature increase experiment under a controlled environment. The temperature gradient is set to five temperature levels from 30°C to 150°C (increases by 30°C per level), and each temperature level is kept stable for 1 hour to ensure the formation of thermal stability. During the experiment, the data acquisition system automatically records the temperature changes of the pipeline at each temperature level and simultaneously obtains the data of the displacement sensor. The deformation state acquisition includes: 1) linear expansion changes, that is, the extension of each section of the pipeline along the axis, which is mainly derived from the data of the laser displacement sensor; 2) angular deformation, that is, the angle deflection caused by uneven thermal stress at the pipeline connection, and the fiber Bragg grating sensor provides continuous angle change values; 3) spatial displacement changes, through the three-dimensional coordinate system analysis of the output of the displacement sensor and combined with the known coordinate system mapping transformation, the spatial morphological change data of the entire pipeline are obtained. After filtering, interpolation and temperature stratification, these data form a high-resolution thermal measurement data set, which provides reliable input for subsequent thermal trend modeling.

[0037] Step S14: sorting the thermal state measurement data under multiple temperature conditions in ascending order of temperature to form a thermal state change sequence;

[0038] The embodiment of the present invention is based on the thermal measurement data obtained in step S13, and sorts the data in order from low to high according to the collected temperature to form a thermal change sequence. The data at each temperature level is grouped into a "thermal snapshot unit", and each unit includes a temperature field distribution diagram, the displacement of each measuring point, the angle change value and the time label. In order to ensure the continuity and comparability of each unit in the sequence, all data points are interpolated and normalized so that the distribution of spatial measuring points is consistent between each stage. This sequence can be regarded as a dynamic trajectory of the thermal response of the pipeline system, which contains the deformation evolution law of the pipeline under different thermal loads, and is the core data support for the subsequent inference of thermal gradient distribution and stress concentration location. Finally, a thermal change sequence of a time-temperature-spatial displacement multidimensional array structure is formed and exported to a data format that can be directly read by a structural thermodynamic modeling platform (such as ANSYS or COMSOL).

[0039] Step S15: extracting the temperature gradient distribution through the reference dimension data and the thermal state change sequence, and determining the thermal expansion constraint boundary to form boundary condition data.

[0040] Based on the thermal change sequence, the embodiment of the present invention compares the temperature field distribution in each temperature section with the reference dimension data, and extracts the expansion ratio of each pipe section at different temperatures, that is, the linear expansion rate is equal to the actual length of the pipe section at that temperature minus the reference length at room temperature divided by the reference length. Based on this, a temperature gradient diagram is drawn to represent the spatial distribution slope of the temperature change. For pipe sections whose expansion ratio is significantly smaller than the average value or shows a negative displacement trend, it can be preliminarily determined that there is a phenomenon of thermal expansion restriction. Combined with the installation structure information, it is identified whether these areas are near known high-constraint components such as fixed supports, nested corners or welded nodes. Through the coupled analysis of constraint points and temperature gradient changes, a "thermal expansion constraint boundary" is established, that is, the positions in the pipeline system that may force intervention in thermal deformation are marked, and they are output according to coordinates and constraint types (such as anchoring, sliding, semi-rigid) to form boundary condition data. This data not only provides a basis for boundary setting for subsequent modeling, but also provides structural constraints for compensation path planning.

[0041] By precisely measuring key structural parameters of the piping system, such as diameter, wall thickness, length, and angles, at room temperature, this method establishes complete benchmark dimensional data, providing an accurate basis for comparison in subsequent thermal analysis. Subsequently, temperature sensors and displacement measurement equipment are installed on the piping system, and a data acquisition network is established. This not only enables real-time monitoring but also lays a solid foundation for high-frequency data acquisition during thermal changes. The piping system is tested under different operating temperature conditions. The data acquisition network systematically records temperature changes and corresponding deformations at each location. This thermal measurement data covers multiple dimensions, including linear expansion, angular deformation, and spatial displacement, facilitating a comprehensive reconstruction of the true structural response under thermal stress. By ascendingly sorting the measurement results under multiple temperature conditions to form a thermal change sequence, the dynamic evolution of the piping system during temperature rise can be clearly characterized. Finally, combining the benchmark dimensional data with the thermal change sequence to extract temperature gradient distribution information, further identifying thermal expansion conduction paths and limiting factors, thereby precisely defining the thermal expansion constraint boundaries and constructing boundary condition data reflecting the actual operating conditions. This series of steps lays a reliable data and analytical foundation for subsequent thermal stress modeling and structural compensation design.

[0042] Preferably, step S15 includes the following steps:

[0043] Step S151: Compare the reference dimension data with the thermal change sequence, calculate the displacement of each measuring point at different temperatures, and establish a temperature-displacement relationship table;

[0044] Based on the obtained thermal change sequence and reference dimension data, the embodiment of the present invention selects a steam pipeline of a chemical plant as an example, compares the difference between the actual coordinates of the same measuring point at different temperatures and the coordinates under the normal temperature reference state, and calculates the displacement of the measuring point at the temperature. The displacement here includes three components: axial (along the centerline direction of the pipeline), radial (perpendicular to the pipeline surface direction) and spatial displacement (total displacement based on three-dimensional coordinate transformation), which are obtained by displacement sensors and spatial reconstruction algorithms respectively. The displacement values ​​of each measuring point at temperatures of 30°C, 60°C, 90°C, 120°C and 150°C are recorded respectively, and a "temperature-displacement relationship table" is established with the measuring point number as the primary key. The table has a temperature column, a corresponding displacement column in each direction and a measuring point position coordinate column. The data in the table is output in CSV format for subsequent use in displacement trend analysis and thermal field simulation modeling.

[0045] Step S152: constructing a temperature distribution cloud map of the pipeline system based on the temperature-displacement relationship table and extracting temperature gradient distribution data;

[0046] The embodiment of the present invention uses the temperature-displacement relationship table in step S151 as the data source, and uses a visual modeling tool (such as Tecplot or Matlab visualization module) to interpolate and map the spatial displacement data under different temperature conditions to construct a three-dimensional temperature distribution cloud map. In the implementation, the inverse distance weighted method is used to spatially interpolate the scattered temperature data, and vector superposition is performed in combination with the displacement direction information of each point to form a thermal field layer with a color gradient change. In the cloud map, the depth of the color represents the temperature, and the vector arrows indicate the displacement direction and relative amplitude of the corresponding point, thereby intuitively displaying the thermal strain trend and heat conduction direction. Furthermore, by analyzing the temperature change rate along the axial direction and branch direction of the pipeline in the cloud map, the temperature gradient distribution data is extracted. The data is represented in the form of a five-tuple of "starting point coordinates-end point coordinates-temperature difference value-distance value-gradient value", which is used to identify areas with more drastic temperature changes and serves as a thermal driving basis for subsequent expansion path and compensation design.

[0047] Step S153: By analyzing the relative motion of each pipe segment in the thermal state change sequence, the fixed constraint points and free expansion areas in the pipeline system are identified to obtain thermal displacement constraint identification data;

[0048] The embodiment of the present invention identifies fixed constraint points and free expansion areas by analyzing the relative movement between each pipe section on the basis of the thermal change sequence and temperature gradient distribution data. The specific method is: compare the relative displacement between adjacent measuring points (i.e., the position of the end measuring point after heating minus the position of the adjacent front measuring point) with their relative positions in the reference state. If the relative displacement between the measuring points of a certain section is constant or close to zero, and there is a bracket, welding or supporting structure near the section, the position can be determined to be a fixed constraint point; if a certain section produces significant stretching or bending deformation during the heating process, and the displacement increases linearly with the temperature rising, it is determined to be a free expansion area. In the above analysis process, the concept of "displacement invariance coefficient" is introduced, which is defined as the variance of the relative displacement at multiple temperatures. The variance is lower than a certain threshold (such as 0.01mm 2 The final output of thermal displacement constraint identification data includes the fixed point number, spatial coordinates, constraint type (completely fixed or limited movement) and free zone range.

[0049] Step S154: determining the main direction and constraint limit of thermal expansion based on the reference size data and the temperature gradient distribution data, and marking the thermal expansion boundary point;

[0050] The embodiment of the present invention further determines the main direction and constraint limit of thermal expansion based on the temperature-displacement relationship data obtained in step S151 and the temperature gradient distribution information extracted in step S152. During the operation, the displacement vector field of the entire pipeline at the highest operating temperature (150°C) is selected, and all displacement vectors are normalized and superimposed for analysis to obtain the main direction of global thermal expansion, which usually extends along the main axis of pipeline transportation. This direction is cross-checked with the fixed constraint point information determined in step S153 to calculate the maximum deformation of each free expansion segment and the start and end positions of its constrained area. Based on this data, the thermal expansion boundary points are marked in the pipeline model, specifically the "contact surface or turning point between the free expansion path and the constraint point". Their coordinates are annotated in three dimensions, and a "boundary point-constraint attribute" comparison table is formed in conjunction with the constraint type to provide a positioning basis for subsequent compensation path planning.

[0051] Step S155: Determine the thermal expansion constraint boundary based on the thermal displacement constraint identification data and the expansion boundary points to form boundary condition data.

[0052] Based on the clarification of the thermal expansion boundary points, the embodiment of the present invention combines the thermal displacement constraint identification data to systematically construct the thermal expansion constraint boundary of the entire pipeline system. The operation process is: each section of the free expansion area is expanded outward to the boundary points at both ends, and the temperature gradient and constraint strength (such as rigidity, semi-rigidity, sliding) between the boundary nodes are introduced as attribute parameters, and these boundaries are defined as "thermal boundary conditions" using structural modeling tools (such as SolidWorks Simulation or Abaqus) for subsequent thermal-mechanical coupling analysis. The thermal expansion constraint boundary not only reflects the physical deformation limit, but also contains the range of thermal stress distribution allowed during system operation. The boundary condition data finally output is described in a JSON structure, which includes the spatial position of the boundary point, the pipe section number to which it belongs, the temperature gradient value, the corresponding constraint type, and the recommended compensation mechanism (such as sliding bracket, corrugated expansion joint, etc.), providing key basic data support for optimizing the thermal expansion path and alleviating thermal stress accumulation.

[0053] By comparing the dimensional changes of each measured point in a thermal change sequence with baseline dimensional data, the present invention accurately calculates the displacement of each point at different temperatures. This allows for the establishment of a detailed temperature-displacement relationship table, providing a quantitative basis for analyzing the impact of temperature changes on structural deformation. Furthermore, a temperature distribution cloud map is constructed, which visually displays the temperature distribution characteristics of different parts of the pipeline system. Temperature gradient distribution data is further extracted, providing a spatial distribution basis for thermal stress analysis. Dynamic analysis of the relative motion of each pipe segment in the thermal change sequence effectively identifies fixed constraint points and free expansion regions in the system, thereby obtaining thermal displacement constraint identification data that characterizes thermal expansion behavior. Combining baseline dimensional and temperature gradient distribution data further clarifies the dominant direction and spatial development boundary of thermal expansion, scientifically identifies key thermal expansion boundary points, and provides precise constraint boundary input conditions for subsequent design. Ultimately, the thermal expansion constraint boundary is determined based on the thermal displacement constraint identification data and boundary points, forming boundary condition data that accurately reflects the actual thermal stress propagation path and the distribution of structural degrees of freedom, laying a solid foundation for thermal expansion analysis, compensation strategy formulation, and structural optimization.

[0054] Preferably, identifying fixed points and free points of the pipeline system according to the boundary condition data in step S2 includes:

[0055] Identify physical fixed anchor points and rigid support points in the piping system based on boundary condition data and generate an initial fixed point list;

[0056] Analyze the displacement constraint characteristics in the boundary condition data, determine the constraint degree of each support point in different directions, and establish a constraint type database;

[0057] Based on the constraint type database, the support points in the piping system are classified into fully fixed points, semi-fixed points and sliding support points to form a support point classification table;

[0058] Identify the unconstrained pipe segment areas in the boundary condition data, mark them as free expansion areas, and generate a preliminary list of free points;

[0059] By analyzing the displacement potential of each point in the preliminary list of free points, the movable direction and distance of each point in three-dimensional space are calculated to generate a table of degree of freedom values;

[0060] Combine the support point classification table with the degree of freedom value table to assign degree of freedom parameters to each key node in the piping system to form a node degree of freedom matrix;

[0061] Based on the node degree of freedom matrix, the degree of freedom information of each node is marked on the pre-acquired pipeline system topology diagram. Different colors and symbols represent different levels of freedom, thereby obtaining a degree of freedom distribution diagram.

[0062] Based on boundary condition data, this embodiment of the present invention uses a petrochemical enterprise's steam main pipeline system as an example to identify and extract all boundary points marked as "fully restricted deformation." Combined with the support structure data in the design drawings, nodes with "zero displacement" characteristics are considered physical fixed anchor points, while nodes with "displacement restricted but with heat conduction compensation devices" are identified as rigid support points. Specifically, each boundary point record in the boundary condition data is traversed and its constraint type field is read. Points with a constraint attribute of "full rigid constraint" or "full axial constraint" and connected to a civil anchor structure are identified as fixed anchor points; points with a constraint attribute that restricts only a certain direction or achieves structural damping through a rigid support are identified as rigid support points. The identification results are tabulated and output as an "initial fixed point list." The table includes fields such as point number, spatial coordinates, constraint type, and corresponding support structure number, which serve as basic data for subsequent classification. Based on the initial fixed point list, the displacement constraint characteristics of each point in the boundary condition data in three coordinate directions (i.e., X, Y, and Z) are further analyzed to establish a three-dimensional constraint degree description. To this end, the concept of "constraint degree identification vector" is introduced, and a vector is composed of Boolean values ​​(such as 0 for allowed and 1 for not allowed) to express whether displacement is allowed in three directions. For example, [1,1,0] means that the point is completely constrained on the X and Y axes and can move in the Z axis. By parsing the "constraint direction" field of each point in the boundary conditions and combining the displacement limitation capability of the support structure description (such as sliding bearings, limiters, expansion joint brackets, etc.), the constraint vector data of each support point in three directions is formed. Finally, a "constraint type database" is established. The database uses the point number as the primary key and records the spatial coordinates, support structure type, three-directional constraint vector, constraint level (such as full constraint, partial constraint) of each point for automatic classification of support point types. Using a constraint type database, all support points are classified into three categories based on their degree of constraint: fully fixed, semi-fixed, and sliding. A "fully fixed point" is a point where no relative displacement is allowed in any three directions (vector [1,1,1]); a "semi-fixed point" is a point where displacement is prohibited in two directions but free expansion is permitted in only one direction (e.g., [1,1,0]); and a "sliding point" is constrained in only one direction or the zero direction, while free expansion is permitted in all other directions. The classification process utilizes batch rule matching combined with logical reasoning, with the algorithm automatically assigning the types. Finally, a "support point classification table" is generated, recording each support point's number, location, constraint vector, category, and recommended compensation device type (e.g., bellows, sliding bracket, etc.). This table provides a basic structural distribution map for optimizing compensation design. After support point classification is completed, unconstrained or weakly constrained regions, known as "free expansion zones," are extracted from the boundary condition data. Points in these regions are initially identified as "free points."The identification method involves traversing all points in the boundary point data whose constraint degree identification vector is [0,0,0] or restricted in only one direction. Simultaneously, based on the thermal expansion boundary points and temperature gradient trends generated in step 10, the point is determined to be at the end of the heat transfer path or in a pipe section not connected to a supporting structure. If so, it is classified as a "potential free point." All points meeting these criteria are added to a "preliminary list of free points," and each point's spatial coordinates, adjacent fixed point numbers, temperature value, and displacement trend are recorded as input for subsequent spatial degree of freedom analysis. Using the preliminary list of free points as input, the potential movement trend of each free point in three-dimensional space is analyzed to determine its degree of freedom direction and maximum allowable displacement range. The calculation method involves linearly fitting the coordinate differences of the point at each temperature in the temperature-displacement relationship table to obtain the displacement increments in the three axes. If the fitted trend increases within the linear range and the fitting error is small (e.g., mean square error less than 0.05 mm), the direction is considered "movable." Otherwise, if the change is insignificant or the trend is irregular, the direction is considered restricted. Combining the analysis results in the three directions, a "degree of freedom vector" is generated for each free point. For example, [1,0,1] indicates that the point has free displacement in the X and Z directions and is constrained in the Y direction. Simultaneously, the maximum movement distance is estimated using the slope of the fitting function, forming a "degree of freedom numerical table." Each row contains the point number, degree of freedom vector, displacement range in each direction (in mm), and the corresponding temperature range. The support point classification table is merged with the degree of freedom numerical table generated in step 15 to assign degree of freedom parameters to each key node in the piping system. This merging operation is based on node number alignment. For support points, degree of freedom vectors are assigned according to their classification (e.g., [0,0,0] for a fully fixed point and [1,0,0] for a sliding support point). For free points, the vectors and movement range data in the degree of freedom numerical table are directly used. This fusion results in a "node degree of freedom matrix." This matrix is ​​indexed by node number and contains columns such as coordinate position, degree of freedom vector, maximum movement distance, and node type (supported / free). This matrix structure is suitable for stress simulation and compensation strategy deployment in structural simulation analysis software. The node degree of freedom matrix is ​​loaded into a pre-built 3D piping system topology diagram, and the degree of freedom attributes are annotated using graphical visualization software (such as AutoCAD Plant 3D or ANSYS Design Modeler). Each node is represented by a different color and symbol to indicate its degree of freedom. For example, a red circle represents a fully fixed point (with a degree of freedom vector of [0,0,0]), a yellow square represents a semi-fixed point, a green triangle represents a sliding support point, and a blue five-pointed star represents a free point. The color depth indicates the maximum displacement capacity. A legend is then used to clarify the meaning of different categories and degree of freedom levels, generating a "degree of freedom distribution diagram" that can be used for visual analysis of thermal expansion paths and optimal design of support systems.Finally, the degree of freedom distribution diagram, temperature distribution cloud diagram and thermal displacement path. Figure 3 The linkage display provides a graphical decision-making basis for formulating more efficient compensator layout plans and fixed point location strategies.

[0063] The present invention uses boundary condition data to identify physical fixed anchor points and rigid support points in a pipeline system, accurately generating an initial list of fixed points and providing a foundational framework for subsequent support structure analysis. This in-depth analysis of the displacement constraint characteristics within the boundary conditions allows for the identification of the constraints imposed on each support point in the X, Y, and Z directions. This allows for the construction of a comprehensive constraint type database, revealing the thermal expansion restriction mechanisms at different locations within the system. The constraint type database is further utilized to functionally classify support points into fully fixed, semi-fixed, and sliding support points, clarifying the hierarchy of support structure functions. This allows for the construction of a support point classification table, facilitating targeted structural adjustments. Furthermore, unconstrained pipe sections are identified and marked as free expansion zones, creating a preliminary list of free points and providing a reference for key locations for dynamic response research. By further analyzing the displacement potential of free points, calculating their movable directions and corresponding distances in three-dimensional space, and establishing a degree-of-freedom numerical table, the deformation capacity of each free point is quantified. By combining the support point classification table with the degree-of-freedom numerical table, specific degree-of-freedom parameters are assigned to each key node, forming a node degree-of-freedom matrix, thereby quantifying the deformation capacity of the entire system during thermal expansion. Finally, the degree of freedom information of each node is marked on the existing pipeline topology diagram and distinguished by different colors and symbols to generate an intuitive degree of freedom distribution diagram, making the rigid and flexible layout of each part of the system clear at a glance, facilitating optimization design and dynamic analysis.

[0064] Preferably, analyzing the displacement transfer relationship of each pipe segment based on the degree of freedom distribution diagram in step S2 includes:

[0065] Based on the topological structure of the pipeline system, the pipeline is divided into several continuous pipe segments and a pipe segment division table is established;

[0066] Analyze the degree of freedom difference of the nodes at both ends of each pipe segment in the pipe segment division table according to the degree of freedom distribution diagram, determine the dominant direction of displacement transmission, and generate a directional displacement vector;

[0067] Adjacent pipe sections with displacement transfer relationships are connected according to the pointing relationship of the directional displacement vectors to form a preliminary displacement transfer path;

[0068] Calculate the length change of each pipe section during thermal expansion and establish a pipe section expansion data table;

[0069] Calculate the value and direction of displacement transfer based on the pipe expansion data table and the preliminary displacement transfer path, and generate a displacement transfer vector diagram;

[0070] Analyze the continuous transfer path in the displacement transfer vector diagram and identify the displacement transfer chain from the high degree of freedom area to the low degree of freedom area;

[0071] Calculate the cumulative displacement on each displacement transfer chain, evaluate the attenuation or amplification effect of displacement during transmission along the chain, and form a displacement transfer effect evaluation table;

[0072] Assign priority weights to each displacement transfer chain according to the displacement transfer effect evaluation table, and determine the primary displacement transfer chain and the secondary displacement transfer chain;

[0073] Based on the displacement time series, displacement transfer chain data is generated according to the spatial distribution, transfer direction, cumulative displacement amount and priority weight information of the main displacement transfer chain and the secondary displacement transfer chain.

[0074] The present invention divides the entire system into several continuous pipe segments based on the topological structure of the pipeline system. The topological structure refers to the abstract representation of each node in the pipeline and its connection relationship, which is usually achieved through graph structure modeling. The nodes represent the connection points of the pipeline, such as interfaces, elbows, and tees, and the edges represent the pipe segments between adjacent nodes. This structure is used to perform a traversal analysis on all connection relationships. On the basis of identifying the pipe segments between adjacent nodes, the starting node and the ending node of each pipe segment are recorded, and a structured pipe segment division table is generated in combination with the geometric parameters of the pipe segment (such as length, material, and pipe diameter). Each row in the table represents an independent pipe segment and contains information such as the segment number, the start and end node numbers, the length, and the material number, providing a basic structural framework for subsequent displacement calculations. According to the degree of freedom distribution diagram generated in the previous stage, the degree of freedom information of the nodes at both ends of each pipe segment in the pipe segment division table is read, and the dominant direction of displacement that may be formed during thermal expansion is analyzed by comparing the constraint level differences of the nodes at both ends (such as one end is completely free, and the other end is semi-fixed or completely fixed). In specific implementation, a positive direction weight is assigned to the end with a higher degree of freedom value, and a negative direction weight is assigned to the end with a lower degree of freedom value. The directional displacement vector represents the main movement trend when thermal expansion stress is released. For example, if the degree of freedom of the starting node of a certain section of pipeline is 6 (completely free) and the degree of freedom of the ending node is 0 (completely fixed), the generated directional displacement vector points to the ending node. Finally, the directional displacement information of all pipe sections is written into a directional displacement vector table, which contains data fields such as pipe section number, start and end nodes, displacement direction and direction weight. Based on the directional displacement vector table, adjacent pipe sections with continuous displacement transfer relationships are connected in this step to form a preliminary displacement transfer path. The specific approach is: traverse each section of the pipeline. If the ending node of the section is the same as the starting node of another section of the pipeline, and the ending and starting directions of the directional displacement vector are consistent (that is, the displacement direction transfer between adjacent sections is continuous), then the two sections are regarded as a set of transfer relationships. Similarly, a complete set of paths is formed using a depth-first search algorithm (DFS) or a graph traversal method to obtain a preliminary displacement transfer path network diagram. Each path in the diagram represents a set of continuous pipe segments whose displacement is transferred by thermal expansion. After forming the preliminary transfer path, it is necessary to further calculate the length change of each pipe segment during the thermal expansion process. According to the thermal expansion formula, the length change of the pipe segment depends on its original length, the linear expansion coefficient of the material, and the temperature change. In actual operation, real engineering parameters can be introduced. For example, a steel pipe segment is 12 meters long and the material linear expansion coefficient is 1.2×10 -5 / °C, and a temperature rise of 80°C, the length increase is approximately 11.52 mm. The original length, linear expansion coefficient, and temperature difference of all pipe segments are substituted into the corresponding formula to batch calculate the expansion of each segment. This generates a pipe segment expansion data table, with each record containing the segment number, original length, temperature rise value, material number, linear expansion coefficient, and calculated thermal expansion length value. After determining the thermal expansion of each pipe segment, the expansion along the path is superimposed according to the directional displacement vector based on the preliminary displacement transfer path, and the magnitude and direction of the transferred displacement along each path are calculated. In specific implementation, the displacement transfer relationship of consecutive pipe segments within each path is accumulated in order, with the direction uniformly directed from the free end to the fixed end. For example, if the expansion of the first two segments in a path is 6 mm and 8 mm, respectively, and the directions are consistent, the accumulated transfer amount is 14 mm. To achieve automatic processing, the system needs to establish logical judgment rules to identify inconsistent directions and address the resulting displacement cancellation effects. The final output result is a displacement transfer vector diagram, in which each path is represented by a directional arrow line, and the value of the transferred displacement is marked to facilitate the subsequent positioning of thermal expansion risks. Based on the generated displacement transfer vector diagram, this embodiment further analyzes the continuous paths extending from the high-degree-of-freedom area to the low-degree-of-freedom area in the diagram, and identifies the "displacement transfer chain" where potential structural stress concentration exists. The "displacement transfer chain" here refers to a group of continuously connected, directional, and cumulatively displaced pipe sections. The starting points of these chains are usually areas with strong thermal expansion sources or high degrees of freedom, and the end points are nodes with restricted or completely fixed degrees of freedom. The graph search algorithm is combined with the path direction filtering rules for screening, and the paths that meet the requirements are numbered one by one and the relevant parameters are recorded, including the chain number, starting and ending nodes, path length, and number of structural nodes, to form a preliminary chain identification table. Subsequently, the cumulative displacement of each displacement transfer chain identified above is calculated, and its attenuation or amplification effect during the path transfer process is evaluated. Cumulative displacement is calculated by superimposing the thermal expansion of each pipe segment in the chain according to its directional vector. If some segments in the path have sliding supports or compensating devices, their displacement will be partially absorbed, requiring an "attenuation factor" to correct for this. Furthermore, if some segments in the path have flexible connections, "displacement amplification" may occur, requiring an "amplification factor" to correct for this. For example, if a path segment with sliding supports is set to an attenuation factor of 0.7, its thermal expansion of 8 mm will be adjusted to 5.6 mm and included in the cumulative displacement. After all paths have been adjusted, a complete displacement transfer effect evaluation table is generated, recording information such as the chain number, original displacement, adjusted displacement, and the type of path attenuation or amplification. Based on the displacement transfer effect evaluation table, each chain is assigned a priority weight, dividing it into primary and secondary displacement transfer chains. During implementation, priority is determined based on multiple factors, including the chain's cumulative displacement, the degree of freedom at the path's starting point, the path length, and whether it crosses critical structural nodes.A multi-layer weighted scoring mechanism is set up to mark the chains with a total evaluation score greater than a certain threshold (such as 75 points) as primary chains, and the rest as secondary chains. The execution of this step ensures that subsequent compensation measures give priority to covering critical transfer paths, effectively reducing the risk of thermal expansion stress in the pipeline system. In this step, all information of the primary and secondary displacement transfer chains is integrated to generate a systematic displacement transfer chain data set. This data set is organized in the form of a structured table or graph database, recording the number, spatial start and end positions, path direction, cumulative displacement value, path length, degree of freedom gradient change, priority weight and other fields of each chain, and is visually represented in the system topology diagram, with each chain marked with a primary or secondary level using different colors and line types. This data provides a quantitative basis for the subsequent formulation of thermal compensation plans, setting compensator positions and specifications, and ensuring that compensation measures accurately match the actual thermal expansion behavior of the pipeline system.

[0075] The present invention divides the pipeline system into multiple continuous pipe segments according to its topological structure and establishes a pipe segment division table, which helps to clearly present the structural relationships and connection units within the system. By analyzing the degree of freedom differences at the nodes at both ends of each pipe segment in combination with the degree of freedom distribution diagram, the dominant direction of the pipe segment displacement during thermal expansion can be clarified, and directional displacement vectors can be generated accordingly, thus laying the directional foundation for the subsequent displacement conduction mechanism. Through the directional relationship of these displacement vectors, adjacent pipe segments with a continuous conduction relationship are further connected to construct a preliminary displacement transmission path. Subsequently, the length change generated by each pipe segment under different temperature conditions is calculated to form a pipe segment expansion data table, providing numerical support for quantifying displacement. On this basis, combined with the preliminary path and expansion data, the actual direction and value of each segment displacement in the transmission path are further calculated to form a displacement transmission vector diagram, thereby revealing the propagation mechanism of thermal deformation in the system. Through the analysis of the displacement vector diagram, the displacement chain that is transmitted step by step from the high degree of freedom area to the low degree of freedom area is identified, making the main channel of the thermal expansion effect more clear. Calculating the cumulative displacement along each transfer chain can identify whether there are amplification or attenuation trends during the conduction process and generate a corresponding effect assessment table, providing a basis for stress management. Based on the assessment results, priority weights are assigned to each transfer chain to clarify which chains dominate the thermal stress distribution and which are secondary pathways. Ultimately, by integrating the spatial distribution, transfer direction, cumulative displacement, and weight information of the transfer chains, a complete displacement transfer chain data set is generated, making the deformation path of the system more predictable during thermal operation and providing data support for structural optimization and thermal stress control.

[0076] Preferably, identifying the concentrated release area of ​​thermal expansion through the displacement transfer chain data and performing node resonance detection in step S2 includes:

[0077] Extract the time series data of displacement changes of each node in the displacement transfer chain data with temperature, and filter out the node set whose displacement change rate exceeds the preset threshold;

[0078] Calculate the displacement differences between nodes in the adjacent node set, mark the pipe sections where the differences suddenly and continuously accumulate, and generate a list of candidate areas for concentrated thermal expansion release;

[0079] Perform frequency domain analysis on the nodes in the candidate list of concentrated thermal expansion release areas, extract the frequency characteristics of displacement changes, match them with the natural frequency database of the piping system, and identify frequency resonance points;

[0080] Count the number of nodes at the frequency resonance point where the vibration amplitude exceeds the safety limit and the duration, and calculate the vibration aggravation coefficient based on the temperature change rate to generate a vibration intensity distribution map;

[0081] The risk level of the candidate list of concentrated thermal expansion release areas is divided according to the vibration intensity distribution diagram and frequency resonance points, and nodes with a vibration aggravation coefficient ≥ 0.8 and a frequency match are marked as high-risk vibration sources;

[0082] Vibration risk assessment data including risk level, vibration mode and trigger conditions is generated based on the location of high-risk vibration sources, vibration frequency characteristics and corresponding temperature range.

[0083] After generating displacement transfer chain data, the present embodiment extracts time-series data on the displacement of each node in each transfer chain as a function of temperature. A high-precision sensor acquisition system records the node displacement values ​​at different temperatures within a set time interval (e.g., every 5 minutes) and synchronizes this data with the temperature change data for the pipeline layout area. To identify nodes most sensitive to thermal expansion, the system calculates the average rate of change of displacement per unit temperature change, or "displacement change rate," for each node. Nodes with a rate of change greater than 0.5 mm / °C are classified as abnormal response nodes. This threshold is set based on pipeline design standards and the material's linear expansion coefficient. It represents critical response nodes that will exhibit significant deformation during actual operation, providing input data for subsequent identification of potential concentrated expansion areas. For the selected set of nodes with high displacement change rates, the system analyzes whether these nodes belong to the same pipe segment or between adjacent pipe segments. For any two adjacent sampling points in the time series, the displacement difference between the corresponding nodes is calculated. If this difference remains greater than a set sudden change threshold (e.g., 2 mm) for multiple consecutive time periods (e.g., three consecutive hours), stress sudden change transmission is considered to be occurring in that pipe segment, potentially leading to concentrated release of thermal expansion energy. The system summarizes the pipe segment numbers and start and end node information that meet the mutation judgment conditions to form a "list of candidate areas for concentrated thermal expansion release". The pipe segments in this list serve as key analysis objects for further identification of subsequent vibration risks. For each node in the list of candidate areas for concentrated thermal expansion release, the original data sequence of its displacement changing with time is extracted, and the fast Fourier transform (FFT) method is used to convert the time domain signal into a frequency domain signal, and the main frequency value and its corresponding amplitude in the frequency component are extracted. The main frequency component of each node is compared with the pre-established "pipeline system natural frequency database". The database contains the resonant frequency range (such as 3Hz to 10Hz) under different pipe diameters, materials, and support methods. If the deviation between the node main frequency and a resonant frequency in the database is less than 0.2Hz, the node is considered to have a frequency resonance risk and is marked as a "frequency resonance point", laying the frequency identification foundation for subsequent vibration intensity assessment. After identifying the frequency resonance points, the system further counts whether the vibration amplitude of each resonance point exceeds the safety limit (generally set to 1.5 mm according to the pipeline fatigue standard), and records the total time that the over-limit state lasts (such as lasting more than 30 minutes). Combined with the temperature change rate of the node (the amplitude of the temperature increase or decrease per minute, for example, more than 0.3 degrees Celsius per minute), the "vibration aggravation coefficient" of the node is calculated, which represents whether the vibration caused by thermal expansion becomes more intense under rapid temperature changes. The vibration aggravation coefficients and corresponding spatial positions of all nodes are summarized to form a "vibration intensity distribution map", which is used to identify which areas in the pipeline system have severe vibrations caused by thermal expansion superimposed on resonance. Based on the vibration intensity distribution map, the risk level of each area in the "list of candidate areas for concentrated release of thermal expansion" is divided into risk levels based on the distribution of resonance points.The high-risk judgment rule is set as follows: the node belongs to the frequency resonance point, and its vibration aggravation coefficient is greater than or equal to 0.8 (indicating a significant coupling effect between frequency and temperature changes), and the vibration amplitude of the node exceeds the limit for a long time (such as the continuous exceeding of the limit for more than 1 hour). Nodes that meet this rule are marked as "high-risk vibration sources" and the pipe sections where they are located are classified as high-risk areas, while other nodes and pipe sections that do not meet this condition are classified as medium- and low-risk areas. This classification result facilitates the subsequent formulation of targeted compensation and optimization measures. Based on the location of the high-risk vibration source marked above (including spatial coordinates and the pipe section where it is located), its main frequency component (such as 6.8Hz), and the temperature fluctuation range (such as frequent switching between 80 and 95 degrees Celsius), the system generates a "vibration risk assessment data", which records the risk level (high, medium, low), vibration mode (main frequency and frequency multiples), and trigger conditions (temperature change rate threshold, heat flux density, etc.) of each high-risk source. For example, in a gas-heating pipeline network, multiple nodes on a free pipe section with support spacing greater than 10 meters frequently experienced excessive vibration amplitudes and frequency coupling within the initial 20 minutes of heating. The system assessed this as a typical high-risk vibration source and recommended adding flexible compensators or changing support structure parameters in this area to reduce the risk of thermal expansion stress concentration.

[0084] Preferably, step S3 includes the following steps:

[0085] Step S31: Analyze the distribution of high-risk nodes and vibration frequency characteristics in the vibration risk assessment data, screen out areas with concentrated thermal stress and sensitive displacement response, and generate a priority list for thermal stress relief;

[0086] After completing the generation of vibration risk assessment data, the embodiment of the present invention performs a spatial cluster analysis on the nodes marked as high-risk vibration sources, and uses a density-based clustering method (such as DBSCAN) to identify the concentrated areas of high-risk nodes in the pipeline network. Combined with its main vibration frequency characteristics (such as whether it is concentrated in the range of 5Hz to 8Hz) and temperature range distribution, it screens out areas with both high thermal stress concentration characteristics and strong displacement response characteristics. Specifically, if there are more than three consecutive high-risk nodes in a certain area, and their vibration frequencies are concentrated within the range of ±0.3Hz of the resonant frequency, and the average displacement amplitude exceeds 1.2 mm, then the area is determined to be a "thermal stress concentration and response sensitive area". The system generates a "thermal stress relief priority list" based on the result, sorts it by risk level, node density and frequency consistency, and determines the thermal expansion sensitive areas that need priority treatment to guide the next step of thermal stress path design.

[0087] Step S32: designing a thermal expansion guiding path along the pipeline based on the thermal stress relief priority list, determining the expansion direction and displacement release node, and forming a thermal stress relief path;

[0088] The embodiment of the present invention designs a path along the pipeline direction in the pipeline design model based on each sensitive area in the thermal stress relief priority list, with the goal of providing a low-resistance path for thermal expansion guidance. The system first analyzes structural parameters such as pipeline direction, bracket spacing, and variable structural nodes, and identifies all potential "displacement release nodes", that is, nodes that allow a certain degree of free movement under temperature changes, such as expansion joint setting points, T-tube free ends, etc.; then, based on the pipe segment connection relationship and structural continuity, the thermal expansion guidance direction is set so that thermal stress can be transferred to the displacement release node along the pipeline's path of minimum resistance. Taking the long-distance pipeline in a petrochemical plant as an example, if a high-risk area is found close to a free end with sparse bracket structure and large thermal displacement space, a thermal stress relief path is designed to bypass the dense bracket area and lead to the free end, forming a thermal stress relief channel, and output the thermal stress relief path data structure in the system for subsequent structural optimization.

[0089] Step S33: According to the constraint types of the fixed points and free points in the boundary condition data, flexible constraint units are installed between the free expansion area and the semi-fixed points to construct an initial balanced force network;

[0090] Based on the designed thermal stress relief path, the embodiment of the present invention systematically extracts boundary condition data, identifies the constraint attributes of each node in the path, and distinguishes them into "fixed points" (completely restricting displacement in three dimensions) and "free points" (no constraints or only axial constraints), and identifies "semi-fixed points" as potential installation locations for flexible connections. Subsequently, flexible constraint units, such as bellows expansion joints, sliding brackets, or metal hose connection devices, are inserted between the free expansion area (such as the thermal displacement concentration section on the relief path) and the semi-fixed point. These units are structurally capable of allowing thermal expansion but controllable displacement release. The flexible constraint unit is initially set to a medium stiffness state to simulate its partial absorption of thermal stress, and finally a fully connected "initial balanced force network" is constructed. This network covers all flexible adjustment interfaces on the thermal displacement path, laying the foundation for subsequent force balance optimization.

[0091] Step S34: simulating the conduction path of the thermal expansion force in the initial balanced force network through the displacement transfer chain data, and adjusting the stiffness parameters of the flexible constraint unit in real time so that the stress difference value of each pipe segment is ≤15%, thereby forming a balanced force network;

[0092] The embodiment of the present invention is based on the constructed initial balanced force network. The system calls the displacement transfer chain data to simulate the dynamic path of the thermal expansion force transmitted from the source node to the release node under different temperature conditions. The finite element method is used to iteratively solve the entire force network. In each simulation of temperature condition changes, the stress difference value of each pipe segment node is recorded. If it is found that the stress difference between certain pipe segments exceeds the allowable threshold (for example, the stress difference within a single segment exceeds 15%), the system will automatically adjust the stiffness parameters of the flexible constraint unit connecting the two ends of the pipe segment (for example, from the initial 5kN / mm to 3kN / mm), and repeat the simulation until the stress difference of all adjacent pipe segments in the entire network meets the control conditions. This process forms a "balanced force network", the key feature of which is that it can achieve uniform stress distribution and eliminate local concentration during the thermal expansion of the pipeline, thereby effectively reducing fatigue and vibration risks.

[0093] Step S35: selecting the type and installation location of the compensation device based on the thermal stress relief path and the optimized balanced force network, and designing a guided compensation solution including compensation amount and expansion and contraction direction parameters;

[0094] Based on the stable balanced force network, the embodiment of the present invention combines the thermal stress dissipation path. The system selects the type of compensation device according to the displacement release characteristics of each node, including sleeve expansion joints (suitable for axial release), universal ball expansion joints (suitable for three-dimensional free displacement), etc., and matches the installation position accordingly. Based on the adjusted response stiffness value of the flexible unit, the local temperature variation amplitude and the pipe expansion coefficient, the system calculates the maximum theoretical compensation amount for each position (such as the maximum displacement to be absorbed is 8 mm), determines the expansion and contraction direction of the compensation device (axial, radial or composite direction), and integrates it into a "guided compensation scheme". For example, the high-temperature section in a certain thermal energy pipeline network is equipped with a sleeve expansion joint (compensation amount ±10 mm, installed in the middle of the dissipation path). Its direction is consistent with the dissipation path, ensuring that the thermal displacement can be released in a controlled manner and slowly released within the design range. The scheme is finally output as a list of structural design parameters for use in engineering construction.

[0095] Step S36: Calculate the regional distribution density of thermal expansion energy under different temperature conditions based on the guided compensation scheme and the displacement transfer chain data, and generate a thermal energy distribution optimization data table and a thermodynamic map.

[0096] The embodiment of the present invention combines the guided compensation scheme with the original displacement transfer chain data. The system calculates the thermal expansion displacement in each pipe section and the change in thermal energy on the conduction path for different typical temperature conditions (such as normal temperature, operating temperature, and extreme high temperature), and statistically calculates the cumulative distribution of thermal expansion forces in different spatial regions. Through thermomechanical coupling analysis, the concentration of thermal expansion energy in a unit length pipe section is calculated in joules per meter to form a "thermal energy distribution optimization data table". At the same time, the system draws a "thermal map" to identify the thermal energy density of different areas with light and dark colors, and intuitively shows the improvement in thermal stress distribution after the implementation of the compensation scheme. For example, a certain area in the original thermal map is a red high-density area, which becomes an orange medium-density area after adjustment, indicating that the thermal energy release effect is significant. The image and data table are used to assist in the subsequent compensation device effect evaluation and maintenance decision analysis.

[0097] Preferably, step S32 includes the following steps:

[0098] Step S321: extracting high-response nodes whose displacement exceeds a threshold from the thermal stress relief priority list and generating a key node coordinate list;

[0099] In an industrial high-temperature heat exchange piping system, this embodiment of the present invention uses a Python script to read the thermal stress simulation results output by structural analysis software, based on a thermal stress mitigation priority list generated in a previous stage. This script then identifies high-response nodes where, under typical operating conditions (e.g., ambient temperature fluctuations above 50°C), thermal stress gradients experience dramatic changes, resulting in node displacements exceeding 10mm. During data processing, a threshold parameter of 10mm is set, and the maximum displacement component of each node along the three-dimensional (X, Y, and Z) axes is calculated. A list of key node coordinates is generated based on each node's 3D coordinates in the piping system CAD model. This list also records information such as the node number, displacement, and displacement direction vector for subsequent thermal expansion path design steps.

[0100] Step S322: marking the positions of the key nodes on the pipeline system topology map according to the key node coordinate list, and drawing a main direction vector diagram of thermal expansion in combination with the displacement direction in the displacement transfer chain data;

[0101] The embodiment of the present invention imports the key node coordinate list extracted in step S321 into the AutoCADPlant 3D environment, and marks the key nodes one by one in the established three-dimensional topology diagram of the pipeline system, and uses color weighting to distinguish different displacement levels (such as yellow represents 10-15mm, orange represents 15-20mm, and red represents greater than 20mm). At the same time, by reading the main displacement direction vector (i.e., thermal expansion direction) between each node in the displacement transfer chain data, it is visualized in the form of arrows on the three-dimensional topology diagram to form a complete thermal expansion main direction vector diagram. This diagram shows the expansion trend of each pipe section driven by thermal energy, which helps engineering personnel understand the displacement direction and release direction of the thermal stress concentration area.

[0102] Step S323: Divide the pipeline into a number of thermal expansion guiding sections according to the main direction vector diagram, each section including at least one high-response node as a displacement release starting point;

[0103] This embodiment of the present invention divides the pipeline system into sections based on the main direction vector diagram drawn in step S322. The specific method is as follows: with each high-response node as the center, the pipeline is divided into several thermal expansion-guided sections according to the continuity of its main thermal expansion direction and the displacement of adjacent nodes. Each section contains 13 high-response nodes, and each section of the pipeline is ensured to have a clear starting displacement release point during the thermal expansion process. In this embodiment, taking a typical heat exchange loop as an example, its pipe length is approximately 180 meters, divided into five sections, each approximately 3040 meters long, and the thermal expansion direction is extended along the X-axis and Z-axis respectively. This division ensures that the subsequent path design has a clear node starting point and thermal stress release target.

[0104] Step S324: Connecting displacement release starting points of adjacent sections along the pipeline to generate a preliminary thermal stress relief path;

[0105] Based on the aforementioned thermal expansion guiding sections, the present embodiment connects the displacement release starting points of adjacent sections according to the pipeline's direction. The connection path follows the actual connection logic of the pipeline topology and avoids crossing fixed points or areas not actively subject to thermal expansion. In this example, ArcGIS was used to construct a three-dimensional path. By invoking the NetworkAnalyst module to achieve the shortest possible connection between the start and end points while maintaining directional continuity, a preliminary thermal stress relief path was generated that runs through five thermal expansion guiding sections. The path begins with a high-displacement starting point and sequentially connects each release starting point to form a conduction channel for thermal expansion energy.

[0106] Step S325: Check the conflict between the preliminary thermal stress relief path and the fixed point constraints, adjust the release node position or add an intermediate compensation node for the conflicting path section, and form a thermal stress relief path without constraint conflicts.

[0107] After completing the preliminary thermal stress relief path, the embodiment of the present invention uses the path and boundary condition data comparison and analysis module to detect whether the release node in the path is within the range of a fixed point or a semi-fixed point. If there is a path passing through a fixed end or a displacement-restricted area, it will cause the path to fail or the expansion force cannot be effectively released. In this embodiment, by calling the RevitMEP plug-in to compare the boundary attributes of each node position, it was found that the second section of the path had a problem of overlapping with the fixed bracket position. According to the path adjustment strategy, the engineering staff offset the release starting point by 0.8 meters to the adjacent non-constrained node, and added a compensator node in the middle of the path to buffer the displacement, thereby regenerating an unconstrained conflict thermal stress relief path that meets the boundary conditions, continuity and heat energy transfer laws, and finally forming a stable and effective thermal expansion guiding path structure.

[0108] It is particularly important that step S36 includes the following steps:

[0109] Step S361: Importing the compensation amount, expansion direction parameters, and displacement transfer chain data of the guided compensation solution into the mechanical model, configuring the material elastic modulus, pipe segment connection method, and constraint condition parameters to obtain a parameterized mechanical model;

[0110] After completing the design of the guided compensation scheme, the embodiment of the present invention needs to conduct mechanical verification and thermal expansion energy distribution analysis on the installation effect of the compensator. In this embodiment, the key parameters output from the guided compensation scheme (including the compensation amount of each compensator set in the range of 10mm to 40mm, and the expansion and contraction direction mainly along the X-axis and Y-axis) are imported into the ANSYS Workbench platform to establish a three-dimensional parametric pipeline mechanical model. The elastic modulus of different materials is configured in the model, such as 2.1×10^11Pa for the carbon steel pipe section and 1.9×10^11Pa for the stainless steel section. The connection mode is set according to the welding rigid connection and the flange flexible connection. The constraint conditions are set in combination with the boundary condition data file to set the fixed support, sliding support and free end position. At the same time, the Python script is used to import the displacement transfer chain data constructed in the early stage as the initial thermal expansion load input to ensure that the simulation conditions are consistent with the actual operation thermal cycle conditions.

[0111] Step S362: running a multi-condition simulation in the parameterized mechanical model, outputting the stress distribution, displacement, and energy accumulation density of each pipe segment under the action of thermal expansion, and obtaining simulation result data;

[0112] The parameterized model established in the embodiment of the present invention is used to carry out multi-condition simulation, mainly simulating the thermal expansion response when the temperature gradually increases from room temperature (25°C) to high-temperature operating state (200°C). Each 10°C is a working condition step, and the ANSYS structural analysis module is used to calculate the displacement field, stress field and energy distribution under each working condition. The output results include the maximum displacement of each pipe section (such as the displacement of a certain node at 180°C is 18.3mm), equivalent stress distribution (such as the stress of some elbows is close to 70% of the yield strength) and node energy density (that is, the value of the accumulated heat energy per unit volume converted into deformation power, in joules per cubic meter). These data are summarized as a simulation result data set to provide a quantitative basis for subsequent model calibration and thermal energy distribution analysis.

[0113] Step S363: Compare the simulation result data with the displacement reference value of the displacement transfer chain data. If the error exceeds 5%, modify the model constraint parameters and rerun the simulation until the error is ≤5%, thereby obtaining the optimized simulation result data.

[0114] In order to verify the reliability of the simulation results, the embodiment of the present invention compares the displacement of each node output by the simulation with the on-site reference value in the displacement transfer chain data. If the error exceeds 5%, the correction mechanism is triggered. For example, in this embodiment, it was found that the displacement error in some Z-axis directions reached 6.8%, mainly concentrated in the compensator setting area. By modifying the boundary constraint parameters, the engineers replaced the nodes originally set as "sliding support" with "limited sliding" and fine-tuned the initial prestress setting value of the compensator, thereby enhancing the simulation accuracy of the structural model to the actual thermal response. After the update, all working condition simulations are rerun until the displacement errors of all key nodes in the three-dimensional direction are less than 5%. At this time, the model optimization is considered to be completed, and the optimization simulation result data is output as the basis for formal analysis.

[0115] Step S364: extracting energy cumulative density data based on the optimization simulation result data, calculating the thermal expansion energy value per unit length according to the pipeline topology partition, and generating a thermal energy distribution thermodynamic map with color depth representing energy density;

[0116] After obtaining the optimization simulation result data, the embodiment of the present invention uses the pipeline topology analysis script written in Matlab to match the energy accumulation density data of all nodes with the pipeline structure diagram, and classifies and counts the unit length thermal expansion energy value by section (such as every 10 meters or every elbow to support structure section). For example, the average unit length energy of section A (12.5 meters long) is 4.2×10^4 joules / meter, and that of section B (8.3 meters long) is 7.6×10^4 joules / meter. By normalizing these values ​​and assigning colors according to the gradient (such as light blue represents <3×10^4 joules / meter, and red represents >8×10^4 joules / meter), a thermal energy distribution thermogram is drawn. The graphics are displayed in three-dimensional form in the Revit platform, making the thermal expansion trend and energy concentration area clear at a glance, providing precise guidance for compensator and structural adjustment.

[0117] Step S365: Generate heat energy distribution optimization data including compensator supplementary position and constraint adjustment according to the position and value of the high energy density area in the heat energy distribution thermogram.

[0118] In combination with the high energy density areas identified in the thermal energy distribution thermogram (such as the obvious red areas in sections B and D, with energy densities exceeding 8×10^4 joules / meter), engineers in the embodiment of the present invention have developed corresponding compensation strategies: two compensators are added to the original compensation scheme, and their positions are located in the middle of section B and near the free end of section D, while the fixed bracket at the end of section D is replaced with a semi-fixed support to release some axial stress. The generated thermal energy distribution optimization data includes the recommended installation position coordinates, direction (such as the compensation direction along the Y axis), compensation range (recommended value is 15 to 25 mm), and force adjustment scheme (such as limiting slip in the Z axis) of each newly added compensator. This data can be imported into the BIM system for design updates and used as the parameter basis for the final compensation installation drawing.

[0119] Preferably, step S4 includes the following steps:

[0120] Step S41: deploying temperature sensors and displacement monitoring devices at key nodes of the pipeline system to collect temperature change information during operation in real time to form temperature change cycle data;

[0121] In order to monitor the temperature changes and displacements of the pipeline caused by thermal expansion during operation in real time, the embodiment of the present invention installs high-precision temperature sensors and displacement monitoring devices at key nodes of the pipeline system. The temperature sensor uses a thermocouple sensor with an accuracy of up to ±0.5°C. It is arranged at locations such as straight pipe sections, elbows and support points of the pipeline. A sensor is arranged every 5 meters, and each sensor is connected to the data acquisition system to achieve real-time monitoring of the pipeline temperature. The displacement monitoring device uses a laser displacement sensor with an accuracy of ±0.1mm. It is arranged at key nodes on both sides of the pipeline and can record the radial and axial displacements of the pipeline in real time. The data collected by all sensors is uploaded to the monitoring platform in real time to form temperature change cycle data and displacement data. These data are analyzed and stored by data analysis software to obtain periodic temperature change trends and corresponding displacement response data, ensuring comprehensive tracking of the pipeline's thermal expansion process.

[0122] Step S42: extracting high energy density areas from the thermal energy distribution optimization data, matching the temperature change cycle data of the corresponding areas, analyzing the hysteresis relationship between thermal expansion displacement and temperature change, and generating a dynamic response association table;

[0123] According to the thermal energy distribution optimization data obtained in the early stage, the embodiment of the present invention determines the high energy density areas in the pipeline system and extracts the temperature change cycle data of these areas. By analyzing the hysteresis relationship between the temperature fluctuations and the displacement response of the pipeline in these high energy density areas, the thermal expansion reaction characteristics in different areas are further identified. For example, section B shows obvious displacement hysteresis during the temperature rise process. This hysteresis may be caused by the material and structural characteristics of the pipeline. The temperature cycle data of these areas are matched with the corresponding displacement monitoring data to generate a dynamic response association table, which includes the hysteresis time of different temperature intervals and displacement responses (such as when the temperature changes at 100°C, the displacement lags for about 3 minutes). These data provide a basis for subsequent dynamic response analysis and optimization of compensation devices.

[0124] Step S43: fitting the displacement-time variation curves of different temperature intervals based on the dynamic response association table, marking the displacement acceleration mutation points, and forming a thermal expansion dynamic response curve diagram;

[0125] After completing the dynamic response association table, the embodiment of the present invention fits the displacement-time change curves of the pipeline at different temperatures based on the data in different temperature ranges. These curves show the displacement response during the temperature change process. For example, when the temperature rises to 150°C, the displacement will show a more prominent acceleration change. By analyzing these curves, especially the mutation points of displacement acceleration, the inflection points of the displacement response change of the pipeline at a specific temperature are identified. For example, at 160°C, the acceleration of the displacement suddenly changes, indicating that the thermal expansion of the pipeline has entered the acceleration stage. These mutation points are used to draw a thermal expansion dynamic response curve diagram. The relationship between temperature change and displacement acceleration change is marked in the diagram, which helps to understand the nonlinear characteristics of the pipeline during thermal expansion and provides a basis for setting the control parameters of the compensation device.

[0126] Step S44: Calculating the advance triggering time of the compensation device action according to the displacement acceleration mutation point in the thermal expansion dynamic response curve, and generating an advance compensation parameter including a compensation correction coefficient and a trigger threshold;

[0127] According to the thermal expansion dynamic response curve diagram drawn in step S43, the embodiment of the present invention further calculates the advance triggering time of the compensation device after identifying the displacement acceleration mutation point. For example, if the pipeline displacement suddenly changes at 150°C, it is expected that within this period, the compensation device should be triggered in advance to effectively control the pipeline displacement. Based on this information, the advance amount of the compensation device is calculated, which is usually obtained by analyzing the difference between the displacement acceleration mutation point and the response time of the system. After calculation, it is found that the compensation device should be started in advance when the temperature reaches 140°C to keep the system stable. These advance triggering times and their corresponding compensation amount correction coefficients (such as the compensation amount needs to be increased by 5mm at 160°C) are summarized as advance compensation parameters to ensure that the compensation device intervenes at the right time to avoid excessive stress on the pipeline.

[0128] Step S45: Delimiting a candidate temperature gradient buffer zone range based on the high energy density region boundary in the thermal energy distribution optimization data, and selecting a buffer zone interval distance that matches the advance compensation parameter;

[0129] The embodiment of the present invention identifies areas with large temperature gradients based on the boundaries of high energy density areas in the thermal energy distribution optimization data, and defines candidate ranges for temperature gradient buffer zones. The interval distance of the buffer zones is determined by further analyzing the thermal stress distribution of the pipeline system and the working range of the compensation device. For example, the temperature change rate in high energy density areas (such as section D) is large, so the selected buffer zone should be located 10 meters before and after the section, and ensure that the temperature change in the buffer zone does not exceed ±5°C. These buffer zones will provide appropriate response space for the compensation device to ensure that it can effectively respond to the impact of temperature changes on the pipeline system.

[0130] Step S46: generating a temperature buffer configuration scheme including buffer coordinates, widths, and compensation parameters according to the buffer interval distance.

[0131] The embodiment of the present invention generates a temperature buffer configuration scheme including buffer coordinates, width, and compensation parameters based on the buffer interval distance screened out in step S45. In specific implementation, the high energy density area is divided into multiple buffer zones based on the pipeline layout and heat energy distribution optimization data to ensure that each buffer zone can effectively respond to the needs of thermal expansion. For example, the buffer width of section D is set to 12 meters, and combined with the characteristics of the compensation device, the compensation amount in each buffer zone is set to 20 mm, and the trigger threshold of the compensator is set to start when the temperature change reaches ±3°C. A temperature buffer configuration scheme is generated based on these data, which will provide a specific reference for the installation location and operation of the compensation device during pipeline design and construction.

[0132] It is particularly important that step S45 includes the following steps:

[0133] Extracting the boundary coordinates of the high energy density area from the thermal energy distribution optimization data and generating a regional boundary coordinate table;

[0134] Overlay the region boundary coordinates with the pipeline system topology map, mark the starting and ending points of the high energy density area, and form a schematic diagram of the buffer zone candidate range;

[0135] The initial buffer zone interval is calculated based on the compensation correction coefficient and trigger threshold in the advance compensation parameter and the thermal expansion rate of the pipeline material;

[0136] Compare the initial buffer interval distance with the space margin of the actual pipeline layout, screen out feasible interval distance values, and generate a list of effective interval distances;

[0137] According to the effective interval distance list and the buffer zone candidate range diagram, the recommended interval distance value is marked, and the buffer zone interval distance of the temperature gradient is output.

[0138] When extracting the boundary coordinates of high-energy-density areas from the thermal energy distribution optimization data, the embodiment of the present invention first analyzes the thermal energy distribution of the pipeline system to identify the energy density distribution of each part of the pipeline. High-energy-density areas are usually parts of the pipeline system with large temperature changes, concentrated thermal expansion stress, and strong displacement response. To this end, the specific coordinate ranges of these high-energy-density areas are extracted using the results of thermodynamic simulation analysis, especially the starting and ending points where the thermal stress is more concentrated. The data processing method used includes regional segmentation based on thermal energy density thresholds and calibration of the boundary coordinates of each area. For example, if the energy density of a section of the pipeline system exceeds a certain standard (such as the thermal energy density per meter of pipe section is greater than 50J / m) during thermal expansion, the section of the pipeline is identified as a high-energy-density area. Finally, the starting and ending coordinates of each high-energy-density area are summarized to form a regional boundary coordinate table, which includes the name of each area, the starting point coordinates, the ending point coordinates, and the relevant thermal energy density data. When superimposing the regional boundary coordinates extracted in step S1 with the pipeline system topology map, first ensure that the pipeline plan layout map and three-dimensional topology map data have been completed. The pipeline system topology map contains important information such as each pipeline connection point, elbows, support points, and transition sections, and clearly marks the starting and ending points of each pipe section. Next, using GIS technology, the boundary coordinates of high-energy-density areas are imported into the topology map, and the specific location of each high-energy-density area is marked. For example, in a certain section of the pipeline (such as Section D), based on the results of the thermal energy distribution analysis, it is determined to be a high-energy-density area, and the starting and ending points of this area are marked. To further assist in the design and optimization of the compensation scheme, a schematic diagram of the candidate buffer range is drawn. This diagram vividly illustrates the spatial distribution of high-energy-density areas in the pipeline, helping to better identify the location of buffer zones in subsequent steps. When calculating the initial buffer interval distance, based on the compensation correction factor and trigger threshold in the lead compensation parameters, as well as the thermal expansion coefficient of the pipeline material, the thermal expansion coefficient of the pipeline material (such as steel pipe or plastic pipe) is first obtained. For example, the thermal expansion coefficient of steel pipe is 12×10^-6 / °C, while that of plastic pipe is 70×10^-6 / °C. By combining these material properties with the compensation correction coefficient, the displacement of the pipeline and the required compensation under different temperature changes are calculated. In addition, based on the changes in thermal expansion stress and the displacement response characteristics of the pipeline, the initial buffer interval is calculated. For example, assuming that the displacement of the pipeline at 100°C is 20mm and the correction coefficient of the compensation device is 1.5, the initial buffer interval may need to be set to 15m. The key formula in the calculation process is to infer the linear expansion of the pipeline based on the thermal expansion coefficient and temperature change, and adjust it according to the response time requirements of the compensation device to ensure that the buffer setting can effectively absorb the stress caused by thermal expansion.When comparing the initial buffer zone spacing with the spatial margin of the actual pipeline layout, it is first necessary to obtain the spatial data of the actual pipeline layout, specifically including the actual installation location of the pipeline, the length of the straight pipe section, the location of the elbows and support points, etc. In the actual pipeline layout, due to the space limitations during installation, the buffer zone setting cannot violate the actual space requirements. Therefore, by comparing the calculated initial buffer zone spacing with the actual available space, the effective spacing distance that can be implemented is screened out. Assuming that the actual space margin of a certain section of pipeline is 10m, and the calculated initial buffer zone spacing is 15m, the buffer zone setting needs to be adjusted to match the actual space. In this way, it is ensured that the compensation plan will not be unable to be implemented due to space limitations during design. When marking the recommended spacing distance values ​​based on the effective spacing distance list and the buffer zone candidate range schematic, the buffer zone setting plan is first updated based on the effective spacing distance screened in step S4, combined with the location of each high-energy density area in the pipeline. In this step, the recommended spacing distance for each buffer zone is determined based on the specific layout of the pipeline. For example, in the high-energy-density area of ​​pipeline section A, after calculation and screening, the recommended buffer spacing is 8 meters. In section B, due to more ample space, the recommended spacing is 12 meters. Ultimately, the generated buffer spacing data for the temperature gradient is displayed on the temperature gradient map to guide the specific layout and installation of the compensation device. The spacing and associated compensation parameters for each buffer are output as the final design solution, providing a scientific basis for pipeline thermal expansion compensation.

[0139] Preferably, step S5 includes the following steps:

[0140] Step S51: Implement pipeline system transformation according to the guided compensation scheme and the temperature buffer configuration scheme, install compensation devices and set temperature buffer zones to obtain an optimized pipeline system;

[0141] When the embodiment of the present invention implements the transformation of the pipeline system according to the guided compensation scheme and the temperature buffer configuration scheme, it is first necessary to select the appropriate type of compensation device and determine its installation position based on the previously calculated temperature buffer configuration scheme and the compensation device installation requirements. The compensation device includes thermal expansion compensators, expansion joints, etc., and its type is selected based on factors such as the material properties of the pipeline, the temperature range it can withstand, and the flow rate of the fluid in the pipeline. Taking steel pipes as an example, when the pipeline is at a higher temperature (such as above 100°C), it is necessary to select a high-temperature and pressure-resistant compensator. At the same time, combined with the temperature buffer configuration scheme, temperature buffers are set in the high energy density areas of the pipeline system. These buffers can effectively absorb the displacement caused by thermal expansion, thereby reducing the concentration of thermal stress. When installing the compensation device, it is necessary to accurately determine the installation position of the compensation device based on the structural characteristics of the pipeline to ensure that it is coordinated with the overall layout of the pipeline system. During the installation process, the installation quality of the compensation device and the buffer zone is checked in real time through measuring and monitoring equipment to ensure that it meets the design requirements and finally completes the optimization and transformation of the pipeline system.

[0142] Step S52: collecting thermal snapshots under different temperature conditions on the optimized pipeline system to form thermal data after transformation;

[0143] When collecting thermal snapshots under different temperature conditions on the optimized pipeline system, the embodiment of the present invention first installs temperature sensors and displacement monitoring devices at key positions of the pipeline to collect temperature change information of the pipeline system under different operating conditions in real time. Assuming that in the optimized pipeline system, a section of the pipeline rises from ambient temperature to 100°C, the temperature sensor will record the temperature data of this change process, and the displacement monitoring device will measure the displacement of the pipeline in real time. Through multiple experiments, thermal snapshots are collected for each section of the pipeline under different temperature conditions (such as 40°C, 60°C, 80°C, and 100°C) to form thermal data after the transformation. The thermal snapshot contains information such as the temperature distribution, displacement distribution, and thermal stress distribution of the pipeline at various temperatures. These data provide a basis for subsequent thermal stress calculations and compensation effect evaluations.

[0144] Step S53: Compare and analyze the thermal state data after transformation with the thermal state change sequence, calculate the thermal stress reduction percentage and displacement change, and generate thermal stress improvement rate and compensation effect evaluation data;

[0145] When the embodiment of the present invention compares and analyzes the thermal data after the transformation with the thermal change sequence, it is first necessary to establish a thermal change sequence as a reference. The thermal change sequence is usually calculated based on the thermal data of the pipeline system before the transformation or a standard thermal expansion model. By comparing the thermal data collected at different temperatures of the transformed pipeline with this change sequence, the thermal stress and displacement changes of the transformed pipeline under different temperature conditions are analyzed. Specifically, if the thermal stress of the pipeline system is significantly reduced after optimization, it means that the design of the compensation device and the temperature buffer zone is effective. If the percentage of thermal stress reduction exceeds a predetermined standard (such as more than 50%), it means that the compensation effect is obvious. The percentage of thermal stress reduction is calculated through comparative analysis, and then the displacement change of the pipeline is calculated. These data are used to generate thermal stress improvement rate and compensation effect evaluation data, which help evaluate the actual effect of the optimization plan and provide a basis for subsequent adjustments.

[0146] Step S54: Identify areas with insufficient thermal stress improvement rates based on compensation effect evaluation data, adjust compensation device parameters or types, implement optimization adjustments, verify the effects, and obtain construction acceptance data;

[0147] When identifying areas with insufficient thermal stress improvement rates based on compensation effect evaluation data, embodiments of the present invention first determine which areas have insufficient thermal stress improvement rates by comparing and analyzing the compensation effect evaluation data. Typically, the thermal stress reduction in such areas is less than 50%, or the displacement change does not meet the design requirements. For example, in a high-energy-density area of ​​a certain section of pipeline, the thermal stress remains high despite the installation of a compensation device. In this case, it is necessary to identify the problem in that area, analyze the operating status of the compensation device, and determine whether it is caused by an improper selection of the compensation device type or insufficient parameter settings. Depending on the insufficient thermal stress improvement rate, the parameters of the compensation device can be adjusted or replaced with a more suitable type (e.g., using a compensator with a greater pressure-bearing capacity). After the adjustment, the pipeline system needs to be verified again, and post-construction thermal data collected to evaluate whether the adjusted effect has achieved the expected goals. Finally, construction acceptance data is generated. This acceptance data includes the specific type of compensation device, installation location, adjusted compensation parameters, optimized thermal stress and displacement data, etc.

[0148] Step S55: establishing a parameter library for different operating conditions based on the construction acceptance data and the temperature change cycle data to form a seasonal compensation parameter set.

[0149] When establishing a parameter library for different operating conditions based on construction acceptance data and temperature change cycle data in an embodiment of the present invention, it is first necessary to collect all data during the construction process, including the actual temperature change cycle data of the pipeline, the operating data of the compensation device, thermal data, construction acceptance data, etc. Utilizing these data, a systematic parameter library is established, which contains pipeline thermal expansion displacement data, thermal stress data, and compensation effect data under different seasons and temperature conditions. Based on the temperature change characteristics of different seasons, compensation parameters under different working conditions are designed and recorded. For example, when the temperature is higher in the summer, the action time of the compensation device may need to be advanced, while when the temperature is lower in the winter, the action time of the compensation device needs to be delayed. In this way, a seasonal compensation parameter set is formed to provide a basis for the long-term operation of the pipeline system, ensuring that the pipeline can always be in an optimized working state under different temperature conditions, and avoiding pipeline damage or failure caused by temperature changes.

[0150] The present invention is therefore intended to be illustrative and non-restrictive in all respects, with the scope of the invention being defined by the appended claims rather than the foregoing description, and all changes that come within the meaning and range of equivalents of the application documents are intended to be embraced therein.

[0151] The foregoing description is intended only to provide specific embodiments of the present invention, which will enable those skilled in the art to understand and implement the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention is not intended to be limited to the embodiments shown herein, but is to be construed in the widest possible manner consistent with the principles and novel features disclosed herein.

Claims

1. A displacement analysis, evaluation and compensation method for optimizing pipeline thermal expansion, characterized in that: The following steps are involved: Step S1: Collecting multiple temperature thermal snapshots to form a thermal state change sequence; determining the thermal expansion constraint boundary according to the thermal state change sequence to form boundary condition data; Step S2: Identify fixed points and free points of the piping system based on the boundary condition data and construct a degree of freedom distribution diagram; analyze the displacement transfer relationship of each pipe segment based on the degree of freedom distribution diagram to generate displacement transfer chain data; identify the concentrated release area of ​​thermal expansion through the displacement transfer chain data and perform node resonance detection to generate vibration risk assessment data; Step S3: Design a thermal stress relief path based on the vibration risk assessment data, set flexible constraints to form a balanced force network; design a guided compensation scheme based on the thermal stress relief path and the balanced force network, calculate the thermal expansion energy distribution, and generate thermal energy distribution optimization data; Step S4: Modeling a thermal expansion dynamic response curve based on the thermal energy distribution optimization data; generating an advance compensation parameter based on the thermal expansion dynamic response curve; and generating a temperature buffer configuration scheme based on the advance compensation parameter and the thermal energy distribution optimization data. Step S5: According to the guided compensation scheme and the temperature buffer configuration scheme, the pipeline system is modified, and a thermal snapshot is collected to form thermal data after the modification; the compensation efficiency is verified based on the thermal data after the modification to form a seasonal compensation parameter set.

2. The displacement analysis, evaluation and compensation method for optimizing pipeline thermal expansion according to claim 1 is characterized in that: Step S1 includes the following steps: Step S11: measuring the diameter, wall thickness, length and angle of the pipeline system at room temperature to form reference dimension data; Step S12: Install temperature sensors and displacement measurement equipment on the pipeline system and establish a data acquisition network; Step S13: The pipeline system is tested and operated under different operating temperature conditions. The temperature changes of various parts of the pipeline system are recorded through a data acquisition network. The deformation state of the pipeline system under different temperature conditions is also collected to generate thermal measurement data, where the deformation state includes linear expansion, angular deformation, and spatial displacement. Step S14: sorting the thermal state measurement data under multiple temperature conditions in ascending order of temperature to form a thermal state change sequence; Step S15: extracting the temperature gradient distribution through the reference dimension data and the thermal state change sequence, and determining the thermal expansion constraint boundary to form boundary condition data.

3. The displacement analysis, evaluation and compensation method for optimizing pipeline thermal expansion according to claim 2 is characterized in that: Step S15 includes the following steps: Step S151: Compare the reference dimension data with the thermal change sequence, calculate the displacement of each measuring point at different temperatures, and establish a temperature-displacement relationship table; Step S152: constructing a temperature distribution cloud map of the pipeline system based on the temperature-displacement relationship table and extracting temperature gradient distribution data; Step S153: By analyzing the relative motion of each pipe segment in the thermal state change sequence, the fixed constraint points and free expansion areas in the pipeline system are identified to obtain thermal displacement constraint identification data; Step S154: determining the main direction and constraint limit of thermal expansion based on the reference size data and the temperature gradient distribution data, and marking the thermal expansion boundary point; Step S155: Determine the thermal expansion constraint boundary based on the thermal displacement constraint identification data and the expansion boundary points to form boundary condition data.

4. The displacement analysis, evaluation and compensation method for optimizing pipeline thermal expansion according to claim 1 is characterized in that: Identifying fixed points and free points of the pipeline system according to the boundary condition data in step S2 includes: Identify physical fixed anchor points and rigid support points in the piping system based on boundary condition data and generate an initial fixed point list; Analyze the displacement constraint characteristics in the boundary condition data, determine the constraint degree of each support point in different directions, and establish a constraint type database; Based on the constraint type database, the support points in the piping system are classified into fully fixed points, semi-fixed points and sliding support points to form a support point classification table; Identify the unconstrained pipe segment areas in the boundary condition data, mark them as free expansion areas, and generate a preliminary list of free points; By analyzing the displacement potential of each point in the preliminary list of free points, the movable direction and distance of each point in three-dimensional space are calculated to generate a table of degree of freedom values; Combine the support point classification table with the degree of freedom value table to assign degree of freedom parameters to each key node in the piping system to form a node degree of freedom matrix; Based on the node degree of freedom matrix, the degree of freedom information of each node is marked on the pre-acquired pipeline system topology diagram. Different colors and symbols represent different levels of freedom, thereby obtaining a degree of freedom distribution diagram.

5. The displacement analysis, evaluation and compensation method for optimizing pipeline thermal expansion according to claim 1 is characterized in that: Analyzing the displacement transfer relationship of each pipe segment based on the degree of freedom distribution diagram in step S2 includes: Based on the topological structure of the pipeline system, the pipeline is divided into several continuous pipe segments and a pipe segment division table is established; Analyze the degree of freedom difference of the nodes at both ends of each pipe segment in the pipe segment division table according to the degree of freedom distribution diagram, determine the dominant direction of displacement transmission, and generate a directional displacement vector; Adjacent pipe sections with displacement transfer relationships are connected according to the pointing relationship of the directional displacement vectors to form a preliminary displacement transfer path; Calculate the length change of each pipe section during thermal expansion and establish a pipe section expansion data table; Calculate the value and direction of displacement transfer based on the pipe expansion data table and the preliminary displacement transfer path, and generate a displacement transfer vector diagram; Analyze the continuous transfer path in the displacement transfer vector diagram and identify the displacement transfer chain from the high degree of freedom area to the low degree of freedom area; Calculate the cumulative displacement on each displacement transfer chain, evaluate the attenuation or amplification effect of displacement during transmission along the chain, and form a displacement transfer effect evaluation table; Assign priority weights to each displacement transfer chain according to the displacement transfer effect evaluation table, and determine the primary displacement transfer chain and the secondary displacement transfer chain; Based on the displacement time series, displacement transfer chain data is generated according to the spatial distribution, transfer direction, cumulative displacement amount and priority weight information of the main displacement transfer chain and the secondary displacement transfer chain.

6. The displacement analysis, evaluation and compensation method for optimizing pipeline thermal expansion according to claim 1 is characterized in that: Identifying the concentrated release area of ​​thermal expansion through displacement transfer chain data and performing node resonance detection in step S2 includes: Extract the time series data of displacement changes of each node in the displacement transfer chain data with temperature, and filter out the node set whose displacement change rate exceeds the preset threshold; Calculate the displacement differences between nodes in the adjacent node set, mark the pipe sections where the differences suddenly and continuously accumulate, and generate a list of candidate areas for concentrated thermal expansion release; Perform frequency domain analysis on the nodes in the candidate list of concentrated thermal expansion release areas, extract the frequency characteristics of displacement changes, match them with the piping system natural frequency database, and identify frequency resonance points; Count the number of nodes at the frequency resonance point where the vibration amplitude exceeds the safety limit and the duration, and calculate the vibration aggravation coefficient based on the temperature change rate to generate a vibration intensity distribution map; The risk level of the candidate list of concentrated thermal expansion release areas is divided according to the vibration intensity distribution diagram and frequency resonance points, and nodes with a vibration aggravation coefficient ≥ 0.8 and a frequency match are marked as high-risk vibration sources; Vibration risk assessment data including risk level, vibration mode and trigger conditions is generated based on the location of high-risk vibration sources, vibration frequency characteristics and corresponding temperature range.

7. The displacement analysis, evaluation and compensation method for optimizing pipeline thermal expansion according to claim 6, characterized in that: Step S3 includes the following steps: Step S31: Analyze the distribution of high-risk nodes and vibration frequency characteristics in the vibration risk assessment data, screen out areas with concentrated thermal stress and sensitive displacement response, and generate a priority list for thermal stress relief; Step S32: designing a thermal expansion guiding path along the pipeline based on the thermal stress relief priority list, determining the expansion direction and displacement release node, and forming a thermal stress relief path; Step S33: According to the constraint types of the fixed points and free points in the boundary condition data, flexible constraint units are installed between the free expansion area and the semi-fixed points to construct an initial balanced force network; Step S34: simulating the conduction path of the thermal expansion force in the initial balanced force network through the displacement transfer chain data, and adjusting the stiffness parameters of the flexible constraint unit in real time so that the stress difference value of each pipe segment is ≤15%, thereby forming a balanced force network; Step S35: selecting the type and installation location of the compensation device based on the thermal stress relief path and the optimized balanced force network, and designing a guided compensation solution including compensation amount and expansion and contraction direction parameters; Step S36: Calculate the regional distribution density of thermal expansion energy under different temperature conditions based on the guided compensation scheme and the displacement transfer chain data, and generate a thermal energy distribution optimization data table and a thermodynamic map.

8. The displacement analysis, evaluation and compensation method for optimizing pipeline thermal expansion according to claim 7 is characterized in that: Step S32 includes the following steps: Step S321: extracting high-response nodes whose displacement exceeds a threshold from the thermal stress relief priority list and generating a key node coordinate list; Step S322: marking the positions of the key nodes on the pipeline system topology map according to the key node coordinate list, and drawing a main direction vector diagram of thermal expansion in combination with the displacement direction in the displacement transfer chain data; Step S323: Divide the pipeline into a number of thermal expansion guiding sections according to the main direction vector diagram, each section including at least one high-response node as a displacement release starting point; Step S324: Connecting displacement release starting points of adjacent sections along the pipeline to generate a preliminary thermal stress relief path; Step S325: Check the conflict between the preliminary thermal stress relief path and the fixed point constraints, adjust the release node position or add an intermediate compensation node for the conflicting path section, and form a thermal stress relief path without constraint conflicts.

9. The displacement analysis, evaluation and compensation method for optimizing pipeline thermal expansion according to claim 8, characterized in that: Step S4 includes the following steps: Step S41: deploying temperature sensors and displacement monitoring devices at key nodes of the pipeline system to collect temperature change information during operation in real time to form temperature change cycle data; Step S42: extracting high energy density areas from the thermal energy distribution optimization data, matching the temperature change cycle data of the corresponding areas, analyzing the hysteresis relationship between thermal expansion displacement and temperature change, and generating a dynamic response association table; Step S43: fitting the displacement-time variation curves of different temperature intervals based on the dynamic response association table, marking the displacement acceleration mutation points, and forming a thermal expansion dynamic response curve diagram; Step S44: Calculating the advance triggering time of the compensation device action according to the displacement acceleration mutation point in the thermal expansion dynamic response curve, and generating an advance compensation parameter including a compensation correction coefficient and a trigger threshold; Step S45: Delimiting a candidate temperature gradient buffer zone range based on the high energy density region boundary in the thermal energy distribution optimization data, and selecting a buffer zone interval distance that matches the advance compensation parameter; Step S46: generating a temperature buffer configuration scheme including buffer coordinates, widths, and compensation parameters according to the buffer interval distance.

10. The displacement analysis, evaluation and compensation method for optimizing pipeline thermal expansion according to claim 9, characterized in that: Step S5 includes the following steps: Step S51: Implement pipeline system transformation according to the guided compensation scheme and the temperature buffer configuration scheme, install compensation devices and set temperature buffer zones to obtain an optimized pipeline system; Step S52: collecting thermal snapshots under different temperature conditions on the optimized pipeline system to form thermal data after transformation; Step S53: Compare and analyze the thermal state data after transformation with the thermal state change sequence, calculate the thermal stress reduction percentage and displacement change, and generate thermal stress improvement rate and compensation effect evaluation data; Step S54: Identify areas with insufficient thermal stress improvement rates based on compensation effect evaluation data, adjust compensation device parameters or types, implement optimization adjustments, verify the effects, and obtain construction acceptance data; Step S55: establishing a parameter library for different operating conditions based on the construction acceptance data and the temperature change cycle data to form a seasonal compensation parameter set.

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